Nonlinear dynamics of the development of density fluctuations upon glass transition in one-component polymeric systems

The existence of a solution of the type of a traveling-kink that propagates with a low phase velocity was proved for the equation of glass transition in polymers. An analytical expression was derived for the kink traveling velocity which depends on the attraction (repulsion) force of a polymer chain on infinitely distant walls and the rate of change in the derivative of the chemical potential in the vicinity of the phase separation point. For the nonlinearized set of nonlinearly coupled glass transition and heat transfer equations, conditions for the existence of heat switching waves were established, whose parameters (amplitude and velocity) depend on the characteristics of traveling waves of polymer-chain density upon instantaneous heat supply with allowance for heat withdrawal into a sink. The possibility of the quasi-local, exponentially fast heat supply at the semispace boundary was considered, and conditions for the rise in the Onsager coefficient and in the rate of heat supply at the boundary of a semi-infinite sample at which the penetration of the density wave into a finite depth becomes possible were determined.