A new mean-field theory for dilute polymer solutions: Phase diagram, conformational behavior and interfacial properties

Abstract

A new mean-field theory for dilute polymer solutions is presented. The approach is based on looking at a polymer molecule in the mean-field of the solution. This has the advantage of allowing the conformational behavior of the chain molecules and the thermodynamic properties of the solution to be studied within the same theoretical framework. The phase diagram predicted by the theory has a critical temperature which is lower, and a width of its coexistence curve which is larger, than those obtained from the simpler mean-field (Flory) theory. The critical volume fraction is found to scale with the degree of polymerization n as φc∼n−0.40, in excellent agreement with experimental results. The theory allows one to study the size and shape of the polymer molecules as functions of the thermodynamic state of the solution. It is found that on the concentrated side of the coexistence curve the average shape of the molecules is an elongated ellipsoid, while in the dilute side the molecules are smaller in size and their shape becomes more sphere-like as the concentration is reduced. The theory is extended to study the properties of the interface separating two phases at coexistence. In particular, it is applied to study the variation of the sizes, shapes and orientations of the polymer molecules due to the inhomogeneous density in the interfacial region. It is found that as the interface is approached from the polymer-rich side the molecules tend to slightly decrease their size and their longest axes tend to orient parallel to the interface. At the edge of the polymer-poor side of the interface the molecules are very elongated and their long axes are oriented almost exclusively perpendicular to the interface. It is argued that the orientation profile in the interfacial region is a general property of nonspherical molecules.