Modeling of many-body interactions between elastic spheres through symmetry functions

Abstract

Simple models for spherical particles with a soft shell have been shown to self-assemble into numerous crystal phases and even quasicrystals. However, most of these models rely on a simple pairwise interaction, which is usually a valid approximation only in the limit of small deformations, i.e. low densities. In this work, we consider a many-body yet simple model for the evaluation of the elastic energy associated with the deformation of a spherical shell. The resulting energy evaluation, however, is relatively expensive for direct use in simulations. We significantly reduce the associated numerical cost by fitting the potential using a set of symmetry functions. We propose a method for selecting a suitable set of symmetry functions that capture the most relevant features of the particle environment in a systematic manner. The fitted interaction potential is then used in Monte Carlo simulations to draw the phase diagram of the system in two dimensions. The system is found to form both a fluid and a hexagonal crystal phase.

10 pages, 9 figures

References in corpus (4)

• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• Phase diagram of Hertzian spheres
• A new look at effective interactions between microgel particles
• Coating thickness and coverage effects on the forces between silica nanoparticles in water

Cited by in corpus (3)

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• A neural network potential with self-trained atomic fingerprints: a test with the mW water potential