Elsevier

Analytica Chimica Acta

Volume 917, 21 April 2016, Pages 19-26
Analytica Chimica Acta

Evaluation of the availability of bound analyte for passive sampling in the presence of mobile binding matrix

https://doi.org/10.1016/j.aca.2016.02.039Get rights and content

Highlights

  • The mathematical expression of the lability factor of bound analyte was deduced.

  • Effective average diffusion coefficient was introduced.

  • The lability factors of PAHs in the diffusion boundary layers surrounding SPME fibers were estimated.

  • The lability factors of PAHs were successfully used to predict the mass transfer efficiencies of PAHs.

Abstract

Elucidating the availability of the bound analytes for the mass transfer through the diffusion boundary layers (DBLs) adjacent to passive samplers is important for understanding the passive sampling kinetics in complex samples, in which the lability factor of the bound analyte in the DBL is an important parameter. In this study, the mathematical expression of lability factor was deduced by assuming a pseudo-steady state during passive sampling, and the equation indicated that the lability factor was equal to the ratio of normalized concentration gradients between the bound and free analytes. Through the introduction of the mathematical expression of lability factor, the modified effective average diffusion coefficient was proven to be more suitable for describing the passive sampling kinetics in the presence of mobile binding matrixes. Thereafter, the lability factors of the bound polycyclic aromatic hydrocarbons (PAHs) with sodium dodecylsulphate (SDS) micelles as the binding matrixes were figured out according to the improved theory. The lability factors were observed to decrease with larger binding ratios and smaller micelle sizes, and were successfully used to predict the mass transfer efficiencies of PAHs through DBLs. This study would promote the understanding of the availability of bound analytes for passive sampling based on the theoretical improvements and experimental assessments.

Introduction

Passive sampling techniques are very popular for sampling analytes of interest from various complex sample matrixes, such as environmental waters [1], sediments [2] and biological samples [3], [4], [5], [6], [7], [8]. For the implementation of passive sampling in complex sample matrixes, it has long been a concern among the scientific community whether the bound analytes are available for passive sampling in complex sample matrixes, which might complicate the passive sampling kinetics and influence the passive sampling efficiency [9], [10], [11].

For over a decade, a series of studies revealed that the presence of diverse mobile binding matrixes, such as humic substances [12], [13], [14], [15], [16], [17], surfactant micelles [16], [17], nanoparticles [18], [19], and proteins [9], [10], [11], [19], could accelerate the mass transfer kinetics through the diffusion boundary layers (DBLs) in the sample matrixes, which was regarded as a “shuttle effect” of the mobile binding matrixes, indicating that the bound analytes also contributed to the overall mass transfer through DBLs adjacent to passive samplers [9], [10], [11], [15], [18], [19]. These studies emphasized the importance of full awareness of the effects of binding matrixes, and showed profound influence on the development of calibration methods for passive sampling techniques [11], [20].

Several pioneer studies were committed to quantify the effects of the binding matrixes on the mass transfer through DBLs adjacent to solid-phase microextraction (SPME) fibers [9], [10], [15], [18], [19]. All these studies agreed that, to make the bound analytes available for the mass transfer through DBLs, the desorption kinetics of analytes from the binding matrixes should be fast when compared to the time scales that the free analytes diffuse through DBLs [9], [10], [15], [18], [19]. ter Laak et al. [15] who were cautious about the desorption kinetics, made a remarkable progress by introducing a lability factor in their theoretical model to correct the possibly inefficient desorption of the analytes from the binding matrixes during the time period of the complexes diffusing in DBLs. The lability factor was assigned to range from zero to unity, which at each endpoint value was corresponding to the completely inert and completely labile complexes. When the complexes were completely inert, the bound analytes would not desorb form the binding matrixes during the time period of the complexes diffusing in DBLs, and thus, would not participate in the mass transfer through DBLs. On the contrary, when the complexes were completely labile, the bound analytes would totally participate in the mass transfer through DBLs. In other words, the lability factor also measures the availability of the bound analytes in the mass transfer through DBLs [12], [13], [18], [19]. The model developed by ter Laak et al. [15] coincided well with the experimental results of several completely labile systems developed by van Leeuwen, Town and their colleagues [18], [19]. However, the desorption kinetics of analytes from the binding matrixes might not be that fast, as the desorption kinetic coefficients reported by Kopinke et al. were in the range of 0.0017–1.1 s−1 [21]; while the time scales for the free and bound analytes to diffuse through DBLs are probably at second levels or even subsecond levels. Then, the incompletely labile systems might also be common in real situations according to the Damköhler Number [22]. To our knowledge, the availability of any incompletely labile analyte-binding matrix complexes for passive sampling have not been studied yet. In addition, the lability factor was introduced conceptually, not through rigorous mathematical derivation.

In the present study, the mathematical expression of the lability factor was deduced for the first time. Based on the upgraded interpretation of the lability factors, an effective average diffusion coefficient was used to establish a model to describe the enhanced mass transfer in DBLs. Thereafter, the lability of the polycyclic aromatic hydrocarbon (PAH)-micelle complexes in the DBLs adjacent to SPME fibers under different SDS concentrations and salinities were figured out according to the model. SDS micelles were selected as the binding matrix since SDS micelles are well known as spherical permeable nanoparticles, whose diameters and diffusion coefficients are constant in a certain concentration range and are tunable under different salinities [23], [24]. The lability factors of PAHs clarified the availability of the bound PAHs for SPME.

Section snippets

Materials

Phenanthrene (PHE), anthracene (ANT), fluoranthene (FLA), and pyrene (PYR) were all purchased from Supelco Inc. (Bellefonte, PA, USA). Stainless steel wires (SSWs, 127 μm in diameter, medical grade) were purchased from Small Parts Inc. (Miami Lakes, FL, USA). Sylgard 184 silicone elastomer base was purchased from Dow Corning Co. (Midland, MI, USA). Polydimethylsiloxane (PDMS) tubing (i.d. 212 μm, o.d. 300 μm) was purchased from Helixmark (Carpinteria, CA, USA). Sodium dodecylsulphate (SDS) was

Mathematical expression of the lability factor

Considering the simplest situation, i.e. supposing a planar configuration of the passive sampler, the following mathematical derivation is based on a planar DBL. For a cylinder SPME fiber, if the thickness of the DBL is far smaller than the radius of the fiber, the DBL adjacent to the SPME fiber can be treated planar as well. Generally, the thickness of a DBL would be declined by increasing the flow rate of the water.

For a planar DBL, the continuity equations for the free and bound analytes in

Binding of PAHs to SDS micelles

In this study, the partition coefficients between the PDMS fiber and the solutions, Kfs were determined as described in the Experimental section. As shown in Table 1, the binding of PAHs to SDS micelles decreased the partition coefficients between the PDMS fiber and the solutions. When SDS micelles presented in the solutions (all above the critical micelle concentration of SDS), the Kfs values were dramatically reduced. The percentages of the free PAHs in SDS solutions were calculated according

Conclusions

Lability factor is a very important parameter for measuring the availability of the bound analyte for the mass transfer through DBLs adjacent to passive samplers. In this study, we promoted the understanding of the availability of bound analyte by (a) presenting the mathematical expression of the lability factor; (b) using the effective average diffusion coefficient to make the mass transfer model consistent to the extreme assumption about the completely inert complexes; and (c) for the first

Acknowledgments

We acknowledge financial support from the projects of NNSFC (21225731, 21377172, 21477166), the NSF of Guangdong Province (S2013030013474).

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