Time-dependent nonlinear growth theory of linear chains

A theory was developed for the nonlinear growth of linear chains by incorporating the chain dynamics into the rate equation. This was achieved by using a modified Boltzmann equation. The chains were first divided into two groups as reacting and unreacting chains in any time interval. The contribution of reacting chains to the chain growth was accounted by using a time propagator. The nonlinearity in growth introduced by reacting chains was expressed in velocity space as a kind of enhanced diffusion. The space-independent and the space-dependent solutions of chain growth were obtained by using an almost unchanging quantity, the “fractional change of length per collision”. The statistical mechanics of chain growth was studied and the chain growth distance was determined