**Author details**

104 Nitroxides – Theory, Experiment and Applications

cholesteric order exists in the medium. The OP method can be applied for analysis of polydomain samples only in the case of statistical (chaotic) orientation of the domains. Such

The most essential weakness of the OP method is the interdependence of determined parameters. The coefficients of rotation diffusion and the characteristics of ordering potential are not independent when single EPR spectrum is treated. As a result, few different optimal set of parameters produce almost the same calculated spectra. Hence, it is impossible to determine unambiguously the rotation diffusion coefficients and orientation parameters by means of simulation of a single EPR spectrum. This problem is solved to some extent by simultaneous simulation of a series of spectra recorded at various orientations of the sample in the magnetic field. However, such experiment cannot always be performed. For example, recording of the spectrum angular dependence of spin probes in a nematic liquid crystal at the temperature of mesophase is impossible, as the nematic phase is oriented by the magnetic field of the spectrometer. In such case, to record the angular dependence, it is necessary to undertake additional efforts: to align the sample by electric field, to put liquid crystal into the polymer pores, etc. The mutual correlation of different coefficients *c*jm, which characterize the ordering potential, prevents the reliable determination of the order parameters with a rank more than two even when the set of

The data presented in this chapter lead to the following conclusions. Owing to the modern computing technique that allows simultaneous simulation of the set of EPR spectra, some methods for extraction of the quantitative information from the spectra were developed. These methods broaden significantly the area of application of the spin probe technique and make it possible to investigate subtle features of the structure and molecular dynamics of various materials. On the other hand, it is clear that possibilities opened are not used quite

First of all, it is necessary to note that at present, there is no method for reliable distinction of the influences of rotation and orientation of the radicals on the shape of EPR spectra. One more problem that is close to solution by means of the spin probe method is the determination of the high-rank order parameters. There is no theoretical prohibition for determination of these parameters by the EPR method. However, the existing approach based on the ordering potential is unable to provide reliable values of high-rank order parameters. The direct expansion of the orientation function in a series of generalized spherical harmonics (a model-free technique) overcomes this drawback but is unable to use the spectra recorded at high molecular mobility. One more basic problem in the field is the elaboration of the accurate mathematical criteria for calculation of errors that appear in the

In our opinion, insufficient attention is paid to consideration of the concentration broadening of the EPR spectra. Whereas the simulation of the exchange-broadened spectra

course of solving the inverse problem during the spectra simulation.

approach is called microscopic order–macroscopic disorder (MOMD).

spectra with different sample orientation is simulated.

**5. Conclusions** 

effectively.

Andrey Kh. Vorobiev and Natalia A. Chumakova *Department of Chemistry, M.V. Lomonosov Moscow State University, Leninskie Gory, Moscow, Russia* 
