2005/09/27 by Christian Wald, Paul M. Goldbart, Annette Zippelius +1 · 2 citations
Materials Science · Physics and Astronomy · #Block Copolymer Self-Assembly #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.1063/1.2200697
19 pages, 10 figures. Submitted to the Journal of Chemical Physics (http://jcp.aip.org)
arxiv created 2005/09/27 · openalex publication_date 2006/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent cross-links are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerge upon sufficient cross-linking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of cross-linking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellas or random structures with a unique wavelength, can be energetically favorable.