Free energy of singular sticky-sphere clusters.

  title={Free energy of singular sticky-sphere clusters.},
  author={Yoav Kallus and Miranda C. Holmes-Cerfon},
  journal={Physical review. E},
  volume={95 2-1},
Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential and complex fluids near jamming, to self-assembled lattices and various metamaterials. Under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero-frequency vibrational modes, yet such singular modes are at the epicenter of many interesting behaviors in the systems above. We consider a… 

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This work uses 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 to compare clusters obtained by continuation with different potentials.

Simulating sticky particles: A Monte Carlo method to sample a Stratification

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Gregory-Newton problem for kissing sticky spheres

All possible non-isomorphic arrangements of 12 spheres kissing a central sphere (the Gregory-Newton problem) are obtained for the sticky-hard-sphere (SHS) model, and subsequently projected by

Coupling between long ranged repulsions and short ranged attractions in a colloidal model of zero shear rate viscosity

In this work, we analyzed an isotropic colloidal model incorporating both shortrange sticky attractions and long-range electrostatic repulsions. We computed the zero-shear viscosity and second virial

Application of a Simple Short-Range Attraction and Long-Range Repulsion Colloidal Model toward Predicting the Viscosity of Protein Solutions.

The application of a hard-sphere colloidal model with SALR interactions toward predicting the viscosity of dilute to semi-dilute protein solutions is shown and it is shown that it is the coupling between attractions and repulsions that gives rise to the observed experimental trends in solution viscosities as a function of pH, concentration, and ionic strength.

Calculating the Symmetry Number of Flexible Sphere Clusters

A numerical algorithm is introduced to compute the sticky symmetry group and symmetry number of a flexible sphere cluster using a definition of symmetry that arises naturally when calculating the equilibrium probability of a cluster of spheres in the sticky-sphere limit.

Thermodynamic stability versus kinetic accessibility: Pareto fronts for programmable self-assembly.

A genetic algorithm is developed to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable short-ranged interaction energies.

Colloquium : Toward living matter with colloidal particles

This Colloquium examines whether the essential properties of living matter could emerge by programming interactions between colloidal particles, an approach that bootstraps off of recent advances in DNA nanotechnology and in the mathematics of sphere packings.

From sticky-hard-sphere to Lennard-Jones-type clusters.

A more realistic extended Lennard- Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.



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

This work compute the asymptotic limit of the Fokker–Planck equation and shows that it becomes restricted to the low-dimensional manifolds connected by “sticky” boundary conditions, providing a complete description of the lowest-energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom.

Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements.

The success of this model, which requires no fitting parameters or measurements of the potential, shows that the free-energy landscape of colloidal systems and the dynamics it governs can be understood geometrically.

Geometric frustration in small colloidal clusters

The yield of clusters of specific structure in a model colloidal system with competing interactions using Brownian dynamics simulations is considered as a function of the strength of the interactions, for clusters with m = 3,4,5,6,7,10 and 13 colloids.

The Free-Energy Landscape of Clusters of Attractive Hard Spheres

It is found that highly symmetric clusters are strongly suppressed by rotational entropy, whereas the most stable clusters have anharmonic vibrational modes or extra bonds, many of which are subsets of close-packed lattices.

Structure and dynamics of model colloidal clusters with short-range attractions.

  • R. Hoy
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
The structure and dynamics of small isolated N-particle clusters interacting via short-ranged Morse potentials are examined, showing nontrivial temperature dependence and nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures.

Sticky spheres and related systems

Some properties of a system of hard-core particles with attractive wells in the Baxter sticky-sphere limit and a related limit are considered, as is the approach to these limits. A demonstration of

Dynamical properties of two- and three-dimensional colloidal clusters of six particles.

It is shown that the interaction energies between the particles are probably greater than previously assumed, and the rates predicted by transition state theory using harmonic vibrational densities of states are off by four orders of magnitude.

Entropy favours open colloidal lattices.

An analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices is described.

Phonon contribution to the entropy of hard-sphere crystals.

  • V. Elser
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2014
A "sticky-sphere" model by which the system interpolates between hard spheres in one limit and a harmonic crystal in the other, and the value for the net entropy difference is in excellent agreement with the best previous estimate.

Mechanical instability at finite temperature.

The investigation of the mechanical instability in a lattice model at finite temperature T using a square lattice with a φ(4) potential between next-nearest-neighbour sites and an 'order-by-disorder' effect that favours the rhombic over other zigzagging configurations is reported.