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.

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We located the melting line of the Yukawa system by determining the free energy of both fluid and solid phases by computer simulations. At the high densities the fluid freezes into a body-centered-cubic (bee) solid, whereas for low densities it freezes into a face-centered-cubic (fee) solid. For both the bee-fluid and the fee-fluid part of the melting line two coexistence points were determined. We observed that the relative root-mean-square displacement in the solid (Lindeman ratio) varies considerably along the melting line. At the bee-fluid part of the melting line the Lindeman ratio equals 0.19, whereas at the fee-solid part of the melting line it is smaller than 0.16.

Acid-base chemistry of clay minerals is central to their interfacial properties, but up to 10 now a quantitative understanding on the surface acidity is still lacking. In this study, with first principles 11 molecular dynamics (FPMD) based vertical energy gap technique, we calculate the acidity constants of 12 surface groups on (010)-type edges of montmorillonite and kaolinite, which are representatives of 2:1 13 and 1:1-type clay minerals, respectively. It shows that ≡Si-OH and ≡Al-OH 2 OH groups of kaolinite 14 have pKas of 6.9 and 5.7 and those of montmorillonite have pKas of 7.0 and 8.3, respectively. For each 15 mineral, the calculated pKas are consistent with the experimental ranges derived from fittings of 16 titration curves, indicating that ≡Si-OH and ≡Al-OH 2 OH groups are the major acidic sites responsible to 17 pH-dependent experimental observations. The effect of Mg substitution in montmorillonite is 18 investigated and it is found that Mg substitution increases the pKas of the neighboring ≡Si-OH and ≡Si-19 OH 2 groups by 2~3 pKa units. Furthermore, our calculation shows that the pKa of edge ≡Mg-(OH 2 ) 2 is 20 as high as 13.2, indicating the protonated state dominates under common pH. Together with previous 21 adsorption experiments, our derived acidity constants suggest that ≡Si-O-and ≡Al-(OH) 2 groups are the 22 most probable edge sites for complexing heavy metal cations.