From canyons to valleys: Numerically continuing sticky hard sphere clusters to the landscapes of smoother potentials

Abstract

We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6\le N\le 12$ hard spheres that are "sticky", i.e. they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30\% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events, and find that most rearrangements occur when a pair of non-bonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.

References in corpus (14)

• Extended corresponding-states behavior for particles with variable range attractions
• A geometrical approach to computing free energy landscapes from short-ranged potentials
• Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements
• Deriving Finite Sphere Packings
• Enumerating rigid sphere packings
• Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation
• Geometric frustration in small colloidal clusters
• From Sticky-Hard-Sphere to Lennard-Jones-Type Clusters
• Structure and dynamics of model colloidal clusters with short-range attractions
• Free energy of singular sticky-sphere clusters
• Contact numbers for congruent sphere packings in Euclidean 3-space
• Properties of Kinetic Transition Networks for Atomic Clusters and Glassy Solids
• Spaces of convex n-partitions
• The Gregory-Newton Problem for Kissing Sticky Spheres

Cited by in corpus (1)

• Simulating sticky particles: A Monte Carlo method to sample a stratification