We map dilute or semidilute solutions of nonintersecting polymer chains onto a fluid of “soft” particles interacting via a concentration dependent effective pair potential, by inverting the pair distribution function of the centers of mass of the initial polymer chains. A similar inversion is used to derive an effective wall-polymer potential; these potentials are combined to successfully reproduce the calculated exact depletion interaction induced by nonintersecting polymers between two walls. The mapping opens up the possibility of large-scale simulations of polymer solutions in complex geometries.

Dilute or semidilute solutions of nonintersecting 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 semidilute regime—of the standard Asakura–Oosawa approximation based on the assumption of noninteracting polymer coils.

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_g is sufficiently large compared to the diameter of the colloidal particles σ_col (2R_g/σ_col≥0.45), 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 present LCBOPII, an improvement of the long-range carbon bond-order potential (LCBOP) by Los and Fasolino [Phys. Rev. B 68, 024107 (2003)]. LCBOPII contains a coordination dependent medium range term for bond distances between 1.7 and $4\mathrm{\AA }$, meant to reproduce the dissociation energy curves for single, double, and triple bonds and improve the reactive properties as well as the description of the liquid and of low coordinated phases. Other features of LCBOPII are a coordination dependent angular correlation, a correction for antibonding states, and a conjugation dependent torsional interaction based on ab initio calculations of the torsional barriers for a set of molecular configurations. We present results for the geometry and energetics of the graphite-to-diamond transformation and of the vacancy in diamond and graphite as well as the prediction of the energy barrier of the 5-77-5 defect in graphite and graphene for which ab initio results are available only for unsuitably small samples. In the accompanying paper (Ghiringhelli et al., Phys. Rev. B 72, 214103 (2005) we use LCBOPII to evaluate several properties, including the equation of state, of liquid carbon.