6533b7dcfe1ef96bd12731eb

RESEARCH PRODUCT

Phase separation of symmetrical polymer mixtures in thin-film geometry

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Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two “neutral” repulsive walls are presented for chain lengthNA=NB=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesTc(D) of unmixing are located by finite-size scaling methods, and it is shown that\(T_c (\infty ) - T_c (D) \propto D^{ - {1 \mathord{\left/ {\vphantom {1 {v_3 }}} \right. \kern-\nulldelimiterspace} {v_3 }}} \), wherev3≈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\(\phi _{cocx}^{(2)} - \phi _{cocx}^{(1)} = \hat B(D)\left[ {1 - {T \mathord{\left/ {\vphantom {T T}} \right. \kern-\nulldelimiterspace} T}_c (D)} \right]^{\beta _2 } \), whereβ2 is the critical exponent of the two-dimensional Ising universality class (β2=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofTc(D), one observes in practice “effective” exponents which gradually cross over fromβ2 toβ3 with increasing film thickness. This anomalous “flattening” of the coexistence curve should be observable experimentally.