Electron Spin Resonance Volume 6

A Review of the Literature Published between June 1978 and November 1979

By P. B. Ayscough

The Royal Society of Chemistry

Copyright © 1981 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85186-801-1

Contents

Chapter 1 Chemical Analysis by E.P. R. By I. B. Goldberg, 1,
Chapter 2 Theoretical Aspects of E.S. R. By A. Hudson, 24,
Chapter 3 ENDOR and ELDOR By K. Mobius, 32,
Chapter 4 Triplets and Biradicals By A. Hudson, 43,
Chapter 5 Transition-metal Ions By A. L. Porte, 50,
Chapter 6 Inorganic. and Organometallic Radicals By M. C. R. Symons, 96,
Chapter 7 Organic Radicals: Structure By B. C. Gilbert, 133,
Chapter 8 Organic Radicals: Kinetics and Mechanisms of their Reactions By R. C. Sealy, 177,
Chapter 9 Organic Radicals in Solids By T. J. Kemp, 208,
Chapter 10 Spin Label Studies By B. M. Peake, 233,
Chapter 11 Biological and Medical Studies (Metalloproteins) By N. J. Blackburn, 295,
Chapter 12 Applications of ESR in Medicines By N. J. F. Dodd, 319,

CHAPTER 1

Chemical Analysis by E.P.R.

BY I. B. GOLDBERG

1 Introduction

In recent years, electron paramagnetic resonance has become a widely used technique for chemical analysis. Although many applications have appeared, there have been few reviews devoted to this topic. Since this is the first chapter on this subject in ‘Specialist Periodical Reports’, the essential articles up to November 1979 are included in this volume. We anticipate having a sufficient number of reports to review every second volume.

This Chapter covers the theory and methods of quantitative chemical analysis and applications to liquids, solids, and gases. The separation of applications by physical state is arbitrary, but was selected because there are particular nuances associated with measurements on each state. Subjects which I do not anticipate reviewing include qualitative analyses and analyses in which only relative signal amplitudes are used to determine relative concentrations; these studies are usually covered in better context in other reviews in this volume. The methods are described in many texts on e.p.r., such as references. Tabulations of e.p.r. data are available for qualitative identification of spectra. Comparison of the relative signals in order to determine concentrations has become a routine method. However, in many cases the concentrations of the unknowns are not verified so that the validity of the method is somewhat uncertain. Thus, we review here articles of a general nature, those which report proven analytical methods, or those applicable to chemical analyses.

Some chemical analysis techniques which make use of e.p.r. spectroscopy are reported in the continuing bibliography in Analytical Chemistry. Work prior to 1965 was reviewed by Bard and Flockhart. Only a few critical reviews are available. Goldberg and Bard reviewed the fundamental theory, techniques, and several applications in an introductory chapter. Randolph has discussed many different procedures for sample handling treatment of data, and sources of computational error. Eaton and Eaton 14 have presented a concise review of experimental techniques.

2 Theory of Absolute Concentration Measurements

The principal advantage of magnetic resonance techniques over other instrumental methods is that standards which are chemically different from the unknown can be used, subject to certain constraints. Although the relationship of the e.p.r. signal to the microwave susceptibility is well known, the principal relationship between the e.p.r. signal and the radical concentration of a dilute system was developed by Westenberg for gas-phase studies starting from the general definition of power absorption. Under the conditions that kBT [??] hv, where T is the absolute temperature and v is the frequency of the. e.p.r. measurement, and that the microwave absorption does not significantly affect the Q-factor of the cavity, the concentration C, of a particular species is related to the double integrated e.p.r. spectrum (first derivative) according to equation (1), for a transition between states i and j.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The right-hand side of equation (1) can be broken into portions that depend on the experimental conditions (first parenthesis), the molecule (bracketed portion), and the instrumental parameters and signal (final parentheses). The important properties of the radical are geff = h/µB(dv/dB) which relects the change of resonant frequency with magnetic field and converts magnetic field units to frequency units; the partition function Z which includes the line degeneracy and different electronic and rotational or vibrational states; and the energy of the state undergoing the transitions. The Zeeman energy is neglected from EJ,MJ· µij is the transition-dipole matrix element, J and MJ have their usual meaning, and gJ is the spectroscopic splitting factor. The important instrumental parameters include the incident microwave power, P, the amplification of the e.p.r. signal, A, the magnetic-field modulation, Bm, and the double integral of the e.p.r. signal S(B). It is assumed that experiments are carried out in the linear region of the microwave detector, thus S α P1/2. The parameter KI includes the Q-factor of the cavity, the filling factor, and numerous other properties of the instrument, which remain constant during the analysis.

In most cases, the transition probability can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

for the transition from J, MJ to J, MJ + 1.

For paramagnetic species in which J = S, i.e., no orbital or rotational angular momentum, such as radicals or transition metals in condensed phases, the first and second parts of equation (1) yield

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where Ik is the total spin of nk equivalent nuclei and Dl, is the degeneracy of each of the lines used in the double integration. If the substitution hv0 = g µB B can be made, it is found that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. However, this is not generally the case, Aasa and Vanngard pointed out that the intensity of spectra of randomly oriented solids is proportional to g, not to g2, if the field is scanned at a fixed frequency; this occurs because the energy difference between both states is constant. This result is also implicit in the derivations given by Westenberg and by Goldberg and Bard.

Different methods can be used to determine the double integral. Most common are numerical calculations of first moment or double integral of the line or the product of the square of the linewidth, w, and the amplitude, a, of the signal. Chesnut showed that the lineshapes must be identical if the product aw2 is to be a suitable analytical parameter. In view of this criterion and the problem that the peak-to-peak linewidth, ΔHPP, which is often used is, in general, not accurately determinable, Kwan and Yen suggested that parameters other than the peak-to-peak linewidth may be preferable. They recommended the use of the parameter S10 = w210 a, where w10 is the width of the line across one lobe of the derivative curve at height of 1/10 of the amplitude measured between the baseline and the peak of the line. At this point, the value of S10 is approximately equal for Gaussian and Lorentzian lines of the same integrated area. Not all lineshapes, however, fall between Gaussian and Lorentzian, particularly in randomly oriented anisotropic systems.

The derivations of equations (l) and (3) are based on the assumption that the Q-factor of the cavity does not vary significantly across the resonance. This is generally valid for dilute paramagnetic samples. Vigoroux and his co-workers pointed out that if this condition (4πnQox” [??] 1, where n is the filling factor of the samples and Q0 is the Q-factor off-resonance) is not fulfilled, the measured linewidth will increase with sample size or concentration.

The linearity of analytical parameters determined from e.p.r. spectra with sample quantity was analysed by Goldberg and Crowe. For Lorentzian lines, the product a·ΔH2pp was found to be linear to approximately ten-fold larger concentrations than the amplitude of the derivative. The range of linearity of the double integral with concentration falls between a and aΔH2pp depending on the limits of the integration. For Gaussian lineshapes, a similar trend was observed.

3 Experimental Methods in Analytical Measurements

Treatment of E.P.R. Data. – The most important parameter in concentration determinations is to obtain a signal from the spectrometer that is a function of concentration. It is often desirable for the signal to be linear with concentration. Parameters that are commonly used, in order of increasing difficulty of computation, are: (i) the peak-to-peak amplitude of the line, a; (ii) the square of the peak-to-peak linewidth, ΔHpp, multiplied by a ; (iii) the first moment of the derivative line, m, defined by equation (4),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where B0 is the resonance field and B1 and B2 are the high- and low-field limits of the integration; (iv) the double integral of the first-derivative signal, d. It is easily shown that m [right arrow] d as the limits of integration become very large. Calculation of m or d requires greater instrumental stability than does measurement of the peak-to-peak amplitude.

The merits of these parameters have been discussed in detail. With the provisions that the sample does not overload the cavity 22 and that there is no significant broadening due to concentration, a is the simplest parameter; this is used for many measurements of transition-metal ions in liquids or solids. The parameter a·ΔH2pp is only valid if the lineshape does not change, and thus is often used for gas-phase concentrations in which the lineshape is almost precisely Lorentzian. Randolph showed that both m and d are particularly subject to errors as a result of incomplete spectral scans (also see ref. 23), baseline drift, and inaccuracies of the initial baseline. In all cases, the error due to these artifacts is about twice as great for the double integral as for the first moment. This conclusion is based on the premise that the initial pain t of the recorded signal is chosen as the baseline. If d is corrected to the proper initial baseline, the errors become equal. Gaussian lines, which exhibit sharper fall-off than Lorentzian lines, are less subject to these errors. Several methods for minimizing these computational or instrumental errors have been suggested. Loveland and Tozer developed a numerical method that takes baseline drift into account. In order to minimise the errors due to finite limits of integration, double integrals of Lorentzian lines can be multiplied by a factor,f, [equation (5)]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where integration is carried out over the magnetjc field between B1 and 2B0 -B1 and Γ is the half width at half-height, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Calculation of m and d is facilitated by using digital computers to analyse data, either on-line or off-line. While the developments in e.p.r. computer interfacing are beyond the scope of this review, several programs are available. With the use of digitised data, the sampling increment becomes an important parameter to consider. Hall showed that the double integral converges rapidly for a theoretical line, when the ratio of the sample increment to the peak-to-peak linewidth is less than 0.4. This work was based on points taken symmetrically about the centre of the line. In actual implementation of remote data acquisition, the field is usually allowed to change at a uniform rate, so that the data points may not be symmetrically disposed. Convergence was calculated for asymmetric distributions of data points, which showed that for increments smaller than ca. 0.17 of the linewidth, the double integral is within I% of the theoretical value for scans larger than three times the linewidth on either side of resonance.

Methods of determining m or d without computational facilities include a moment balance in which the spectrum can be cut and placed along a balance arm in order to determine the first moment of the deviative, and a nomogram for determining double integrals. A method for calculating first moments of e.p.r. spectra on a desk or programmable calculator was also reported.

Experimental Methods in Quantitative E.P.R. – Sample Cells and Positioning. The objective of many experiments is to obtain a sufficient signal-to-noise ratio and reproducibility for a particular measurement, preferably at minimum cost. Numerous cell designs have been proposed for this purpose. The appropriate combination of cell design and microwave cavity minimises the effect of dielectric loss, which is particularly important for liquid samples. Since different liquids exhibit different microwave properties, analysis must be carried out in the same solvent. Typically, TE011 or TE102 mode cavities are used. Varian and Bruker now manufacture a TM110 mode cavity which permits larger liquid-sample quantities to be used than the conventional flat cells with a TE102 mode cavity. The signal-to-noise ratio of the TM110 cavity is reported to be approximately twice that of the TE102 cavity for aqueous samples of the same concentration, and approximately six-fold more for sulphuric acid samples.

An alternative method for improving the sensitivity to aqueous samples was recommended. A metal cylinder (8.53 mm o.d.) was placed coaxially in a tube (8.79 mm i.d.) so that the layer of solution was ca. 0.13 mm. This was then placed along the sample axis of a conventional TE011 cavity. The metal cylinder causes the electric field to be zero at the surface of the conductor rather than at the cavity centre; this allows a much large amount of liquid sample to be used than can be placed in a normal 3 mm o.d. tube. This arrangement has been reported to give approximately twice the signal for aqueous samples as the TE102 cavity with a flat cell.

Several inexpensive cells for TE 102 mode cavities have been constructed. A piece of flattened heat-shrinkable Teflon, onto which a tube is sealed at either end, was used for radical ions. Reproducibility of cell positioning and cell dimensions would be difficult. A 3 mm o.d. tube held in place by Teflon plugs which fit into the collets of the cavity was found to give good reproducibility and provide sufficient sensitivity for most purposes. Three sections of rectangular cross-section glass (two 0.4 x 3 mm and one 0.4 x 4 mm), filled with solution and supported in a quartz or Teflon container, gave 2.5 times the intensity of a melting-point capillary filled with the same solution. Reproducibility was approximately 10% between cells, including uncertainties due to repositioning.

Sample positioning is also important for reproducible analytical results for liquid and solid samples. For gaseous samples, very large volumes are usually used; thus positioning is not critical. Small solid samples can be placed on the axis of the cavity, and the sample is then adjusted vertically to obtain the largest signal. Sample sizes larger than a few millimetres and smaller than the cavity dimension must be corrected for filling factor and dielectric loss. It is important to realise in correcting for the length of the sample that the intensity does not follow the behaviour predicted 3 by S α cos2(πx/L), where x is the deviation from the centre of the cavity along the r .f. magnetic-field axis and L is the length of the axis. Because of the modulation amplitude, the signal falls off more rapidly as the sample is moved. An empirical calibration of the amplitude as a function of position was recommended to account for finite sample length.

Positioning the flat cell in rectangular cavities constitutes the largest single source of non-systematic errors in the analyses of liquid samples. It is common to leave the cell fixed in the cavity if refilling can be done in the presence of air.

Sources of Instrumental Uncertainties. Some of the important instrumental parameters in obtaining reproducible signals are evident from equation (1). The magnitude of these errors depends on the specific spectrometer. A detailed analysis44 of measurements carried out on a Varian E-3 spectrometer gave the following uncertainties: amplification factor, A, 4.3%; modulation amplitude, Bm, 6.2%; scan rate, 4.0%; measurements oflinewidth, 2.1%. Some of these uncertainties were attributed to attenuators for signal amplification and modulation amplitude being constructed from ± 5% resistors, and to audio-amplifiers for the modulation coils not having sufficient power to be linear at the higher settings.

(Continues…)Excerpted from Electron Spin Resonance Volume 6 by P. B. Ayscough. Copyright © 1981 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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