A geometrical approach to computing free energy landscapes from short-ranged potentials

Abstract

Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free energy landscape of such systems as the range of the potential goes to zero. In this limit, the landscape is entirely defined by geometrical manifolds, plus a single control parameter. These manifolds are fundamental objects that do not depend on the details of the interaction potential, and provide the starting point from which any quantity characterizing the system -- equilibrium or non-equilibrium -- can be computed for arbitrary potentials. To consider dynamical quantities we compute the asymptotic limit of the Fokker-Planck equation, and show that it becomes restricted to the low-dimensional manifolds connected by "sticky" boundary conditions. To illustrate our theory, we compute the low-dimensional manifolds for n<=8 identical particles, providing a complete description of the lowest-energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom. The results can be directly tested on colloidal clusters. This limit is a novel approach for understanding energy landscapes, and our hope is that it can also provide insight into finite-range potentials.

References in corpus (2)

• Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation
• Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions

Cited by in corpus (27)

• Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements
• Enumerating rigid sphere packings
• Holographic Measurements of Anisotropic Three-Dimensional Diffusion of Colloidal Clusters
• Sticky Brownian Motion and its Numerical Solution
• From Sticky-Hard-Sphere to Lennard-Jones-Type Clusters
• Sticky-sphere clusters
• Morphometric approach to many-body correlations in hard spheres
• Free energy of singular sticky-sphere clusters
• Structure and dynamics of model colloidal clusters with short-range attractions
• Mutation at Expanding Front of Self-Replicating Colloidal Clusters
• Metastable distributions of Markov chains with rare transitions
• Close encounters of the sticky kind: Brownian motion at absorbing boundaries
• Modeling aggregation processes of Lennard-Jones particles via stochastic networks
• A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains
• Simulating sticky particles: A Monte Carlo method to sample a stratification
• The Gregory-Newton Problem for Kissing Sticky Spheres
• Coupling between long ranged repulsions and short ranged attractions in a colloidal model of zero shear rate viscosity
• The polyhedral structure underlying programmable self-assembly
• Visualizing Free Energy Landscapes for Four Hard Disks
• From canyons to valleys: Numerically continuing sticky hard sphere clusters to the landscapes of smoother potentials
• Calculating the symmetry number of flexible sphere clusters
• Energy landscapes for the self-assembly of supramolecular polyhedra
• Geometric and Topological Entropies of Sphere Packing
• Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity
• Thermal Fluctuations of Singular Bar-Joint Mechanisms
• Rigidity for sticky disks
• Efficient Atlasing and Search of Configuration Spaces of Point-Sets Constrained by Distance Intervals