Critical Depletion, Adsorption, and Intersurface Interaction in Polymer Solutions: A Mean-Field Theory Study

Abstract

Using a self-consistent field theory, we examine the thermodynamics and interfacial properties of a homopolymer solution, either close to a single hard surface or confined between two parallel surfaces, in equilibrium with a bulk reservoir. We focus on the bulk critical regime and find that various physical quantities therein exhibit qualitatively different behaviors from those in the off-critical regime. For the single-surface system, the surface-excess Γ diverges as ln|ϕb – ϕc| and ln|χc – χ| when approaching the bulk critical point, where χ and ϕb are the Flory–Huggins interaction parameter and the volume fraction of polymer segment in bulk solution, respectively, and χc and ϕc are their respective values at the critical point. Γ diverges to +∞ when the surface–polymer interaction eₛ is larger than the depletion–adsorption transition (DAT) point ec, and to −∞ when eₛ < ec. As such, the DAT at ec in the critical regime is rather sharp and ec = 0.1824 + 0.1359N–¹/² at large N. For the two-surface system, the intersurface potential W at the critical point is purely attractive for both depleted and adsorbed cases and follows a D–³ power-law decay at large intersurface separations D; when eₛ is close to ec, the strength of W becomes rather weak. This nonmonotonic dependence of W on eₛ has important experimental implications on the stability of colloidal suspensions.