Dilute or semi-dilute solutions of non-intersecting self-avoiding walk (SAW) polymer chains are mapped onto a fluid of ``soft'' particles interacting via an effective pair potential between their centers of mass. This mapping is achieved by inverting the pair distribution function of the centers of mass of the original polymer chains, using integral equation techniques from the theory of simple fluids. The resulting effective pair potential is finite at all distances, has a range of the order of the radius of gyration, and turns out to be only moderately concentration-dependent. The dependence of the effective potential on polymer length is analyzed in an effort to extract the scaling limit. The effective potential is used to derive the osmotic equation of state, which is compared to simulation data for the full SAW segment model, and to the predictions of renormalization group calculations. A similar inversion procedure is used to derive an effective wall-polymer potential from the center of mass density profiles near the wall, obtained from simulations of the full polymer segment model. The resulting wall-polymer potential turns out to depend strongly on bulk polymer concentration when polymer-polymer correlations are taken into account, leading to a considerable enhancement of the effective repulsion with increasing concentration. The effective polymer-polymer and wall-polymer potentials are combined to calculate the depletion interaction induced by SAW polymers between two walls. The calculated depletion interaction agrees well with the ``exact'' results from much more computer-intensive direct simulation of the full polymer-segment model, and clearly illustrates the inadequacy -- in the semi-dilute regime -- of the standard Asakura-Oosawa approximation based on the assumption of non-interacting polymer coils.Comment: 18 pages, 24 figures, ReVTeX, submitted to J. Chem. Phy

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We report a computer-simulation study of a simple model for a colloid dispersed in a polymer solution. The simulations were performed using a computational scheme that allows simulation at constant osmotic pressure of the polymers. We present results for the polymer-induced interaction, the equation-of-state, and the phase diagram. The simulations show that when the radius of gyration of the polymers R, is sufficiently large compared to the diameter of the colloidal particles a,.,l (2 R,la,,,20.45), addition of polymer induces a colloidal "liquid-vapor" phase separation. For shorter polymers, only the solid-fluid transition is observed. In addition, we find that the nonpairwise additivity of the polymer-induced attraction between the colloidal particles has a pronounced effect on the equation-of-state and the phase behavior of a colloid-polymer mixture. The perturbation theory of Lekkerkerker et al. [Europhys. Lett. 20, 559 (1992)] is found to perform well, except at low densities.

We have tested the performance of three frequently used density functionals (LDA, LDA+B, and LDA+B+LYP) in a study of the intermolecular interactions of benzene. Molecular geometries are satisfactory, with the gradient-corrected density functionals yielding slightly better results. The quadrupole moment is significantly underestimated by all three functionals. LDA performs fortuitously comparatively well for both binding energies and geometries of the dimer and the solid, whereas in LDA+B, and LDA+B+LYP the dimer interaction is purely repulsive, leading to the complete absence of cohesion in the solid. These results are consistent with density-functional theory calculations for noble gas dimers. However, when the dispersion energy calculated from a model potential is included, LDA fails. Binding energies are overestimated by unacceptable amounts, and intermolecular distances are too small. In contrast, dispersion corrected LDA+B and LDA+B+LYP perform reasonably well, although discrepancies are still large when measured on the thermal energy scale at room temperature.

We computed the phase-separation behavior and effective interactions of colloid-polymer mixtures in the "protein limit," where the polymer radius of gyration is much larger than the colloid radius. For ideal polymers, the critical colloidal packing fraction tends to zero, whereas for interacting polymers in a good solvent the behavior is governed by a universal binodal, implying a constant critical colloid packing fraction. In both systems the depletion interaction is not well described by effective pair potentials but requires the incorporation of many-body contributions.