Structure and tension of the interface between dilute polymer solutions

摘要

We treat a lattice model of phase separation in polymer solutions in meanhyphen;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 squarehyphen;gradient contribution to the freehyphen;energy density that is of de Gennesrsquo; form, and thus to an interfacial tension that varies with polymerization indexNand temperature distance below the critical pointTcminus;Tas in the theories of Nose and of Vrij and Roebersen. In the scaling regimeNrarr;infin; andTcminus;Trarr;0 at fixedx=constN1/2(Tcminus;T) the surface tension sgr; is of the formNminus;1Sgr;(x), with Sgr;(x) a scaling function that we display and that has the asymptotic behavior Sgr;(x)sim;constx3/2forxrarr;0 and Sgr;(x)sim;constx2forxrarr;infin;. The latter contrasts with thex5/2found earlier when no account was taken of the chainhyphen;conformation biases. These biases are displayed as functions of location in the interface. On the concentratedhyphen;phase side of the interface the concentration of horizontal links is greater, and on the dilutehyphen;phase side it is less, than in a random chain.