Y. Rouault et al., PHASE-SEPARATION OF SYMMETRICAL POLYMER MIXTURES IN THIN-FILM GEOMETRY, Journal of statistical physics, 80(5-6), 1995, pp. 1009-1031
Monte Carlo simulations of the bond fluctuation model of symmetrical p
olymer blends confined between two ''neutral'' repulsive walls are pre
sented for chain length N-A = N-B = 32 and a wide range of film thickn
ess D (from D = 8 to D = 48 in units of the lattice spacing). The crit
ical temperatures T-c(D) of unmixing are located by finite-size scalin
g 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. Cont
rary to this result, it is argued that the critical behavior of the fi
lms 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 bet
a(2), is the critical exponent of the two-dimensional Ising universali
ty class (beta(2) = 1/8). Since for large D this asymptotic critical b
ehavior is confined to an extremely narrow vicinity of T-c(D), one obs
erves in practice ''effective'' exponents which gradually cross over F
rom beta(2) to beta(3) with increasing film thickness. This anomalous
''flattening'' of the coexistence curve should be observable experimen
tally.