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Incorporating Fluctuations and Dynamics in Self-Consistent Field Theories for Polymer Blends

  • Marcus MüllerEmail author
  • Friederike Schmid
Chapter
Part of the Advances in Polymer Science book series (POLYMER, volume 185)

Abstract

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 such as 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 one 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 a 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 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.

Polymer blends Self-consistent field theory External potential dynamics Field-theoretic polymer simulations Polymeric microemulsion Polymer dynamics  

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Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WisconsinMadisonUSA
  2. 2.Fakultät für PhysikUniversität BielefeldBielefeldGermany

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