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Typical good nonpolar solvents for nonpolar polymers have values of the Flory interaction parameter χ of 0.3 or higher. This is striking since miscible nonpolar polymer blends exist with well-matched solubility parameters and resulting very small χ values of 10 -2 or less. Using a cell model, it has been previously argued that there is a generic contribution to χ in polymer-solvent systems of about 0.3, which ultimately arises from the difference in affinity for free volume of bonded chain mers and otherwise identical solvent mers. We explore this result with off-lattice MC simulations of hard-sphere freely jointed chains in identical hard-sphere solvent. We observe reductions in chain radii of gyration and of virial coefficients for dimers among hard-sphere solvents versus in vacuum, consistent with the cell model results. Finally, we extract free volume distributions and observe reduced free volume of chain mers compared to solvent. With a model of a single mer in a fluctuating cell surrounded by hard-sphere fluid, we construct free volume distributions in good agreement with our MC results and previous work of Sastry et al. on hard-sphere liquids.

From a single chain in a dilute solution to an entangled polymer melt, from bulk systems to more complex interfacial problems, computer simulations have played a critical role not only in testing the basic assumptions of various theoretical models but also in interpreting experimental results. Early computer simulations of polymers were mostly carried out on a lattice using Monte Carlo methods. This approach has led to significant progress in recent years and will continue to do so in many areas. In some cases however, for example in the study of shear, lattice models have serious limitations. For this reason and also due to the availability of more powerful computers, continuum, off-lattice polymer models have recently become popular. In this article, we review some of the recent progress in studying polymers at surfaces and interfaces using continuum models.

The dynamical critical exponent of the two-dimensional spin-Qip Ising model is evaluated by a Monte Carlo renormalization-group method involving a transformation in time. The results agree very well with a finite-size scaling analysis performed on the same data. The value of z = 2.13+ 0.01 is obtained, which is consistent with most recent estimates.

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