6533b854fe1ef96bd12afcb0

RESEARCH PRODUCT

Critical phenomena in polymer mixtures: Monte Carlo simulation of a lattice model

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A lattice model of a symmetrical binary (AB) polymer mixture is studied, modelling the polymer chains by self-avoiding walks withN A =N B =N steps on a simple cubic lattice. If a pair of nearest neighbour sites is taken by different monomersAB orBA, an energye ab is won; if the pair of sites is taken by anAA or aBB pair, an energye is won, while the energy is reduced to zero if at least one of the sites of the pair is vacant. To allow enough chain mobility, 20% of the lattice sites are vacancies. In addition to local motions of the chain segments we use a novel “grand-canonical” simulation technique:A chains are transformed intoB chains and vice versa, keeping the chemical potential difference fixed. The phase diagram is obtained forN=4, 8,16 and 32; the critical behaviour is analysed by finite-size scaling methods. It is shown that the critical exponents are those of the Ising model (β=0.32,ν=0.63) rather than those of the Flory-Huggins meanfield theory (β=γ=1/2). Implications of these results for real polymers are briefly discussed.