The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems

Abstract

We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the "Langevin Hull", can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work.

Figure 1

Affine scaling methods use box-length scaling to adjust the volume to adjust to under-or over-pressure conditions. In a system with a uniform compressibility (e.g. bulk fluids) these methods can work well. In systems containing heterogeneous mixtures, the affine scaling moves required to adjust the pressure in the high-compressibility regions can cause molecules in low compressibility regions to collide.

Figure 2

The external temperature and pressure bath interacts only with those atoms on the convex hull (grey surface). The hull is computed dynamically at each time step, and molecules can move between the interior (Newtonian) region and the Langevin Hull.

Figure 3

The resistance tensor Ξ for a facet comprising sites i, j, and k is constructed using Oseen tensor contributions between the centoid of the facet f and each of the sub-facets (i, f, j), (j, f, k), and (k, f, i). The centroids of the sub-facets are located at 1, 2, and 3, and the area of each sub-facet is easily computed using half the cross product of two of the edges.

Figure 4

The response of the internal pressure and temperature of gold nanoparticles when first placed in the Langevin Hull (T_bath = 300K, P_bath = 4 GPa), starting from initial conditions that were far from the bath pressure and temperature. The pressure response is rapid (after the breathing mode oscillations in the nanoparticle die out), and the rate of thermal equilibration depends on both exposed surface area (top panel) and the viscosity of the bath (middle panel).

Figure 5

Compressibility of SPC/E water

Figure 6

At low pressures, the liquid is in equilibrium with the vapor phase, and isolated molecules can detach from the liquid droplet. This is expected behavior, but the volume of the convex hull includes large regions of empty space. For this reason, compressibilities are computed using local number densities rather than hull volumes.

Figure 7

Distribution of cos θ values for molecules on the interior of the cluster (squares) and for those participating in the convex hull (circles) at a variety of pressures. The Langevin Hull exhibits minor dewetting behavior with exposed oxygen sites on the hull water molecules. The orientational preference for exposed oxygen appears to be independent of applied pressure.

Figure 8

Density profiles of gold and water at the nanoparticle surface. Each curve has been normalized by the average density in the bulk-like region available to the corresponding material. Higher applied pressures de-structure both the gold nanoparticle surface and water at the metal/water interface.

Figure 9

When the sites are distributed among many nodes for parallel computation, the processors first compute the convex hulls for their own sites (dashed lines in left panel). The positions of the sites that make up the subset hulls are then communicated to all processors (middle panel). The convex hull of the system (solid line in right panel) is the convex hull of the points on the union of the subset hulls.