An algorithm previously used for the computer simulation of nuclear magnetic resonance (NMR) spectra of liquid crystals was developed to apply to the case when the atomic nuclei of the molecular system of interest possess different chemical shifts. The improved algorithm has led to the obtaining of very good theoretical simulated spectra for the monomer corresponding to the polymer under study, and these are the basic spectra which, upon consideration of the elastic modes, should transform to the line shapes experimentally found for the polymer samples. A general theory was developed to describe the phenomenon of nuclear magnetic absorption, responsible for the observed NMR spectra, in the presence of the complex cooperative movements of the liquid crystal molecules, generally embraced under the designation of elastic modes. To construct such a general theory, some approximations are needed for reasons of mathematical tractability. The validity and quality of these approximations have been extensively tested and the conclusion is that the theory applies to all but the highly viscous liquid crystals, which means that this theory and the previous empirical one are in fact complementary.
The theory leads to a number of complex mathematical formulae describing the nuclear magnetic absorption as a function of frequency. A computer program was then devised to simulate a spectrum for a given set of values of the input parameters, and it was concluded that only 2 independent parameters affect the shape of the output spectrum, for a given choice of the basic spectrum input (fixed by the molecular structure, conformation and ordering tensor in the sample considered): the nematic order parameter S and a relaxation time expressible in terms of 2 viscoelastic parameters, an average viscosity eta and an average elastic constant k. Because S, eta and k can be measured independently for each temperature, it was possible to test the theory by comparing the simulated and the experimental spectra. For polymer samples in general, accurate measurements of eta and k are impossible to make.
A modified version of the general theory has permitted the simulation of powder spectra, like those produced by nematic liquid crystals in their solid phases. The results were then successfully applied to the fluorine NMR spectra of teflon. What is particularly interesting is that teflon is not a liquid crystalline compound, but nevertheless excellent agreements were obtained between simulated and experimental spectra. The conclusion is that this and many other conventional polymers exhibit a nematic order on a microscopic scale (short range), the macromolecules ordering and aligning themselves locally just as happens in nematic polymers over larger (macroscopic) dimensions.