Aqueous flat-cells perpendicular to the electric field for use in electron paramagnetic resonance spectroscopy, II: design

https://doi.org/10.1016/j.jmr.2004.11.006Get rights and content

Abstract

This paper builds on the work of Mett and Hyde [J. Magn. Reson. 165 (2003) 137]. Various aqueous flat-cell geometries in the perpendicular orientation have been studied using Ansoft High Frequency Structure Simulator (version 9.0, Pittsburgh, PA) and Computer Simulation Technology Microwave Studio (version 5.0, Wellesley Hills, MA). The analytic theory of Mett and Hyde has been refined to predict optimum dimensions of multiple sample cell structures including the effect of the sample holder dielectric properties and the interaction of the cells with each other on EPR signal strength. From these calculations and simulations we propose a practical multiple cell sample structure for use in commercial rectangular TE102 cavities that yields 2.0–2.3 times higher sensitivity relative to a single flat-cell in the nodal orientation. We also describe a modified TE102 resonator design with square rather than cylindrical sample-access stacks that is predicted to give a factor of 2.2–2.7 enhancement in EPR signal strength of a single flat-cell in the nodal orientation. These signal enhancements are predicted with sample holders fabricated from polytetrafluoroethylene. Additional improvement in EPR signal of up to 75% can be achieved by using sample holder materials with lower dielectric constants.

Introduction

A conventional procedure for observation of aqueous EPR samples at X-band is to introduce the sample to a flat-cell cuvette that is placed in a rectangular TE102 cavity as shown in Fig. 1A. The cell lies in a nodal plane where the RF electric field intensity is zero and the RF magnetic field is maximum. Sample placement is very critical and only a few degrees of misalignment of the cell with respect to the x-axis results in a sharp decrease in the Q-value of the cavity. However, by rotating the cell precisely 90° from the so-called parallel orientation in the electric field node, Fig. 1A, to the perpendicular orientation, Fig. 1B, the Q-value recovers and good EPR signals can be obtained. Aqueous sample flat-cells oriented such that the RF electric field is perpendicular to the surface of the cell, Fig. 1B, were first studied by Hyde [1] and further discussed by Eaton and Eaton [2]. In both of these papers, experiments using more than one cell in perpendicular orientation were reported. More recently, Mett and Hyde [3] carried out a detailed theoretical analysis of the microwave fields when aqueous sample flat-cells are in the perpendicular orientation. They predicted that by placing multiple parallel flat-cells in a TE102 cavity with cell thickness (x-dimension), width (y-dimension), and the spacing between cells carefully optimized, a significant (3–6 times) EPR signal improvement can be achieved compared with a single optimized flat-cell in the parallel orientation of Fig. 1A.

The present paper builds on the analytic work of Mett and Hyde [3]. Extensive use is made of finite-element modeling of electromagnetic fields and analytic equations to calculate the optimum sample cluster dimensions. The analytic theory of Mett and Hyde [3] is extended and refined to make predictions of optimum sample cluster sizes and dimensions in the presence of a dielectric sample holder. Several practical multiple cell sample geometries are proposed for the X-band Varian Multipurpose TE102 cavity. Dimensions of this cavity are given in the caption of Fig 1. Extension to the similar Bruker cavity is straightforward.

Predicted EPR signals consistent with [3] were obtained using an assembly of identical flat-cells that extended from side-wall to side-wall when the relative dielectric constant of the sample holder was close to unity. These EPR signals were found to be 3.9–4.7 times that of a single flat-cell in standard orientation for 15–27 cells. We found that a sample holder of larger dielectric constant significantly lowered performance. For a polytetrafluoroethylene (PTFE) sample holder, the corresponding predicted EPR signal enhancement ratios were 2.2–2.7. We also found that the geometrical constraints imposed by the cylindrical 11 mm diameter sample-access stacks, see Fig. 1, further lowered performance by 8–24%, depending on the number of cells. Results using a 15-cell sample structure yielded about a factor of 2 better than the standard flat-cell geometry. Thus we propose a new TE102 resonator design with a square rather than circular sample-access stack, which is shown here to give a factor of 2.7 enhancement in EPR signal strength using a 27-cell sample assembly relative to the conventional flat-cell geometry of Fig 1A. Finally we consider the rectangular uniform field mode, TEU02, [4], [5], [6] as well as the cylindrical TM110 cavity, both of which are compatible with aqueous sample flat-cell geometry in the perpendicular orientation [1].

Three types of power loss in an aqueous sample flat-cell were identified by Mett and Hyde, Types I, II, and III. Type I loss is the only type that is active in the parallel flat-cell geometry of Fig. 1A. There are no Ez components and negligible Ey components of the electric field, only Ex. All lines of RF electric field in the cavity are parallel to the flat-cell surface. The boundary condition at the cell surface is that the electric field tangential to the surface Etan be continuous across the surface. Power loss is determined by integration of E2 within the sample volume. This geometry was analyzed by a number of workers in the early literature (see particularly Stoodley’s paper [7]). It was recently reconsidered in the context of Uniform Field rectangular cavities in a paper from this laboratory [8].

All three types of power loss occur in the perpendicular orientation, Fig. 1B, and are defined below. Finite-element simulations that illustrate the electric fields giving rise to these sources of loss are shown in Fig. 2. The sample boundary is outlined in black in this figure, and the relative dielectric constant of the sample holder is unity. Dimensions of the sample cell are 0.4 × 8 × 22.9 mm, which are the same as commercial cells for use in the geometry of Fig. 1A. Fig. 2A shows the electric field magnitude in an x–y plane with the nodal electric field null portrayed as a dark blue band. The flat-cell is perpendicular to the nodal plane. Fig. 2B shows only the component of electric field perpendicular to the surface, Ex, in an expanded view, while Figs. 2C and D show the electric field tangential to the surface, Ey.

A major and perhaps surprising finding of Mett and Hyde [3] was that Type I loss exists when the flat-cell is in the perpendicular orientation, which requires that Ey be non-zero. This component of the RF electric field is strictly zero in the empty cavity. The existence of non-zero Ey is understood as follows: polarization charges terminate the lines of RF electric field in the x-direction because of the discontinuity in Ex occurring at the sample surface, noting the high dielectric constant of water. Because Ex changes approximately linearly along the sample in the y-direction, the density of polarization charges also changes approximately linearly in the y-direction along the surface of the sample. This gives rise to a component of E along y, and thus to Type I loss. For this effect to occur, it is necessary that ∂Ex/∂y > 0—that the sample lie in a gradient of the RF electric field.

Fig. 2C shows that the polarities of Ey on either side of the sample are opposite creating a zero at the center of the sample slab (green color). A major finding of Mett and Hyde [3] is that tangential electric field nulls exist within each cell in the multiple cell configuration. Fig. 2C also shows that Ey peaks half way between the y-edges of the sample with a maximum value occurring at y = 0, which is the nodal plane for Ex and the point of maximum gradient in Ex.

Type II loss can be seen in Fig. 2B. Although Ex is discontinuous at the sample surface because of the high dielectric constant of water and is greatly reduced inside the sample, it nevertheless has a finite value and results in loss. There is a small variation of Ex across the sample thickness predicted by the analytical equations of Mett and Hyde [3]. It is an effect that depends on the wavelength in water at X-band. When optimum, Type I loss plus the cavity wall power loss is approximately equal to the Type II loss when the samples are in the perpendicular orientation as predicted in Mett and Hyde.

Type III loss refers to the regions of complexity at the edges of the sample where local electric field intensities become quite high. Polarization charges on opposite corners of an edge give rise to electric field vectors that tend to oppose the applied electric field in free space. Nevertheless, there is a residual component of Ex at the edge that penetrates the sample because it is tangential to the edge surface. This penetration increases the total electric field in the sample near the edge about two times relative to what would be expected from Type II loss alone. Type III loss was analyzed extensively by Mett and Hyde [3].

Section snippets

Methods

The results of this paper are based on finite-element simulations of electromagnetic fields. Two commercial programs were available to us: Ansoft High Frequency Structure Simulator (HFSS) (version 9.0, Pittsburgh, PA) and Computer Simulation Technology (CST) Microwave Studio (version 5.0, Wellesley Hills, MA). Both programs permit “driven mode” and “eigenmode” solutions of Maxwell’s equations. The eigenmode method was used exclusively in the work described here. Although these programs are

Single-cell to n-cell analysis

A major finding of Mett and Hyde [3] is that each individual sample cell has a tangential electric field node within it. Sample cell placement within the cavity was found to have a major influence on the position of this node. Because of the linear variation of the tangential electric field within the sample, Type I loss is four times smaller if the node is perfectly centered within the sample than if the node is on the sample surface. This factor of four reduction in dielectric loss results in

Other resonator types

Other resonator types, such as the uniform field resonator [4], [5], [6] developed in this laboratory, have been considered. The uniform field resonator is desirable for EPR spectroscopy because the RF magnetic field is uniform along two free dimensions X and L (the cavity central section z-dimension) and saturates the sample evenly. The multiple sample analysis done here and in Mett and Hyde [3] carries over to the uniform field resonator without modification. Around a 10% reduction in EPR

Conclusions

The multiple flat-cell clusters in perpendicular orientation proposed by Mett and Hyde [3] have been simulated and analyzed with the use of finite-element codes. Modifications of the analytic theory of Mett and Hyde [3] that include the effects of the sample holder dielectric and the interaction of the cells with each other resulted in improved predictions of optimum flat-cell cluster dimensions. The analysis resulted in sample clusters that produce gains of 2.0–2.7 times the EPR signal

Acknowledgments

This work was supported by Grants EB001417 and EB001980 from the National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health.

References (13)

  • R.R. Mett et al.

    Aqueous flat cells perpendicular to the electric field for use in electron paramagnetic resonance spectroscopy

    J. Magn. Reson.

    (2003)
  • J.S. Hyde

    A new principle for aqueous sample cells for EPR

    Rev. Sci. Instrum.

    (1972)
  • S.S. Eaton et al.

    Electron paramagnetic resonance sample cell for lossy samples

    Anal. Chem.

    (1977)
  • R.R. Mett et al.

    Axially uniform resonant cavity modes for potential us in electron paramagnetic resonance spectroscopy

    Rev. Sci. Instrum.

    (2001)
  • J. Anderson et al.

    Cavities with axially uniform field for use in electron paramagnetic resonance. II. Free space generalization

    Rev. Sci. Instrum.

    (2002)
  • J. Hyde et al.

    Cavities with axially uniform field for use in electron paramagnetic resonance. III. Re-entrant geometries

    Rev. Sci. Instrum.

    (2002)
There are more references available in the full text version of this article.

Cited by (20)

  • Benchtop X-band electron paramagnetic resonance detection of melanin and Nitroxyl spin probe in zebrafish

    2022, Free Radical Biology and Medicine
    Citation Excerpt :

    We found that both types of capillaries produce a similar type of signal to noise ratio (Fig. S8). It was reported previously that the use of 0.5 mm flat capillaries for aqueous samples led to the decrease of the EPR signal and problems with tuning [30]. However, in the case of zebrafish embryos or larvae, in addition to water, samples contain approximately 30–40% of fish tissue (lipid environment).

  • Extruded dielectric sample tubes of complex cross section for EPR signal enhancement of aqueous samples

    2017, Journal of Magnetic Resonance
    Citation Excerpt :

    The bundle is either a set of 0.1 mm wall thickness quartz capillaries or a single PTFE extrusion, depending on the version. It was shown in Sidabras et al. [4] that the optimum EPR signal enhancement will occur when the sample holder has the lowest dielectric constant, due to an increase of electric field charge gradient. Therefore, measurements and simulations are performed on the PTFE extrusion version.

  • Cavity- and waveguide-resonators in electron paramagnetic resonance, nuclear magnetic resonance, and magnetic resonance imaging

    2014, Progress in Nuclear Magnetic Resonance Spectroscopy
    Citation Excerpt :

    The authors showed that by placing multiple flat-cells with optimized dimensions and spacing within the TE102 cavity, an increase in SNR can be achieved compared to a single cuvette in a parallel orientation. From a geometric point-of-view it is more favourable to use a square hole for sample access, and in a later paper [10] the authors showed that an increase of a factor of 2.7 in SNR, with respect to the conventional flat geometry, could be obtained using a 27 cell sample assembly. The key element in their SNR analysis was to consider the different loss mechanisms in the parallel and perpendicular orientations.

View all citing articles on Scopus
View full text