**1. Introduction**

56 Nitroxides – Theory, Experiment and Applications

Technology

[128] Hussain T, (2009) Pressure and Temperature Dependence of Spin- and Electron-Exchange Reactions Measured by ESR Spectroscopy. Dissertation, Graz University of

> The present chapter is devoted to methods of extraction of quantitative data from slow-motion EPR spectra of nitroxides in viscous and rigid media. Slow-motion spectra correspond to the range of rotation relaxation times in which the EPR spectra cannot be reduced to superposition of the Lorentzian lines, which is typical of the range of fast rotation. In the case of the X-band EPR spectra of nitroxides, this range lies approximately from 10−6 to 10−9 s. In the limit of slow motions the movements of the probe do not influence the EPR spectrum shape (rigid-limit conditions). The aim of the present chapter is to describe the methods of yielding quantitative data on molecular mobility and orientation alignment. Such data can be obtained most reliably by means of numerical simulation of the spectra. In the appendix of this chapter, we describe the homemade software used for spectra simulation.

> The methods of extraction of quantitative data on molecular mobility from EPR spectra have been developed rather intensively during the last decades. In the case of fast rotation (characteristic time shorter than approximately 10−9 s), the simple measurements of line widths and intensities of spectral components are enough to estimate the isotropic rotation correlation time. The corresponding procedures and formulas can be found elsewhere [1-3]. When more exact data are desirable and in the case of anisotropic rotational mobility, the well-known method developed by Freed and collaborators for numerical simulation of the spectra can be used [4, 5]. Examples of applications of this technique to different systems can be found in works [6-11].

> In the present chapter, we focus the reader's attention on obtaining quantitative data when the conventional methods produce incorrect or unreliable results. Section II describes the method of determining the translational diffusion coefficient. The technique is simple and

© 2012 Vorobiev and Chumakova, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Vorobiev and Chumakova, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

does not require spectra simulation. It was suggested in [12] about 20 years ago but has not found wide application. We illustrate this technique on samples of ordinary solvents and ionic liquids. The methods of spectra simulation are considered in section III. First, in the rigid-limit spectra of the isotropic samples, we showed the possibility to achieve agreement between experimental and calculated spectra within errors of spectrum recording. The magnetic and line width characteristics of the nitroxide probe are determined in the course of this simulation. The obtained values are necessary for the analysis of spectra recorded in more complicated conditions. The spectra simulation and determination of the rotational characteristics of the probes in polymer matrices are presented as examples. The quantitative description of EPR spectra in a wide temperature range up to the glass transition point was found to require consideration of quasi-libration movements. Section IV deals with the study of orientation alignment of paramagnetic probes. The section describes the orientation distribution functions that can be determined by simulation of spectrum angular dependencies. Liquid crystalline, polymeric, and low-molecular glassy systems are considered. The model-free method of characterizing orientation distribution function is compared with the mean-force approach realized in the known software [4, 5]. The advantages and drawbacks of both approaches are discussed.
