**5. Conclusions**

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 effectively.

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 course of solving the inverse problem during the spectra simulation.

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 is possible in the program package [4], the description of the spectral line broadening in the case of dipole-dipole interaction of radicals and, moreover, in the cases of dipole-dipole and exchange interactions is impossible. Elaboration of appropriate methods would be useful for determination by means of spin probe technique of not only orientational but also translational order of liquid crystal materials, biological membranes, and films. In such case, one could see the whole spectrum of intermediate states appearing during formation of one or another ordered phase.

We hope that the methods presented in this chapter and the proposed open-code computer programs will serve to develop more complete methods of analysis of the EPR spectra of spin probes.
