PHASE-SEPARATION OF SYMMETRICAL POLYMER MIXTURES IN THIN-FILM GEOMETRY

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two ''neutral'' repulsive walls are presented for chain length N-A = N-B = 32 and a wide range of film thickness D (from D = 8 to D = 48 in units of the lattice spacing). The critical temperatures T-c(D) of unmixing are located by finite-size scaling methods, and it is shown that T-c(infinity) - T-c(D) proportional to D--1/nu 3, where nu(3) approximate to 0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as phi(coex)((2)) - phi(coex)((1)) = B(D)[1-T/T-c(D)](beta 2), where beta(2), is the critical exponent of the two-dimensional Ising universality class (beta(2) = 1/8). Since for large D this asymptotic critical behavior is confined to an extremely narrow vicinity of T-c(D), one observes in practice ''effective'' exponents which gradually cross over From beta(2) to beta(3) with increasing film thickness. This anomalous ''flattening'' of the coexistence curve should be observable experimentally.