Cluster self-assembly condition for arbitrary interaction potentials
arXiv:2010.04631 · doi:10.1039/D0SM00650E
Abstract
We present a sufficient criterion for the emergence of cluster phases in an ensemble of interacting classical particles with repulsive two-body interactions. Through a zero-temperature analysis in the low density region we determine the relevant characteristics of the interaction potential that make the energy of a two-particle cluster-crystal become smaller than that of a simple triangular lattice in two dimensions. The method leads to a mathematical condition for the emergence of cluster crystals in terms of the sum of Fourier components of a regularized interaction potential, which can be in principle applied to any arbitrary shape of interactions. We apply the formalism to several examples of bounded and unbounded potentials with and without cluster-forming ability. In all cases, the emergence of self-assembled cluster crystals is well captured by the presented analytic criterion and verified with known results from molecular dynamics simulations at vanishingly temperatures. Our work generalises known results for bounded potentials to repulsive potentials of arbitrary shape.
arXiv comment9 pages, 5 figures
References in corpus (25)
- Type-1.5 Superconductors
- Exact Criterion for Determining Clustering vs. Reentrant Melting Behavior for Bounded Interaction Potentials
- Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent systems
- Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
- Phase diagram of the Gaussian-core model
- Soft Spheres Make More Mesophases
- Defect-induced supersolidity with soft-core bosons
- Microscopic theory of type-1.5 superconductivity in multiband systems
- Type-1.5 superconductivity in multiband systems: the effects of interband couplings
- Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors
- Computer Assembly of Cluster-Forming Amphiphilic Dendrimers
- The Elasticity of Nuclear Pasta
- Reentrant and Isostructural Transitions in a Cluster-Crystal Former
- Muon-spin rotation measurements of the vortex state in SrRuO: type-1.5 superconductivity, vortex clustering and a crossover from a triangular to a square vortex lattice
- Hexatic phase and cluster crystals of two-dimensional GEM4 spheres
- Interactions and design rules for assembly of porous colloidal mesophases
- Hierarchical structure formation in layered superconducting systems with multi-scale inter-vortex interactions
- Quantum Cluster Quasicrystals
- Microphase Equilibrium and Assembly Dynamics
- Glass transitions in monodisperse cluster-forming ensembles: vortex matter in type-1.5 superconductors
- Hierarchies of Length Scale Based Typology in Anisotropic Multiband Superconductor
- Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors
- Cluster crystals for Brownian particles with combined soft and hard-core repulsive interactions
- Phase-change switching in 2D via soft interactions
- Melting of a two-dimensional monodisperse cluster crystal to a cluster liquid