Gradient Monte Carlo simulations: hard spheres in spatially varying temperature and gravitational fields

Pulling simulation predicts mixing free energy for binary mixtures

Predicting the mixing free energy of mixing for binary mixtures using simulations is challenging. We present a novel molecular dynamics (MD) simulation method to extract the chemical potential μ(X) for mixtures of species A and B. Each molecule of species A and B is placed in equal and opposite harmonic potentials ±(1/2)U_ex(x) centered at the middle of the simulation box, resulting in a nonuniform mole fraction profile X(z) in which A is concentrated at the center, and B at the periphery. Combining these, we obtain U_ex(X), the exchange chemical potential required to induce a given deviation of the mole fraction from its average. Simulation results for U_ex(X) can be fitted to simple free energy models to extract the interaction parameter χ for binary mixtures. To illustrate our method, we investigate benzene-pyridine mixtures, which provide a good example of regular solution behavior, using both TraPPE united-atom and OPLS all-atom potentials, both of which have been validated for pure fluid properties. χ values obtained with the new method are consistent with values from other recent simulation methods. However, the TraPPE-UA results differ substantially from the χ obtained from VLE experimental data, while the OPLS-AA results are in reasonable agreement with experiment, highlighting the importance of accurate potentials in correctly representing mixture behavior.

Monodisperse hard rods in external potentials

We consider linear arrays of cells of volume V(c) populated by monodisperse rods of size σV(c),σ=1,2,..., subject to hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In one application we also examine effects of contact forces between rods. We employ two distinct methods of exact analysis with complementary strengths and different limits of spatial resolution to calculate profiles of pressure and density on mesoscopic and microscopic length scales at thermal equilibrium. One method uses density functionals and the other statistically interacting vacancy particles. The applications worked out include gravity, power-law traps, and hard walls. We identify oscillations in the profiles on a microscopic length scale and show how they are systematically averaged out on a well-defined mesoscopic length scale to establish full consistency between the two approaches. The continuum limit, realized as V(c)→0,σ→∞ at nonzero and finite σV(c), connects our highest-resolution results with known exact results for monodisperse rods in a continuum. We also compare the pressure profiles obtained from density functionals with the average microscopic pressure profiles derived from the pair distribution function.

Field induced gradient simulations: a high throughput method for computing chemical potentials in multicomponent systems

We present a simulation method for direct computation of chemical potentials in multicomponent systems. The method involves application of a field to generate spatial gradients in the species number densities at equilibrium, from which the chemical potential of each species is theoretically estimated. A single simulation yields results over a range of thermodynamic states, as in high throughput experiments, and the method remains computationally efficient even at high number densities since it does not involve particle insertion at high densities. We illustrate the method by Monte Carlo simulations of binary hard sphere mixtures of particles with different sizes in a gravitational field. The results of the gradient Monte Carlo method are found to be in good agreement with chemical potentials computed using the classical Widom particle insertion method for spatially uniform systems.