A mean-field approach to simulating anisotropic particles

Abstract

We introduce a mean-field theoretical framework for generalizing isotropic pair potentials to anisotropic shapes. This method is suitable for generating pair potentials that can be used in both Monte Carlo and molecular dynamics simulations. We demonstrate the application of this theory by deriving a Lennard-Jones (LJ)-like potential for arbitrary geometries along with a Weeks–Chandler–Anderson-like repulsive variant, showing that the resulting potentials behave very similarly to standard LJ potentials while also providing a nearly conformal mapping of the underlying shape. We then describe an implementation of this potential in the simulation engine HOOMD-blue and discuss the challenges that must be overcome to achieve a sufficiently robust and performant implementation. The resulting potential can be applied to smooth geometries like ellipsoids and to convex polytopes. We contextualize these applications with reference to the existing methods for simulating such particles. The pair potential is validated using standard criteria, and its performance is compared to existing methods for comparable simulations. Finally, we show the results of self-assembly simulations, demonstrating that this method can be used to study the assembly of anisotropic particles into crystal structures.

A theory of entropic bonding

“…This mathematical device provides a quantifiable proxy for excluded volume, which facilitates the development of the theory. Explicit molecular dynamics simulations ( 48 – 50 ) of a system of NPs and pPs interacting via the derived effective potential ( Eq. 7 ) —while not necessary for crystal structure prediction—provide additional validation of the reasonableness of this ansatz ( SI Appendix , section VI ).…”

coxeter: A Python package for working with shapes

“…Furthermore, since these shapes may be used in physics-based simulations, any calculations must be robust enough to handle any numerical issues that may arise across a wide range of different geometries. Some of the applications of coxeter to date include: the development of equations of state for polyhedral particles (Irrgang et al, 2017); the calculation of physical properties for dynamical simulation of anisotropic particles (Ramasubramani et al, 2020); and the orientational ordering of ellipsoidal colloids in a magnetic field (Kao et al, 2019).…”

Controlling morphology in hybrid isotropic/patchy particle assemblies

“…Numerous computational studies have been undertaken to better understand the mechanistic aspects of assembly of patchy particles and their emergent selfassembled structures. Their phase behavior and kinetics have been studied extensively using Monte Carlo and Molecular Dynamics (MD) methods [22][23][24][25][26][27][28][29][30] . Majority of those studies have discussed structures obtained by direct binding between anisotropic particles.…”