Conformation and deformation of linear macromolecules in concentrated solutions and melts in the self‐avoiding random walks statistics

Abstract

AbstractA strict statistics of self‐avoiding random walks in the d‐measured lattice and continuous space for intertwining chains in the concentrated solutions and melts was proposed. On the basis of this statistics the thermodynamics of conformation and isothermal and adiabatic deformation of intertwining chains was described. The equation of conformational state has been obtained. It was shown that in the field of chains overlap they are stretched increasing its conformational volume. In this volume there are other chains with the formation of m‐ball. Free energy of a chain conformation does not depend upon the fact, if the chains intertwined or they are isolated in the m‐ball. Mixing entropy is responsible to the chains interweaving in the m‐ball. Dependencies of the conformational radius, free energy, and conformation pressure on respective concentration of polymeric chains have been determined. Using the thermodynamics of intertwining polymeric chains of m‐ball conformational state and also the laws of isotropic media deformation into linear differential form the theoretical expressions for elasticity modules (namely, volumetric volume, Young's module and shift's module) and for the main tensions appearing at the equilibrium deformation of the m‐ball were obtained. Poisson's coefficient is a function only on the Euclidean's space and for the real three‐dimensional space is equal to 3/8. A simple model explaining the tensile strength of the m‐ball by the chains intertwining effect and, thereafter by the loss of the mixing entropy, but not by the chemical bonds breaking was proposed. Calculations of the elastic properties, the main tensions, and tensile strength of natural rubber carried out without using the empirical adjusting parameters are in good agreement with the experimental data. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008