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

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.