ИСТИНА

Dynamic and static light scattering are modern and widely used in science and application experimental techniques to investigate polymeric materials. Light scattering with some other methods are often used to determine the molecular weight (Mw), molecular weight distribution function, averaged sizes, radius of gyration of polymers etc. The collection of all the data allows one to characterize polymers in detail and to obtain fundamental concepts of structure – properties relations, which in turn helps to produce new materials with the desired properties. However, in common, not applicable for many macromolecules model of ideal (freely-jointed or Gaussian) chain (or sub-chain) is used to analyze experimental data (e.g. from light scattering). There should be striking inconsistence between the ideal chain model and more realistic models for a new class of polymer molecules of small size, dendrimers. For polymers which obey Gaussian statistics, the method of obtaining a conformationally-dependent properties is developed in some detail [1]. In this paper, more realistic model that takes into account the hindrance of rotation around individual bonds and volume effects, is developed with the help of the approach of transition matrices, proposed by Flory [2], and mathematical theory of formal grammars [3], which operates with non-commute among themselves elements. A one-to-one mapping between the forest and a grammar was constructed to obtain explicit analytical expressions for the generating function F2, which makes it easy to calculate various sizes for non-ideal polymers. Of course, from function F2 the well-known Gaussian statistics are automatically kept track of for ideal macromolecules.