# Free energy of singular sticky-sphere clusters.

@article{Kallus2016FreeEO, title={Free energy of singular sticky-sphere clusters.}, author={Yoav Kallus and Miranda C. Holmes-Cerfon}, journal={Physical review. E}, year={2016}, volume={95 2-1}, pages={ 022130 } }

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…

## 18 Citations

### Physical interpretation of the partition function for colloidal clusters

- PhysicsPhysical Review E
- 2018

Colloidal clusters consist of small numbers of colloidal particles bound by weak, short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is…

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

- PhysicsPhysical review. E
- 2020

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

- PhysicsThe Journal of chemical physics
- 2020

This work introduces a Monte Carlo method to handle the case when constraints can break and form, and samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher- dimensional manifolds.

### Gregory-Newton problem for kissing sticky spheres

- MathematicsPhysical Review E
- 2018

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

- Physics
- 2021

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…

### Thermal Fluctuations of Singular Bar-Joint Mechanisms.

- PhysicsPhysical review letters
- 2022

A bar-joint mechanism is a deformable assembly of freely rotating joints connected by stiff bars. Here we develop a formalism to study the equilibration of common bar-joint mechanisms with a thermal…

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

- BiologyMolecular pharmaceutics
- 2022

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

- Computer ScienceJ. Nonlinear Sci.
- 2019

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.

- Computer ScienceSoft matter
- 2021

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.

### Sticky Brownian Motion and its Numerical Solution

- PhysicsSIAM Rev.
- 2020

This article introduces a simple and intuitive sticky random walk to simulate sticky Brownian motion, that also gives insight into its unusual properties, and outlines possible steps to extend this method towards simulating multi-dimensional sticky diffusions.

## References

SHOWING 1-10 OF 69 REFERENCES

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

- MathematicsProceedings of the National Academy of Sciences
- 2012

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.

- PhysicsPhysical review letters
- 2015

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.

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

- PhysicsPhysical 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

- Physics
- 1991

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.

- PhysicsPhysical chemistry chemical physics : PCCP
- 2016

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.

- PhysicsNature materials
- 2013

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.

### Mechanical instability at finite temperature

- Materials Science, PhysicsNature Communications
- 2015

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.

### Phonon contribution to the entropy of hard-sphere crystals.

- PhysicsPhysical 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.

### Energy landscapes of colloidal clusters: thermodynamics and rearrangement mechanisms.

- PhysicsNanoscale
- 2012

Calculations suggest that distinct features characteristic of short-ranged interactions should be observable in terms of the structure, thermodynamics and dynamical properties, and analysis of a kinetic transition network for the 19-particle cluster reveals super-Arrhenius behaviour in the dynamics.

### Colloidal matter: Packing, geometry, and entropy

- PhysicsScience
- 2015

The wide range of self-assembled structures seen in colloidal matter can be understood in terms of the interplay between packing constraints, interactions, and the freedom of the particles to move—in other words, their entropy.