TIME-DEPENDENT NONLINEAR GROWTH THEORY OF LINEAR-CHAINS

A theory was developed for the nonlinear growth of linear chains by in corporating the chain dynamics into the rate equation. This was achiev ed by using a modified Boltzmann equation. The chains were first divid ed into two groups as reacting and unreacting chains in any time inter val. The contribution of reacting chains to the chain growth was accou nted by using a time propagator. The nonlinearity in growth introduced by reacting chains was expressed in velocity space as a kind of enhan ced 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 me chanics of chain growth was studied and the chain growth distance was determined.