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Phase separation in binary mixtures containing polymers: A quantitative comparison of single-chain-in-mean-field simulations and computer simulations of the corresponding multichain systems

Authors

  • Marcus Müller,

    Corresponding author
    1. Department of Physics, University of Wisconsin–Madison, 1150 University Avenue, Madison, Wisconsin 53719
    • Department of Physics, University of Wisconsin–Madison, 1150 University Avenue, Madison, Wisconsin 53719
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  • Grant D. Smith

    1. Department of Materials Science and Engineering, University of Utah, 122 South Central Campus Drive, Room 304, Salt Lake City, Utah 84112
    2. Department of Chemical Engineering, University of Utah, 122 South Central Campus Drive, Room 304, Salt Lake City, Utah 84112
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Abstract

We discuss a phenomenological, coarse-grained simulation scheme, single-chain-in-mean-field (SCMF) simulation, for investigating the kinetics of phase separation in dense polymer blends and mixtures of polymers and solvents. In the spirit of self-consistent-field calculations, we approximate the interacting multichain problem by that of a single chain in an external field, which, in turn, depends on the local densities of the components. To study the time evolution of the mixture, we perform an explicit Monte Carlo (MC) simulation of an ensemble of independent chains in the external field and periodically calculate the average densities and update the external field. Unlike dynamic self-consistent-field theory, these SCMF simulations do not assume that the chain conformations relax much more quickly than the density and incorporate the single-chain dynamics explicitly rather than via an Onsager coefficient. This allows us to study systems with large spatial inhomogeneities and dynamic asymmetries. To assess the accuracy and limitations of the simulation scheme, we compare the results of SCMF simulations using a discretized Edwards Hamiltonian with computer simulations of the corresponding multichain system for (1) the early stages of spinodal decomposition of a symmetric binary polymer blend in response to a quench from χN = 0.314 to χN = 5 (where χ is the Flory–Huggins parameter and N is the number of segments), for which the growth rate of composition fluctuations is compared with MC simulations of the bond fluctuation model and alternative dynamic self-consistent-field calculations, and (2) the evaporation of a solvent from a low-molecular-weight thin polymer film, for which a comparison is made with molecular dynamics (MD) simulations of a bead-necklace model with a monomeric solvent. In the latter case, the polymer conformations are extracted from MD simulations and modeled in the SCMF simulations by a discretized Edwards Hamiltonian augmented by a chain-bending potential. From the MD simulations of thin polymer films in equilibrium with its vapor, phase coexistence has been determined, and the second- and third-order virial coefficients in the SCMF simulations have been adjusted accordingly. Finally, MD simulations of bulk solutions of a polymer and a solvent over a range of compositions, as well as the pure solvent at various densities, have been performed to determine self-diffusion coefficients that enter the SCMF simulations in the form of density-dependent segmental mobilities. A comparison of the polymer and solvent profiles in a thin film as a function of time and the fraction of the solvent evaporating from a solvent-swollen film, as obtained from MD simulations and parameterized SCMF simulations, shows satisfactory agreement for this simple mapping procedure. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 934–958, 2005

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