chapter  1
22 Pages

Distribution of internal Links of the Polymer Chain in the Self-Avoiding Random Walks Statistics

Summary ................................................................................................... 2 1.1 Introduction ...................................................................................... 2 1.2 Initial Statements ............................................................................. 4 1.3 Sarw Statistics for the Internal Links of a Chain ............................. 9 1.4 Structure of the Polymer Chain Conformational Space ................. 13 1.5 Free Energy of Conformation of Polymer Chain Sections ............ 17 1.6 The Most Probable Distance between Two Internal Links of

a Polymer Chain ............................................................................. 18 1.7 Conclusions .................................................................................... 20 Keywords ................................................................................................ 20 References ............................................................................................... 20

SUMMARY

Within the frame of the self-avoiding random walks statistics (SARWS), the derivation of the internal n-link (1 < n < N) distribution of the polymer chain with respect to the chain ends is suggested. The analysis of the obtained expressions shows, that the structure of the conformational volume of the polymer chain is heterogeneous; the largest density of the number of links takes place in conformational volumes nearby the chain ends. It can create the effect of blockage of the active center of the growing macroradical and manifest itself as a linear chain termination. The equation for the most probable distance between two internal links of the polymer chain was obtained as well. The polymer chain sections, separated by fixing the internal links, are interactive subsystems. Their total conformational volume is smaller than the conformational volume of undeformed Flory coil. Therefore, total free energy of the chain sections conformation equals to free energy of the conformation of deformed (i.e., compressed down to the total volume of the chain sections) Flory coil.