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BY-NC-ND 4.0 license Open Access Published by De Gruyter January 18, 2023

Methods for the SI-traceable value assignment of the purity of organic compounds (IUPAC Technical Report)

  • Steven Westwood ORCID logo EMAIL logo , Katrice Lippa , Yoshitaka Shimuzu , Beatrice Lalerle , Takeshi Saito , David Duewer , Xinhua Dai , Stephen Davies , Marina Ricci , Annarita Baldan , Brian Lang , Stefan Sarge , Haifeng Wang , Ken Pratt , Ralf Josephs , Mikael Mariassy , Dietmar Pfeifer , John Warren , Wolfram Bremser , Stephen Ellison , Blaza Toman , Michael Nelson , Ting Huang , Ales Fajgelj , Ahmet Gören , Lindsey Mackay and Robert Wielgosz

Abstract

The “purity” of an organic compound typically refers, in practice, to an assignment of the mass fraction content of the primary organic component present in the material. The “purity” value of an organic primary calibrator material is the ultimate source of metrological traceability of any quantitative measurement of the content of that compound in a given matrix. The primary calibrator may consist of a Certified Reference Material (CRM) whose purity has been assigned by the CRM producer or a laboratory may choose to value-assign a material to the extent necessary for their intended application by using appropriately valid methods. This report provides an overview of the approach, performance and applicability of the principal methods used to determine organic purity including mass balance, quantitative NMR, thermal methods and direct-assay techniques. A statistical section reviews best practice for combination of data, value assignment as the upper limit values corresponding to 100 % purity are approached and how to report and propagate the standard uncertainty associated with the assigned values.

Acronyms and abbreviations

APCI

atmospheric pressure chemical ionization

APPI

atmospheric pressure photoionization

CAD

charged aerosol detector

CCQM

Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology

CIPM

International Committee for Weights and Measures

CMC

calibration and measurement capability

CRM

Certified Reference Material

DIN

Deutsches Institut für Normung

DSC

differential scanning calorimetry

DoF

Degrees of freedom

DI

Designated Institute

ECN

effective carbon number

ELSD

evaporative light-scattering detector

EQN

equation

FDA

U.S. Food and Drug Administration

FID

flame ionization detection

FLD

fluorescence detection

FPD

freezing point depression

FWHM

full width at half maximum

GC

gas chromatography

GUM

Guide to the expression of Uncertainty in Measurement

HPLC

high-performance liquid chromatography

HRGC

high-resolution gas chromatography

HRMS

high-resolution mass spectrometry

HS-GC/MS

head space gas chromatography/mass spectrometry

HSQC

single quantum coherence spectroscopy

ICH

International Conference on Harmonization

ICP

inductively coupled plasma

IDMS

isotope dilution mass spectrometry

IMP

peptide impurity molecule

ISO

International Organization for Standardization

IUPAC

International Union of Pure and Applied Chemistry

JCGM

Joint Committee for Guides in Metrology

KFT

Karl Fischer titration

KHP

Potassium hydrogen phthalate

LC

liquid chromatography

LOD

limit of detection

LOQ

limit of quantification

MCM

Monte Carlo Method

MS

mass spectrometry

MS/MS

tandem mass spectrometry

MSD

mass selective detection

NIST

National Institute of Standards and Technology, U.S.A.

NMI

National Metrology Institute

NMIJ

National Metrology Institute of Japan

NMR

nuclear magnetic resonance

OAWG

(CCQM) Working Group on Organic Analysis

PAD

pulsed amperometric detection

PAWG

(CCQM) Working Group on Protein Analysis

ppm

measure in parts per million using δ-scale of relative NMR signal frequency shift

PC

Primary Component (of organic material for purity assignment)

PRM

Primary Reference Material

PRT

platinum resistance thermometer

qNMR

quantitative nuclear magnetic resonance

QC

quality control

RF

radiofrequency

RRF

relative response factor

RI

differential refractive index

RM

Reference Material

S

Internal- or external-standard for a qNMR assay

S/N

signal-to-noise ratio

SC

Secondary Component (aka “impurity”)

SCNV

total non-volatile secondary component

SCOS

organic solvent secondary component

SCRS

related-structure secondary component

SCtotal

total secondary component content as determined by thermal methods

SCW

water impurity component

SI

International System of Units

SRM

Standard Reference Material (a CRM produced by NIST)

TGA

Thermogravimetric analysis

TOF-MS

time-of-flight mass spectrometry

UV/Vis

ultraviolet/visible UV absorbance detection

VIM

International Vocabulary of Metrology

VOC

volatile organic compound

WHO

World Health Organization

XRF

X-ray fluorescence spectrometry

Symbols
C

analyte concentration (mol/L) or subunits thereof

c i

measurement uncertainty sensitivity coefficient of generic variable xi

f

electrolysis efficiency (coulometry), fraction melted (thermal methods)

F

Faraday constant

i

index

I

electric current (coulometry), integrated signal (qNMR)

J(I,S)

heteronuclear coupling (qNMR)

k

amount-of-substance content (mol/kg),[1] partition constant (thermal methods), expansion factor (measurement uncertainty), constant (qNMR)

K

Kelvin, SI-unit of thermodynamic temperature

m

mass (kg or subunits thereof)

M

molar mass (g/mol)

n

amount-of-substance (mol); stoichiometric ratio of electrons to analyte (coulometry)

N

number of equivalent nuclei contributing to a signal quantified for a 1H-qNMR measurement

p

purity of the primary component of a material stated as a percentage on a mass fraction basis

p’

numerical value corresponding to a percentage purity p when defined as above

pKOW

negative log10 of the octanol: water partition coefficient

Q

amount of charge (coulometry); mass of water by a coulometric KFT (water content)

R

molar gas constant (thermal methods); ratio (various)

S

Internal- or external-standard for a qNMR assay

S i

Signal intensity due to component i in an external standard qNMR measurement

t

time

T

thermodynamic temperature in Kelvin

T eq

equilibrium temperature in Kelvin

T*

melting point of pure PC in Kelvin

u(…)

standard uncertainty of the quantity within the “(…)”

U 95%(…)

expanded uncertainty at the 95 % level of confidence of the quantity within the “(…)”

v

degrees of freedom

V

volume of the solution, subscript specifies of what

w

mass fraction content (g/g or subunits, especially mg/g, thereof)

x

amount-of-substance fraction (mol/mol)

x i

generic variable i

Y

number of residues of a given amino acid in a peptide impurity

z

ratio of charge numbers (coulometry)

Z

number of residues of a given amino acid in a peptide

α

pulse angle applied (NMR), correction term (thermal methods)

ΔfusH

molar fusion enthalpy

ΔfusHpartial

partial fusion enthalpy at the equilibrium condition during fusion

ΔfusHtotal

total fusion enthalpy of the sample

ΔT

melting point depression

Ө

360° pulse width (NMR)

Disclaimer

Commercial products or companies identified within this report are provided for purposes of description of a particular method or procedure only. They are not intended to imply a recommendation by the Bureau International des Poids et Mesures (BIPM), National Institute of Standards and Technology (NIST) or other National Metrology Institute contributing to this Report nor are they intended to imply that the named products or companies are necessarily the best available for the purpose.

1 Introduction

The delivery of reliable measurements in organic analysis requires the availability of well-characterized pure organic materials. Over 40 years have elapsed since the original publication of the IUPAC Monograph “Characterization of Chemical Purity of Organic Compounds” which summarized the methodologies for higher-order purity assignment of organic compounds that were then available [1]. The Monograph was restricted to materials of relatively high absolute purity, where the mass fraction or amount-of-substance fraction of the primary component (PC) expressed as percent was in excess of 98 %.

Measurement capabilities for the assignment of organic purity have been enhanced considerably and their applicability broadened in the intervening decades. This has resulted primarily from two separate but complimentary developments: the widespread application of high-performance liquid chromatography coupled to sensitive systems with broad selectivity for analyte detection and quantification and the improvement in the accuracy and precision, as well as the wider availability, of quantitative nuclear magnetic resonance (qNMR) spectroscopy. Both approaches enable quantitative characterization of organic compounds without preliminary chemical derivatization under mild, ambient conditions even in cases where there is a limited supply of material. Depending on factors including the level of uncertainty required in the final purity assignment, the amount of material available and the resources that can be dedicated to method development and validation, suitable approaches are now available for the purity assignment of most materials which contain a single, stable organic compound as the primary component.

In addition to a much broader range of applications compared to the methods described in the original IUPAC Monograph, these approaches provide greater confidence in the trueness and precision of the assigned value. Lower levels of measurement uncertainty in the assigned values can be achieved and assignments can be made in cases where only limited amounts, larger levels of impurity and/or labile material are involved.

These technical advances in the methodology for organic purity assessment occurred concurrently with an increasing recognition that a solid metrological infrastructure was needed to underpin the diverse array of measurement standards required for the analysis of organic chemicals [2]. The value assignment of Certified Reference Materials (CRMs) intended for use as Primary Reference Materials (PRMs) to establish a calibration hierarchy for results of organic analysis has recently been the focus of guideline development [3] and benchmark studies. The Working Group on Organic Analysis (OAWG) of the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology [4] (CCQM) of the International Committee for Weights and Measures (CIPM) [5] has coordinated a series of international studies designed to benchmark and improve the capabilities of National Metrology Institutes (NMIs) and Designated Institutes (DIs) for organic purity analysis [6].

1.1 Scope

The recommendations in this Report relate to procedures for the characterization of the mass fraction content of the primary component present in non-volatile, homogenous, stable organic liquids and solids, whose primary structure can be characterized by physicochemical techniques. The approaches should also be applicable to stable organometallic compounds. A survey is provided of the measurement approaches for the characterization and assessment of the purity of organic chemicals in the context of their value assignment for use as reference materials (RMs), CRMs or PRMs within a calibration hierarchy.

Excluded from the scope of this Report are purity assessments of heterogeneous materials such as organic polymers, complex carbohydrates and mixtures of structurally-related components, even where these can be separated chromatographically. In addition, the application of specialized methodology for isotopomer characterization, in particular carbon isotope ratio determinations of individual organic compounds, and enantiomeric analysis by chromatographic separation, while being recognized as potentially important in specific applications for the complete characterization of an organic compound, are excluded from this Report. These are specialized classes of “impurity” and their assessment has been the subject of IUPAC Technical Documents [7, 8]. Likewise the determination of the optical purity of a compound [9], while recognized as a related but indirect measure of chemical purity, is not addressed in this Report.

An important distinction also exists between the characterization of the purity of an organic material and the full assignment of the property value for a pure-substance CRM. The latter includes, in addition to characterization of the purity of the material, an assessment of and allowance for the homogeneity and stability of the assigned value within a production batch of the CRM. Guidance for these aspects of the production of RMs and CRMs is provided in ISO Standard 17034:2016 [10] and ISO Guide 35:2017 [11]. They are not addressed in this Report.

The specific aims of this Report are to:

  1. outline approaches for the assignment of the mass fraction content of the primary component in an organic material;

  2. provide examples of the estimation of the measurement uncertainty associated with an assigned purity value;

  3. assist analytical chemistry laboratories accredited to or operating in conformity with ISO 17025:2017 [12] to address their requirement to establish the metrological traceability of the RMs they use to deliver their measurement services.

1.2 Overview

This Report comprises four sections that address different aspects of the process of the purity assignment of organic compounds. The first section discusses concepts and definitions. It describes the role of a pure-substance RM in the calibration of measurement systems for a specific organic analyte and provides some guidance and recommendations on the associated nomenclature.

The second section comprises the major technical section of this Report and provides an overview of approaches for purity characterization for approaches in common use, namely:

  1. indirect assay by mass balance through the quantification of total impurities;

  2. direct assay of the PC by quantitative NMR (qNMR);

  3. direct assay of the PC by techniques other than qNMR;

  4. direct assay of total impurities by thermal methods.

The third section provides recommendations for estimating and reporting the measurement uncertainty of the assigned purity values.

A short fourth section outlines the role of international comparisons in developing and demonstrating the utility of the techniques presented in this report.

The appendices to this report provide worked examples for purity assignment, drawing on illustrative results derived from individual participant results obtained during the CCQM-K55 series of key comparisons.

2 Concepts, Definitions and Glossary

For the purposes of this document the general definitions, concepts and terminology given in the International Vocabulary of Metrology [13] apply, unless otherwise stated.

2.1 analyte

Component specified in a measurand [14].

In the context of organic purity assignment, the analyte is the compound of defined regio- and stereo-chemical structure that comprises the primary component (see below) of a high-purity material.

2.2 Reference Material (RM)

Material, sufficiently homogeneous and stable with reference to specified properties, which has been established to be fit for its intended use in measurement (Clause 5.12 in [13]).

2.3 Certified Reference Material (CRM)

Reference material, accompanied by documentation issued by an authoritative body and providing one or more specified property values with associated uncertainties and traceabilities, using valid procedures (Clause 5.14 in [13]).

Certified Reference Materials (CRMs) are, by definition, traceable to an accurate realization of the unit in which the property values are expressed. For a high-purity organic material the assigned property value must be accompanied by an associated uncertainty estimate at a stated level of confidence.

2.4 Primary Reference Material (PRM)

High-purity material, certified for the amount-of-substance fraction or mass fraction of the analyte in the material, that constitutes a realization of the International System (SI) unit for amount-of-substance, mole (if expressed as amount-of-substance content) or for mass, kilogram, (if expressed as mass fraction) for the PC [2]. A primary reference material (PRM) shall have its value assigned either directly by a primary reference measurement procedure [15] or indirectly by quantifying the impurities present in the material by appropriate analytical methods (Clause 3.24 in [16, 17]).

Although the ISO/REMCO Guide 30: 2015 Reference materials — Selected terms and definitions [18] does not refer specifically to the concept of a PRM, it does furnish an important clarification in clause 2.1.5 of a primary measurement standard (or primary standard) as being, in the context of Reference Materials, a “measurement standard that is designated or widely acknowledged as having the highest metrological qualities and whose property value is accepted without reference to other standards of the same property or quantity, within a specified context.” A PRM is a pure organic substance CRM that meets the additional metrological requirements of a primary measurement standard.

2.5 Calibrator

Measurement standard used in the calibration of a measuring system according to a specified measurement procedure [19, 20].

Note: The term “calibrant” is synonymous with “calibrator.”

2.6 Primary Calibrator

Calibrator established without reference to another calibrator for the same analyte [19, 20].

A CRM for a high-purity organic compound, having an assigned value obtained using a primary reference measurement procedure or by a higher-order mass-balance approach, can constitute a PRM for that analyte. A PRM is typically used in the preparation of a primary calibrator consisting of a standard solution of the analyte which becomes the reference point for a calibration hierarchy for measurements having the compound as the target analyte in the final measurand. Gravimetry is generally used as the primary reference measurement procedure to prepare the primary calibrator solution. The primary calibrator may be used in a reference measurement procedure to value assign the property values of a secondary calibrator or RM or in the simplest case directly for measurement of a sample.

Figure 1 displays a simple example of the use of a PRM in a calibration hierarchy for the measurement of the amount concentration of an analyte in a test sample. The measurement result on the test sample is traceable to the primary calibrator, which itself is traceable to the value of the PRM.

Figure 1: 
            Calibration hierarchy and SI traceability. The boxes and arrows trace the measurement of the amount concentration of an organic analyte in a test sample in units of nmol/L. The trapezoid to the left represents the magnitude of the combined standard uncertainty of the assigned value in successive components of the calibration hierarchy. Figure adapted from Section 4.2.2 of ref. [16].
Figure 1:

Calibration hierarchy and SI traceability. The boxes and arrows trace the measurement of the amount concentration of an organic analyte in a test sample in units of nmol/L. The trapezoid to the left represents the magnitude of the combined standard uncertainty of the assigned value in successive components of the calibration hierarchy. Figure adapted from Section 4.2.2 of ref. [16].

The calibration hierarchy in real situations may be extended further, either because: 1) the primary calibrator is used exclusively for value assigning secondary calibrators, with several levels of calibrators also possible when several measurement methods or instruments require calibration, or 2) routine measurement procedures require matrix matched or commutable calibrator materials.

It should be noted that terminology describing high-purity organic materials and their intended uses is congruent but not consistent across various sectors, written standards and regulatory requirements. The terminology proposed in this Report has been taken from that developed with the concept of Reference Measurement Systems [16] which has evolved within the Metrology and Clinical Chemistry communities. There are well-characterized, high-purity organic materials that meet the International Conference on Harmonization (ICH) [21] and U.S. Food and Drug Administration (FDA) [22] definitions of “primary reference standards” or the World Health Organization (WHO) [23] definition of “primary chemical reference substances” that currently lack important requirements for classification as a PRM as defined in this Report. These requirements include the 1) assignment of the measurement uncertainty associated with the purity value and 2) establishment of the traceability of the assigned value to the SI.

The term PRM as defined here should not be confused with its use in ICH Guidelines [24] and more widely in the pharmacopoeial sector [25] to designate a material characterized for internal use by a manufacturer either by comparison with a “primary reference standard” or by in-house procedures if a higher-order reference standard for the analyte is not available.

2.7 primary component (PC)

For this Report, the PC is the regio- and stereo-chemically defined organic compound of interest in a material subject to a purity characterization. “Analyte” and “PC” are used synonymously herein when referring to a material subject to a purity characterization, although “analyte” has the broader general meaning of being the component of any system subject to a particular analysis. As noted previously, the specialized approaches required for the characterization of the enantiomeric and isotopomeric composition of a PC are not included within the Scope of this Report.

2.8 secondary component (SC)

A SC consists of any chemical component of a material subject to a purity assignment that is not the PC. “Impurity” is widely and commonly used in the literature, and where appropriate in places in this Report, as a synonym for SC. However, a SC may be an intrinsic component of the stable form in which a high-purity organic material normally exists (e.g. water content of an organic hydrate, counter ion in salts of organic acids and bases) and not extraneous or undesirable in the common sense of the word “impurity”.

2.9 measurand

Particular quantity subject to measurement [13]. In the case of a high-purity organic material, the measurand is either the mass fraction or amount-of-substance fraction of the PC of the material.

2.10 purity

The 1971 IUPAC Organic Purity Monograph [1] included a discussion of the concept and definition of purity in the context of organic compounds. This discussion was developed further in NIST Special Publication 1024[2] and more recently by Pauli et al. in the context of the evaluation of the content of a material by qNMR spectroscopy [26].

The notion of a “pure” material as one consisting exclusively of a single, defined molecular species is neither readily achievable nor of particular practical value for most applications requiring high-purity materials in organic analysis. Although some of the procedures described in this Report can be used for the characterization of ultra-high-purity materials, that is not the primary focus or purpose of this Report. Building on the original IUPAC Monograph and recognizing that a material may be considered “pure” when it meets specifications required to avoid the introduction of error and bias into a measurement result, the following practical definition of “purity” is proposed in the context of this Report:

An organic material is sufficiently pure when the content of its primary component has been assigned and the amount of secondary components (impurities), which may interfere with the purpose for which the material is required, is so low or so well characterized that their combined effect has negligible impact on the intended application of the material.

Applying this definition allows expansion of the scope of this Report beyond that of the original Monograph to encompass materials containing, in addition to an organic PC, significant amounts of SC consisting of some or combinations of total related-structure impurities (SCRS), water (SCw), residual organic solvent (SCos), inorganic salts and counter-ions (SCNV). Even if the content of the organic PC is below 95 % on a mass fraction basis the material can comply with the proposed definition and be suitable for use as a PRM for the establishment of a calibration hierarchy for SI-traceable measurement results of the organic analyte that constitutes the PC of the material.

For organic PRMs the abstract concept of “purity” is most commonly delivered in practice by reporting the mass fraction, w [27, 28], of the PC in the material. The value is expressed either as a percentage or in units of g/g or its submultiples such as mg/g. As noted in Section 2.10 in the definition of purity as it applies in this context it is necessary to identify and quantify the mass fraction of the major SCs present in the material. It should be noted that a material having an assigned value for the PC in units of mass fraction (w) can be converted into units of amount-of-substance content (k), from knowledge of its molar mass.

In any material the upper limit for the mass fraction of the PC, equivalent to “100 % purity” in the common but ambiguous usage often found in the general literature, is 1 g/g. For numerical convenience, in particular when reporting levels of impurity content, the limit value of 1000 mg/g is often used in practice. A reported purity value and its associated uncertainty range should not exceed this value. The issue of appropriate practice in reporting is discussed further in Section 4.1.1 below.

Purity can also be reported as the amount-of-substance fraction (x) in units of mol/mol of the PC in a material. This is common practice for the results of methods such as coulometry or calorimetry that provide a direct measure of the PC content. The closer a material approaches 100 % “purity” the closer the agreement of the numerical values of the mass fraction and amount-of-substance fraction of the PC.

A more literal definition of purity as the ratio of the mass (or other measure) of a specified component divided by the mass (or other measure) of the system is proposed in the document IUPAC Provisional Recommendations: Metrological and Quality Concepts in Analytical Chemistry [14].

2.11 direct assay

A procedure that relies solely on measurement of the PC to assign the mass fraction content, amount-of-substance content or amount-of-substance fraction of the PC in a material subject to a purity characterization.

2.12 indirect assay

A procedure or set of procedures that measure the total amount-of-substance content or mass fraction content of the SCs in a material subject to assignment and, by difference from the limit value of 1.0, of the PC content in a material subject to a purity characterization. The “mass balance” method discussed in Section 3.1 is the most important example of this approach.

3 General Approaches to Organic Purity Assignment

Estimates of the mass fraction content of the PC in an organic material can be obtained by one of four general approaches or by the combination of results obtained by two or more of these approaches. These involve determination of one or more of:

  1. mass fraction (w1,w2, ….wn) for each SC present in the material followed by subtraction of their summation from the limit value of 1.0. This is commonly referred to as the mass balance method;

  2. mass fraction of the PC by a direct assay based on qNMR spectroscopy;

  3. mass fraction of the PC by a direct assay using a technique other than qNMR;

  4. combined mass fraction, Σwi, of all impurities in the material obtained using a thermal measurement followed by subtraction from the limit value.

3.1 Mass Balance

The implementation of this strategy for purity assignment requires application of an ensemble of orthogonal techniques capable of quantifying each class of impurity present in the material [3, 29], [30], [31], [32]. Summation of the individual impurity quantification values furnishes a value for the total impurity content of the material and by difference from the limit value for the mass fraction of the PC. The mass fraction value for the PC is traceable to the SI when the results for each contributing impurity class determination are also SI-traceable. For a given organic compound, the individual classes of SC that require assessment and quantification of their mass content are:

  1. total related-structure impurities, SCRS, with mass fraction wRS, where wRS=1nwRS,i and wRS,i is the assigned mass fraction content of each discrete related-structure impurity i (SCRS,i) present in the material;

  2. water, SCW, with mass fraction wW;

  3. residual organic solvent and volatile organic compounds, SCOS, with mass fraction wOS, where wOS=1nwOS,i and wOS,i is the assigned mass fraction content of each discrete residual solvent impurity i (SCOS,i) present in the material

  4. non-volatiles, SCNV, with mass fraction wNV, with potential contributions from either or both:

    1. total inorganic impurities,

    2. total non-volatile organics.

The mass fraction assignments of the contributing impurities must orthogonal, in the sense of there being no overlap of impurities quantified by the measurement methods used, and the assignments must cover the totality of impurities present in the material. In this case the mass fraction of the PC in the material, wPC, when the final value and the impurity class mass fractions are reported in units of mg/g, is given by:

(1)wPC=1000 mg/g(wRS+wW+wOS+wNV)mg/g

The combined standard uncertainty of wPC is obtained by a simple quadratic combination of the uncertainties associated with each contributing impurity assignment:

(2)u(wPC)=u(wRS)2+u(wW)2+u(wOS)2+u(wNV)2

An alternative measurement model that is often used for mass-balance purity assignment [3] (in the case shown for a result reported in units of mg/g) is:

(3)wPC=(1000wRS,rel)(1000 mg/g(wW+wOS+wNV)mg/g1000 mg/g)

The value for wRS,rel in eq. 3 is the ratio of the combined peak area response due to the SCRS components to the combined peak area response from the PC and total SCRS when a high resolution chromatographic method is used to separate and detect the PC and related structure impurities. Where wRS,rel is expressed in units per mille and wW, wOS and wNV in units of mg/g, as the latter were defined for eq. 1, then the assigned value for wPC is obtained in units of mg/g.

Because wRS,rel is a relative ratio and is not linked to an external calibrator it does not have SI-units, distinct from the value in mass fraction units associated with wRS in eq. 1. As the combined value of wW, wOS and wNV decreases the correction factor due to their contribution in eq. 3 approaches unity and wRS,rel approaches wRS numerically.

The assignment of results for each separate impurity class and the use of their summed value to assign by difference the value for the mass fraction content of the PC and its associated measurement uncertainty is referred to as the mass balance method. The implementation of this method is discussed below.

3.1.1 Total related-structure impurities (SCRS)

Chromatographic techniques can be used to separate components of a chemical mixture. The sample is dissolved in a fluid mobile phase that flows through a stationary phase contained in a column. Sample components partition between the mobile and stationary phases and are differentially retained by the column depending on their relative solubilities in the two phases and their relative affinity for the column coating.

High-resolution gas chromatography (HRGC) and high-performance liquid chromatography (HPLC) [33] techniques coupled to the use of one or more detectors with suitably broad selectivity and sensitivity are routinely used to detect and quantify each related-structure impurity i (SCRS,i) present in a high-purity material [34, 35]. It is assumed that SCRS,i exhibits broadly similar chromatographic behavior and detector response to the PC and will have a similar molar mass (MPC ≈ MRS,i). Where an unbiased result with small associated measurement uncertainty is required and the structures of the impurities are known, the assumption of equivalent relative response factors (RRFs) of the individual impurities to the PC should be tested through other techniques (use of multiple detection methods or 2D-chromatography, qNMR, elemental analysis).

3.1.1.1 Liquid Chromatography methods

High-performance liquid chromatography systems (including “ultra-performance” systems) typically provide lower resolution compared with separations achievable by capillary HRGC. However, LC systems enable the use of a greater diversity of stationary and mobile phases and are performed under near-ambient conditions. As a result HPLC methods can be applied to a wider range of organic analytes including the many that are thermolabile. As mentioned in the Introduction, the ready availability of HPLC equipment and suitable detector systems since the 1980s was a key driver in the increased availability of accurate, precise methodology for organic purity assignment.

For purity assignment purposes, wherever feasible, baseline resolution is sought for each of the components under investigation as potential related structure impurities – both from each other and from the PC. If this is not achievable then baseline separation from the PC is the priority. By optimizing chromatographic separation and determining performance characteristics using a gravimetrically prepared test solution containing the main PC and anticipated related structure SCs it is possible to establish with a degree of confidence that all such SCs will elute within an appropriate retention time window and can be resolved from the PC [29]. At least one chromatographic method should utilize a “universal detector” that responds with a readily-modeled RRF to each organic component present at a significant level (above 0.5 mg/g) in the column effluent. Examples of “universal detectors” that have been used for purity assignment by GC based methods are flame ionization detection (FID) [36] and mass spectrometry (MS) [37, 38]. For LC-based methods a wider range of detection options having broad selectivity are available [39]. These include evaporative light-scattering detection (ELSD) [40, 41], differential refractive index (RI) detection [42], charged aerosol detection (CAD) [43, 44], detection by direct mass spectrometry (MS) [45, 46] and by time-of-flight mass spectrometry (TOF-MS) using electrospray ionization (EI) [47, 48], atmospheric pressure chemical ionization (APCI) or atmospheric pressure photoionization (APPI) [49, 50]. Identification and quantification of related structure impurities in a material can also be achieved using LC with tandem MS (or MS/MS) [51, 52]. Applications of the MS/MS methods provide precise mass-to-charge ratios of the selected precursor and product ions, which in combination with knowledge of the structure and reactivity of the PC can be used to assign a molecular formula for each impurity. Methods based in LC-NMR [53] have also been used for the detection and quantification of separated sample components, but the relatively low sensitivity of NMR limits its usefulness. A recent interesting variant on the “universal detector” approach is absolute quantification using online carbon isotope ratio mass spectrometry (IRMS) as a detection system coupled to LC systems [54], [55], [56].

Liquid chromatography methods using ultraviolet/visible absorbance detection (LC-UV/Vis) or fluorescence detection (LC-FLD) cannot serve as “universal” detectors, as impurities lacking a suitable chromophore or fluorophore will not be detectable and the RRFs between those impurities that can be detected may diverge considerably. However, where the PC and the major related-structure SCs contain a common chromophore or fluorophore, LC-UV/Vis is a robust and sensitive technique. The use of LC-UV/Vis and LC-FLD produces results demonstrating better linearity and a higher level of precision compared with LC-CAD and related methods [3, 57, 58].

Liquid chromatography with UV/Vis detection can be used to optimize chromatographic conditions for the separation of components that can be transferred for use with other detection systems. Where the compound is sufficiently stable and volatile, the combination of data obtained by LC-UV/Vis with analysis by GC-FID, LC-CAD or LC- or GC-MS techniques has been shown to be a reliable approach for the detection and quantification of the SCRS profile of high-purity materials [29].

Recently LC methods reliant on an aerosol-based detection have found increasing application for the detection and quantification of organic impurities lacking any suitable chromophore [59, 60]. Although LC-ELSD and LC-RI are in principle “universal” detection methods, they are relatively insensitive and have a limited dynamic range. Liquid chromatography with charged aerosol detection generally exhibits higher sensitivity and better linearity of response than the other aerosol-based detection systems and is suitable for both non-volatile and semi-volatile components [41, 61]. The linearity and sensitivity of the CAD response depends primarily on the mass concentration of each analyte and is broadly, but not entirely, independent of chemical structure. It does have the drawback of requiring use of either an isocratic elution profile or post-column adjustment of the eluant composition prior to introduction to the CAD to avoid interference from or drift of the baseline response.

Pre- or post-column derivatization techniques improve detection sensitivity and selectivity by chemical coupling of a readily detectable functional group (typically a chromophore or fluorophore) onto a reactive functional group present in the organic components in the material [62], [63], [64]. This approach is limited for use in purity assignments to materials where it can be demonstrated that both the PC and each individual SCRS,i are readily derivatized. Despite this limitation the approach has important practical applications for the purity characterization of significant general classes of organic compounds, including amino acids [65], carbohydrates [66] and steroids [67]. Pre-column derivatization will often have an additional advantage by enhancing the chromatographic separation of the derivatized components compared to the underivatized analytes. The quantification of derivatized amino acids can be used both in the purity assignment of individual amino acids and as the basis for the indirect assignment of the purity of protein and peptides via the quantification of the component amino acids released during exhaustive hydrolysis of the source material that are stable under the hydrolysis conditions [68].

Detection based on electrochemical methods has also been reported for use in related structure impurity detection and quantification. Applications based on pulsed amperometric detection (LC-PAD) can in principle be applied to polar aliphatic compounds containing amine, hydroxyl or sulfur containing functional groups and have been reported for the analysis of carbohydrates [69] and tetracyclines [70].

Regardless of the detection method, authentic pure substances of each putative impurity should be used to develop and validate the separation methods and quantitative response either in an absolute sense or relative to the PC for each component. Knowledge of the source of the material subject to purity assessment, especially the synthesis pathways used for its preparation or extraction or the purification processes if it is a natural product, is useful when attempting to identify the related structure impurities associated with the PC.

If authentic standards of each of the individual SCRS,i components are available, one approach is to optimize the initial separation of the components using an LC-UV/Vis or LC-CAD detection system. If sufficient this method can be used to quantify the main component. It can also be the basis for the chromatographic separation required for the quantification of SCRS by more sensitive LC-MS, LC-HRMS or LC-MS/MS based methods. In addition to quantification, the information derived from the various MS detection techniques can be used to confirm the assigned identity of the individual SCRS components present in the material or to identify otherwise unknown impurities [29].

Developing chromatographic conditions able to resolve a range of known or potential SCRS,i components having longer and shorter retention times relative to the PC increases confidence that the co-elution of a specific SCRS,i with the PC is unlikely to be a significant issue. If examination of the material by HPLC on at least two columns having different stationary phase chemistries and using different detectors fails to reveal additional organic components, it can be assumed that no significant “co-eluting” SCRS,i is present. This conclusion should be investigated and confirmed by an independent technique such as HRGC or NMR.

Provided each SCRS,i has a unique decomposition pathway after ionization when compared with the PC, LC-MS/MS methods can provide identification and even quantification information in cases where a SCRS,i co-elutes with the PC or is not fully resolved from it.

3.1.1.2 Gas Chromatography methods

In general, only non-polar compounds of relatively low molar mass are suitable for direct GC analysis, on the proviso that they can be volatilized without decomposition. In selected cases where artefact formation can occur in the heated sample inlet, “cool-on-column” injection may be used to mitigate or avoid this problem [71]. The range of compounds amenable to GC analysis is enhanced and the performance characteristics increased in terms of peak resolution and detection sensitivity by sample pre-derivatization involving alkylation, acylation or silylation of reactive functional groups [72]. The caveats for the limitations of the use of pre-derivatization in LC-analysis for purity assessment apply equally in the case of GC. In addition, the introduction of excess derivatization reagent onto the column can result in artefact peaks and problems with baseline stability that may interfere with the implementation of this approach for high-accuracy purity assessment studies.

Volatilized carbon compounds in the GC mobile phase have been observed using thermal conductivity, nitrogen-phosphorous, flame photometric, electron capture and atomic emission detectors [46, 73], [74], [75], [76]. However, in the context of purity evaluation of organic compounds, detection and quantification by FID and MS have historically been the most suitable “universal” detection methods. They each exhibit sufficiently high linearity and sensitivity to provide reliable quantification of both the PC and individual impurity components of SCRS [36], [37], [38].

By providing a measure of total ionized carbon for each successive organic eluent FID acts in effect as a carbon counter. The ability to calculate RRFs for analyses utilizing the FID is of fundamental importance for accurate quantification. Relative response factor data is obtained from the GC-FID chromatogram for a compound introduced in either neat or derivatized form. To estimate the expected response based on the carbon content, by comparison with the observed value and where authentic standards are not available to establish an external calibration, the effective carbon number (ECN), equal to the number of carbons in an alkane producing an identical FID response to the compound, can be used for calculating a fit-for-purpose estimate of the RRF for each identified impurity [77]. Because this factor assumes the completeness of reaction if a derivatization step is used, as well as the potential for decomposition on injection or adsorption by the column, experimentally determined RRFs may be significantly different from those anticipated based simply on the ECN.

Because it combines high sensitivity with a broad linear range, GC-FID remains the most widely used system for the measurement of volatile organic compounds. Its utility for assignment of the related structure impurity profile of a given material is dictated by the characteristics of the PC and the assumption that all impurities are equally efficient and responsive to the same GC-FID conditions. In the case of impurities for which external calibrators are not available, at least the molecular formula of the impurity should be established so that an RRF based on its ECN can be assigned.

3.1.1.3 Impurity assignment by direct calibration

Establishing a purity assessment of the PC that is SI-traceable using the mass balance measurement model of necessity requires an SI-traceable assignment of the mass fraction content for each class of secondary component present in the material.

Quantitative assignment of the SCRS content can be achieved using an external calibration for the quantification of each resolved impurity. This approach is conceptually straightforward, all be it potentially time-consuming and resource intensive. Ideally it requires the availability of an authentic standard of each impurity and the determination of its RRF against the PC using the same conditions and equipment as those used to evaluate the material subject to the purity assignment. The performance characteristics of precision, linearity, limit of detection (LOD) and limit of quantification (LOQ) [14] for each impurity should be determined over a mass fraction range representative of the levels at which the impurity occurs in the material [78, 79]. Procedures to follow in cases where the structure of an impurity is unknown or an authentic external calibration standard is not available are discussed below.

Using modern tandem chromatographic systems, the relative standard uncertainty achievable in the mass fraction values of individual related structure SCs in a material by external calibration are often comparable to those that can be obtained for the PC itself using the same method. Relative uncertainties in the range 1 to 2 % can typically be achieved for the quantification of individual related structure impurities present above the 10 mg/g level and in the range 2 to 5 % for each SCRS,i present at levels of 1 to 10 mg/g [29]. Although larger relative uncertainties are often associated with the quantification of related structure impurities present at levels below 1 mg/g, their contribution in absolute terms to the overall standard uncertainty of the assigned value of the PC is generally small (see example below). The uncertainty associated with an individual SCRS,i quantification should be expanded appropriately where the identity of the SC has not been established or external calibration standards for the impurity are not available.

When SCRS components are the predominant class of impurity in the material, the mass balance approach can often achieve levels of measurement uncertainty in the assignment of the mass fraction of the PC smaller than those obtained by direct quantification of the PC using the same method. In a case where each related structure impurity has been identified and pure substance RMs for each are available to use as external calibration standards, appropriate RRFs are readily determinable. This is not the case when no pure substance RM is available for a significant related structure impurity and even less so if the structure is unknown. However, even in these cases pragmatic RRF estimates can usually be made.

The RRF is determined using the most closely-related compound structurally for which suitable RMs are available. If two or more such compounds are evaluated, the standard deviation of the RRFs provides a reliable uncertainty. If no suitable RMs are available, assume the RRF is unity but with a larger relative uncertainty. In this situation access to an LC-CAD or similar “universal detector” is useful since by LC-CAD the observed response depends primarily on the molar mass of the molecule, regardless of its chemical structure.

It is also useful to have access to a UV/Vis diode array detector so that the full absorbance spectrum of each resolved impurity can be compared with that of the PC. This provides evidence to validate the assumption that compounds containing a similar chromophore will have a similar RRFs. It can also be used to identify impurities for which this assumption is not justified. A Type-B estimate of the uncertainty in the RRF for each unassigned impurity must be evaluated based upon all the available evidence.

3.1.1.4 Impurity assignment by relative response

By comparison with the calibration approach described by eq. 1, application of the model described in eq. 3 proceeds through assignment of the observed SCRS response relative to the combined response of the PC and SCRS followed by conversion of this relative value to an absolute value after correction for contributions due to the other SC classes. This provides a measurement of the mass fraction of SCRS when the concentrations of all components are within the detector’s linear response range for each analyte and the observed detector response for each SCRS,i is adjusted by an appropriate RRF against the PC response.

It is critical that the concentration of both the PC and each SCRS,i in the sample subject to analysis are within the linear response range of the detector. If the concentration of the PC is too high, the detector response for the PC will be saturated leading to an overestimation of the relative response of related structure impurities in the sample. Similarly if the concentration of an SCRS,i component in the sample subject to analysis is below its LOD then evidently it makes no contribution to the final value of SCRS.

The relative response approach commences from an assumption that the PC and each SCRS,i display equivalent RRFs on a mass basis towards the detector linked to the chromatographic system. This is assumed to be valid for impurities of similar structure and molar mass to the PC. However, there are numerous examples in the literature where this assumption does not hold [31]. For this reason either the RRFs should be investigated, at least for the major impurity components, or an appropriate allowance should be made in the measurement uncertainty budget.

In practice for the SCRS,i present at low levels, deviations from the assumption of equivalent RRF to the PC have only a small impact on the final purity estimate for the PC. In this case the uncorrected relative peak area response provides a practical measure of the contribution to wRS,rel of these impurity components. The detection methods used in the chromatography of organic compounds typically do not detect water and can have difficulty to distinguish SCRS of organic components that elute with the solvent front. In addition some SCRS in the material under investigation may be retained on the column. Therefore, evaluation of the chromatographic response is not valid as a stand-alone method to assign an SI-traceable purity value. An independent cross check is required to validate the chromatographic data. The description of a material as, for example, “> 99 % pure by GC-FID” is insufficient to establish SI-traceability of the content of the material unless there is additional evidence to demonstrate that there is a negligible content of potential impurities that would not in principle be detected by GC-FID.

The relative peak area response does provide a useful independent check where an external calibration method is used for the SCRS quantification and also as a consistency check when the PC content is assigned by a direct assay method.

3.1.1.5 Control for bias due to artefact formation

Artefacts can be created during sample preparation and chromatographic analysis that can be mistaken for genuine SCRS,i. Solution preparations can induce isomerization, solvolysis or solvent-catalyzed degradation that generate artefact components [80]. On-column reactions can also produce artefact peaks [81] and they can form in the ion source of a mass spectrometer during the MS ionization process [82] with potential impact on the results of LC-MS based quantifications. A common approach to controlling for the formation of artefacts is to apply the procedure to a RM of the analyte having an assigned value for PC content and confirming that the value obtained is consistent with that reported by the RM producer.

Impurities may co-elute with the PC. A reasonable level of confidence that co-elution is unlikely to be a significant issue can be achieved by use of two or more chromatographic separation principles (differing stationary and mobile phases, columns, flow rates, temperature programs, etc.) that can resolve the PC from potential impurities having both longer and shorter retention times [29]. Where possible, the absence of co-eluting SCRS,i components should be supported by an independent direct assay. In the absence of evidence of the presence of related structure impurities, the level of contribution of “non-detectable” impurities to SCRS can be treated as zero with negligible associated uncertainty.

3.1.1.6 Measurement uncertainty and SI traceability

“Metrological traceability” is formally the “property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty.” [13] Throughout this report when a result or purity value of a material is described as “SI-traceable” it implies that the result or assigned value is related by an unbroken calibration chain to a reference for each SI unit in which it is expressed.

In the case of quantification by external calibration, the references required to establish SI-traceability are the materials used to determine the calibration response for each contributing impurityi. Thus, establishment of SI-traceability requires a fit-for-purpose, SI-traceable mass fraction assignment for each external calibrator material.

The concept of “fit-for-purpose” assignment is key in order to achieve a pragmatic implementation of the mass balance method. The smaller the contribution of a particular SCRS,i to SCRS overall and the larger the acceptable overall u(wPC) of the final assignment, the less stringent the required assessment of the external calibrator material used as the reference point for the quantification of the SCRS,i.

Three categories of materials are used as calibrator materials for quantifying an SCRS,i:

  1. pure substance CRMs prepared in compliance with ISO 17034 [10] requirements and having assigned mass fraction values with established traceability to the SI;

  2. pure substance RMs prepared in compliance with ISO 17034 supplied with information on the characterization of the material, including a reliable limit value for its purity (e.g. “> 99 %”);

  3. uncharacterized materials having either no assigned purity or where the reported value (e.g. “> 99 %”) has not been established at a suitable level of confidence.

Case 1 is the simplest and in principle requires no additional supporting investigation.

Case 2 is more common. In this case, after an independent confirmation that the stated lower limit is consistent with the chromatographic or spectral properties of the material, a fit-for-purpose value assignment can be calculated [29]. When the lower-limit purity is stated as a percentage value (p) this value can be converted to a mass fraction, w, using eq. 4:

(4)w=(1000p+10001000p2)mg/g

where p’ is the numerical value corresponding to the percentage purity p of the material.

An example is given below of the assignment for material having p > 99 %:

(5)w=(1000×0.99+10001000×0.992)mg/g=(990+102)mg/g=995 mg/g

A fit-for-purpose assignment of the standard uncertainty in this value is obtained applying eq. 6, assuming a rectangular distribution of possible values over the range 0.99 to 1.00 [83]:

(6)u(w)=(10001000p23)mg/g

The uncertainty calculation for a material having a purity in excess of 99 % is shown in eq. 7:

(7)u(w)=(10001000×0.9923)mg/g=1023mg/g2.9mg/g

Case 3 differs from Case 2 in that additional characterization must be undertaken by the user to establish at a suitable level of confidence the minimum content of the primary component in the material. Once a minimum value has been established eq. 4 and eq. 6 can be used to assign a fit-for-purpose, SI-traceable value with its associated measurement uncertainty for the purity of the calibrator material.

3.1.2 Water content (SCW)

The most widely used methods for quantification of the water content of a high-purity organic material are Karl Fischer titration (KFT) [84, 85] and thermogravimetry [86].

3.1.2.1 Coulometric Karl Fischer titration (KFT)

Karl Fischer titration relies on the principle that the oxidation in solution of sulphur dioxide by free iodine in the presence of a weak organic base (usually imidazole) requires the presence of H2O, one mol of I2 being required for each mole of H2O consumed. Either volumetric or coulometric titration techniques can be used. The water content in the sample subject to titration is delivered into the titration cell either by introducing the bulk sample directly into the KFT reagent prior to titration or through its release from an aliquot of the sample when heated by an oven with the liberated water vapour being transferred quantitatively into the titration cell using a flow of dry gas [87].

Coulometric determination provides a versatile approach for quantification of water present in the range 0.1 to 50 mg/g (0.01 to 5 %) in the material subject to purity characterization, which covers the levels encountered in most organic compounds. Volumetric titration is more suitable in the less frequent cases when the water content exceeds 50 mg/g (5 %).

Coulometric KFT measures the quantity of electric charge (in coulombs) required to generate in situ free iodine (I2) for conversion into iodide ions by reaction with water in the presence of the KFT reagent. Quantification of the water content is based on the stoichiometry of the oxidation reaction requiring the generation of one molar equivalent of iodine for each molar equivalent of water consumed. Provided an accurate gravimetric determination was undertaken of the mass of the sample aliquot analyzed, the measured amount of electric charge can then be related to the mass fraction of water by application of Faraday’s law [88]. Through implementation of a validated procedure ensuring that the quantity values of all input parameters are traceable to their relevant SI units, a direct, SI-traceable relation is established between the amount of electric charge consumed, the amount of I2 generated and the water content of the sample subject to the analysis.

3.1.2.1.1 Oven-transfer methods

The oven method is recommended for use with materials not amenable to direct contact with the KFT reagent because they:

  1. undergo side reactions with the reagent,

  2. release water too slowly at ambient temperatures,

  3. are insufficiently soluble in the KFT reagent,

  4. contain matrix constituents which cause interference.

If there is a possibility that reactive volatile material other than water is released (e.g., reducing substances that react with the I2 of the KFT reagent or low-boiling aldehydes, ketones, siloxanes or sulfur-containing compounds that can interfere with the KFT reaction), the standard KFT reagent can be replaced by a sulfur dioxide-free reagent. Use of a two-compartment cell with a diaphragm is recommended for very accurate determinations, measurements of samples containing less than 50 µg of water content and measurements of samples with easily reducible functionalities (e.g. nitro-compounds, unsaturated hydrocarbons). Atmospheric moisture is an ever-present source of potential contamination which, for hygroscopic materials, can influence the trueness of the final measurement result. Working with heated oven gas transfer using sealed sample vials has the important advantage that the titration cell will not be contaminated by the sample, which should limit the possibility of carryover or memory effects.

The oven temperature and the duration of heating are optimized in method development studies to ensure complete water extraction in reasonable time without decomposition of the sample. It is critical to establish that all water can be released from the sample upon heating. If larger quantities of the sample are available, volumetric KFT can be used to confirm that all water (including any strongly bound) in the material has been detected. The heating temperature should be as high as possible, but at least 20 °C below the decomposition temperature of the compound under investigation. For a given material, the oven conditions can be optimized using a temperature gradient or, for example, by independently investigating the stability of the sample by thermogravimetry.

The initial oven temperature should be set as high as the respective sample permits (the higher the temperature, the faster the analysis). A typical gradient for a stable compound with high melting point would be from 50 to 250 °C with a heating rate of 10 °C/min. The temperature should be held steady at the melting point of the material. The flow rate of the carrier gas should also be pre-assessed, a typical range being between 40 and 60 mL/min. The oven method must be used with care with thermolabile materials that can potentially release water through chemical breakdown on excessive heating, for example through intra- or inter-molecular condensation reactions [6c].

Water release-curves are obtained that describe the kinetics of water discharge as a function of temperature. These curves provide useful information regarding the nature of water in the sample i.e., distinguishing between adsorbed water and more tightly bound hydrates or water of crystallization. The latter can be tightly or loosely bound as well as with a fixed stoichiometry or as a variable hydrate that may equilibrate its moisture content with the environment. For unstable samples or compounds potentially subject to condensation reactions, water may be an artefact of thermal decomposition rather than inherently present in the material.

Relative humidity and temperature in the laboratory should be controlled and monitored. Conditioning of the instrument until the drift has stabilized below a pre-set value (typically below or equal 10 μg H2O per minute), and performing a suitable number of blank determinations (determination of the humidity present in the sample vessel dead volume and the inevitable moisture adhering to the vessel walls, vial cap and septum), are recommended before starting any water content determination with a heated oven-transfer system.

The performance of the entire measurement procedure, including sample preparation, can be validated and monitored using as RMs solid powders certified for water content relevant to the material under assessment. The performance of the titration cell should be separately validated and monitored by direct addition of solutions with certified water content into the titration cell. If oven temperatures greater than 160 °C are applied, dry nitrogen instead of dry air should be used as carrier gas for organic samples to prevent oxidation reactions.

For high accuracy, the size of the sample for coulometric KFT by heated oven transfer should be such that it contains between 100 and 5000 µg of water per sample. A relative precision better than 1 % can usually be achieved when optimized transfer conditions are applied with aliquots of materials containing an absolute water content above 500 µg. The precision decreases for samples containing lower absolute levels of water content, while if the water content is too high it may lead to condensation in the transfer tubing and loss in the transfer process. If dealing with small sample masses, accurate weighing is critical.

Under optimized conditions it is possible to determine water contents down to 10 µg (provided that the titration cell drift value is low), although the relative precision of such determinations inevitably increases. The minimum total sample mass required for an individual analysis should reflect the observation that in practice it is difficult to distinguish water content in a material from the natural variation in the vial blank correction value when the absolute water content in the sample aliquot is below 50 µg. The maximum sample mass is limited by the water-reactive capacity of the KFT reagent and the amount of material available for analysis.

3.1.2.1.2 Direct addition methods

Direct addition KFT requires that an accurately known mass of sample is introduced into the titration cell and that the sample is freely soluble in the titration solution. The rate of dissolution may be important. In general, the end-point of the titration is determined by the instrument, based on set drift levels or time limits. If the dissolution rate is slow, the drift levels may be reached and the titration stopped prematurely.

The background drift, usually expressed in terms of microgram of water per minute, must be stable before the sample is introduced into the titration cell. It will usually be significantly lower than that observed with oven-transfer KFT (< 5 µg H2O per minute). The drift should be consistent throughout the sequence of samples.

Although the blank correction will be smaller than for oven transfer, addition of the sample to the titration cell exposes the system to the atmosphere and introduces ambient moisture. This is accounted for by analyzing a series of blanks, in which the cell is opened and closed in the same manner as though a sample were being introduced. Subtraction of the correction value calculated from the results for these blanks from the mass of water determined for a given sample gives the blank-corrected value corresponding to the water content estimate for the sample subject to titration.

Care must be exercised when choosing the titration solution, depending on the solubility and functionality of the analyte of interest. Since carbonyl groups produce water as a by-product from reaction with methanol, special methanol-free reagent is required for the titration of ketones and aldehydes [89].

Provided the material is readily soluble in the KFT reagent, direct addition of the sample to the titration cell avoids the need to evaluate the efficiency of a transfer process and the effectiveness of the release of water from the sample. Direct addition also minimizes the possibility of thermal elimination of water from the organic compound. Because the system is sealed, the drift levels in the titration cell are typically lower and reestablish more rapidly than when using heated oven transfer. Thus, the direct addition approach generally has a lower LOD and LOQ for a given material than the oven method.

3.1.2.1.3 Measurement uncertainty and SI traceability

In cases where there is no significant difference found between results observed with sample-containing vials and blank vials, the water content of the materials can be assigned a value of zero with an asymmetric uncertainty assigned from the LOD.

The combined uncertainty of a KFT result above the LOQ of the method can be estimated by quadratic combination of the major contributions from the repeatability/intermediate precision and the uncertainty of the trueness estimate. Uncertainty sources to be considered are weighing, electrolytic efficiency (in principle, 100 %), stoichiometric variability (in theory, the mole ratio of H2O consumed to I2 generated should be 1:1) caused by side reactions, the efficiency of water transfer and the accuracy of the titration end point [90], [91], [92].

The amount-of-substance fraction water content in the sample (xH2O) is given by eq. 8:

(8)xH2O=MH2OQ2mFf

where MH2O is the molar mass of water, Q is the amount of charge in coulombs; m the mass of sample; F is the Faraday constant and f is a combined factor representing the electrolysis efficiency in generating I2 and the exclusivity of reaction of water with I2 as it is generated in situ. The factor f is generally assigned a value of unity and for estimation of the standard uncertainty of the final result a Type-B estimate should be included that allows for the accuracy of this assumption.

During method validation, a check for systematic error should be carried out using a solid reference material certified for water content. If a systematic error is detected, the method should be modified as necessary to eliminate it. Even if no error is detected, an uncertainty component for the assumption of quantitative recovery linked to the uncertainty in the CRM value for water content should be introduced into the measurement equation used to calculate the KFT result.

If suitable oven-transfer standards or CRMs for water content are not available, the quantitative release of water from the matrix in the oven-transfer KFT should be cross-checked against direct titration and/or volumetric KFT (if the percentage water content of the material is greater than 0.05 g/g). The uncertainty related to the water release upon heating is variable depending on the substance analysed and can be difficult to estimate. If the result is cross-checked by an independent method, this uncertainty source could be omitted.

A linear regression check using different sample intakes, plotting the observed response to amount of sample added, should be undertaken to check for systematic errors. If there is a significant deviation of the zero-point coordinates of the y-axis (intercept), there has been a systematic error. An attempt should be made to correct for the observed bias and optimize the system [93].

3.1.2.2 Thermogravimetric analysis (TGA)

Thermogravimetric analysis (TGA) can be used for the determination of the release of total volatiles from a material [86]. The premise for this application is that only adsorbed volatile compounds (water or residual organic solvent) desorb from the substrate as the sample is heated at temperatures below the decomposition point. The sample is subjected to an optimized heating rate and the mass of the sample as a function of temperature recorded. The resulting temperature versus mass plot allows for the determination of the: 1) total mass loss, equivalent to the mass fraction of volatile material in the original sample, and 2) the temperature at which the volatiles are released from the sample. This can give insight into the compounds evolved from the sample matrix since the temperature of mass loss is often near the boiling point of individual volatile compounds. If desired, explicit identification of volatile components released from a material subject to TGA can be obtained using MS or infrared spectroscopy [94].

The experimental equipment used in TGA consists of a temperature-controlled furnace able to apply uniform heating to the test sample and an analytical balance recording the dynamic changes in the sample mass. The sensitivity of the balance varies depending on the target sample size but should be no less than a few tenths of a percent of the target sample mass. The larger the ratio of the sample mass to the mass sensitivity of the balance the greater the discrimination of changes in mass and the greater the decrease in the uncertainty of the result. The thermobalance should be able to sustain a controlled inert atmosphere purge gas (e.g., nitrogen) to prevent oxidation during the initial heating process. Crucial to the measurements is the use of sample containers that are inert with respect to the sample and that will remain stable throughout the experimental temperature range (i.e., void of phase transitions). The sample container is removable, but during normal measurements will be in direct contact with the balance and should be positioned in the center of the furnace for even and consistent heating. To ensure the overall accuracy of TGA results, the thermobalance should be appropriately calibrated.

The operation of the TGA system should be validated using a reference compound that provides a known mass loss over a set temperature range. Calcium oxalate hydrate and sodium tartrate dihydrate are often used for this purpose.

When interpreting TGA data, it is important to recognize the biases that may arise in the measurement process due to chemical interactions or physical changes that occur during the measurement process. Potential problems include shifts in vaporization temperature, inconsistent release of intercalated water and the effect of buoyancy in the thermobalance. The transition temperatures of solvent loss can yield some information about the identity of the solvent, but this data should be treated with caution because the mass transition temperature may be shifted higher if there are significant intermolecular interactions between the sample and the volatile compound. For instance, compounds that have a strong hydrophilic component or high surface area may retain water at significantly higher temperatures than its boiling point. For applications where it is necessary to determine the identity of a released volatile component, instruments coupled with mass spectrometric detectors are used.

The apparent mass of the sample can fluctuate due to a buoyancy effect caused by a change in the density of the air column within the sample furnace over the course of a normal TGA experiment. Where high accuracy is required, it is recommended that a baseline correction be acquired at the same ramp rate and temperature profile as the sample.

3.1.2.1.3 Measurement uncertainty and SI traceability

In principle, the measurement uncertainty of a TGA result is that associated with the gravimetric measurement of the difference between the initial and final mass of the sample. However, an additional recovery factor should be included to account for the uncertainty contribution associated with the assumption of quantitative release of volatile material from the material under the temperature program used for the TGA. The reference materials used in the validation of the extent of quantitative recovery of water using an oven-transfer KFT method (see Section 3.1.2.1.3) can be used in a similar role for the validation of TGA methods. They allow for a practical estimation of this additional uncertainty contribution linked to the assumption of quantitative release of the volatile contents from a material.

3.1.3 Residual organic solvent (SCOS)

3.1.3.1 Methods for total residual organic solvent

Various methods based on the extraction of volatile organic compounds (VOCs) from a sample head-space [95] for transfer, trapping and subsequent analysis by GC are suitable for the detection and quantification of residual organic solvent content, SCOS, present as a SC in a high-purity organic material. These include static and dynamic purge-and trap-systems [96] and solid-phase microextraction [97].

Residual solvent content can also be determined in a material using standard GC-MS or GC-FID equipment by direct injection of a solution of the material onto a capillary GC column suitable for the analysis of VOCs, the column outlet being connected to the detector. If this approach is used, two independent solutions, one in a volatile solvent (methanol or methylene chloride) and the other in a non-volatile solvent (dimethyl sulfoxide, dimethylformamide) should be analyzed [29].

Quantitative nuclear magnetic resonance spectroscopy (qNMR) is a convenient alternative method to identify and quantify solvent residue present in organic material. Thermogravimetric analysis should also give information when the residual organic solvent content is significant, provided independent methods establish that the observed mass loss on heating the sample is not due to water. Systems where the TGA oven effluent is passed into a mass spectrometer have been used to identify the chemical nature of volatile components [98, 99].

3.1.3.2 Measurement uncertainty and SI traceability

The approach involved in establishing the measurement uncertainty and traceability to the SI of the value for SCOS are essentially the same as those for the traceability of the SCRS content as discussed in Section 3.1.1.4. The use of HPLC-grade pure solvent as the calibration standard for the quantification of an individual SCOS suffices for quantifications based on GC methods. If a qNMR approach is used, the SI-traceability of the result arises from that of the mass fraction content assignment of the (internal) standard used for the quantification of the integration of the unique 1H NMR signal from the solvent.

3.1.4 Non-volatile content (SCNV)

3.1.4.1 Methods for determining total non-volatile content

The quantity of non-volatile impurities in a material can be assessed by combining data from several complementary methods. A traditional approach is by weighing the residue remaining after exhaustive combustion of a gravimetrically defined sample of the material [100]. Oxidative combustion of the material at high temperature by TGA can be used as an accurate surrogate for ashing analysis and requires a significantly smaller amount of material.

Individual levels of the more common elemental impurities (Na, K, Mg, Ca, Al, Si, Fe) can be determined by X-ray fluorescence, inductively coupled plasma (ICP) optical emission spectrometry and ICP-MS [101]. The LODs for these vary by chemical element and technique but generally do not exceed 0.1 μg/g.

Size-exclusion chromatography [102] can be used to quantify polymeric and oligomeric organic impurities not readily detected by other techniques. Ion-exchange chromatography can be used to quantify common charged species, as would be encountered with salts of organic acids and bases [103]. Supporting data from microanalysis for non-metal content (C, H, O, N, P, S, Cl, etc.) can be used as an independent check for any significant deviation from, at least, the empirical formula of the PC.

3.1.4.2 Measurement uncertainty and SI traceability

When results for SCNV determinations are indistinguishable from blank analyses, the wNV can be assigned a value of zero with an asymmetric u(wNV) bounded by zero and a conservative estimate based on the LOD of the analytical method used [29]. Alternatively, assign the wNV as one-half of the LOD with an u(wNV) corresponding to a rectangular distribution over the range up to the LOD.

For estimates based on ashing or TGA residue, the uncertainty associated with observed mass of the residue should be expanded by an additional factor to allow for the uncertainty associated with the assumption of completeness of oxidation of the organic content.

Since ashing and elemental analysis techniques quantify residual mass rather than the quantity of the oxide or salt impurity (ies) associated with metals and other elemental impurities, the mass fraction of these impurities should be regarded as a lower-bound to the mass fraction of the SCNV. Estimating wNV therefore requires chemical insight informed by knowledge of the origin and processing history of the material. Determine the likely impurity compounds associated with each impurity (e.g., NaCl, KCl, MgCl2, CaO, Al2O3, SiO2, Fe2O3) and estimate wNV from the quantified mass fraction of the impurity present multiplied by the molar mass of the most likely impurity compound divided by the molar mass of the parent element. If the composition of the residue is unknown, estimate wNV from the mass fraction of the residue multiplied by the largest of the likely molar mass ratios for (impurity compound)/(impurity). The u(wNV) can be based on the molar mass differences among the potential impurities.

Appendix A provides examples of the implementation of mass balance methods for purity assignment.

3.2 Direct Assay by Quantitative Nuclear Magnetic Resonance (qNMR)

Nuclear magnetic resonance (NMR) is a spectroscopic technique that provides information about the electronic environment around measurable nuclei in a chemical substance. When placed within a strong magnetic field, a nucleus not containing even numbers of both protons and neutrons (most commonly 1H or 13C) distributes between non-equivalent energy states. The energy required for transition between these states corresponds to specific radio wave frequencies that are in turn correlated to the influence of the opposing magnetic field due to electrons surrounding the nucleus magnetic field on the applied field. The relaxation of each distinct nuclear spin resonance is detected with a radiofrequency receiver and provide a spectrum rich in structural information about the molecule.

It has been widely used as a tool for the identification and characterization of the chemical structures of organic compounds since it was commercially introduced in 1952 [104]. For qualitative assessment of chemical structure, NMR makes use of the nature and variation in chemical shifts, spin-spin coupling and the proportionality of signal area from resonating nuclei. The uniformity of signal response from each nucleus is the most important property for quantitative measurements which, when combined with a suitable degree of chemical shift dispersion, enables accurate assessment of sample composition. Although the potential for use of the proportionality of signal response for quantitative purposes has been known for many years [105], the application of NMR for quantitative analysis was limited due to its inherent insensitivity compared to that achievable by modern chromatographic systems. However recent advances in instrumental design coupled with a migration to higher magnetic-field instruments and the routine deployment of cryoprobes has significantly improved the accuracy and sensitivity of NMR signal quantification. As a result, in the last decade applications of quantitative NMR assay (qNMR) have become increasingly more popular and widespread [106].

The uniformity of NMR signal response eliminates the need to determine relative response factors for individual compounds as is required for chromatographic systems using UV/Vis or MS detection [107]. While 1H is the most widely used nucleus for quantitative NMR assays due to its virtual omnipresence in organic molecules, other nuclei, particularly 19F and 31P, have also been used where applicable [108, 109].

Quantitative NMR methods are potentially primary reference measurement procedures as they do not require a reference material of the substance subject to quantification.

Under conditions of quantitative measurement which allow the induced magnetization to reestablish the equilibrium state before each cycle of signal accumulation, the integration area of an individual signal, I, can be expressed as shown in eq. 9:

(9)I=kNCcos(α)=kNnVcos(α)=kNmwMVcos(α)

where I is the integration area (integral) of a signal, C is the concentration of the analyte in the sample solution, N is the number of equivalent nuclei giving rise to the signal, n is the amount of substance of the analyte in the solution, V is the volume of the solution, M is the molar mass of the analyte, m is the mass of material used to prepare the analyzed solution, w is the mass fraction of the analyte in the material, α is the pulse angle applied and k is a constant.

For I corresponding to unique, resolved signals arising from different molecules, the ratio of the two signal areas is proportional to the number of nuclei giving rise to the signal. Knowledge of the number of equivalent nuclei giving rise to each signal allows for a simple calculation of the relative amount of substance of the two analytes in the solution subject to qNMR analysis. If the mass fraction content of one of the analytes (the standard) is known the mass fraction content of the other analyte can readily be assigned (see Sections 3.2.2 and 3.2.3 below).

As for any technique, qNMR methods have advantages and disadvantages regarding the type of sample to be analyzed and the practicalities of its use in providing a fit for purpose quantification method.

Among the significant advantages:

  1. no need to detect or identify impurities,

  2. general applicability for uncomplicated small molecules,

  3. short method development time,

  4. non-destructive,

  5. no specific RM for an individual analyte is required.

Among the disadvantages:

  1. limited choice of solvent,

  2. low sensitivity,

  3. application can be difficult for complex large molecules and mixtures,

  4. high capital cost for instrumentation requiring specialized technical support.

Since qNMR is usually employed as a direct assay of the PC, there is no bias due to undetected impurities provided these do not interfere with the NMR signals from either the analyte or the standard. Quantitative nuclear magnetic resonance can also be used to quantify minor organic impurities present down to levels of a few hundred μmol/mol if the impurity possesses a unique resonance suitably isolated from other signals.

As the sensitivity of 1H NMR is inherently low compared with the detection methods used with most tandem chromatographic techniques, the analyte sample concentrations subject to qNMR analysis are significantly higher. As there is only a limited choice of suitable NMR-compatible solvents, the solubility of the analyte and standard is an important factor for achieving a successful qNMR application.

The compromises routinely made to enhance the signal and reduce the analysis time in routine qualitative NMR reduce the uniformity of signal response and are not compatible with quantitative accuracy [109]. Recent comparisons have demonstrated that care needs to be taken to ensure instrumental and experimental parameters are properly investigated and validated for an intended qNMR analysis [106, 110].

This summary of applications of qNMR is restricted to solution state measurements and describes experimental considerations to ensure its appropriate use in quantitative purity assessment of organic materials. Three qNMR methodologies have been used for the assignment of purity:

  1. relative quantification;

  2. internally standardized assay;

  3. externally standardized assay.

Appendix B provides examples of the experimental design and optimization for each qNMR method.

3.2.1 Relative quantification

The most straightforward qNMR purity analysis method is quantification of hydrogen-containing organic impurities from the intensity of their 1H-qNMR signals relative to those from the PC. When the structure of the impurity and the signal assignments are known, an estimate of the relative ratio of the mass of the impurity to the mass of the PC in the material can be derived from the integration ratio of NMR signals unique to each analyte.

This approach is insufficient to obtain an absolute purity value as it only provides a quantification of NMR-visible impurities relative to the PC and thus the result is not directly SI-traceable. These impurities will in general encompass the SCRS and SCOS, but not water, fully halogenated solvents or impurities, nor unidentified impurities. However, this method can usefully contribute to a comprehensive indirect purity assignment approach. In ideal cases due to the absence of gravimetric steps it can provide a relatively small measurement uncertainty estimate for the sum of wRS and wOS.

The measurement equation for relative quantification of the identified organic impurities that provide a unique NMR signal is given by eq. 10:

(10)wRS+OS=wPC×inISC,iIPCNPCNSC,iMSC,iMPC

where:

  • wRS+OS: mass fraction of n related structure and residual solvent impurities providing a unique NMR signal,

  • wPC: mass fraction content of PC in the material,

  • IPC: integral of the quantified signal for PC,

  • ISC,i: integral of the quantified signal for the ith known organic impurity,

  • NPC: number of 1H nuclei contributing to the PC quantification signal,

  • NSC,i: number of 1H nuclei contributing to the signal for the ith known organic impurity,

  • MPC: molar mass of PC,

  • MSC,i: molar mass of the ith known organic impurity.

This open-form equation can be solved iteratively.

3.2.2 Internally standardized assay

For the internal standard method, a gravimetrically defined amount of sample and internal standard are dissolved in an appropriate solvent to prepare the sample solution subject to analysis. Quantification is realized by comparing the integral areas of unique signal(s) from the PC in the material under analysis with unique signal(s) from an internal standard, S.

The measurement equation for internal standard qNMR is given by eq. 11:

(11)wPC=IPCISNSNPCMPCMSmSmPCwS

where:

  • wPC: mass fraction of the PC in the material,

  • wS: mass fraction content of internal standard S,

  • IPC: integral of the quantified signal for PC,

  • IS: integral of the quantified signal for internal standard S,

  • NPC: number of 1H nuclei contributing to the PC signal,

  • NS: number of 1H nuclei contributing to the internal standard S signal,

  • MPC: molar mass of PC,

  • MS: molar mass of internal standard S,

  • mPC: mass of material used in the preparation of the solution,

  • mS: mass of internal standard used in the preparation of the solution.

3.2.2.1 Reference standards

Internal standards for qNMR should meet as many as possible of the following criteria:

  1. high level of assigned purity with small associated uncertainty,

  2. precisely weighable (non-hygroscopic, non-volatile and non-electrostatic),

  3. chemically inert with respect to the NMR solvent used and the matrix analyzed,

  4. suitably stable in the chosen NMR solvent,

  5. absence of tautomeric or dynamic properties that broaden or split its NMR signals,

  6. possess a distinct NMR signal well resolved from all other signals,

  7. have no signals that obscure PC quantification signal(s) and

  8. mass fraction content contribution from nuclei giving rise to the quantification signal below 50 mg/g

The final criterion results from the requirement for gravimetric preparation of the qNMR sample. If the mass content contribution from the 1H-nuclei in the standard giving rise to the quantified signal exceeds 50 mg/g, the aliquot size for a typical analysis is limited to small amounts and the uncertainty associated with gravimetric operations involving the standard becomes a limiting factor in the overall uncertainty of the resultant 1H-qNMR purity assignment.

Benzoic acid is widely used as the ultimate source of SI-traceability for many qNMR measurements [111] despite being of somewhat limited use for direct measurements. A comprehensive suite of compounds for use as qNMR internal standards allowing greater flexibility in the source of SI-traceability for a given analysis have also been proposed [112]. From this group an internal standard can be selected for use with most organic compounds suitable for qNMR purity analysis. Regardless of the internal standard chosen it should either be a CRM produced by an NMI or a supplier accredited to ISO 17034 [10] or it should be linked through a calibration hierarchy with appropriate metrological rigor to such a material.

3.2.2.2 Solvent

The solvent for an internally standardized assay must solubilize both the analyte and internal standard and be non-reactive with either. The residual proton signal arising from the solvent must not interfere with either peak to be quantified. For externally standardized assay, it is preferable but not strictly necessary that the same solvent be used to minimize between solvent variability and potential bias from differences in tuning, lineshape, etc.

3.2.2.3 Spectrum quality

Central to successful qNMR with either internal or external standards is careful shimming, tuning and matching of each sample prior to the acquisition of quantitative spectra. This is required to ensure linear excitation, uniform signal amplification, detection of induced decay and reestablishment of equilibrium magnetization between pulses.

3.2.3 Externally standardized assay

Quantification can be carried out using an external standard, where the quantification reference is not in the same solution as the analyte. As well as methods for the direct comparison of the integrals of analyte and standard signals in separate NMR solutions, alternative methods are available:

  1. quantification against a calibration curve established using a different analyte [113].

  2. separation of solutions within a single NMR tube (e.g. coaxial tubes [114])

  3. use of proxy electronic signals [115], [116], [117], [118].

The proxy-signal PULCON (PUlse Length–based CONcentration) determination method [117], often used when achieving the smallest possible levels of measurement uncertainty, is not essential.

As well as its relative speed and simplicity, externally standardized assay has the advantage that the analyte is not combined in solution with an internal standard. This is a benefit for potentially reactive materials and can be important if analyte recovery is desired due to cost or rarity. Externally standardized qNMR assay also allows for greater flexibility in the choice of reference standard. Unless a simultaneous determination is being made using co-axial NMR tubes, the chemical shift of the quantified signal from the reference standard does not need to be fully resolved from that of the sample.

Where higher-accuracy assay results are required, the internal standard calibration method is preferred because it avoids the additional biases and uncertainty contributions introduced by variation in the experimental conditions when the analyte and standard are measured separately.

The fitness-for-purpose specifications for a specific measurement task guide the decision between the use of an approach based on an internal standard, external standard with common solvent or external standard with different solvents.

3.2.4 Measurement uncertainty and SI-traceability

The measurement uncertainty associated with a qNMR result can be calculated based on the combination of contributions from the orthogonal input factors (gravimetry, preparation, measurement, processing, calculations, etc.). The uncertainty contribution of the reference value of the standard underpinning the assay must also be included.

An uncertainty calculation for an internally standardized qNMR purity determination derived from eq. 11 and based on a published approach [119] is shown in eq. 12:

(12)u(wPC)wPC=(u(IPC)IPC)2+(u(IS)IS)2+(u(MPC)MPC)2+(u(MS)MS)2+(u(mPC)mPC)2+(u(mS)mS)2+(u(wS)wS)2

where:

  • u(MPC): uncertainty in molar mass of analyte;

  • u(MS): uncertainty in molar mass of internal standard;

  • u(mPC): uncertainty in mass of analyte sample;

  • u(mS): uncertainty in mass of internal standard sample;

  • u(IPC): uncertainty in integration of analyte;

  • u(IS): uncertainty in integration of internal standard signal;

  • u(wS): uncertainty in mass fraction content of internal standard.

A combined estimate for u(IPC) and u(IS) can be derived from the standard deviation of the ratio of the integrals, R = IPC/IS, for the replicate analyses. The uncertainty equation becomes as shown in eq. 13:

(13)u(wPC)wPC=(u(R)R)2+(u(MPC)MPC)2+(u(MS)MS)2+(u(mPC)mPC)2+(u(mS)mS)2+(u(wS)wS)2

There is a component of the uncertainty due to gravimetric sample preparation duplicated in the u(R) term that could be removed with a more vigorous approach to the uncertainty budget, however this contribution is relatively small and any double counting involved generally makes a negligible contribution to the result of the quadratic combination of the relative uncertainty terms.

The uncertainty of the masses of analyte and internal standard can be calculated in a variety of ways and are dependent on the laboratory’s calibration and mass determination procedures [120]. Because of the difference in density between organic compounds, corrections to the observed mass for the buoyancy effect due to differences in the mass of displaced air should be included for highest accuracy measurements. Additional contributions to the uncertainty budget can be made for uncertainty due to variation in the 1H/2H isotopic ratios of the H-nuclei contributing to the quantified signals and to allow for bias due to the potential presence of unresolved peaks below LOD.

The molar masses, M, and their uncertainties, u(M), are calculated from the assigned values for the contributing atomic masses. These should be calculated as recommended in the recent IUPAC report [121].

A Bayesian approach to assigning the uncertainty of a qNMR determination from the results of replicate analysis has also been described [122].

An uncertainty calculation for the externally standardized qNMR purity determination based on a published approach [119] is given by eq. 14:

(14)u(wPC)wPC=(u(R)R)2+(u(MPC)MPC)2+(u(MS)MS)2+(u(mPC)mPC)2+(u(mS)mS)2+(u(wS)wS)2+(u(mPC,sol)mPC,sol)2+(u(mS,sol)mS,sol)2

where the symbols are as for eqs. 12 and 13 and:

  • u(mPC,sol): uncertainty in mass of the analyte solution;

  • u(mS,sol): uncertainty in mass of the external standard solution.

The traceability of a qNMR result to the kilogram is realized via the materials certified for mass fraction purity or for percent content by mass that are used as the standards, by undertaking gravimetric operations using analytical balances certified for mass accuracy through appropriate calibration, by the implementation of appropriate maintenance and quality assurance and by the application of a validated qNMR measurement procedure to obtain the qNMR result. As noted for any mass fraction purity assignment, the result is also traceable to the mole through knowledge of the molar mass of the purity-assigned component.

3.3 Direct Assay by Other Techniques

In addition to qNMR, there are other direct assay methods for organic purity assignment. These fall into two categories:

  1. primary reference measurement procedures providing a de novo value of the purity of the material without reference to a standard of the same compound [123].

  2. secondary reference measurement procedures where the assignment is achieved through calibration (directly or indirectly) against a PRM of the same compound [124, 125].

Primary direct reference measurement procedures are not, by definition, linked to a calibrator of the material subject to value assignment. Only a relatively small number of compounds are suitable for purity assignment by primary direct methods. However, because the techniques can produce results at high levels of accuracy accompanied by low levels of uncertainty, they are critical for the assignment of simple, ultrapure materials which can be used for the calibration and method validation of purity assignment techniques applicable to a wider range of organic compounds. Examples include:

  1. benzoic acid [111] or potassium hydrogen phthalate (KHP) as primary calibrators for qNMR [126].

  2. creatinine and urea as PRMs in routine clinical chemistry [127].

  3. amino acids as calibrators in protein quantification [128].

Two methods for the assignment of ultrapure PRMs that produce results having small associated uncertainties are titrimetry [129] and coulometry [130]. Both techniques measure directly the amount-of-substance content (k) [131] of the PC in the bulk material, based on a well-defined chemical reaction. The mass fraction content (w) is readily calculated from the amount-of-substance content (k) given the molar mass of the PC.

Neither titrimetry nor coulometry can determine the organic molecule as a molecular entity. Rather, these methods determine the amount-of-substance content of a specific moiety present in the analyzed sample. To convert the result of the assay into a mass fraction, the identity and molar mass of the primary component of the material must be established independently. As an example, an acidimetric titration of KHP determines directly only the amount-of-substance content of replaceable H+ in the sample. The composition of the remaining material (in this case phthalate as its mono potassium salt) is assumed. If the assay is expressed on an amount-of-substance content basis, it is also assumed that a stoichiometric relationship exists between the detected species (replaceable H+ for KHP) and the remaining portion of the molecule [132].

Titrimetry and coulometry are best applied for the direct assay of nominally pure compounds containing non-reactive impurities. The functional group-specific character of titrimetry and coulometry means that no direct distinction is possible between the PC and any SCRS present containing the same reactive moiety. For an SI-traceable result for the mass fraction content of the PC, information from other methods on the nature and amount of these impurities is required. Consequently, approaches based on these techniques are not suited to the assignment of materials containing significant amounts of SCRS.

For some substances the consumption of sample may be limiting: more than 1 g of material is generally required to undertake titration methods at optimal accuracy. For materials with very high purity assigned with small associated uncertainty, appropriate care also needs to be taken in drying and handling the material to avoid the introduction of bias in the assigned values due to inhomogeneity or instability in the water content of the material [133].

3.3.1 Titrimetry

Titrimetry [129] meets the requirements for classification as a primary ratio measurement procedure [15]. It is based on the fundamental stoichiometric relationship of the underlying chemical reaction utilized in the titration. The analyte (the PC of a high-purity organic material, suitable for characterization by assay procedures) reacts with added titrant according to this stoichiometric relationship. Generally, the titrant is added as a solution to a gravimetrically prepared solution of the material subject to titration. Solutions have the advantage that they are homogeneous if mixed immediately before use. For any aliquot, the amount of titrant may be calculated exactly from the volume or mass added and the concentration (moles of solute per litre of solution) or the amount of substance content (moles of solute per kilogram of solution) of the titration agent.

Traditional use of titrimetry involves measurement of the volume of added titrant. The volumetric approach has the disadvantage that the concentration is temperature dependent, owing to the possibility for thermal expansion of the solution. Addition of solution by mass (gravimetric titrimetry or “weight titration”) eliminates this problem [134], as mass readings are effectively independent of temperature. Gravimetric titrimetry has the further advantage that balances yield a more objective measurement with a smaller uncertainty and higher resolution than that routinely accessible using volumetric measurements. If the titrant is available as a solid with accurately characterized homogeneity, the pure (neat) solid may be added gravimetrically as bulk material followed by incremental additions of a dilute solution of the solid (gravimetrically or volumetrically) to reach the equivalence point. This approach avoids evaporation of the solution, which can occur during the addition of a bulk solution. The total volume of solution is often smaller, resulting in a sharper endpoint in many titrations. A recent publication examined the relative performance of coulometric and volumetric methods for the mass fraction assignment of KHP [130].

Traceability to the SI of a result obtained by titrimetry relies on three factors:

  1. an exact stoichiometric relationship between the titrant and the analyte, such that any side-reactions that consume titrant must be negligible or at least quantifiable;

  2. the assay value of the titrant used being itself traceable to the SI;

  3. the masses/volumes of the sample and added titrant also being traceable to the SI.

The results of titrimetric measurements are thus traceable to the stoichiometry of the titration reaction, mass, volume (where relevant), the molar masses of the analyte, and the assay of the titrant. If the measured quantity for the sample and/or the titrant is the amount-of-substance content of analyte, rather than the mass fraction, the respective molar masses (which have non-zero uncertainties) can be eliminated from the calculation, decreasing the overall uncertainty. Although the component of uncertainty associated with the molar masses is usually negligible, this treatment yields a noticeably decreased uncertainty for very precise titrations.

The critical traceability of the titrant to the SI can be obtained either directly (e.g., if a CRM is used) or indirectly through a separate standardization titration, with the concentration or amount-of-substance content of the titrant assigned from its calibrator. In this latter case, the calibrator can be a CRM (or other SI-traceable material) either identical to the compound being characterized or a different compound that reacts with the titrant in an exact stoichiometric manner. For example, a standard NaOH solution could be used for an acidimetric titrimetric assay of maleic acid, with the NaOH solution itself standardized against (hence, traceable to) a CRM for KHP (or potentially even a separate CRM for maleic acid) as the calibrator.

The strict requirement for a well-defined stoichiometry has the consequence that titrimetry of organic compounds is generally limited to use with organic acids and, to a lesser extent, bases. A relative precision of 0.002 % is attainable in cases of a homogeneous, high-purity sample with an overall relative combined uncertainty including the uncertainty of the titrant standardization of the order of 0.03 %. Oxidation-reduction titrations have also found limited use with organic compounds [135] but are not as frequently used as acidimetric titrations, owing to stoichiometric limitations.

3.3.2 Coulometry

Coulometry is a type of titrimetry using electrochemical generation of the titrant. As such it is also potentially a primary direct measurement procedure [15, 136]. The titrant reacts with the analyte in the same way that volumetrically- or gravimetrically-added titrant reacts in a conventional titration. Coulometry thus incorporates most of the advantages and shortcomings of titrimetry.

The generation of titrant in coulometry is governed by Faraday’s Laws of electrolysis [137] relating the charge passed through an electrode to the amount of titrant that is generated. In practice, a sample of mass, m, is titrated. The amount-of-substance content of the PC, kPC, is calculated directly from the electric current, I, passing through the electrode; the time, t; the ratio of electrons consumed per mole of analyte, n (including its reaction with electrogenerated titrant); and the Faraday constant, F, a fundamental physical constant as shown in eq. 15 [138], [139], [140]:

(15)kPC=t0tfIdtnFm.

This incorporates both the electrochemical generation of the titrant and its stoichiometric reaction with the analyte moiety.

The equation for calculation of mass fraction from amount-of-substance content is given by eq. 16:

(16)wPC=kPCMPC

Corrections based on the mass fractions of interfering impurities are assigned as shown in eq. 17:

(17)wPC=MPC(kPC(winiMi))

Most high-accuracy coulometry is performed using a constant electric current, which can result in assigned values that have very small associated uncertainties [141] To make optimal use of the potential precision achievable, the bulk of the titrant is often added at high constant electric current (known very accurately), with the remainder required added at a lower constant electric current. Constant-current coulometry has the further advantage that the titrant is generated and used virtually immediately, avoiding the potential for changes in concentration during storage.

The traceability of results obtained by coulometry relies on the same factors that govern titrimetry, except that the source of traceability are the quantities in eq. 15 rather than a chemical titrant. This equation is only valid if no side reactions generate other species at the electrode or consume titrant. This property is often referred to as “100 % current efficiency.”

Provided these requirements are fulfilled, the traceability of coulometry is to the measured electric current, time, sample mass applicable to the titration (SI units A, s and kg respectively) and to the stoichiometry of the titration reaction. The inherent measurand in coulometry is the amount fraction, not the mass fraction. As in the case of standard titrimetry, a smaller uncertainty is achieved if the measurand is the amount fraction of the PC in place of the mass fraction.

Coulometry achieves a relative precision better than 0.001 % in optimal cases [141]. Typical relative uncertainties are of the order of 0.01 to 0.02 % for the assignments of high-purity, homogeneous CRM materials. Frequently the precision and uncertainty of results are limited by the inherent homogeneity of the material being assayed. Most of the CRMs used as calibrants in titrimetry are certified using coulometry. High-purity CRMs for benzoic acid and KHP, having been value assigned by coulometry, are also being used to underpin the SI-traceability of quantitative NMR techniques [111].

A number of publications and review articles provide further information on the applications of coulometry for organic purity assignment [130, 142, 143].

Appendix C provides a detailed example of a titrimetric method for purity assignments.

3.4 Indirect Assay by Direct Assessment of Total Impurities

3.4.1 Density and specific gravity measurements

Measurements of the ratio of the density of a substance to the density of a reference substance, equivalent to the ratio of the mass of a substance to the mass of a reference substance for the same given volume, provides a straightforward and inexpensive means of obtaining information about the mass fraction content of organic fluids [144]. The overview of the theory of its use for purity determinations and summary of its applications provided in the relevant chapter of the first IUPAC Organic Purity Characterization monograph [1] remains relevant as a basic description of the approach.

Reference hygrometers can measure liquid density as the specific gravity using a gravimetric method with a relative expanded uncertainty approaching 0.01 %. The reference substance used is nearly always water at its densest state (4 °C). The temperature and pressure must be specified for both the sample and the reference. Tables of the relationship of observed specific gravity to the percentage mass fraction content of the liquid of interest are available for many organic liquids [145]. If necessary, a calibration function can be defined through gravimetric preparation of spiked materials.

The compound density is significantly affected by the major impurity (e.g., water impurity in ethanol modifies the density). The resolution of the densimeter should be at least 10−5 g/cm3 according to the target uncertainties needed for the purity determination. To reach these values, the sample preparation technique is critical and requires that there be no water residue on glassware. Sonication of the sample often helps to stabilize the hygrometer signal.

3.4.2 Thermal Methods

Calorimetry and thermal analysis are well-established methodologies for determining the physical properties of matter. These techniques, which measure the quantity changes associated with a temperature change to a substance can in suitable cases also be related to the total impurity content of the material, SCtotal. This, by difference, provides an assignment of the purity of the PC. Because the quantities are directly measured, the traceability of the measurement result is readily established.

Within thermal analysis, applications based on the freezing point depression method [146, 147] and the related method of differential scanning calorimetry [148] are popular for purity assay. Both methods have been proposed to meet the requirements for primary direct purity measurement procedures [123, 149, 150]. These methods relate the observed extent of melting (freezing) point depression to SCtotal and rely on the ideal assumption that all impurities exist only in the liquid phase during fusion and have equivalent properties to each other and to the PC.

In real samples, SCs may remain in the solid phase, evaporate into the headspace in the sample container or be insoluble. In these cases, further evidence from supporting techniques may be required to determine the impurities not amenable to quantification by the freezing point depression method. A classification of the possible types of impurities present during the fusion process and the changes they undergo during fusion is shown in Figure 2.

Figure 2: 
              Schematic diagram of impurities before, during and after fusion. Circle: insoluble impurities; triangle: volatile impurities; diamond: solid soluble impurities; square: solid insoluble impurities.
Figure 2:

Schematic diagram of impurities before, during and after fusion. Circle: insoluble impurities; triangle: volatile impurities; diamond: solid soluble impurities; square: solid insoluble impurities.

Only impurities of the “diamond” and “square” category in Figure 2 are investigated using thermal methods. Application of these methods assume the contribution from volatile [“triangle”] impurities and insoluble impurities not taken into the liquid phase [“circle”] are negligible or can be estimated by other means.

The freezing point depression method also does not take into account any PC and/or SCs released into the gas phase due to volatility. When the components comprise an ideal solution, the ratio of PC and SCs will be the same in either phase. However, if the volatility of each component differs this may bias the observed purity due to changes in the liquid phase composition. For real samples, the amount-of-substance fraction in the gas phase relative to the liquid phase is dependent on the activity of each component and can be estimated from the activity coefficients of each component.

3.4.3 Freezing Point Depression

The freezing point depression method relies on the establishment of a thermodynamic equilibrium between solid and liquid phases undergoing fusion. It is assumed that the amounts of PC and SCtotal are constant and that all impurities exist in the liquid phase only. The bias and resultant additional uncertainty arising from these assumptions becomes larger as the purity of the material decreases [151] and methods for their estimation are described in the literature [152].

The simplified equation to calculate the amount-of-substance fraction of SCtotal in solution, xB, which can be used by difference for the assignment of the PC purity, is given in eq. 18:

(18)xB=ΔfusH(T*)R(T*)2(T*T)

where ΔfusH is the molar fusion enthalpy, R is the gas constant, T* is the melting point of the pure PC and T is the sample temperature. This relation is realized in every condition during fusion. The amount-of-substance fraction of SCtotal is obtained when the fusion is completed. In this case T = Tfus and eq. 19 applies:

[19]xB*=ΔfusH(T*)R(T*)2(T*Tfus)=ΔfusH(T*)R(T*)2ΔT.

where xB is the amount-of-substance fraction of SCtotal at Tfus and ΔT is the melting point depression.

The melting point of the pure PC (T*) and ΔfusH are intrinsic thermodynamic properties of the PC whose values can generally be readily found in the literature. The ΔT is a sample composition-dependent value. Measurement of ΔT is thus the most critical experimental parameter for purity assay by the freezing point depression method.

Although ΔT can be determined from observing the melting point change achieved by spiking a sample with known amounts of impurities [153], this approach is not widely used. A more general procedure is to utilize the relation between fraction melted, f, and the equilibrium temperature, Teq, observed during a controlled, gradual melting of the sample. Figure 3 is a schematic representation of the phase changes assumed to be taking place during a sample fusion.

Figure 3: 
              Schematic diagram for purity assay by freezing point depression method.
Figure 3:

Schematic diagram for purity assay by freezing point depression method.

The equilibrium temperature (Teq) can be derived as shown in eq. 20:

(20)Teq=T*ΔTxBxB*.

When all impurities are assumed to be in the liquid phase, the amount-of-substance fraction of impurities in the liquid phase is inversely proportional to the fraction melted, xB=xB*/f. eq. 20 can be rearranged into eq. 21:

(21)Teq=T*ΔTf.

This equation derives from the assumption of no solid-soluble impurities present in the sample. In cases where it is necessary to consider the effect of solid-soluble impurities, the Lewis and Randall differential equation can be used as shown in eq. 22 [147, 154]:

(22)dTdxB=(k1)RT2ΔfusH

where k is the partition constant of the concentration of the impurities in the solid and the liquid phase. This introduces the correction term α into eq. 23:

(23)Teq=T*ΔT/(f+α);α=k1k.

From f and temperatures at selected equilibrium conditions, ΔT and T* can be determined. For the evaluation, the reciprocal of the f versus Teq plot (a van’t Hoff plot), is used. Teq is measured with a calorimeter. The fraction melted (f) is evaluated from the ratio of partial fusion enthalpy at the equilibrium condition during fusion, ΔfusHpartial and the total fusion enthalpy of the sample, ΔfusHtotal according to eq. 24:

(24)f=ΔfusHpartial(T)ΔfusHtotal(Tfus)

The molar fusion enthalpy can be measured by a standard procedure using the calorimeter. Therefore, temperature and enthalpy measurements are the minimum requirements for the purity assay by freezing point depression method with calorimeters. For the evaluation of ΔfusH, the sample mass is needed in addition to the enthalpy measurement.

There are three established freezing point depression methods for obtaining obtain f and Teq:

  1. fractional melting with an adiabatic calorimeter [155], [156], [157].

  2. stepwise scan method with a DSC [158], [159], [160].

  3. continuous scan method with a DSC [161, 162].

These techniques involve common procedures for relating the enthalpy change during the fusion process to the SCtotal content. Detailed examples of their implementation are described in Appendix D.

3.4.4 Converting amount-of-substance fraction to mass fraction purity

The freezing point depression method provides a direct measure of xB. However, for optimal use as a PRM the amount-of-substance fraction of the PC, xPC, must be converted into a mass fraction value, wPC. The values for xPC and wPC are equal when all the components have the same molar mass. When the molar masses differ they can be interconverted as follows provided an estimate of the average molar mass of the SCs, MSC, is available in addition to the (known) molar mass of the PC, MPC. In this case eq. 25 applies:

(25)wPC=MPC(1xB*)MPC(1xB*)+MSC(xB*)(1xB*).

For the estimation of the average molar mass of impurities information is required using other techniques. The accuracy of the conversion increases as more information about the impurities is available, although as the amount fraction of the PC approaches 1.0, the uncertainty in the value for mass fraction decreases regardless of information on the structure of the impurities. For lower purity samples, inaccurate identification and determination of the nature of the impurities potentially introduces a significant bias in the derived mass fraction purity assignment.

It is good practice to check a material separately for impurities undetectable by the freezing point depression method. If present, they should be quantified by other measurement techniques. To account for the mass fraction of insoluble and volatile impurities in the case where the contributions from these impurities are significant, the mass fraction, wPC is adjusted as follows from eq. 26:

(26)wPC=(1wOSwNV)wPC, fpd

where wOS is the mass fraction of volatile impurities, wNV is the mass fraction of insoluble, residual impurities and wPC,fpd is the value for mass fraction of the PC obtained from eq. 25.

3.4.5 Measurement uncertainty and SI traceability

The parameters in eq. 18 are common to the three techniques. The uncertainty sources associated with these inputs are summarized below.

The gas constant, R, is a physical constant and its value is available from CODATA [163, 164]. The molar fusion enthalpy, ΔfusH, is derived from the enthalpy measurement. The contribution to ufusH) due to calibration of the instrument and sample weighing must be accounted for. The melting point depression, ΔT, and melting point of the pure PC, T*, are obtained from the van’t Hoff plot. The measurement uncertainty due to the regression analysis and the temperature measurement contribute to the uncertainties of both parameters.

When multiple parameters are evaluated simultaneously, the measurement variation of each parameter should not be accounted for independently as the parameters are correlated. In such a case, the measurement variation of xB should be evaluated instead of that of each parameter. An additional uncertainty source is the range of the fraction melted. An appropriate estimate for the van’t Hoff plot can be obtained by undertaking a purity assay using a CRM of a high-purity substance.

To account for the small value of ΔfusHpartial, data obtained during the initial step of fusion should be excluded for purposes of purity assay. Although the appropriate range of fraction melted is sample dependent, it is impossible to determine the most appropriate range without knowledge of the purity obtained by the freezing point depression method. This generally requires iterative measurements in order to assess the influence on assigned purity of variation in the selected range of fraction melted.

3.5 Bio-oligomer Purity Assessment

While the higher-order reference measurement procedures for the content assignment of pure-substance CRMs are well-established for small organic molecules, difficulties and challenges remain in the assignment of such materials for larger molecules such as peptides, proteins, carbohydrates and oligonucleotides. The application of traditional mass-balance based approaches can be particularly challenging for these materials due to difficulties in handling them and limitations in the amount available for characterization.

Quantification of larger molecules is also complicated by the fact that they can exhibit higher-order structures such that characterization of the primary structure of the molecule may be insufficient to allow for correlation of the observed amount of substance of the molecule to its biological activity. Nevertheless, quantification of the primary structure purity of such biomolecules is the first step in establishing a PRM for that analyte. The measurand of interest is the mass fraction of the biopolymer present in the bulk material.

3.5.1 Peptide purity by amino acid assay

In general, pure peptides/proteins cannot be obtained in sufficiently large quantities for the implementation of a range of different characterization techniques. This has resulted in a reliance for the harmonization of many large-molecule measurements using standard methods and/or reference substances. Traditionally, the parent material is subject to exhaustive hydrolysis and the concentration of the liberated monomers (amino acids, carbohydrate, nucleotides) is measured and related to the initial concentration of the compound of interest [165]. Recently, strategies have been developed based on the determination of protein amount via quantification of prototypic peptides released by enzymatic hydrolysis from the protein subject to assignment [166], [167], [168]. These approaches have been investigated in depth for the routine analysis of human growth hormone and its biomarkers [169]. Several NMIs are developing higher-order measurement procedures for the analysis of purified protein calibrators [170] and serum-based matrix materials. These approaches show promise for the standardization of priority protein measurands. However, they in turn require RMs of assigned purity for each measured proteolytic peptide.

In principle, the purity of any peptide can be assessed by use of a mass-balance approach. However, this could require impractically large quantities of precious peptide material. A simpler alternative to the full mass-balance approach is a peptide impurity-corrected amino acid analysis. This involves quantification of the constituent amino acids released following hydrolysis of a sample of the material with correction for the contributions due to amino acids originating from impurities [171], [172], [173].

The CCQM-K115 comparison, which investigated the purity assignment of a sample of human C-peptide, provides examples of assignment using both mass balance and peptide-hydrolysis based methods [174].

The quantification of the individual amino acid mass fraction content in the hydrolysate by exact matching liquid chromatography-single point isotope dilution tandem mass spectrometry (LC-IDMS/MS) is described as follows, assuming no isotopic overlap between the analyte and isotopic spike:

(27)wx=wzmzmycmymxRBRBc

where:

  • wx: mass fraction of amino acid in sample,

  • wz: mass fraction of original amino acid in calibration blend,

  • mz: mass of original amino acid solution in calibration blend,

  • myc: mass of the labelled amino acid solution in calibration blend,

  • my: mass of the labelled amino acid solution in sample blend,

  • mx: mass of sample used,

  • RB: sample peak area ratio,

  • RBc: calibration peak area ratio.

A general approach to uncertainty budget and measurement uncertainty calculations for the double IDMS method have been reported [175].

The equation for the conversion of the amino acid concentrations determined using eq. 27 value for the original mass fraction of the parent peptide is given by eq. 28:

(28)wP=(MPZ1)[nAAmmiYSC,iwSC,iMSC,i]

where:

  • wP: mass fraction of peptide in the source material,

  • MP: molar mass of peptide,

  • Z1: number of residues of the amino acid of interest per peptide molecule,

  • nAA: amount of substance of the amino acid of interest measured in the sample analyzed,

  • mm: mass of the material sample analyzed,

  • Yi: number of residues of the amino acid of interest per peptide impurity molecule (IMPi),

  • wSC,i: mass fraction of the peptide impurity SCi,

  • MSC,i: molar mass of the peptide impurity SCi.

This approach requires identification and a fit-for-purpose quantification of the peptide impurities present in the material for accurate results. The source of SI-traceability of the amino acid analysis results is to a PRM for each amino acid. A simplified approach where all peptide impurities are measured relative to the parent peptide has also been reported [176].

3.5.2 Peptide purity by other techniques

Other approaches for the assessment of purity have been applied when only a small quantity of peptide material is available. These include qNMR and elemental analysis (%C,H,N,S) with correction for non-peptide nitrogen-containing impurities. Both qNMR and elemental analysis require a correction of the raw result or allowance for contributions due to related structure components [117, 173, 177, 178].

A strategy for correcting both LC-MS/MS and 1H-qNMR results for related peptide impurities and combining results from both methods using a Bayesian statistical approach using mass balance results as prior knowledge has been reported recently for the assignment of a calibrator for angiotensin II [176].

4 Traceability and Uncertainty of Purity Assignment

4.1 Interpreting Purity Statements

As discussed in the Introduction, for the purposes of this report the focus has been on the assigned value for the mass fraction of the PC in a PRM reported in units of mg/g or expressed as a percentage. The value should be reported as a mass fraction, w, with an associated uncertainty at a stated level of confidence [179].

The associated uncertainty is usually stated as a 95 % expanded uncertainty, U95%(w), understood to specify the symmetric interval w – U95%(w) ≤ w ≤ w + U95%(w) and more compactly stated as w ± U95%(w). However, asymmetric intervals may be encountered, particularly with very pure materials.

Such intervals are defined by lower and upper bounds, w – UL95%(w) ≤ w ≤ w + UU95%(w) – more compactly stated as w{UL95%(w), +UU95%(w)} or as wUL95%(w)+UU95%(w) [191].

In either case, the true value of the mass fraction of the component in any given unit of the PRM is expected, with about 95 % confidence, to lie within the specified interval.

4.1.1 Achieving SI-traceable purity assignments

An assigned purity, wPC ± U95% (wPC) is traceable to the SI when the results obtained for each contributing measurement is traceable to the SI; that is:

  1. calibrated to appropriate references;

  2. suitably documented;

  3. reported with an appropriately estimated uncertainty.

When stated as an SI-traceable mass fraction, w + U95%(w) should not exceed the limit value of 1 g/g. If the interval does extend beyond the natural limit, a w ± U95%(w) symmetric interval can be treated as specifying the asymmetric interval w – U95%(w) ≤ w ≤ 1 g/g. Clearly a value for w > 1 g/g is physically impossible and cannot provide traceability to the SI.

Note that zero is also a limit value of mass fractions. However, for all useful PRMs w – U95%(w) for the PC will be much greater than zero and there is no need to consider this boundary condition further. Therefore, since the mass fraction interval between 0 and w will always be much wider than the interval between w and 1, if the expanded uncertainty is specified as an asymmetric interval, then UL95%(w) will be larger than UU95%(w) and the ratio UL95%(w)/UU95%(w) > 1.

In some application areas, notably the pharmaceutical sector, the content of higher-order reference standards is commonly stated on a relative basis. Such purity values are not directly metrologically traceable to the SI but rather to the specified artefact RM, often representative of the first commercial preparation of a material. Such purities are relative to the assay of the artefact. As a result there is no natural limit to the achievable purity and uncertainty intervals that include values greater than 100 % are valid. However, these results cannot be regarded as SI-traceable in the absence of a reference value for the purity of the artefact.

4.1.2 Degrees of freedom

Certified Reference Material certificates should provide values for the standard uncertainty, u(w), the 95 % coverage factor, k95%, and possibly the number of degrees of freedom, v, associated with u(w) [180]. These values are related through the equations U95%(w) = k95%·u(w) and k95% = t95%,v, where t95%,v is the Student’s t two-sided 95 % coverage factor for v degrees of freedom. Degrees of freedom can be interpreted as one less than the number of independent determinations of w. Knowledge of v is useful in the more sophisticated uncertainty propagation methods.

When a certificate only provides U95%(w), assume that k95% = 2, u(w) = U95%(w)/2 and v is “large.” Likewise, if k95% is stated to be 1.96 (the value for t95%,) or 2, v is “large.” In such cases, a numerical value of v = 60 can be used since t95%,v first becomes less than 2 for v = 61. When v is not stated but k95% = U95%(w)/u(w) > 2, ν can be determined by comparing k95% to tabulated values for t95%,ν.

4.2 Assigning Purity and its Uncertainty

There are two general approaches to establishing the mass fraction of the main component, PC, in a nominally pure material: 1) “mass balance” approaches where everything in a material except the PC is quantified as described in Sections 3 and 3.1) “direct assay” approaches where the PC is itself quantified as discussed in Sections 3.2 through 3.4 [3]. For any given material, many quantitative analytical techniques can contribute to one or the other (or both) of these approaches. Once the necessary quantitative values are available then combining them into a metrologically traceable estimate of the mass fraction of the PC in the material is (relatively) straightforward. For a less metrologically intricate discussion of these issues, see also the paper by Gates et al. [181].

4.2.1 Metrological traceability

For some measurands by some techniques, the necessary references may be independent of the nature of the material; e.g., for water by mass loss on drying the references are to mass and temperature. Some techniques enable calibration of many different compounds to a structurally unrelated CRM; e.g., qNMR. However, other techniques require calibration with an RM containing the same analyte at a known mass fraction; e.g., external standard chromatography.

When calibration requires the use of an RM, the assigned mass fraction of the analyte in the RM must also be SI-traceable. Ideally, a suitable CRM is available to use in this role. However, often no appropriate CRM is available and a less-well-characterized material must be used. It will therefore be necessary to establish a fit-for-purpose traceable estimate of the mass fraction of the measurand in the calibrant. Fortunately, the level of effort required for such secondary purity determinations need not be excessive. If the measurand makes a relatively small contribution to the final purity of the PC in the material subject to assignment then an evaluation using a method providing a relatively large uncertainty may be suitable. A suggested approach is described in Section 3.1.1.4 of this Report.

4.2.2 Mass balance assignment

In principle, the indirect mass-balance approach requires detection and quantitative evaluation of all SCs, including: structurally-related organic contaminants and degradation products introduced during preparation and purification, SCRS; water, SCW; residual organic solvents, SCOS; and inorganics, SCNV. Given an exhaustive list of n unique SCs evaluated as Gaussian N(wi, u(wi)) probability distributions, the mass fraction purity of the analyte is shown in eqs. 29 and 30 respectively:

(29)wPC=1000 mg/ginwi
(30)u(wPC)=inu2(wi)

where wi represents the quantified mass fraction of the ith impurity and u(wi) its standard uncertainty.

In practice, biases in the mass balance approach can arise due to the challenges of identifying and quantifying all SCs. Even with complete knowledge of a material’s source and history it is possible that:

  1. impurities are present at levels below the LOD of the available analytical method(s);

  2. impurities are present but cannot be detected;

  3. unsuspected impurities are at detectable levels but overlooked;

  4. analysis artefacts are mistakenly interpreted as impurities.

While there are several computational approaches to dealing with non-quantified SCs [29, 182], the completeness of the mass-balance approach will rely on “informed judgement” [183]. The completeness of the quantification of the SCs can be tested by comparison of the mass balance value with the result of a direct assay of the material based on an independent measurement principle.

4.2.2.1 Known but not quantified impurities

When an SC is known to be present but at a level too small to be quantitatively evaluated, wi can be characterized as being somewhere between zero and the LOD of the analytical method in use. In the absence of any other information about the likely value for wi, the 0 < wi < LOD interval can be interpreted as a symmetric U(0, LOD) rectangular distribution, with wi = LOD/2 and u(wi) = LOD/2√3. When wi is believed to be very small compared to those of other known impurities, wi can be assigned a value at or near 0 and the uncertainty treated as an asymmetric triangular, gamma, or other appropriate probability distribution that has its maximum at or near zero and descends to provide 95 % coverage at the LOD.

Regardless of the probability distribution used to describe the SC, non-quantified SCs known to be present should be allowed for in the uncertainty calculation. Provided the relative uncertainty contribution from such SCs is small, their impact on the effective degrees of freedom associated with u(wPC) will be negligible.

4.2.2.2 Plausible but not detected impurities

Analysts are likely to look for some potential SCs that are structurally related to the PC without having much expectation of their presence. When such a “fishing expedition” fails to detect such a compound’s presence and (in retrospect) it is thought that there is little or no likelihood of the potential SC being present in the material, then that potential SC need not be considered further. However, if there remains doubt about its presence then wi can again be characterized as being somewhere between 0 and LOD, but with a much greater likelihood of being 0. The wi can be assigned 0 and, as above, the associated uncertainty treated as an asymmetric triangular, gamma, beta or other appropriate distribution with maximum at zero and continuously decreasing to provide 95 % coverage at the LOD.

4.2.2.3 Overlooked Impurities and analytical artefacts

Detecting unsuspected SCs and discriminating analysis artefacts from “real” analytical signals requires diligence, skill and chemical insight. There is no statistical magic that can compensate for incomplete or inaccurate chemical analysis. However, any bias introduced by such problems may be detected by comparison to results from direct assays.

4.2.2.4 Combining two or more estimates for the same impurity

When there are two or more quantitative estimates for the same SC (e.g., from qNMR and chromatography or different chromatographic methods), the individual estimates must be reduced to a single estimate that represents the state of knowledge about that SC. How to best accomplish this again requires technical judgement.

If one of the methods is believed to be more reliable than the other(s), then it may be valid to assign wi and u(wi) using just that method’s result. However, when there is no single clearly superior method then all the potentially valid results should be combined.

There are many well-characterized methods for estimating consensus location and dispersion values from independent estimates of the same measurand [184], [185], [186]. Linear pooling [187] is among the more appropriate in that it can be used with as few as two results and is relatively easy to calculate. The NIST Consensus Builder [188] provides an open-access online calculator for implementation of this and other potentially appropriate consensus calculation methods.

4.2.3 Quantitative NMR assignment

Quantitative NMR compares signals from structurally dissimilar molecules, thus potentially enabling the use of a single calibrant for a range of different analytes.

The necessary conditions of this method are described in Section 3.2, including the requirement that when the PC and internal standards materials are combined in the same NMR test sample, each must have at least one stable, non-exchangeable proton moiety that provides a structurally-distinct, well-resolved NMR resonance for quantification. Since the integrated area of each 1H-qNMR peak is, in principle, exactly proportional to the number of resonant protons of the corresponding moiety in the test sample, the mass fraction purity of the PC, wPC, in the material can be determined using the measurement eq. 11 described in Section 3.2.2 and reproduced here:

wPC=IPCISNSNPCMPCMSmSmPCwS

The quantities to the right-hand side of the measurement function can be independently established with reliable uncertainty estimates as described in Section 3.2.4 and references therein.

Biases in the qNMR approach can arise due to the challenges of completely integrating a signal that is unique for the PC. Where resources allow, the presence of potential biases should be tested by independent assessment of the PC content of the material by a mass balance approach or by a direct assay based on a different physicochemical principle.

4.2.4 Combining purity values and uncertainties from different methods

For materials intended for use as PRMs, it is recommended practice to undertake purity assessments using both direct and indirect determinations. Combining the results from multiple methods provides a result that is more likely to be accurate and provide greater confidence than does any single estimate.

When multiple results for the PC are available, the first step is to confirm that they all estimate the same measurand (the mass fraction of the PC in the material, wPC), then compare the 95 % uncertainty intervals. If the intervals for results substantially overlap, the consensus result can be estimated as a weighted mean. Metrologically appropriate tools for assigning a consensus value are readily available.

If the indirect estimate is significantly closer to the limit value than the estimate from direct assay, it is possible that some SCs have escaped detection or were underestimated. If the indirect result is farther from the limit value, it is possible that two or more of the wi represent the same impurity or that some have been overestimated. In either case, the cause may also be bias in the direct result. If resources permit, these possibilities should be investigated and, if possible, the discordance resolved.

If no further experimental effort can be justified or no explanation can be found for the discordance, then the 95 % uncertainty interval for wPC extends from the UL95% (wPC) of the smaller estimate to UU95% (wPC) of the larger. The uncertainty intervals for the individual methods do not capture the loss of confidence from the discordance of the two methods.

If neither of the estimates is believed to be more reliable, then wPC can be estimated as the midpoint of this range. If one of the estimates is believed to be more likely than the other, estimate wPC as that value. When one of the estimates is believed to be somewhat more reliable, techniques are available that can use this information and produce an appropriate consensus estimate [189, 190].

4.2.5 Reporting and propagating purity uncertainty

The minimum information that must be reported is the purity value of the primary component, wPC, its 95 % uncertainty interval, wPC ± U95% (wPC) and the reporting units. If generated during the statistical analysis, it may be useful to report the standard uncertainty, u(wPC), and its degrees of freedom, ν(wPC).

The purity and its uncertainty should be estimated using the most appropriate measurement model and tools available. However, when the purity is intended to be traceable to the SI rather than to an artefact, the interval that is reported must not exceed the natural limit value of 1 g/g.

Should the initially estimated uncertainty interval extend beyond 1 g/g, there are several options:

  1. reduce the uncertainty of the major contributor(s) to the uncertainty through further analysis;

  2. recalculate the purity using a Monte Carlo model (MCM) [191, 192] that enables constraining the estimate to be between limits [122, 193];

  3. identify the largest sources of uncertainty in the calculation. Check that the probability distributions used to describe them are appropriate. If the experimental data for any significant contributor are not symmetrically distributed, consider using an MCM.

  4. truncate the reported interval at 1 g/g.

The latter three options will result in the reporting of an asymmetric uncertainty interval. While requiring more effort on the part of users of the purity information (see the “Using Purity Estimates” below), asymmetric intervals reflect reality for measurement results that abut natural limits.

4.2.5.1 Propagating a symmetric uncertainty

The uncertainty calculated for the mass fraction of the PC can be propagated through the measurement equation of any subsequent calibration used in the measurement process.

The propagation approach described in the “Guide to the expression of uncertainty in measurement” (GUM) [180] assumes that the standard uncertainties for all input parameters are expressed as the standard deviations of Gaussian (normal) N(x,u(x)) probability distributions where x ± u(x) covers about 68 % of the plausible values for x.

When v for all the uncertainties are large, the 95 % expanded uncertainty of the sample material, U95% (wPC), is given by

(31)U95%(wPC)=2u(wPC)

When v are not all large, the U95% should be estimated using the Student’s t expansion:

(32)U95%(wPC)=t95%,v(wPC)u(wPC)

where v(wPC) can be estimated from the Welch–Satterthwaite formula as described in the GUM.

Standard and expanded uncertainties can be estimated using computationally-intensive GUM-Supplement 1 [194] or Bayesian MCMs. These methods enable specification of input parameters using a variety of probability distributions rather than just the Gaussian. Freely available online implementations of MCMs supported by NMIs include the NIST Uncertainty Machine [195, 196] and the LNE-MCM [192].

4.2.5.2 Propagating an Asymmetric Uncertainty

MCM approaches to the propagation of asymmetric uncertainties have been developed [197], [198], [199] for use in cases where estimates that are statistically sound or that provide the narrowest defensible intervals are required for the intended purpose of the PRM.

5 International Comparisons of Purity Assignments

The CCQM OAWG [4] undertakes critical evaluation and benchmarking of NMI and DI capabilities for the execution of “higher order” measurement procedures for well-defined organic analytes for which the SI-traceable amount-of-substance is to be determined. Although the scope of OAWG activities encompasses a wide range of chemical measurements, irrespective of the level at which the analyte is present, the nature of the matrix or the analytical techniques used one of the OAWG’s key roles is to ensure that each measurement comparison is metrologically traceable to a primary calibrator that can be described in relevant units of the SI. For most cases, the relevant unit is the mass fraction purity of the primary calibrator. The purity determination of organic calibrators is thus one of the core activities for the OAWG. Activities to assess individual institutes’ capabilities to characterize SI-traceable organic calibrators have been undertaken within the OAWG for nearly two decades. This was initiated with a series of CCQM pilot studies [200] which led in turn to the CCQM-K55 series which investigated, in a series of separate comparisons, the purity assignment of 17β-estradiol, aldrin, valine and folic acid [6].

The approach used for purity assignment in these comparisons has developed from a relatively basic determination of the mass fraction purity (%) to a comprehensive determination of all impurity contributions present in a material that impact the value of the mass fraction purity of the primary component of the material at least at the mg/g level. The results of these comparisons are used by the participants to underpin and benchmark their core competencies in this area. The evolving metrological challenges lie not simply in the chemical component assignments, but also include how the data are treated within and among the participants in each comparison or pilot study.

The CCQM-K55 series of key comparisons covered the “purity of organics” measurement space across a four-sector model based on the use of molar mass and pKOW as surrogates respectively for structural complexity and polarity. The model was developed as follows:

M<300 g/mol,pKOW<2;300<M<500,pKOW<2;M<300 g/mol,pKOW>2;300<M<500,pKOW>2.

Successful participation in a specific comparison was presumed to demonstrate generic capabilities for the purity assignment of other compounds classified within the same sector. The series was completed in 2017 and the results have been leveraged to support calibration and measurement capability (CMC) claims made by NMIs for the provision of pure organic calibrators. They also indirectly underpin the SI-traceability of the purity assignments of primary calibrators required in turn for CMC claims for the assignment of the mass fraction content of individual analytes present in multi-component calibration solutions and at trace level in complex matrices.

The OAWG has since evolved its model for purity comparisons to map the organic purity space up to a molar mass of 1000 g/mol. The current model assumes that at lower molar masses (below 500 g/mol) the polarity of a specific analyte governs the need for different measurement approaches, e.g. GC- or LC-based methods for direct analysis of non-polar compounds against primarily LC-based for direct analysis of polar molecules. The new model extends the molar mass range covered by the OAWG “core” key comparisons from 500 g/mol up to 1000 g/mol [201]. The shift to assessing capabilities for the purity assignment of larger molar mass compounds reflects the growing need for reference standards of more structurally complex analytes, such as biomarkers, macrolide natural products, small peptides and oligonucleotides.

The OAWG has evolved how it handles both the assessment of chemical purity and the associated measurement uncertainty. National Metrology Institutes (NMIs) with work programmes in organic analysis are increasingly assigning purity through a combination of results obtained using mass balance and qNMR techniques [202], [203], [204], [205]. This approach allows for an effective assessment of biases in either contributing technique [206] and of so-called “dark uncertainties” [207] that exist between methods. Both the mass-balance and qNMR assessments can be subject to biases that are difficult to detect directly.

With the mass balance approach, important questions that have been addressed include:

  1. have all SCs been detected?

  2. for a given technique, how linear is the observed response of each SC relative to that of the PC?

  3. is the response evaluated on the correct mass fraction basis?

  4. are any apparent SCs method-generated artefacts?

For qNMR, extraneous contributions to the analyte or internal standard signals will bias the result. Given the relatively limited resolution and sensitivity of 1H-qNMR methods, even for compounds of moderate structural complexity it can become challenging to differentiate with confidence between signals from the PC and those from structurally related impurities. A range of other factors related to sample preparation and data acquisition need to be effectively controlled to result in a traceable purity estimate by qNMR, particularly if small uncertainties are claimed for the assigned value.

Needs for pure calibrator certification has extended into measurement sectors that merge into the bioanalytical sciences. The CCQM-K104 purity comparison on the purity assignment of avermectin B1a [208] was undertaken to examine how purity assessments for large, structurally complex organic compound had developed from those used in the earlier CCQM-P20.f pilot study of digoxin [200b]. The results obtained highlighted the increased challenges for purity assignment that result from the association of the PC with numerous isomeric or homologous SCRS impurities. In the case of avermectin B1a, molar mass 873 g/mol, in vivo synthesis is associated with the co-production of structurally related analogs which are difficult to remove entirely during purification. The ability to resolve such impurities in a final preparation and quantify them in a fit-for-purpose manner is a significant challenge. The purity assignment of such compounds by qNMR becomes increasingly difficult due to the overlap of structural analogs with the quantification peak for the main compound. These challenges are being addressed by investigating more sophisticated approaches to qNMR such as LC-NMR [209] or adapting 2D NMR techniques for quantification [210, 211].

International comparisons related to peptide purity assignment have been initiated by the CCQM Working Group on Protein Analysis (PAWG) [212]. In addition to amino acid hydrolysis-based and qNMR techniques, the CCQM-K115 study of a synthetic human C-peptide (M = 3020 g/mol) demonstrated that, provided sufficient material is available, the mass-balance approach can be applied to large biomolecules. In this case more than one hundred structurally-related impurities (SCRS) were identified as well as significant levels of water (SCW) and counter ion and inorganic salts (SCNV). A comparison investigating the purity assignment of the cyclic peptide oxytocin (CCQM-K115.b) is nearing completion.


Corresponding author: Steven Westwood, Bureau International des Poids et Mesures (BIPM), Sèvres, France, e-mail:

Article note: Sponsoring body: IUPAC Analytical Chemistry Division (Division V): see more details on page 72. This work was started under the project 2013-025-2-500.


Award Identifier / Grant number: 2013-025-2-500

Appendix A: Examples of Purity by Mass Balance Methods

DISCLAIMER: If any commercial products or company names are identified here it is provided only for adequate description. Such identification is not intended to imply recommendation or endorsement by the Bureau International des Poids et Mesures (BIPM), National Institute of Standards and Technology (NIST) or any other National Metrology Institute nor is it intended to imply that the products or names identified are necessarily the best available for the purpose.

A.1 Related Structure impurities (SCRS)

Illustrative examples are given of the purity assignment by a mass balance approach through the characterization of the secondary component contents of a material. The examples are derived from results reported by participants for the CCQM-K55 series comparison materials where 17β-estradiol (CCQM-K55.a) [6a], aldrin (CCQM-K55.b) [6b] and L-valine (CCQM-K55.c) [6c] were respectively the PC.

A.1.1 Related Structure impurities (SCRS) in L-Valine by external calibration

A representative LC-CAD spectrum obtained for the L-Valine material is shown in Figure A-1.

Figure A-1: 
                Separation and assignment of components of the CCQM-K55.c material by LC-CAD [Note: The peak eluting to the left of Ala is due to an internal standard].
Figure A-1:

Separation and assignment of components of the CCQM-K55.c material by LC-CAD [Note: The peak eluting to the left of Ala is due to an internal standard].

Four significant related structure components (L-Ala, L-Ile, L-Leu and α-aminobutyric acid [Abu]) were separated from the PC and identified in the material. A smaller level (below 0.05 mg/g) of L-Met, co-eluting with the main component peak, was detected separately by LC-MS/MS. These assignments were confirmed by NMR and by LC-FLD and GC-FID of appropriately derivatized samples.

High-purity source materials for L-Ala, L-Ile, L-Leu, Abu and L-Met were obtained from a commercial supplier. For L-Ile and L-Leu assignments of the purity of the reference standards were made by qNMR using a CRM for KHP as the internal standard. The SI-traceability of their assigned values derived from the KHP CRM as transferred to each material via the implementation of a validated qNMR procedure. For α-ABA, L-Ala and L-Met the nominal percent mass content reported by the supplier was in excess of 99 %. Nuclear magnetic resonance spectroscopy, LC-CAD and C/H/N content analysis of each material was consistent with this assignment. For these three materials their assigned purity value for use in calibration calculations was 995 mg/g with a standard uncertainty of 3 mg/g (assumption of a rectangular distribution over the range 990 to 1000 mg/g). The SI-traceability of their assigned values derives from the assignment, confirmed by independent data, of the mass fraction content of the material being in excess of 990 mg/g. The assigned values, SI-traceability and assignment method for each external calibrator used in the quantification of individual SCRS in the CCQM-K55.c material are summarized in Table A-1.

Table A-1:

Purity assignments and source of SI-traceability for calibrators for SCRS in CCQM-K55.c.

SCRS Calibrator purity (mg/g) SI-Traceability source Assignment
L-Ile 990 ± 1 KHP CRM qNMR
L-Leu 998 ± 1 KHP CRM qNMR
L-Ala 995 ± 5 Confirmed > 990 mg/g NMR, LC-UV-CAD
α-ABA 995 ± 5 Confirmed > 990 mg/g NMR, LC-UV-CAD
L-Met 995 ± 5 Confirmed > 990 mg/g NMR, LC-UV-CAD

The individual content of each amino acid SC found in the CCQM-K55.c material was assigned by external calibration using a quantitative LC-MS/MS method. These assigned values were confirmed using a less sensitive LC-CAD method. A mixed primary calibrator solution of the value-assigned minor component amino acid standards was prepared and MS/MS parameters for the detection and quantification of each amino acid using electrospray ionization (EI) were optimized. A primary MRM was identified for quantification purposes for each analyte and a multipoint calibration curve established by triplicate analysis of standard solutions prepared by gravimetric dilution of the primary calibrator solution at four mass levels spanning the mass range 30 to 300 ng/g. The correlation coefficient for the five calibration curves developed for the LC-MS/MS method was in excess of 0.998.

A similar process was followed for LC-CAD. Because of the lower sensitivity of the CAD response the mass levels used to establish the calibration curves were higher, over the range 200 ng/g to 1800 ng/g, and the correlation coefficient for the five calibration curves was lower, being only in excess of 0.990.

A solution of the CCQM-K55.c comparison material having a mass fraction content of ca. 100 μg/g, anticipated to contain SCRS impurities at levels of 50 to 500 ng/g, was prepared and analyzed using both the LC-MS/MS and LC-CAD methods. The mass fraction levels of the related structure impurity components assigned from the LC-MS/MS method are shown in Table A-2. The results obtained by LC-CAD for the main impurities (L-Ala, L-Ile, L-Leu) were consistent with the results by LC-MS/MS. LC-CAD was insufficiently sensitive to detect Abu at the mass fraction present in the material at the sample concentration used. L-Met co-eluted with the PC peak under the chromatographic conditions used but it could be detected and quantified by LC-MS/MS using an MRM based on a unique precursor ion.

Table A-2:

Content assignments for individual SCRS,i and overall value for SCRS in CCQM-K55.c obtained by LC-MS/MS using an external calibration approach.

SCRS,i Mass fraction in CCQM-K55.c material ± U95% (mg/g)
L-Ala 2.68 ± 0.24
L-Ile 2.02 ± 0.12
L-Leu 1.76 ± 0.16
Abu 0.32 ± 0.05
L-Met 0.016 ± 0.003
SC RS 7.14 ± 0.32

The assigned value for total related structure impurity content is the sum of individual contributions. In this case the expanded uncertainty was assigned as the quadratic sum of the expanded uncertainty of each contributing impurity assignment.

A.1.2 Related Structure impurities (SCRS) in L-Valine by relative response

A chromatogram obtained for the CCQM-K55.c comparison material using LC-FLD after pre-column derivatization is shown in Figure A-2. Three major amino acid impurities (Ala, Leu, Ile) and the minor component Abu were identified in the material by comparison of retention time with authentic standards. A separate analysis by LC-MS/MS confirmed the presence of the four impurities identified by LC-FLD and in addition identified a small amount of L-Met and a trace amount of glycine. The relative response factors for the individual impurities to the PC were assigned from the ratio of the molar mass of each amino acid impurity to the molar mass of the main component, L-Val (MSC/MVal) assuming equivalent derivatization efficiency and fluorescence response on a molar basis. A Type B allowance is included for the uncertainty associated with these assumptions.

Figure A-2: 
                Separation and assignment of components of the CCQM-K55.c material by LC-FLD.
Figure A-2:

Separation and assignment of components of the CCQM-K55.c material by LC-FLD.

The relative response on a per mille basis obtained from the LC-FLD method and the final assigned mass fraction levels of each related structure impurity component are reported in Table A-3. Although there are inconsistencies in the assignments of individual components the results obtained for this common material by the separate approaches (external calibration in A.1.1 and relative response in A.1.2) give values for total related structure impurity content that are consistent within their stated uncertainties.

Table A-3:

Content assignments for SCRS,i and SCRS in CCQM-K55.c obtained by relative response using.

SCRS,i ‰ by FLD (rel. area) u (rel. area) RRF u (RRF) Mass fraction content in L-Valine material ± U95% (mg/g)a
L-Ala 3.58 0.106 0.76 0.03 2.72 ± 0.26
L-Leu 2.03 0.034 1.12 0.05 2.27 ± 0.22
L-Ile 1.67 0.052 1.12 0.05 1.87 ± 0.20
Abu 0.60 0.021 0.76 0.03 0.46 ± 0.04
L-Metb 0.08 0.01 1.27 0.05 0.10 ± 0.02
SC RS 7.42 ± 0.40
  1. LC-FLD. aSCRS content = Relative area (‰) * RRF (= MSC,i/MVal). bIdentified and estimated by LC-MS/MS only, not resolved from the PC by LC-FLD.

A.2 Water content (SCw)

The KFT method is the principal method for the water content determination of high-purity organic compounds. Examples are provided of both direct addition and of transfer of the water content from a solid sample via a heated sample oven to the titration cell. Thermogravimetric analysis (TGA) is the other major technique used for water content estimation.

A.2.1 Water content (SCw) in estradiol by oven transfer KFT

The basic equation for a water content measurement of a gravimetrically defined sample is:

SCw=(QsamplerQtsample)QblankmQblank=Qblank,measrQtblank

where SCw is the mass fraction water content in the material, Qsample is the total mass of water detected by the KFT measurement of the sample, rQ is the rate of background drift due to atmospheric water, tsample is the time for the sample analysis, Qblank is the correction required for water introduced from a blank vial, Qblank,meas is the mass of water detected by KFT in the measurement of a blank sample, tblank is the time required for the blank analysis and m is the mass of sample.

The results for four accurately weighed aliquots of the CCQM-K55.b estradiol material, each of approximately 10 mg, using an optimized oven transfer method, are reported in Table A-4. The measurement uncertainty budget for the water content determination is shown in Table A-5.

Table A-4:

Content assignments for SCw in CCQM-K55.a by oven transfer KFT.

Sample m (mg) Q sample (μg) rQ (μg/min) t (min) Q blank (μg) SC W (mg/g)
1 10.24 92.1 3.6 3.14 0.78 7.81
2 10.25 84.7 3.7 2.95 7.12
3 10.07 81.6 3.6 2.99 6.96
4 10.54 78.3 3.6 2.87 6.38
Table A-5:

Measurement Uncertainty (MU) Budget for SCw in CCQM-K55.a by oven transfer KFT.

Uncertainty component u(xi) Source of uncertainty x i u(xi) c i u i(SCw) = |ci| u(xi)
u(SCW) (μg/g) Variation of water concentration 7066 297 1 297
u(Qsample) (μg) End point for sample 84.2 3.1 1/m 302
u(rQ) (μg/min) Drift variation 3.6 μg 0.06 μg -tsample/m 21
u(t) (min) Titration time 2.99 -rQsample/m
u(Qblank) (μg) Water amount of blank 0.78 3.11 1/m 303
u(Qblank,rep) (μg) Repeatability of blank 0.78 0.10 10
u(Qblank) (μg) End point for blank 5.1 3.1 302
u(rQ) (μg/min) Drift variation 3.7 0.06 7
u(t) (min) Titration time 1.16
u(m) (mg) Amount of sample 10.28 0.02 -C water/m 14

The assignment including U95% for water content in the estradiol material was (7.07 ± 1.06) mg/g.

A.2.2 Water content (SCw) in estradiol by direct addition KFT

The measurements were carried out using a commercial coulometric solution as anolyte, and a diaphragm electrode with a commercial coulometric solution specific for use with ketones as catholyte. The drift measurement was allowed to stabilize before commencing each experiment. Two blank runs and one measurement of a water standard were performed for method verification prior to measurement of the material. The blank runs were conducted by exposing the vessel to the atmosphere for a period equivalent to the time needed for addition of the sample through the weighing funnel. The instrument performance was validated over 10 days by different operators, based on the measurement of 80 to 140 mg aliquots of a water standard containing 1 mg/g of water.

To determine the mass fraction of water in the CCQM-K55.a comparison, five aliquots (14.0 to 15.4 mg) of the material were weighed out accurately and titrated after direct addition to the KFT cell using a weighing funnel. The results were corrected for a contribution due to moisture introduced when the titration cell is briefly opened to the atmosphere during addition of the material.

The final assignment for water content in the estradiol material was (7.48 ± 0.88) mg/g.

A.2.3 Water content (SCW) in estradiol by TGA

Samples of the CCQM-K55.a material were transferred onto an aluminium pan and the sample mass determined using the calibrated microbalance of a TGA instrument. The program for measurement of the total volatiles content was: hold for 5 min at 40 °C, heat from 40 to 120 °C at 10 °C/min, hold for 5 min at 120 °C, heat from 120 to 260 °C at 10 °C/min. The resultant thermogram indicated the release of two classes of volatile component. An initial mass loss, assigned to the release of adsorbed (surface) water, taking place on heating up to 120 °C corresponded to 0.105 % of the original sample mass. The mass did not change significantly on further heating up to 180 °C. At this temperature a second mass loss was observed, assigned to the release of water of hydration after fusion of the crystalline estradiol main component and corresponded to 0.623 % of the total sample mass.

As there was no significant volatile organic content observed for the material by GC-MS or NMR analysis, it was justified to ascribe the loss on heating to the water content of the material. This gave a combined mass change from loss of water of 0.728 % corresponding to a SCw assignment of (7.28 ± 0.25) mg/g.

The traceability of the result derives from the traceability of the TGA balance mass determinations.

The measurement uncertainty estimate for the result was derived from the uncertainty of the contributing gravimetric determinations, based in turn on the balance performance parameters, expanded by a Type B estimate for uncertainty associated with the assumption of completeness of and the absence of bias in the release of water from the material.

Note that all three methods give results that are consistent within their estimated expanded uncertainties.

A.3 Residual Solvent (SCOS)

Examples are provided for the determination of the residual solvent content in the aldrin material used as the comparison sample for CCQM-K55.b

A.3.1 Residual solvent (SCOS) in aldrin by Headspace GC/MS

Preliminary GC-MS studies established that the material contained a significant level of methanol. No other volatile compounds were observed. A sample of the aldrin (ca 40 mg) was transferred directly into a head space vial, dissolved in 10 mL of N,N-dimethylacetamide (DMA) and sealed. An HS-GC/MS analysis was undertaken using a sequence including this sample and three blanks (solvent only), a set of calibration standards for methanol in DMA, six injections of the aldrin sample and repeat analysis of the calibration standards. The calibration standards covered concentrations of methanol in the DMA solution at levels from 0.5 to 15 μg/g. The aldrin sample and the calibration standards were prepared and run under the same conditions.

The assigned value for methanol content including U95% thus obtained was (2.33 ± 0.2) mg/g

A.3.2 Residual Solvent (SCOS) in aldrin by direct injection GC

A splitless injection GC method with mass spectrometric detection was applied to a solution in isooctane of the CCQM-K55.b aldrin material. A DB-624 capillary column (30 m × 0.25 μm, solid phase 1.4 μm) suitable for separation of volatile organics was used. Initially solutions of the material at ca 1000 μg/g in methanol, dichloromethane and DMSO were examined separately to investigate the presence of any residual solvent. No detectable amount of larger solvents were observed but analysis of the DMSO solution indicated the presence of methanol. This was confirmed by 1H NMR analysis and by HS-GC/MS.

A standard solution of isopropanol in HPLC-grade isooctane was used as internal standard. As methanol is particularly volatile, preparation of accurate standard calibration solutions was a challenge. All calibrant and sample solutions were handled using glassware, volumetric pipettes and transfer syringes were cooled prior to use. Solutions were analyzed as soon as feasible after preparation and were stored at 4 °C prior to analysis. Fresh calibration solutions were prepared daily. It was observed that although the absolute signal from methanol and the isopropanol internal standard decreased in the course of replicate injections the relative effect on the methanol/isopropanol response ratio was sufficiently small that fit for purpose quantification of the methanol content could be achieved.

The assigned value for the methanol content of the material was (2.5 ± 0.3) mg/g based on the peak area of the methanol response quantified against an external calibration using ultrapure methanol.

A.3.3 Residual solvent (SCOS) in aldrin by relative response NMR

The 1H NMR spectrum of the material in CDCl3 showed a well-resolved signal corresponding to the methyl singlet of methanol at 3.9 ppm. A relative response qNMR analysis on two independent samples, quantifying the methanol peak against the main aldrin peaks provided an estimate of (2.5 ± 0.4) mg/g for the methanol content in the material.

A.4 Non-Volatiles (SCNV)

Representative examples are given for the determination of the non-volatiles organic and inorganic content in valine (CCQM-K55.c) and Aldrin (CCQM-K55.b).

A.4.1 Non-volatiles (SCNV) in estradiol by TGA

Samples of the CCQM-K55.a material were placed in platinum pans and the sample mass was determined using the microbalance of the TGA instrument. Two separate samples (10.5 and 13.0 mg) were each heated from 35 °C (20 min) to 850 °C at a rate of 20 °C min−1, with a final hold time of 60 min. The sample pan was allowed to cool to 35 °C and the residual mass at this pan temperature was determined. Measurements were performed using a dry-air atmosphere as the sample gas and dry-nitrogen as the balance gas. Analytical blanks were estimated between each measurement using empty platinum pans taken through the same TGA cycle. The inorganic/non-volatiles residue weight from each sample determined using the internal balance (0.1 μg readability) corresponded to a percent mass content of 0.012 % or 0.12 mg/g.

A.4.2 Non-volatiles (SCNV) in valine by TGA

Under an initial nitrogen flow, two valine samples (each an accurately weighed sample of around 8 mg) were heated from 30 °C (20 min) to 340 °C at a rate of 5 °C min−1, then to 850 °C at 20 °C min−1 with a final hold time of 60 min. The sample gas was switched to oxygen and the temperature maintained at 850 °C for a further 20 min. The sample pan was reweighed after being cooled back to 35 °C.

The residue amount was below the limit of detection for the instrument (ca. 15 μg). At the sample size used, this corresponded to a level of non-volatile residue in the sample not greater than 2 mg/g. The assigned limit of detection reflected uncertainty introduced due to variation in the mass of the blank pans after the high temperature oxidation cycle. This introduced a level of uncertainty in the accuracy of the baseline corresponding to complete oxidation/ashing of the organic content of the material.

A representative thermogram for the TGA response of the valine CCQM-K55.c material, typical for that observed for simple organic compounds, is shown in Figure A-3.

Figure A-3: 
                TGA thermogram used for estimation of SCNV in valine (CCQM-K55.c).
Figure A-3:

TGA thermogram used for estimation of SCNV in valine (CCQM-K55.c).

A.4.3 Non-volatiles (SCNV) in aldrin by ICP-MS and ICP-OES

Metal content in aldrin

Samples of the CCQM-K55.b material were subjected to microwave digestion in a solution of 1 mL HNO3 and 1 mL H2O2, using a 40 mg aliquot made up to 1 mL. In-house QC materials were used to check the calibration of the instrument response for common inorganic components. The relative standard uncertainty in the final value was estimated to be 25 % for semi-quantitative analysis and values below 0.5 mg/g. The settings of the ICP-OES instrument used were: RF power is 1300 W, plasma gas (argon): 15 L/min; semi-quantitative calibration using one blank and one standard.

A.4.4 Non-volatiles (SCNV) in aldrin by XRF Sample size: 53 mg (n = 1)

The method was calibrated at the original installation using a set of manufacturer and NIST SRM standards and validated using NIST SRM 2855 (Additive Elements in Polyethylene). The method is sensitive to elements from sodium to uranium. It performed well above an estimated LOD below 0.01 mg/g for the one detected element (Si) not intrinsic to aldrin.

A.5 Primary component (PC) purity by mass balance

A.5.1 Purity of β-estradiol

Assignments of the mass fraction content with their associated uncertainty of each impurity present in the material as reported by a participant in the CCQM-K55.a comparison are given in Table A-6. The related structure impurity content was assigned by a quantitative LC-UV method using external calibration against reference standards for each of the identified impurities present in the material.

Table A-6:

Impurity assignment table – Purity of β-estradiol by mass balance (CCQM-K55.a).

Impurity Category Assignment method Content in estradiol material (mg/g) Standard uncertainty (mg/g)
4-Methylestradiol SCRS LC-UV (calibration)a 5.41 0.32
Estrone SCRS LC-UV (calibration)a 1.16 0.03
1-Methylestradiol SCRS LC-UV (calibration)a 0.32 0.02
17β-Dihydroequilenin SCRS LC-UV (calibration)a 0.28 0.01
17α-Estradiol SCRS LC-UV (calibration)a 0.12 0.01
Trace impurities SCRS LC-UV (rel. response)b 1.66 0.03
Ethanol SCOS HS-GC/MSc 0.06 0.02
Water SCW KFT (oven) 7.07 0.53
Non-volatiles SCNV TGA 0 +0.46
Total impurity 16.1 −0.7
  1. aExternal calibration using an authentic standard. bCombined LC-UV response relative to response of PC. cExternal calibration using an ethanol standard.

Water content was determined by both oven transfer KFT and TGA analysis, as described above. Residual solvent (ethanol) was detected and quantified by HS-GC/MS. The assigned value was confirmed by relative response 1H-NMR. No significant non-volatile residue was found after oxidative high temperature TGA. No significant metal content was detected by ICP-MS analysis.

The value for 17β-estradiol content of the material was assigned as (983.9 ± 1.6) mg/g, the difference of the summation of the estimates for individual impurities (16.1 mg/g) from the limit value 1000 mg/g.

The standard uncertainty of the assignment was the quadratic sum (square root of the sum of squares) of the standard uncertainty of each contributing impurity estimate. The expanded uncertainty at 95 % confidence (U95%) of the assigned value was obtained from the standard uncertainty using a coverage factor (k) of two.

A.5.2 Purity of aldrin

The contributing assignments of the mass fraction content of each impurity class reported by a participant in the CCQM-K55.b comparison and their associated uncertainty are shown in Table A-7.

Table A-7:

Impurity assignment table – Purity of aldrin by mass balance (CCQM-K55.b).

Impurity Category Assignment method Content in aldrin material (mg/g) Standard uncertainty (mg/g)
Isodrin SCRS GC-FID (calibration)a 24.7 0.52
Dieldrin SCRS GC-FID (calibration)a 4.1 0.10
Dechlorane SCRS GC-FID (calibration)a 4.5 0.54
Endrin ketone SCRS GC-FID (calibration)a 0.1 0.01
Trace impurities SCRS GC-FID (rel. response)b 1.0 0.3
Methanol SCOS GC-MS (calibration)c 2.5 0.1
Water SCW KFT (oven) 0.5 0.2
Inorganic SCNV TGA and ICP-MS 0 +0.06
Oligomer SCNV SEC-UVd 11 0.56
Total impurity 48.4 1.0
  1. aExternal calibration using an authentic standard. bCombined FID response relative to the PC. cExternal calibration using a methanol standard. dAssigned subsequent to the CCQM-K55.b comparison by size-exclusion chromatography.

The related structure impurity content was estimated using a GC-FID method with external calibration of the response of the identified individual impurities (isodrin, dieldrin and dechlorane) for which value-assigned reference materials were available. For an additional trace level, unidentified impurities also observed by GC-FID and their combined response relative to the main component, was used as the value assignment.

The presence of methanol in the material was identified by HS-GC/MS and 1H NMR. The GC-MS method used for the estimation of methanol content is described in Appendix A.3.2.

The water content was determined by an oven transfer KFT method on 50 mg aliquots of the material. There was no significant non-volatile content observed after high temperature TGA under oxidizing conditions and ICP/MS analysis of a sample showed no significant metal content.

An oligomeric impurity present in the material was not detected initially. See the full discussion of this issue, which was encountered by numerous participants, in the CCQM-K55.b comparison Final Report [6b]. This impurity was detected and estimated subsequent to the completion of the comparison using size-exclusion chromatography (SEC) with UV detection.

The value for aldrin content of the material was assigned as (951.6 ± 2.0) mg/g, the difference of the summation of the estimates for individual impurities (48.4 mg/g) from the limit value of 1000 mg/g.

The standard uncertainty of the assignment was the quadratic sum (square root of the sum of squares) of the standard uncertainty of each contributing impurity estimate. The expanded uncertainty at 95 % confidence (U95%) of the assigned value was obtained from the standard uncertainty estimate using a coverage factor (k) of two.

Appendix B: Examples of purity by qNMR

B.1 Experimental design for internal standard qNMR

The choice of experimental parameters is essential in ensuring a qNMR assay delivers results of appropriate trueness, precision and associated measurement uncertainty estimate [213]. The two basic modes of qNMR analysis, absolute and relative quantification, require the consideration of different factors to ensure an analysis result is fit for its intended purpose.

B.1.1 Selectivity

As with any spectroscopic technique, the analyst must ensure that the resonance signals assigned to the analyte and reference standard are free from interference from signals from other components in the analytical sample. In qNMR this can be achieved in a variety of ways:

  1. checking signal lineshape to identify unexpected asymmetry;

  2. integration of multiple signals from the analyte for internal consistency;

  3. varying solvent, standard or temperature to see if changes in chemical shift reveal any impurities;

  4. performing 2D-NMR experiments including homonuclear correlation spectroscopy (COSY), total correlation spectroscopy (TOCSY) and single quantum coherence spectroscopy (HSQC) [214] can probe for unexplained correlations or identify signals from impurity components coincident with the quantification signals in the 1D spectrum of the PC.

B.1.2 Peak selection

Apart from the obvious necessity to use signals sufficiently resolved from others in the NMR spectrum, other considerations apply to achieve accurate quantification.

Assuming a Lorentzian peak shape, it is necessary to integrate at least 64 times the half width of a peak to quantify in excess of 99.9 % of the signal. If broad signals (FWHM > 3 Hz) are selected, this may lead to unavoidable signal loss or overlap with adjacent signals. This can be especially problematic in the common case when the analyte signal is significantly broader than that of the internal standard. Chemical shift dispersion limits the separation of signals. Signal overlap from impurities may cause a positive bias for a signal area. With all but the simplest spectra, some compromise may be required in the integration ranges used due to interference from other signals. In these cases, either the bias should be corrected for or the potential error factored into the uncertainty budget.

Several common deuterated solvents (e.g., D2O, CD3OD) contain acid, exchangeable deuterons that will equilibrate with any exchangeable hydrogens in the analyte or standard, altering the hydrogen/deuterium ratio and affecting the observed signal intensity in the 1H spectrum. Quantification based on 1H signals from functional groups containing OH, NH and SH should be avoided. Care should be taken when selecting reference 1H signals where, at a certain pH, exchange with the solvent is possible – e.g., the methylene group of malonic acid in basic conditions or protons in aromatic ring systems, such as 1,3,5-trimethoxybenzene, activated for electrophilic proton exchange under acid conditions.

Molecular rearrangements, bond rotations and tautomerizations that occur on similar timescales to the NMR experiment can cause line broadening effects that need to be considered. A common example is amide tautomerism where a major and a minor set of signals due to s-E and s-Z conformations can exist, often with the minor signal broadened and difficult to integrate.

B.1.3 Magnetic field strength

There is no minimum NMR spectrometer field strength requirement for qNMR measurements. However, increasing the field strength enhances signal dispersion and sensitivity, both of which should increase the trueness and precision of qNMR measurements. The increased chemical shift dispersion associated with higher field strength improves the separation of broad or overlapping peaks, assisting in their integration. However dynamic exchange phenomena (e.g. tautomerization) resulting in broader peaks can occasionally occur at higher magnetic field.

B.1.4 Sample preparation and gravimetry – need for replicate analysis

Nuclear magnetic resonance measurements are commonly conducted using an NMR tube with 5 mm internal diameter in which the sample solution volume is usually 0.7 to 1.0 mL. This typically only requires several milligrams of analyte and standard to give an optimal concentration of both the analyte and reference standard in the range of 1 to 50 mg/mL. Too low a concentration may result in an insufficiently high signal-to-noise ratio (S/N). Too high a concentration may lead to a reduction in lock stability, radiation damping or viscosity effects resulting in a deterioration of the observed signal lineshape.

As deuterated solvents are relatively expensive, sample preparation tends to be on a small scale and places emphasis on the trueness and precision of the gravimetric manipulations which become a significant component to the overall uncertainty of the resulting measurement. It was evident in the results of the CCQM-P150.a qNMR pilot study that while there was no evidence of bias in the results due to the type of balance used, the more precise the balance the closer the agreement and the smaller the observed dispersion between individual results and with the reference value [106, 110].

In the majority of 1H-qNMR assays involving well-resolved signals each having adequate S/N, the standard deviation of results obtained between sample preparations generally exceeds that of replicate analyses of individual solutions. This confirms that the gravimetric preparation of samples is a significant source of uncertainty in the process. Sample inhomogeneity, sample transfer losses (particularly with freeze dried ‘fluffy’ materials), hygroscopicity of the sample, interference due to electrostatic effects and incomplete solubility in the selected solvent can also contribute to the measurement uncertainty associated with gravimetric operations.

Depending on the balance facilities available, the mass of samples to be used in the gravimetric preparation of the NMR solutions should be chosen to minimize the uncertainty associated with the sample preparation process rather than solely to match the NMR tube volume [215, 216]. Under these circumstances, the experiment should be designed to maximize the number of separate sample preparations, with no more than four replicate analyses for each individual sample preparation.

Where ‘between replicate’ analyses are less reproducible due to issues such as poor S/N, difficulties in applying suitable baseline correction or the interference of spectrum artefacts, then additional replicates for each solution may help to increase the effective degrees of freedom of the analysis without the burden of additional sample preparation.

B.1.6 Digitization of signals

The digital resolution of an NMR spectrum will impact the reproducibility of measurement primarily due to the potential for the truncation of signals. When the analyte and standard have significantly different signal shapes this can create an analyte-specific bias. For example, a 600 MHz 1H spectrum with 20 ppm spectral width and 64 000 data points will have resolution of approximately 0.2 Hz per point. To produce well-defined signals that give accurate area measurements and suitable precision at typical sampling rates, the resolution should not exceed 0.4 Hz per point.

B.1.7 Relaxation delay and pulse angle

The application of insufficient delay between replicate scans during an NMR experiment is one of the most significant potential sources of error within a qNMR analysis.

During a simple NMR experiment, a single pulse of radiofrequency (RF) energy excites the nuclei to a non-equilibrium population distribution. The energy emitted as the excited spins decay back to the initial state generates the RF signal detected as the NMR resonance signal. The time required for half the excess spins to return to equilibrium is referred to as longitudinal or spin-lattice relaxation time, T1. To ensure quantitative assays, the system should return to equilibrium before a repeat excitation is made. The amount of time required between pulses will be dependent on the amount of excitation delivered (expressed as the pulse angle) and the relaxation properties of the nuclei under analysis.

The 1H-qNMR spectra are usually acquired using excitation pulses that induce a transverse deviation of the bulk magnetization of between 30° and 90°. The exact pulse angle or pulse width does not impact directly on the quantitative nature of the response but do impact on the repetition rate required to ensure accurate quantitative analysis and also on the achievable S/N. A 30° pulse requires a delay between pulses equivalent to at least 5 times the longest T1 to ensure 99.9 % of the signal recovery. For a 90° pulse a delay of at least 10 times the longest T1 is recommended for comparable recovery. Although a 90° pulse requires a longer recovery time, each pulse gives twice the signal intensity compared with a 30° pulse.

Figure B-1 illustrates the effect of both solvent and increasing the relaxation delay on the efficiency of signal recovery evaluated using a solution of two materials (1,3,5-trimethoxybenzene and benzoic acid) of known purity. In this example, the T1 of each signal varies significantly with solvent and complete recovery of both signals required a relaxation delay of almost 20 times the longest T1.

Figure B-1: 
                Influence of relaxation delay and solvent on the efficiency of qNMR assignments of 1,3,5-trimethoxybenzene with benzoic acid as internal standard.
Figure B-1:

Influence of relaxation delay and solvent on the efficiency of qNMR assignments of 1,3,5-trimethoxybenzene with benzoic acid as internal standard.

For externally standardized assays, the equivalence of the pulse angle between samples becomes a source of uncertainty. It is strongly recommended to use a 90° pulse as the impact of inaccuracy in the pulse width is minimized at this pulse angle.

B.1.7 Impact of signal-to-noise (S/N) ratio

A high S/N is required to provide sufficiently precise assay values so that measurement repeatability becomes a relatively small component of the overall measurement uncertainty. The major impacts of poor S/N are the difficulty to correct the baseline and thus integrate the signal accurately, poor signal definition and the inability to detect small impurity signals interfering with analyte signals. Figure B-2 shows the impact of increasing S/N on the precision of replicate analyses of dimethyl terephthalate in solution in CDCl3 as measured by the relative integration of the singlet signal due to the six methyl ester hydrogens versus the singlet resonance due to the four aromatic hydrogens.

Figure B-2: 
                Variability in individual replicate results for the ratio of integration of dimethyl ester signal (6H) to the aromatic signal (4H) in DMTP as function of S/N.
Figure B-2:

Variability in individual replicate results for the ratio of integration of dimethyl ester signal (6H) to the aromatic signal (4H) in DMTP as function of S/N.

For high-accuracy measurements, when feasible, each quantified signal should target a relative standard deviation of replicate measurement results of less than 0.25 % and a S/N ratio for in excess of 1000.

B.1.8 Pulse program

The recommended option for qNMR analysis is a simple single pulse experiment operating at a 90° pulse angle. There are occasions when this approach is not suitable for specific sample types and alternate pulse sequences are used to mitigate these issues. The potential impact on the quantitative nature of the experiment must be understood by the user. Some alternatives include solvent suppression [217], heteronuclear decoupling and multidimensional experiments such as HSQC [218]. Even in the absence of a detectable effect, the degree of confidence in the assumption of uniform efficiency of the spin excitation transfer required for both analyte and standard if using a 2D NMR experiment for quantification should be considered in the uncertainty budget.

B.1.9 Solvent suppression

When a solvent signal (typically water) needs to be suppressed to improve S/N and digitization of signal amplitude a variety of solvent suppression methods may be used. However suppression may severely impact the accuracy of quantification. Signals close to the frequency of the solvent suppression may experience significant signal attenuation. Validation studies would be needed to demonstrate the absence of such an effect. As above for the use of 2D qNMR, even in the absence of a detectable effect, the uncertainty budget for the results should incorporate an allowance for the degree of confidence in the assumption of the lack of significant signal attenuation due to the suppression method.

B.1.10 Heteronuclear decoupling

Heteronuclear decoupling can be considered when such coupling impacts the ability to resolve and integrate relevant NMR signals. The removal of heteronuclear coupling in qNMR applications may help reduce the complexity of an NMR spectrum. It may also improve the resolution of specific signals through suppression of the heteronuclear J(I, S) splitting of multiplets (for a detected NMR nucleus I coupled to a heteronucleus S).

Signal broadening due to heteronuclear couplings in a 1H spectrum from nuclei with high natural abundance (e.g., 19F and 31P) can create significant problems due to the large coupling constants involved. For example, two-bond J(1H, 19F) couplings can be in the region of 48 Hz. Heteronuclear decoupling will see the intensities of the individual lines of a J(I, S) multiplet coalesce into a single peak, improving the S/N of the decoupled signal.

Signal satellites from dilute spins can overlap with adjacent peaks making integration difficult. This is often seen in 1H spectra where one-bond J(1H, 13C) coupling with values sometimes more than 200 Hz result in minor signals from the isotopomer (approximately 0.55 % the size of the parent resonance) potentially interfering with adjacent signals and impeding their accurate integration. The natural Lorentzian linewidths for the 1H-qNMR of small molecules dictate that the frequency range required to accurately quantify a peak extends to include the 13C satellites. It is possible to decouple these heteronuclear couplings, which results in the signals becoming effectively coincident (barring a small isotopic shift) with the 1H signals from the 12C isotopomer.

A potential downside of incorporating decoupling into the pulse sequence is that heteronuclear nuclear Overhauser effects [219] will be generated and affect the intensities of the resultant signals. Since this will not be consistent between individual signals, it will potentially bias the results. This is a larger problem if the heteronucleus has near 100 % abundance rather than for 13C satellites where the impact is only on the 1.1 % abundant natural isotopomer. Care must also be taken when applying heteronuclear decoupling as there is potential for energy from the decoupling pulses to heat the sample during the experiment, particularly in aqueous, high salt solutions. This can adversely affect the lineshape which will impact on the accuracy of the signal integration. Decoupling has a greater potential for impact on externally standardized assays since maintaining a constant temperature between samples is vital to ensure a consistent equilibrium energy state population distribution.

B.1.11 Spectral width

The spectral width and frequency offset should be chosen such that signals targeted for accurate quantification do not fall near the extremities (within 1 ppm) of the excitation band. The intensity of bands close to the excitation frequency will be attenuated by filter effects. Historically, high-accuracy qNMR measurements were designed with the frequency offset chosen to ensure the analyte and reference signals were equidistant from the center of the spectrum to minimize effects from non-linear excitation. Modern NMR instruments have greater RF linearity and such considerations are generally unnecessary for 1H spectra. However, care should still be taken if using nuclei with larger spectral windows.

The natural bandwidth of a RF pulse is proportional to the inverse of its pulse length. A ‘hard’ RF pulse should be used for excitation where the band width of the pulse far exceeds the frequency range of the required spectrum window. For 1H qNMR using a 90° pulse angle, the excitation time is generally in the 7 to 10 μs range and this condition is easily met. However, this can be a problem for the larger chemical shift ranges of many heteronuclei (e.g., 19F and 31P at chemical shifts above 300 ppm). In such cases, the spectrum width is often reduced to limit the range to include only the signals to be analyzed. If thus limited, care should be taken to ensure that peaks outside this window do not fold back into the spectra and interfere with the peaks of interest or distort the baseline and hamper accurate integration.

B.2 Additional considerations for external standard qNMR

In external standard qNMR, samples of analyte and standard are prepared and measured in separate NMR tubes. The absolute instrument molar response determined from the calibration samples is transferred to the response for the analytes measured under identical conditions. This requires the highly stable fields and efficient transmitters and receivers typical of modern spectrometers and careful consideration of operating conditions. Sample volumes and the potential for probe-damping effects should be considered where there are dielectric differences between analytical and calibration samples.

Establishing SI-traceability for the results of external calibration qNMR thus requires greater control of the instrumental and acquisition parameters and sample conditions than for the internal standard assay. Additional factors must be considered, including:

  1. relative efficiency of RF pulse delivery (pulse generation, amplification and transmission)

  2. relative efficiency of signal detection (detection, transmission and digitization)

  3. equivalence of filling factors (dimensions of NMR tube, sample volume and alignment)

  4. uniformity of spin population difference (same temperature of sample)

Such factors introduce additional, in some cases significant, uncertainty components. Externally calibrated assays are likely to yield larger uncertainties than analogous internally standardized assays.

Although relatively few references exist on the use of external standard 1H-qNMR, a critical evaluation of developments to 2014 [220] presents substantial supplemental validation data. The discussion in this reference specifically addresses measurement and correction of probe damping effects due to differences in conductivity and RF susceptibility between sample and standard based on the product of 360° pulse widths and signal intensity.

A detailed experimental and theoretical evaluation of the parameters critical to external standard qNMR (temperature, tube dimensional precision and probe Q-damping correction based on pulse width) in addition to the overall NMR method concluded that relative standard uncertainties of 1 % are achievable [221]. Levels of precision at the order of 1 to 2 % were also claimed using external standard qNMR with pulse length normalization to measure protein concentration [118]. Relative standard uncertainties of 0.6 to 1.1 % have been reported for results obtained using periodic calibration while uncertainties of 0.35 to 0.60 % were reported through separate calibration of each analyte sample [222]. A comparison of internal standard, external standard and electronic referencing methods for qNMR reported that precision of between 0.3 and 0.7 % could be obtained by external qNMR even with multiple operators and calibrations as long as one month apart [223]. While not true for external standard techniques, hybrid transfer standard methods have been reported that calibrate compatible internal standards using pure-material RMs before application to an unknown [224].

B.2.1 Sample preparation

Like with internal standard methods, external standard calibration requires a well-characterized, traceable reference standard with a stated uncertainty and with suitable proton resonances that can be accurately integrated. Where not sample limited, large enough amounts should be weighed such that uncertainties due to gravimetric operations do not make a significant contribution to the overall method uncertainty.

The gravimetric preparation of external samples and standards requires calculating actual concentrations, not just the mass ratio. Therefore the solution volumes must also be determined. Where solvents for both analyte and standard are the same and they are prepared and measured under identical conditions, the weight of each solution is enough (e.g., expressing concentration as mol/g solvent). Where different solvents are used and/or variable laboratory conditions apply between preparation and measurement, careful consideration of the actual solvent volumes and thus analyte and standard concentrations are required. Use of different solvents also requires careful consideration of solvent density as a function of temperature.

Near-identical, high-precision tubes must be used to precisely control the volume of both sample and standard within the sensitive area of the probe. Uncertainties in tube volumes are reported to be 0.25 % or lower [221]. Ideally the tubes should be flame sealed to prevent evaporative concentration of the solutions and the measurements be performed under identical and tightly controlled temperatures following equilibration of the sample to the operating temperature of the NMR probe.

If the tubes are flame-sealed and the standards are stable in solution, an advantage of the external standard method is that the standards can be used repeatedly and need not be freshly prepared for each analytical procedure.

B.2.2 Calibration

The molar response of the measuring system is calibrated as the integrated signal area per proton per mole under defined instrumental conditions and then applied to determine the analyte concentration under identical conditions. For the PC quantified using the external standard S:

(B-1)IPCNPCnPC=IsNsns

Although parameters such as receiver-gain and transient-number can be varied [221], the most robust approach is to keep all parameters constant between samples and standards – including solvents if possible. Although several studies suggest recalibration need not be frequent due to the high intrinsic stability of modern spectrometers, obtaining optimal performance requires calibration between each analyte sample. Independent preparation of multiple replicates of both samples and standards is desired to directly assess the overall method precision including sample preparation.

Where the solvents or ionic composition differ between samples and standards, corrections for probe damping are required. The product of signal intensity (S) and pulse width (θ) is used in place of the integral. Substitution into eq. B-1 gives eq. B-2:

(B-2)SPCθPCNPCnPC=SSθSNSnS

The overall measurement equation for an assignment external by qNMR of the mass fraction purity, wPC, using an external standard of purity wS, with correction for probe damping, is given by eq. B-3:

(B-3)wPC=IPCISNSNPCmSmPCMPCMS[θPCθSVPCVS]wS

where the amount of substance, n, is substituted with sample masses, m, molar masses, M and volumes, V.

B.3 Uncertainty Budget

The measurement uncertainty of a qNMR assignment results from combination of the assessments of the method performance characteristics including trueness, precision and linearity. The uncertainty of measurement predicted by the uncertainty budget must correspond to the uncertainty of multiple independent determinations of purity of the analyte. Several cause and effect diagrams of the factors influencing results and derived uncertainty budgets for qNMR measurements have been published [106, 112, 119].

Table B-1 lists the key parameters and variables that potentially impact on internally and externally standardized absolute qNMR quantification assays. How the factors’ influence on the measurement uncertainty can be evaluated is indicated: Type A (statistically) or Type B (by other means) [225].

Table B-1:

Factors influencing the measurement uncertainty of qNMR assays [226].

Internal Standard External Standard
Between runs Between sample Between compounds Between runs Between samples Between compounds
O1P offset B B B B B B
Pulse calibration A A A
Receiver efficiency A A A
Receiver gain amplification A A
Digitization B B B B B B
Lineshape B B B B
Multiplicity B B B B
Signal/Noise ratio A A A A A A
Gravimetry A A A A
Temperature A A A
Receiver delay B B B B
Tube volume A A
Sample height A A
Operator variation B B B B B B

When no systematic error is detected, the measurement uncertainty of an individual result can be assigned from the intermediate precision estimate for the method. In cases where validation studies reveal a significant bias, the calculated analyte concentration should be adjusted by the estimated recovery values and the measurement uncertainty expanded appropriately.

B.4 Examples

Examples of the three approaches to qNMR applied to the characterization of 17β-estradiol undertaken for the CCQM-K55.a comparison are discussed below.

B.4.1 Purity of 17β-estradiol by relative area quantification 1H-NMR

A relative-area NMR analysis technique was applied to estimate the chemical purity of 17β-estradiol. Individual sample sizes of 10 to 20 mg were used with deuterated dimethyl sulfoxide (DMSO-d6) or deuterated methanol (CD3OD) as solvent. The presence of SCs structurally-related to 17β-estradiol (4-methylestradiol, estrone, 17β-dihyroequilenin, 1-methylestradiol, 9-dehydroestradiol, 17α-estradiol) were established through comparison with the NMR spectra of independent standards of each compound. Figure B-3 provides an overlay of the spectra of the PC with the identified SCRS present in the material. The relative amount-of-substance for the various impurity components (in mg/g) was summed and subtracted from a mass fraction content for the PC (17β-estradiol) initially defined as 1000 mg/g. The assignments were based on the integrated peak areas of the unique 1H-NMR signals of the SCRS of each impurity relative to the integrals of analogous peaks in the primary component.

Figure B-3: 
                Expanded overlay of the 1H-NMR spectrum in the aromatic region of the CCQM-K55.a material with spectra of authentic standards of SCRS components.
Figure B-3:

Expanded overlay of the 1H-NMR spectrum in the aromatic region of the CCQM-K55.a material with spectra of authentic standards of SCRS components.

In addition to allowing for the quantification of SCRS components, assignments of the water content of the material and of a trace level of ethanol were also made that allowed for an assignment of the 17β-estradiol content of the material from 1H-NMR relative quantification. The estimate for the combined SCRS content was 7 mg/g with an additional allowance of approximately 2 mg/g for unidentified/unassigned related structure impurities. The individual impurity quantifications based on this approach are given in Table B-2.

Table B-2:

Impurty assignments by relative area NMR for CCQM-K55.a comparison.

Impurity Category Assignment method Content in estradiol material (mg/g) Standard uncertainty (mg/g)
4-Methylestradiol SCRS 1H-NMRarea 4.9 0.2
Estrone SCRS 1H-NMRarea 1.1 0.02
1-Methylestradiol SCRS 1H-NMRarea 0.30 0.02
17β-Dihydroequilenin SCRS 1H-NMRarea 0.30 0.02
17α-Estradiol SCRS 1H-NMRarea 0.13 0.03
9-Dehydroestradiol SCRS 1H-NMRarea 0.16 0.01
Trace impurities SCRS 1H-NMRarea & LC-UV 2.4 −0.1/+0.9
Ethanol SCOS 1H-NMRarea& HS-GC/MS 0.09 0.02
Water SCW 1H-NMRarea & KFT 6.7 −0.3/+1.2
Non-volatiles SCNV TGA and XRF 0.3 0.08
Total impurity 16.2

The value for 17β-estradiol content was assigned, using the relative area 1H-NMR method, as the difference of the summation of the impurities (16.2 mg/g) from the theoretical maximum of 1000 mg/g.

The uncertainty components were evaluated via Monte Carlo propagation of distributions. Individual component uncertainties were determined by repeated experiment and/or expert opinion for identified impurities. They were extrapolated from experimental evidence and expert opinion for the signals from unidentified impurities. Both of the skewed distributions were represented as triangles extending from the lowest evidential value to the highest; Gaussian distributions were used for all others.

The purity by 1H-NMRarea of 17β-estradiol in the CCQM-K55.a material was 983.82.9+0.3 mg/g

The challenges for this approach are to obtain a suitable S/N for the signals arising from the low-level impurities, given the inherently low sensitivity of the 1H-NMR compared to other organic analysis techniques, and to identify, isolate and integrate the signals of these impurities amongst the signals of the main component (see Figure B-3) [227].

B.4.2 Purity of 17β-estradiol by Internal Standard qNMR

The 17β-estradiol content of the CCQM-K55.a material was assigned by an IS qNMR method using 1,4-bis-trimethylsilyl benzene-d4 (BTMSB-d4) as the standard. Three separate sample preparations were undertaken. The weighing process was performed under controlled temperature (25 °C) and at low relative humidity (2 %). For each individual sample preparation about 5 mg of the internal standard, weighed accurately into an aluminium pan, was placed in a clear glass vial. An accurately weighed sample of about 15 mg of the CCQM-K55.a comparison material, on a separate pan, was placed in the same vial. The vial and its contents were removed from the low humidity conditions used for the gravimetric measurements and about 1.6 mL of CD3OD was added to dissolve the contents until a homogenous solution was obtained. Two 0.75 mL aliquots of the solution were transferred to separate NMR tubes. Each of the six resulting NMR solutions (three sample preparations providing two aliquots per sample) were analyzed in triplicate.

The qNMR data was acquired with a 600 MHz spectrometer equipped with a dual broadband probe. The sample temperature was controlled at 25 °C during the experiment. An equilibration delay of 5 min was applied to ensure the sample was equilibrated to the set temperature each time. In preliminary experiments the longest spin-lattice relaxation time (T1) for the signals subject to quantification was measured in order to establish a relaxation delay setting of 10 times the longest T1. The specific parameters used for the qNMR experiment were spectral width of 100 ppm, audio filter band width of 33 kHz, 90° pulse width of 11.4 μs, 4 s FID acquisition time, 13C decoupling during the acquisition delay to simplify the resulting spectrum simple, 60 s relaxation delay. Thirty-two scans were accumulated and averaged after four initial dummy scans to equilibrate the sample.

After Fourier transformation of the acquired free induction decay data, manual phase correction was carried out, the integration region was established and manual baseline correction performed.

Figure B-4: 
                The 1H-NMR spectrum with signal asssignments used for IS 1H-qNMR of 17β-estradiol in CCQM-K55.a. Signal A is from the IS, BTMSB-d4. Signals B–E are from 17β-estradiol [228].
Figure B-4:

The 1H-NMR spectrum with signal asssignments used for IS 1H-qNMR of 17β-estradiol in CCQM-K55.a. Signal A is from the IS, BTMSB-d4. Signals B–E are from 17β-estradiol [228].

Seventy-four qNMR values were obtained for the 17β-estradiol content (6 samples × 4 quantification signals per sample × 3 runs per sample). The global mean of this data was used as the 17β-estradiol content assignment. The original qNMR measurement equation was rewritten to give eq. B-4:

(B-4)wPC=IPCISNSNPCMPCMSmSmPCwS=MPCMS×g(IS,IPC,NS,NPC,mS,mPC)

where g is a function derived from the input factors to eq. 11, other than the molar masses of the standard and analyte, that permits assignment by ANOVA of an uncertainty component for the overall precision of the qNMR measurement.

The inclusion of additional Type-B uncertainty contributions arising from the individual mass determinations, the efficiency of signal integration, the isotopic composition of the peaks quantified, the estimation of the molar mass of each compound and knowing the uncertainty of the mass fraction content of the internal standard provided the overall uncertainty budget which is summarized in Table B-3.

Table B-3:

Measurement Uncertainty budget for IS 1H-qNMR assignment of 17β-estradiol in CCQM-K55.a.

u(xi) Source of uncertainty x i u(xi) c i u i(wPC) v
u(g) qNMR precision 0.817 94 kg/kg 453.96 μg/g -w PC/g 545.68 8
u(ms) Gravimetry (IS sample) 15.953 mg 0.144 mg w PC/ms 8.875 Large
u(mPC) Gravimetry (PC sample) 5.468 mg 0.125 mg -w PC m PC 22.520 Large
u(IS) Saturation of IS signal 0.983 20 kg/kg 288.68 μg/g w PC I s 288.68 Large
u(IPC) Saturation of PC signal 0.983 20 kg/kg 288.68 μg/g -w PC/IPC 288.68 Large
u(NPC) No. of 1H of PC 7 8.991 7 × 10−5 -w PC/Ns 12.629 Large
u(NS) No. of 1H of IS 18 8.991 7 × 10−5 w PC N PC 4.912 Large
u(MS) Molar mass of IS 272.382 g/mol 8.377 mg/mol w PC M s 3.024 Large
u(MPC) Molar mass of PC 226.499 g/mol 5.601 mg/mol -w s/MPC 24.31 Large
u(wS) Mass fraction of IS 0.999 6 kg/kg 0.001 5 kg/kg -w PC/ws 1480 26
  1. The assigned purity by IS 1H-qNMR for 17β-estradiol in the CCQM-K55.a material was (983.2 ± 1.6) mg/g.

B.4.3 Purity of 17β-estradiol by External standard qNMR

External standard quantitative 1H-NMR was used to determine the mass fraction of the 17β-estradiol content of the CCQM-K55.a material. A correction was applied for contributions due to structurally related impurities as determined separately by LC-UV. Samples of the CCQM-K55.a material (16 to 30 mg) and benzoic acid (NIST SRM 350b, 8 to 15 mg) were dissolved in 3 mL of CD3OD and carefully mixed to obtain a homogenous solution. A 0.7 mL aliquot of each solution was sealed in a precision NMR tube. Spectra were acquired at 400 MHz at 23 °C using 64 scans and 44 915 data points. The NMR spectra obtained after phasing were subject to baseline correction and each signal was integrated manually.

The integrals of the signals for the aromatic proton signals for 17β-estradiol (IPC corresponding to one and two hydrogen atoms respectively) and of benzoic acid (IS corresponding to five hydrogen atoms) were measured including the associated 13C-coupled satellite signals to determine the ratio IPC/IS.

The uncertainty of the result for IPC/IS arises from the variance in the volume of each NMR sample in addition to gravimetric preparation, repeatability, instrument tuning and shimming, manual phasing, baseline correction and integration – as for the internal standard approach. The relative uncertainty due to these components was estimated from the standard deviation of the replicate measurement of the purities of two independently prepared solutions of both the material and of the external standard. The contributions from the uncertainties arising from the molar masses, gravimetry and external standard purity proved insignificant as did the contribution from the correction applied for structurally related impurities not detected by NMR (small components assigned large relative uncertainties) determined by LC-UV based on response factors for estrone and 17α-estradiol. The assignment by ES 1H-qNMR of 17β-estradiol in the CCQM-K55.a material was (984.9 ± 4.6) mg/g.

Appendix C: Example of purity by direct methods

C.1 Titrimetry

An example is given of the use of acidimetric titration for assignment of the L-Val content of the CCQM-K55.c comparison material. The total amount of amine in the sample was determined by a non-aqueous titration in solution in acetic acid. The PC content of L-valine was assigned after correction of the raw result of the titration method for the contribution of amino acid impurities identified separately. Non-aqueous titration grade acetic acid was used as solvent, 0.02 mol/L perchloric acid/acetic acid as titrant, 2 mol/L LiCl/acetic acid as internal solvent and potassium hydrogen phthalate (KHP) as the primary titration reference standard.

C.1.1 Purity of L-Valine by acidimetric titrimetry

The concentration of the titrant, perchloric acid/acetic acid solution, was determined by titration against the KHP primary standard (NMIJ CRM 3001-b). An accurately weighed sample of the KHP (49 mg) was dissolved in 1 mL of formic acid and diluted to 30 mL in acetic acid. The concentration of perchloric acid was calculated applying equation C-1:

(C-1)CHClO4=wKHPmKHP(VKHPVb)MKHP

where:

C HClO4:     concentration of perchloric acid (mol/L),

w KHP:      mass fraction KHP content of primary standard (kg/kg),

m KHP:      mass of primary standard (g),

V KHP:      titration volume for KHP solution (L),

V b:         titration volume of blank (L),

M KHP:      molar mass of KHP (g/mol).

The volume of blank was calculated by regression analysis from the titration results of different concentrations of the KHP solution. The standard uncertainty of the concentration of perchloric acid was evaluated by the combination of the standard uncertainties of the components in the above equation.

In this case approximately 28.5 mg of the L-Val material was weighed accurately and dissolved in 1.0 mL of formic acid. The solution was diluted with approximately 30 mL of non-aqueous titration grade acetic acid. The sample was titrated using the same procedure as for the KHP standard. The total amino acid mass fraction content in the sample was calculated using eq. C-2:

(C-2)wAA=CHClO4(VValVb)MValmVal

where:

w AA:      total amino acid mass fraction content in CCQM-K55.c material (g/g),

m Val:     mass of CCQM-K55.c material (g),

V Val :      titration volume of CCQM-K55.c sample solution (L),

M Val :     molar mass of CCQM-K55.c material (g/mol).

The titration gave wAA as 999.81.7+0.2 mg/g. The mass fraction content, wVal, of L-Val in the CCQM-K55.c material was assigned after correction of wAA for the contribution due to amino acid impurities as shown in equation C-3. For this calculation, the contribution of the amino acid impurities (Cimp) present in the material takes into account their individual molar masses. The mass fraction contribution of individual impurities were estimated separately by GC-FLD as described in Appendix A.1.2 above.

(C-3)wVal=wAAMValCimpMimp

The components of the uncertainty budget for the L-Val assigned value are summarized in Table C-1.

Table C-1:

Measurement Uncertainty budget for L-Val content in CCQM-K55.c by acidimetric titration.

Component Source of uncertainty x i u(xi) c i u i(wAA) (g/g)
C HClO4 (mol/L) Concentration of perchloric acid 0.019 88 0.000 009 w AA/CHClO4 0.000 429
V Val (mL) Titre of sample 12.217 1 0.000 5 w AA/(Vs- Vb) 0.000 041
V b (mL) Titre of blank 0.031 4 0.001 8 -w AA/(Vs- Vb) 0.000 145
m Val (mg) Mass of sample 465.422 0.013 5 -w AA/(ms- m0) 0.000 473
M Val (g/mol) molar mass of L-Val 117.146 0.005 28 w PC/MPC 0.000 045

The L-Val content of the CCQM-K55.c comparison material as determined by impurity-corrected acidimetric titration was (991.8 ± 1.9) mg/g.

Appendix D: Examples of purity by thermal methods

Three techniques are described for use of an indirect purity assay by the freezing point depression method to obtain an assignment of the PC content of a material via determination of f and Teq:

  1. fractional melting using an adiabatic calorimeter [229], [230], [231];

  2. stepwise scan method with a DSC [232], [233], [234];

  3. continuous scan method with a DSC [235, 236].

The three techniques involve common procedures that relate the enthalpy change during the fusion process to SCtotal content. The freezing point depression method assumes that fusion occurs from a single stable crystal phase. Purity assay by freezing point depression is not possible for samples which freeze into multiple crystal phases or do not crystallize. In such cases, crystallization into a single stable crystal phase before the fusion measurement may be achieved by applying a temperature program to pass through several heating-cooling cycles until a single crystal phase is obtained.

After achieving a single stable crystal phase, measurement commences from a temperature lower than the melting point and ends at a higher temperature. When a sample is in a single stable phase (crystal or liquid), the application of heating energy results solely in an increase in the sample temperature. During fusion, supplementary thermal energy input is required to breakdown the sample crystal lattice and as a result the apparent heat capacity of the sample increases. To estimate the additional heating energy required to increase the sample temperature during fusion, the energy trend is measured to establish a baseline over a suitable temperature range for each stable phase. The ΔfusHpartial is evaluated by subtraction of the energy estimated from the baseline observation to simply increase the sample temperature during the fusion process from the total applied heating energy. The equilibrium temperature (Teq) and ΔfusHpartial are measured during fusion. After the fusion is complete, ΔfusHtotal is evaluated at a temperature above the melting point.

The measurement procedures for ΔfusHpartial and Teq differ for the three techniques. A comparison of the three techniques performance characteristics is summarized in Table D-1. The freezing point depression method is based on thermodynamics; purity can only to be evaluated when the system is in thermodynamic equilibrium. Use of an adiabatic calorimeter provides the best realization of thermodynamic equilibrium and can achieve overall levels of standard uncertainty up to an order of magnitude smaller than those of the other techniques. However, there are significant limitations to its use in purity assay. The equipment is highly specialized and not readily available and there are significant restrictions on its application. These include the limited measurement temperature range and its unsuitability for compounds that are insufficiently thermostable or that are potentially reactive with the interior surface of the calorimeter vessels. In addition it requires a relatively large amount of sample. For cases that are sample limited or where the analyte lacks the requisite stability, DSC is the method of choice.

Table D-1:

Comparison of techniques for purity assay by freezing point depression method.

Parameter Adiabatic calorimetry Stepwise scan DSC Continuous scan DSC
Sample condition Equilibrium Quasi-equilibrium Non-equilibrium
Temperature measurement Adiabatic Isothermal Steady rate
Temperature resolution High (10−4–10−3 K) High (10−2 K >)
Equilibration time Very long (1 h–2 d) Long (10 min–3 h)
Measurement time Very long (2–10 d) Long (5 h–1 d) Short (1–10 h)
Sample amount Large (>1 g) Small (1–10 mg) Small (1–10 mg)
Standard uncertainty > 0.00001 mol/mol > 0.0001 mol/mol > 0.0003 mol/mol

Differential scanning calorimetry using a stepwise scan method is preferable to a continuous scan method where the highest accuracy and smallest associated uncertainty is desired. The sample condition in stepwise scan method (quasi-equilibrium condition) is closer to the true thermodynamic equilibrium condition than that in a continuous scan method. As Teq and ΔfusHpartial are measured by the continuous scan method in a manner inconsistent with achieving complete thermodynamic equilibrium, which in turn leads to lower accuracy in measurements of temperature and enthalpy. The larger potential for bias effects due to the measurement procedure and the analysis conditions must be taken into consideration when validating the method and estimating the uncertainty of individual results. On the other hand, the continuous scan method is attractive for the ease of the purity assay and has the significant advantage of being applicable to small sample sizes and to materials subject to some degree of thermal decomposition, which precludes the use of the other techniques.

D.1 Fractional melting with an adiabatic calorimeter

The temperature is measured under thermodynamic equilibrium conditions after heating and Teq is obtained at the equilibrium condition. The heating energy obtained as a joule heat is controlled to achieve a suitable fraction melted. The fusion enthalpy is evaluated at the temperature above melting point.

Measurements with an adiabatic calorimeter are performed through a cycle between two processes – a temperature measurement process and a heating process. A typical temperature profile including a heating process is shown in Figure D-1. In the heating process, the calorimeter vessel is heated by joule heat. The physical quantities determined for purity assay are Teq and the heating energy.

Figure D-1: 
              Temperature profile by adiabatic calorimetry.
Figure D-1:

Temperature profile by adiabatic calorimetry.

D.1.1 Purity of toluene by fractional melting

The heat capacity of the vessel is measured in advance and the thermal energy required for temperature increment of the vessel evaluated from the heat capacity. The molar heat capacity of a substance is typically obtained as the direct measurement result by adiabatic calorimetry. A plot of heat capacity as a function of temperature for a sample of toluene (NMIJ CRM 4003-b) is shown in Figure D-2.

Figure D-2: 
                Heat capacity of toluene by adiabatic calorimetry.
Figure D-2:

Heat capacity of toluene by adiabatic calorimetry.

The fraction melted at each equilibrium condition is calculated from eq. 21 (see Section 3.4.3 above). A van’t Hoff plot for NMIJ CRM 4003-b is shown in Figure D-3. For this sample the 1/f versus T plot shows a concave upward curve, so ΔT and T* are derived from the regression line using a 1/(f + α) versus T plot. Although ΔfusH can be obtained from ΔfusHtotal using the van’t Hoff plot, biases may arise due to the extended measurement time requiring multiple cycles of temperature measurement and heating.

Figure D-3: 
                The van’t Hoff plots of toluene by adiabatic calorimetry. See also eq. D-1.
Figure D-3:

The van’t Hoff plots of toluene by adiabatic calorimetry. See also eq. D-1.

The uncertainty budget for purity assay of a toluene material based on eq. 17 by the fractional melting method is given in Table D-2.

Table D-2:

Measurement uncertainty budget for purity assay of toluene by the fractional melting method.

Component Source of uncertainty x i u(xi) c i c i u i(xi)
x B (mol/mol) Measurement variation 0.000327 0.000008 1 0.000008
ΔT (K) Repeatability, calibration 0.01302 0.002 0.026 0.000052
R (J K−1 mol−1) Literature value [164] 8.314472 0.000 015 3.9E−05 5.9E−10
ΔfusH (J mol−1) Repeatability, baseline, gravimetry, molar mass 6628 5 4.90E−08 2.5E−07
T*(K) Calibration, RM 178.203 0.013 3 3.67E−06 4.9E−08

The uncertainty in xB is obtained from the measurement variation and includes contributions from measurement variation of ΔT and T*. An extended time is needed to reach the thermodynamic equilibrium condition. The equilibrium temperature (Teq) can alternatively be estimated from extrapolation of the temperature profile under a non-equilibrium state, in which case the uncertainty of the estimation should be accounted for in addition to the uncertainty of the temperature measurement.

The uncertainty sources of ΔfusH are measurement variation, measurement of heating energy, baseline, correction of heat leakage and amount of a sample. Heating energy is calculated as a joule heat and its uncertainty sources arise from measurement of the voltage drops, standard resistor and heating time. Heat leakage is estimated from the temperature drift rate and heat capacities of the calorimeter vessel and sample. The estimate of heat required for the temperature increase obtained from the heat capacity of the sample used as the baseline and the actual choice of the baseline contribute to the overall uncertainty. The uncertainty sources of T* are associated with the regression function of the van’t Hoff plot and of the measurement instruments.

In typical cases, the major uncertainty sources in the fractional melting method are the measurement variation of the xB and ΔT. The uncertainty of ΔfusH is usually negligible, but it becomes larger when baseline determination is difficult, such as for low purity samples or samples having a thermal anomaly near fusion.

From this value for xB the value and associated uncertainty of the PC (toluene) amount-of-substance fraction content of the material was determined to be (0.999 673 ± 0.000 016) mol/mol.

D.2 Stepwise scan DSC method

Heating and isothermal processes are repeated using a stepwise temperature program. The DSC signal is displaced from the baseline in the heating cycle and returned to the baseline in the isothermal cycle. The Teq is measured after recovery of the DSC signal to the baseline. The peak area due to the temperature increment corresponds to the enthalpy change arising from the sample fusion and heat for temperature increment.

An example of the DSC thermogram for a sample of dibutyl sulfide is shown in Figure D-4. A peak corresponding to the heat for temperature increment appears in one temperature step and the baseline for the peak is established by the stabilized line in isothermal steps before and after the heating. The amount of heat corresponding to the peak is a sum of the heat difference between a sample and a reference for temperature increment and for fusion. The heat difference due to temperature increment alone is evaluated in the temperature ranges of the solid and liquid phases not affected by fusion. The heat of fusion is evaluated from subtraction of the heat required for temperature increment from the total enthalpy change observed during the fusion. For the sample heating, the heating rate must be constant as the sensitivity of heating for the temperature increment may change with change in the heating rate. The van’t Hoff plot of NMIJ CRM 4221-a is shown in Figure D-5. A correction for solid-soluble impurities is applied for evaluation of ΔT and T*. As heating and isothermal processes alternate and the absolute value of ΔfusHtotal may deviate from the true value, ΔfusH should be measured separately by a continuous scan method.

Figure D-4: 
              The DSC curve of dibutyl sulfide by stepwise scan method.
Figure D-4:

The DSC curve of dibutyl sulfide by stepwise scan method.

Figure D-5: 
              The van’t Hoff plot of dibutyl sulfide by stepwise scan method.
Figure D-5:

The van’t Hoff plot of dibutyl sulfide by stepwise scan method.

D.2.1 Purity of dibutyl sulfide by stepwise scan DSC

Calibration of the temperature and enthalpy are required for DSC measurements. In typical cases, the fusion of high-purity substances with known melting point and fusion enthalpy are used for this purpose. To realize SI-traceability, high-purity CRMs such as NIST SRM 2232 (indium), NIST SRM 1514 (phenacetin), LGC CRM 2605 (acetanilide) and NMIJ CRM 5401 (cyclohexane) are used to calibrate DSC measurements.

An uncertainty budget for assay of dibutyl sulfide by a stepwise DSC scan method is shown in Table D-3.

Table D-3:

Measurement uncertainty budget for purity assay of dibutyl sulfide by stepwise scan method.

Component Source of uncertainty x i u(xi) c i c i u i(xi)
x B (mol/mol) Measurement variation

Range of fraction melted
0.00103 0.000103 1 0.000103
ΔT (K) Regression 0.0178 0.002 0.0579 0.000116
R (J K−1 mol−1) Literature value [164] 8.314462 0.0000075 0.000124 9.3E−10
ΔfusH (J mol−1) Repeatability, RMs, gravimetry, molar mass 18 725 411 5.60E−08 0.000024
T* (K) Regression, RMs 197.33 0.065 1.04E−05 0.000001

The uncertainty sources of xB arise from the variation in ΔT and T* and the range of fraction melted. The uncertainty in ΔT is derived from the regression of the van’t Hoff plot. The contributors to the uncertainty of ΔfusH are measurement variation, the tolerance limit of calibration of heat flow, the uncertainty of enthalpy of phase transition of the RMs used for calibration of the heat flow and the amount of sample used. Likewise, the uncertainty sources of T* are the van’t Hoff plot regression, the temperature calibration and the phase transition temperature of the RMs used for temperature calibration.

The uncertainty of the temperature calibration of the DSC is not accounted for in the uncertainty estimation of ΔT. This is because DSC measurements are over a limited temperature range (1 K or narrower) in contrast to the wide calibration temperature range (100 K or wider). Any bias in the values of temperature differences are assumed to be negligible. In contrast to ΔT, temperature calibration is accounted for in the uncertainty estimation of T*, as the absolute value of temperature is directly affected.

In typical cases, the major uncertainty sources in the stepwise scan method are associated with the values for the xB, ΔT and ΔfusH. The uncertainty of ΔfusH is mainly due to the tolerance of the enthalpy calibration before sample measurement.

From the derived value for the total impurity mole fraction content, xB, the purity and associated uncertainty of the amount-of-substance content of the PC, dibutyl sulfide, was assigned by difference as (0.998 97 ± 0.000 21) mol/mol.

D.3 Continuous scan DSC method

The temperature is increased continuously by applying a constant heating rate. Teq is estimated from a reference temperature and the observed temperature deviation of the sample from the reference due to thermal resistance. The ΔfusHpartial is evaluated from the peak area subdivided by the DSC curve, the baseline and a perpendicular line from the DSC curve to the baseline at a selected temperature [160, 162]. In the continuous scan method, f is not obtained from eq. 23 since a linear relation in the van’t Hoff plot cannot be realized. To linearize the van’t Hoff plot, the equation is modified by the introduction of a constant term to permit evaluation of the fraction melted to give eq. D-1

(D-1)f=ΔfusHpartial(T)+kΔfusHtotal(Tfus)+k

where k is a correction term. One interpretation of k is as an undetected fusion enthalpy at the beginning of fusion or as due to an unrealized thermal equilibrium [237]. The correction is empirical and varies depending on the analysis conditions.

In the continuous scan method, Teq is obtained taking into consideration the thermal resistance of a measurement system in a steady state under a constant heating rate, but it is less satisfactory because sample temperature varies due to the spontaneous endothermic effect of fusion. Another problem is simply setting a perpendicular line is invalid for the evaluation of ΔfusHpartial as it is not fully detected at the corresponding temperature. The detailed contribution of each factor is not considered; their effects are combined into the correction term k. This means that the continuous scan method becomes a “black box” in terms of the process of purity assignment, fundamentally different from the other two techniques. Therefore, it is important to understand that the continuous scan method is an empirical method and measurement under a constant heating rate does not satisfy the theoretical model of the freezing point depression method and the realization of direct metrological traceability for the results obtained.

In the continuous scan method, f and Teq are estimated from a fusion peak measured with a constant heating rate. An example of the measurement result for dibutyl sulfide is shown in Figure D-6 and the associated van’t Hoff plot is shown in Figure D-7.

Figure D-6: 
              The DSC curve of dibutyl sulfide by continuous scan method.
Figure D-6:

The DSC curve of dibutyl sulfide by continuous scan method.

Figure D-7: 
              The van’t Hoff plot of dibutyl sulfide by continuous scan method.
Figure D-7:

The van’t Hoff plot of dibutyl sulfide by continuous scan method.

D.3.1 Purity of dibutyl sulfide by continuous scan DSC

In contrast to the other two techniques, where information on f is obtained over the full range of the fusion process, in continuous scan mode the range f for purity evaluation is typically chosen from the beginning to the inflection point of the fusion peak. In Figure D-7, 1/f versus T is a concave upward curve, but this curvature is corrected assuming there are no solid soluble impurities present in the material. The ΔT and T* are determined from a regression line of the corrected plots. ΔfusH for purity calculation purposes is obtained simultaneously with the van’t Hoff plot, adjusted using the correction factor required for linearization.

An uncertainty budget for the purity assay of dibutyl sulfide (NMIJ CRM 4221-b) by the continuous scan method is shown in Table D-4.

Table D-4:

Measurement uncertainty budget for purity assay of dibutyl sulfide by continuous scan method.

Component Source of uncertainty x i u(xi) c i c i u i(xi)
x B (mol/mol) Repeatability, fraction melted, regression of van’t Hoff plot 0.00226 0.001008 1 0.001008
ΔT (K) Regression 0.0178 0.002 0.0579 0.000116
R (J K−1mol−1) Literature value [164] 8.3144621 0.0000075 0.000272 2.0E−9
ΔfusH (J mol−1) Repeatability, RMs, gravimetry, molar mass 18 725 410 1.21E−07 0.000050
T*(K) Regression, RMs 197.33 0.065 2.29E−05 0.000002

The uncertainty sources of xB are measurement variation of ΔT, ΔfusH and T*, the range of fraction melted and the regression of the van’t Hoff plot. The uncertainty sources of ΔfusH are the tolerance limit of calibration of heat flow, the enthalpy of phase transition of the RMs for calibration of heat flow and the amount of a sample. The uncertainty sources of T* are the tolerable limit of temperature calibration and the phase transition temperature of RMs used for temperature calibration.

From the derived value for the total impurity mole fraction content, xB, the value and associated uncertainty of the amount-of-substance content of the PC, dibutyl sulfide, was assigned by difference as (0.9977 ± 0.0020) mol/mol.

D.4 Converting amount of substance fraction to mass fraction

In most cases, determination of xB by a continuous scan method is obtained using analysis software based on the measurement result of a single fusion peak. The ΔT, T* and ΔfusH are calculated simultaneously with xB and the parameters vary depending on the measurement and analysis conditions. The measurement variations of ΔT, T* and ΔfusH are included in that of xB as the parameters are correlated and it is difficult to separate their contributions. For the same reason, the standard uncertainty of analysis condition of xB include the contributions of the uncertainties associated with ΔT, T* and ΔfusH.

In the case of NMIJ for measurements of dibutyl sulfide, the typical analysis range was from 10 to 50 % of signal height to the peak top. For uncertainty estimation of the analysis range, limits varied from 7 to 13 % (lower) and from 35 to 65 % (higher), respectively. The variation of the value for xB due to the analysis range are shown in Table D-5 and the uncertainty was estimated from the maximum of the deviation from the typical analysis condition. Contributions from measurement variation and the regression of van’t Hoff plot are included in the combined standard uncertainty of xB. The other uncertainty sources of each parameter such as calibration are accounted for separately.

Table D-5:

Variation of amount of substance fraction of total impurities due to range for van’t Hoff plot.

Percentage of higher limit to peak height
35 40 45 50 55 60 65
Ratio of lower limit to peak height as % 7 0.00163 0.00176 0.00190 0.00206 0.00223 0.00241 0.00261
8 0.00169 0.00184 0.00199 0.00216 0.00234 0.00253 0.00275
9 0.00176 0.00191 0.00208 0.00226 0.00245 0.00266 0.00288
10 0.00183 0.00200 0.00217 0.00236 0.00257 0.00279 0.00303
11 0.00191 0.00208 0.00226 0.00247 0.00268 0.00291 0.00317
12 0.00199 0.00216 0.00235 0.00257 0.00280 0.00304 0.00331
13 0.00205 0.00223 0.00243 0.00266 0.00290 0.00315 0.00344
Employed value 0.00236
Maximum deviation 0.00108

In typical cases, the major uncertainty sources in the continuous scan DSC method are xB and ΔfusH. The uncertainty of xB is mainly due to purity variation from the range of the van’t Hoff plot. The uncertainty of ΔfusH is mainly due to the limit of the enthalpy calibration established before undertaking the sample measurement.

The components of the uncertainty for conversion of a purity from amount-of-substance content to mass fraction content (eq. 23) are xB, the molar mass of the PC and the average molar mass of impurities. An uncertainty budget for the purity conversion is shown in Table D-6. The standard uncertainty of the molar mass of the PC i calculated from the IUPAC recommendations [121]. The standard uncertainty of the average molar mass of the impurities is evaluated from their concentrations and individual molar masses.

Table D-6:

Measurement uncertainty budget for toluene amount-of-substance fraction to mass fraction.

x i u(xi) c i c i u(xi) v
Molar mass of main component (g/mol) 92.138 0.004 2.82E−06 1.2E−08
Average molar mass of impurities (g/mol) 73.1 0.9 3.55E−06 3.2E−06
Amount-of-substance fraction of total impurities (mol/mol) 0.000327 0.00015 0.793 0.00012 13 484

The contributions from the uncertainty of xB and of the average molar mass of impurities are dominant while the contribution from the molar mass of the PC is negligible. The uncertainty of the average molar mass can be estimated from the impurity analysis and the magnitude is affected by measurement accuracy of the impurity analysis. The presence of unidentified impurities of necessity significantly increases the uncertainty of the estimate.

Membership of sponsoring bodies

The membership of the Analytical Chemistry Division (Division V) (2020-2021)

President: Zoltán Mester; Past President: Jan Labuda; Vice President: Erico Marlon de Moraes Flores; Secretary: Takae Takeuchi; Titular Members: Medhat A. Al-Ghobashy, Derek Craston, Attila Felinger, Irene Rodriguez Meizoso, Sandra Rondinini, David Shaw; Associate Members: Jiri Barek, M. Filomena Camoes, Petra Krystek, Hasuck Kim, Ilya Kuselman, M. Clara Magalhães, Tatiana A. Maryutina; National Representatives: Boguslaw Buszewski, Mustafa Culha, D. Brynn Hibbert, Hongmei Li, Wandee Luesaiwong, Serigne Amadou Ndiaye, Mariela Pistón, Pedreira, Frank Vanhaecke, Winfield Earle Waghorne, Susanne Kristina Wiedmer.

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Received: 2020-08-06
Accepted: 2022-07-11
Published Online: 2023-01-18
Published in Print: 2023-01-27

© 2022 IUPAC & De Gruyter. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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