Incorporating fluctuations and dynamics in self-consistent field theories for polymer blends

By Marcus Mueller, F. Schmid. 2005

132 citations recorded by the source corpus.

We review various methods to investigate the statics and the dynamics of collective composition fluctuations in dense polymer mixtures within fluctuating-field approaches. The central idea of fluctuating-field theories is to rewrite the partition function of the interacting multi-chain systems in terms of integrals over auxiliary, often complex, fields, which are introduced by means of appropriate Hubbard-Stratonovich transformations. Thermodynamic averages like the average composition and the structure factor can be expressed exactly as averages of these fields. We discuss different analytical and numerical approaches to studying such a theory: The self-consistent field approach solves the integrals over the fluctuating fields in saddle-point approximation. Generalized random phase approximations allow to incorporate Gaussian fluctuations around the saddle point. Field theoretical polymer simulations are used to study the statistical mechanics of the full system with Complex Langevin or Monte Carlo methods. Unfortunately, they are hampered by the presence of a sign problem. In dense system, the latter can be avoided without losing essential physics by invoking a saddle point approximation for the complex field that couples to the total density. This leads to the external potential theory. We investigate the conditions under which this approximation is accurate. Finally, we discuss recent approaches to formulate realistic dynamical time evolution equations for such models. The methods are illustrated by two examples: A study of the fluctuation-induced formation of a polymeric microemulsion in a polymer-copolymer mixture, and a study of early-stage spinodal decomposition in a binary blend.

Subfields: Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/84e4a7207058bd5256ef86f453a470f830eba99d

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Citations in the corpus

Challenges in Multiscale Modeling of Polymer Dynamics (2013, methodology): “One of the most powerful methods to study polymer mixtures at equilibrium in an approximate manner is self-consistent field theory [66].”
Biological and synthetic membranes: What can be learned from a coarse-grained description? (2006, background): “Depending on the system of interest, one can frequently quantify deviations away from the mean-field solution caused by long-wavelength fluctuations, and define the corresponding Ginzburg parameter [254,255].”