End-evaporation dynamics revisited

We present analytical results on the so-called end-evaporation kinetics in equilibrium polymeric systems following a temperature jump (T jump). A T jump prepares the system with a nonequilibrium length distribution, after which it relaxes back to its equilibrium state. Starting from a master equation, we develop a mean-field analytical theory based on a generating function approach, which allows explicit approximate expressions for the monomer and dimer concentrations to be derived in a discrete setting; the concentrations of the other chains as well as the average chain length were shown to be entirely expressible in terms of the monomer and dimer concentrations. We find that the calculated monomer and dimer concentrations as well as the average chain length are in good agreement with numerical simulation results and do not suffer from some of the defects of earlier continuum theories. Furthermore, the relaxation was shown to take place in three different stages. The first stage comprises the very fast relaxation of the monomers to almost their equilibrium concentration; the other polymer chains have hardly relaxed. During the second stage, which is highly nonlinear, a redistribution of material at practically constant monomer density takes place. Only in the final stage of the relaxation process the chain concentrations approach their true equilibrium values. In this stage there are only very small shifts in the concentrations of chains, which are governed by extremely slow "indirect" monomer-mediated processes.