Dynamics of polymeric manifolds in melts: Hartree approximation

TL;DR

This paper develops a theoretical framework using the Martin-Siggia-Rose functional and Hartree approximation to analyze the static and dynamic behavior of polymeric manifolds in melts, deriving a generalized Rouse equation and calculating dynamic exponents.

Contribution

It introduces a novel application of the Hartree approximation to the dynamics of polymeric manifolds, deriving a generalized Rouse equation and analyzing critical dimensions.

Findings

Identification of static upper critical dimension distinguishing Gaussian and non-Gaussian regimes.

Dynamic upper critical dimension separating Rouse and renormalized-Rouse behavior.

Explicit calculation of dynamic exponents matching simulation results for linear chains.

Abstract

The Martin-Siggia-Rose functional technique and the self-consistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds.The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension discriminate between Gaussian and non-Gaussian regimes, whereas its dynamic counterpart discriminates between Rouse- and renormalized-Rouse behavior. The dynamic exponents are calculated explicitly. The special case of linear chains shows agreement with MD- and MC-simulations.