The authors present a method for calculating the chemical potential of arbitrary chain molecules in a computer simulation. The method is based on a generalization of Siepmann's method for calculating the chemical potential of chain molecules with a finite number of conformations. Next, the authors show that it is also possible to extend the configurational-bias Monte Carlo scheme developed recently by Siepmann and Frenkel (1992) to continuously deformable molecules. The utility of their technique for computing the chemical potential of chain molecules is demonstrated by computing the chemical potential of a fully flexible chain consisting of 10-20 segments in a moderately dense atomic fluid. Under these conditions the conventional particle-insertion schemes fail completely. In addition, they show that their novel configurational-bias Monte Carlo scheme compares favourably with conventional Monte Carlo procedures for chain molecules.

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Novel scheme to study structural and thermal properties of continuously deformable molecules

The classical concepts about unmixing of polymer blends (Flory-Huggins theory) and about mesophase ordering in block copolymers (Leibler's theory) are briefly reviewed and their validity is discussed in the light of recent experiments, computer simulations and other theoretical concepts. It is emphasized that close to the critical point of unmixing non-classical critical exponents of the Ising universality class are observed, in contrast to the classical mean-field exponents implied by the Flory-Huggins theory. The temperature range of this non-mean-field behavior can be understood by Ginzburg criteria. The latter are also useful to discuss the conditions under which the linearized (Cahn-like) theory of spinodal decomposition holds. While Flory-Huggins theory predicts correctly that the critical value of the Flory χ-parameter scales with chain length N (for symmetrical mixtures) χc ∝ 1/N, it strongly overestimates the prefactor and its use for fitting experimental data yields spurious concentration dependence. Also the chain radii depend on both χ and the composition of the mixture, thus invalidating the random phase approximation (RPA). Particular strong deviations from the RPA are predicted for block copolymer melts, where chains may stretch out in a dumbbell-like shape even in the disordered phase, before the microphase separation transition is approached. This review concludes with an outlook on interfacial phenomena and surface effects on these systems and other open problems in this field.

Phase transitions in polymer blends and block copolymer melts: Some recent developments

▪ Abstract Polymers offer a wide spectrum of possibilities for materials applications, in part because of the chemical complexity and variability of the constituent molecules, and in part because they can be blended together with other organic as well as inorganic components. The majority of applications of polymeric materials is based on their excellent mechanical properties, which arise from the long-chain nature of the constituents. Microscopically, this means that polymeric materials are able to respond to external forces in a broad frequency range, i.e., with a broad range of relaxation processes. Computer simulation methods are ideally suited to help to understand these processes and the structural properties that lead to them and to further our ability to predict materials properties and behavior. However, the broad range of timescales and underlying structure prohibits any one single simulation method from capturing all of these processes. This manuscript provides an overview of some of the more p...

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Molecular and Mesoscale Simulation Methods for Polymer Materials

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 XN = 0.314 to xN = 5 (where X 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.

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

Recent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies via reconstruction on patterned substrates.

A.K. Kron

Papers

The Monte Carlo method in statistical calculations of macromolecules

Calculation of volume effects in macromolecules by means of a Monte Carlo method: Non-self-intersecting chains on a cubic lattice☆

Dimensions of branched macromolecules in good solvents

Monte-Carlo calculation of volume effects in polymer molecules for chains in a cubic lattice

The Monte Carlo method of calculating volume effects in linear polymer chains