Phase Separation Versus Wetting: a Mean Field Theory for Symmetrical Polymer Mixtures Confined Between Selectively Attractive Walls

Thomas Flebbe; Burkhard Dünweg; Kurt Binder

doi:doi:10.1051/jp2:1996205

Numéro		J. Phys. II France Volume 6, Numéro 5, May 1996


Page(s)		667 - 695
DOI		https://doi.org/10.1051/jp2:1996205

DOI: 10.1051/jp2:1996205
J. Phys. II France 6 (1996) 667-695

Phase Separation Versus Wetting: a Mean Field Theory for Symmetrical Polymer Mixtures Confined Between Selectively Attractive Walls

Thomas Flebbe, Burkhard Dünweg and Kurt Binder

Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55099 Mainz, Germany

(Received 23 November 1995, accepted 2 February 1996)

Abstract
Partially compatible symmetrical ( $N_{\rm A}=N_{\rm B}=N$ ) binary mixtures of linear flexible polymers (A, B) are considered in the presence of two equivalent walls a distnace D apart, assuming that both walls preferentially adsorb the same component. Using a Flory-Huggins type mean field approach analogous to previous work studying wetting phenomena in the semi-infinite version of this model, where $D\to\infty$ , it is shown that a single phase transition occurs in this thin film geometry, namely a phase separation between a A-rich and a B-rich phase (both phases include the "bulk" of the film). The coexistence curve is shifted to smaller values of the inverse Flory-Huggins parameter $\chi^{-1}$ with decreasing D, indicating enhanced compatibility the thinner the film. In addition, due to the surface enrichment of the preferred species (B), the critical volume fraction of A monomers is shifted away from $\phi_{\rm crit}=0.5$ (where it occurs for $D\to\infty$ due to the symmetry of the model) to the B-rich side. This behavior is fully analogous to the results established previously for the Ginzburg-Landau model of small molecule mixtures and to Monte Carlo simulations of corresponding lattice gas models. We argue that for symmetric walls the stable solutions always are described by volume fraction profiles $\phi(z)$ that are symmetric as function of the distance z across the film around its center, but sometimes the system is inhomogeneous in the lateral direction parallel to the film, due to phase coexistence between A-rich and B-rich phases. Antisymmetric profiles obtained by other authors for symmetric boundary conditions are only metastable solutions of the mean field equations. The surface excess of B, whose logarithmic divergence as $\ln \vert\phi-\phi_{\rm coex}\vert$ signals complete wetting for $D\to\infty$ , stays finite (and, in fact, rather small) for finite D: hence studies of wetting phenomena in thin film geometry need to be analyzed with great care.