Kinetics at the collapse transition Gaussian self-consistent approach

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Abstract
We introduce an approximation to the Langevin equation that can be used to study the nonequilibrium dynamics and kinetics of polymer conformational transitions in dilute solution. The approach we describe involves the introduction of a time-dependent effective potential, ΔVq(t), and effective friction ζq. The potential is used to generate a time-dependent Gaussian ensemble and we derive time-dependent self-consistent equations that can be analyzed numerically, or by asymptotic methods. We work out various examples of the homopolymer kinetics, including relaxation of a Flory coil and the collapse transition. For the latter we argue that there are various characteristic regimes after a fast quench that carry us from the Flory to collapsed state. We have explicitly worked out the early stage kinetics where we find a process rather like spinodal decomposition, but where the degrees of freedom are confined to the internal metric of the polymer chain. The chain evolves to produce a chain with a near-periodic arrangement of locally collapsed blobs, which is then believed to coarsen, and we have discussed this phenomenon elsewhere.