Structure and tension of the interface between dilute polymer solutions

Abstract

We treat a lattice model of phase separation in polymer solutions in mean-field (Flory) approximation, taking account of anisotropic biases in the chain conformations in the interface, as in an earlier theory of Helfand. Near the critical point of the phase separation those biases lead to a square-gradient contribution to the free-energy density that is of de Gennes’ form, and thus to an interfacial tension that varies with polymerization index N and temperature distance below the critical point Tc−T as in the theories of Nose and of Vrij and Roebersen. In the scaling regime N→∞ and Tc−T→0 at fixed x=const N1/2(Tc−T) the surface tension σ is of the form N−1 Σ(x), with Σ(x) a scaling function that we display and that has the asymptotic behavior Σ(x)∼const x3/2 for x→0 and Σ(x)∼const x2 for x→∞. The latter contrasts with the x5/2 found earlier when no account was taken of the chain-conformation biases. These biases are displayed as functions of location in the interface. On the concentrated-phase side of the interface the concentration of horizontal links is greater, and on the dilute-phase side it is less, than in a random chain.