Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1008.3068

Phase behaviour of polydisperse spheres: simulation strategies and an application to the freezing transition

Nigel B. Wilding·Peter Sollich
View original source ↗Read source document ↗Export metadata ↓

Abstract

The statistical mechanics of phase transitions in dense systems of polydisperse particles presents distinctive challenges to computer simulation and analytical theory alike. The core difficulty, namely dealing correctly with particle size fractionation between coexisting phases, is set out in the context of a critique of previous simulation work on such systems. Specialized Monte Carlo simulation techniques and moment free energy method calculations, capable of treating fractionation exactly, are then described and deployed to study the fluid-solid transition of an assembly of repulsive spherical particles described by a top-hat "parent" distribution of particle sizes. The cloud curve delineating the solid-fluid coexistence region is mapped as a function of the degree of polydispersity $δ$, and the properties of the incipient "shadow" phases are presented. The coexistence region is found to shift to higher densities as $δ$ increases, but does not exhibit the sharp narrowing predicted by many theories and some simulations.

Explore related subjects

cond-mat.softcond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nigel B. Wilding, Peter Sollich. 2010-08-18. Phase behaviour of polydisperse spheres: simulation strategies and an application to the freezing transition. https://doi.org/10.1063/1.3510534

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Transient Elasticity -- A Unifying Framework for Thixotropy, Polymers, and Granular Media

Thixotropic yield stress fluids, such as paint or ketchup, are traditionally viewed as elastic structures that, under shear rates, break into viscous liquids with lumps, and reconnect at rest. An alternative framework is presented here: Upon shear, structural destruction is incomplete, leaving sufficient connections. As a result, elasticity fundamentally underlies their non-Newtonian behavior, though they do appear purely viscous under a steady shear, displaying little direct evidence of elastic rebound---same as granular media and polymers. Consequently, all three are described by the same set of evolution equations, differing only in their parameters. These equations are set up by starting from solid dynamics and allowing the elastic strain $\varepsilon^e$ to relax, which in effect interpolates between solid and fluid behavior, appropriate for systems that display both types of behavior. Incorporating in addition a two-temperature framework, tracking how energy is dissipated in two consecutive stages, yields the nonlinear model of Transient Elasticity (TE). It describes an elasticity that is transient in time yet persistent under shear. Previously validated for polymers and granular media, TE is here applied to thixotropic yield-stress fluids. As shown, it successfully accounts for a wide range of characteristic phenomena, including over- and undershoot, viscosity bifurcation, shear banding, and oscillatory rheography. Given its appropriateness across structurally diverse systems, TE offers a unified, surprisingly general account of non-Newtonian phenomena.

cond-mat.soft↗
arXiv2026

Deformation and organization of droplet-encapsulated soft beads

Many biological, culinary, and engineering processes lead to the co-encapsulation of several soft particles within a liquid interface. In these situations the particles are bound together by the capillary forces that deform them and influence their biological or rheological properties. Here, we introduce an experimental approach to encapsulate a controlled number of soft beads within aqueous droplets in oil. These droplet-encapsulated gels are manipulated in a deformable microfluidic device to merge them and modify the liquid fraction. In the dry limit the contact surface between the hydrogels is found to be determined by the elastocapillary number $E_c$, with the contact radius following a $E_c^{1/3}$ dependence, indicating that the deformation increases for soft or small particles. When multiple beads are co-encapsulated within a single droplet they can be arranged into linear or three-dimensional aggregates that remain at a local energy minimum.

cond-mat.soft↗
arXiv2026

Flexoelectricity-driven softening of bend elasticity leads to spontaneous chiral symmetry breaking in a polar fluid

The origin of the recently observed spontaneous chiral symmetry breaking in polar fluids composed of achiral molecules is an unsolved problem, raising fundamental questions about how heliconical structures emerge in such systems. Here, we investigate the pretransitional fluctuations leading to the formation of the spontaneously chiral twist-bend ferroelectric nematic phase using dielectric spectroscopy, light scattering, and small-angle X-ray scattering. We observe simultaneous softening of the bend elastic constant and the emergence of a collective dielectric mode on approaching the transition. By developing a theoretical model, we show that these phenomena are signatures of a flexoelectricity-driven transition arising from the coupling between electric polarization and bend deformation.

cond-mat.soft↗