General dynamic theory of macromolecular networks. I. Definitions and classification

Abstract

Abstract The problem of the structural theory of macromolecular networks is formulated and discussed in general terms. The conditions required for a system to become a homogeneous macromolecular network are defined and discussed. Networks are divided according to the nature of their junctions into three classes: energetic (with chemical or quasi‐chemical crosslinks), topological (with entangled chains), and contact (with frictional interactions). The main features of these three classes are discussed. A distribution density function ψ describing the configurations of macromolecules in network systems is introduced. The phase space of variables is 4( N + 1)‐dimensional and includes the coordinates of ( N + 1) vectors h i joining the adjacent network junctions and ( N + 1) contour lengths l i of the network chains. The system of simultaneous equations required for the determination of the function ψ includes the equation of continuity, kinematic equations for the deformation velocity of the individual junctions, the force balance equation needed for the determination of sliding rates l i , kinetic equations for the processes of junction breakage and reformation, and the equilibrium distribution of network junctions defining the initial conditions for the distribution function ψ.