Finite size effects on the phase diagram of a binary mixture confined between competing walls
Abstract
A symmetrical binary mixture AB that exhibits a critical temperature T_{cb} of phase separation into an A and a Brich phase in the bulk is considered in a geometry confined between two parallel plates a distance D apart. It is assumed that one wall preferentially attracts A while the other wall preferentially attracts B with the same strength (“competing walls”). In the limit D→∞, one then may have a wetting transition of firstorder at a temperature T_{w}, from which prewetting lines extend into the one phase region both of the A and the Brich phase. It is discussed how this phase diagram gets distorted due to the finiteness of D: the phase transition at T_{cb} immediately disappears for D<∞ due to finite size rounding, and the phase diagram instead exhibit two twophase coexistence regions in a temperature range T_{trip}< T< T_{c1 }= T_{c2 }. In the limit D→∞ T _{c1},T _{c2} become the prewetting critical points and T_{trip}→ T_{w}. For small enough D it may occur that at a tricritical value D _{t} the temperatures T_{c1 }= T_{c2 } and T_{trip} merge, and then for D< D_{t} there is a single unmixing critical point as in the bulk but with T_{c}( D) near T_{w}. As an example, for the experimentally relevant case of a polymer mixture a phase diagram with two unmixing critical points is calculated explicitly from selfconsistent field methods.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 April 2000
 DOI:
 10.1016/S03784371(99)005257
 arXiv:
 arXiv:condmat/0005060
 Bibcode:
 2000PhyA..279..188M
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 Physica A 279 (2000) 188