Hard-sphere Liquid Research Articles

Morphometric Approach to Many-Body Correlations in Hard Spheres.

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the morphometric calculation of n-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where fivefold symmetric structures appear lower in free energy than fourfold symmetric structures and from a single reaction path predict a dynamical barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.

Effect of quantum dispersion on the radial distribution function of a one-component sticky-hard-sphere fluid

In this short communication we present a possible scheme to study the radial distribution function of the quantum slightly polydisperse Baxter sticky hard sphere liquid at finite temperature thorugh a semi-analytical method devised by Chandler and Wolynes.

Anomalous dynamic arrest of non-interacting spheres ("polymer") diluted in a hard-sphere ("colloid") liquid.

Upon compression, the equilibrium hard-sphere liquid [pair potential uHS(r)] freezes at a packing fraction ϕf = 0.494 or, if crystallization is prevented, becomes metastable up to its glass transition at ϕg ≈ 0.58. Throughout the fluid regime (ϕ < ϕg), we are, thus, certain that this model liquid does not exhibit any form of kinetic arrest. If, however, a small portion of these spheres (packing fraction ϕ2 ≪ ϕ) happen to ignore each other [u22(r) = 0] but do not ignore the remaining "normal" hard spheres [u12(r) = u21(r) = u11(r) = uHS(r)], whose packing fraction is thus ϕ1 = ϕ - ϕ2, they run the risk of becoming dynamically arrested before they demix from the "normal" particles. This unexpected and counterintuitive scenario was first theoretically predicted and then confirmed by simulations.

Crystal nucleation in sedimenting colloidal suspensions.

Homogeneous crystal nucleation from a metastable hard-sphere colloidal liquid has been extensively studied in simulations and experiments. A 12 order of magnitude difference between simulated and experimental nucleation rates is observed, the origin of which remains a puzzle. Here, we experimentally study crystal nucleation at the single particle level in suspensions of hard-sphere-like colloids under the influence of sedimentation. We find that sedimentation significantly enhances the nucleation rate, but contrary to what was previously thought, this is not due to simple density fluctuations, as the nucleation barriers become independent of the local density in a sedimentating fluid. Instead, we find an enhancement of the local dynamics, which suggests that local convective cells are responsible for shear-enhanced crystallization at low volume fractions.

Calculation of critical nucleation rates by the persistent embryo method: application to quasi hard sphere models.

We study the crystal nucleation of the Weeks-Chandler-Andersen (WCA) model, using the recently introduced persistent embryo method (PEM). The method provides detailed characterization of pre-critical, critical and post-critical nuclei, as well as nucleation rates that compare favorably with those obtained using other methods (umbrella sampling, forward flux sampling or seeding). We further map our results to a hard sphere model allowing comparison with other existing predictions. Implications for experiments are also discussed.

Self-consistent generalized Langevin equation theory of the dynamics of multicomponent atomic liquids

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from a ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions.

Splitting of the Universality Class of Anomalous Transport in Crowded Media

We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties depend in a subtle nonuniversal way on the transport through narrow channels. At the same time, the different universality classes are robust with respect to introducing correlations in the obstacle matrix as we demonstrate for quenched hard-sphere liquids as underlying structures. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times, in striking contrast to glassy dynamics.

Static lengths in glass-forming monodisperse hard-sphere fluids from periodic array pinning.

We explore the static length in glass-forming hard-sphere liquids revealed by the response of dynamical properties (diffusion coefficient D and α relaxation time τα) to a regular array of pinned particles. By assuming a universal scaling form, we find data can be excellently collapsed onto a master curve, from which relative length scales can be extracted. By exploiting a crystal-avoiding simulation method that suppresses crystallization while preserving dynamics, we can study monodisperse as well as polydisperse systems. The static length obtained from dynamical property Q (τα and D) scales as log Q ∼ ξ, with ψ ≈ 1.

Topological analyses in APP/PS1 mice reveal that astrocytes do not migrate to amyloid-β plaques

Although the clustering of GFAP immunopositive astrocytes around amyloid-β plaques in Alzheimer's disease has led to the widespread assumption that plaques attract astrocytes, recent studies suggest that astrocytes stay put in injury. Here we reexamine astrocyte migration to plaques, using quantitative spatial analysis and computer modeling to investigate the topology of astrocytes in 3D images obtained by two-photon microscopy of living APP/PS1 mice and WT littermates. In WT mice, cortical astrocyte topology fits a model in which a liquid of hard spheres exclude each other in a confined space. Plaques do not disturb this arrangement except at very large plaque loads, but, locally, cause subtle outward shifts of the astrocytes located in three tiers around plaques. These data suggest that astrocytes respond to plaque-induced neuropil injury primarily by changing phenotype, and hence function, rather than location.

Curvature Dependence and Tolman Length of Surface Tension of Nano-Droplet of Attractive Hard Sphere Liquid

Curvature Dependence and Tolman Length of Surface Tension of Nano-Droplet of Attractive Hard Sphere Liquid

The role of shear in crystallization kinetics: From suppression to enhancement.

In many technical applications crystallization proceeds in the presence of stresses and flows, hence the importance to understand the crystallization mechanism in simple situations. We employ molecular dynamics simulations to study the crystallization kinetics of a nearly hard sphere liquid that is weakly sheared. We demonstrate that shear flow both enhances and suppresses the crystallization kinetics of hard spheres. The effect of shear depends on the quiescent mechanism: suppression in the activated regime and enhancement in the diffusion-limited regime for small strain rates. At higher strain rates crystallization again becomes an activated process even at densities close to the glass transition.

The hard sphere view of the outer core

AbstractThe hard sphere model for liquids attempts to capture the physical behavior of a real liquid in a simple conceptual model: a fluid of fixed size spheres that only interact repulsively when they come into contact. Is the model good enough to use for modeling internal planetary structure? To answer this question, I survey variants of hard sphere liquid theory by applying them to the Earth’s outer core to determine which of them explains wavespeeds in the outer core best. The variants explored here are the Carnahan-Starling hard sphere model, the Mansoori-Carnahan-Starling-Leland extension to hard sphere mixtures, the transition metal hard sphere liquid, and the Lennard-Jones hard sphere liquid with attractive forces. With an empirical addition of a temperature dependence to the liquid’s hard sphere diameter, all of the variants explored can replicate wavespeeds in most of the radius range of the outer core. The hard sphere model for liquid transition metals explains the wavespeed best because it yields a mean liquid atomic weight of 48.8 g mol−1 at 10 wt% light element abundance in the core which is in good cosmochemical agreement with core light element models. Other variants also fit core wavespeeds but require implausibly low liquid mean atomic weight implying excessive incorporation of hydrogen or helium in the core. Applied to the detailed wavespeed structure of the Earth’s outermost outer core, the model suggests that the mean atomic weight could be reduced by up to 1.74% or the temperature could be increased by up to 400 K relative to an adiabatic profile, or there could be 8% fewer valence electrons in the liquid.

Coming Home from a MOOC

My ten-week Massive Open Online Course "Statistical Mechanics: Algorithms and Computations", in early 2014, focused on subjects such as Monte Carlo sampling, molecular dynamics, transition phases in hard-sphere liquids, simulated annealing, classical spin models, quantum Monte Carlo algorithms, and Bose-Einstein condensation, etc. It familiarized a huge international crowd of students with cutting-edge subjects in computational physics. Here, I present the topics of the course, its basic design ideas, its scope and challenges, and compare it with earlier attempts in online teaching.

T1 process and dynamics in glass-forming hard-sphere liquids.

To study the relationship between dynamics and structure in a glass-forming liquid, we introduce a purely geometric criterion for locally mobile particles in a dense hard-sphere fluid: namely, "T1-active" particles, which can gain or lose at least one Voronoi neighbor by moving within their free volume with other particles fixed. We obtain geometrical and dynamical properties for monodisperse hard-sphere fluids with 0.40 < ϕ < 0.64 using a "crystal-avoiding" MD simulation that effectively suppresses crystallization without altering the dynamics. We find that the fraction of T1-active particles vanishes at random close packing, while the percolation threshold of T1-inactive particles is essentially identical to the commonly identified hard-sphere glass transition, ϕg ≈ 0.585.

Characterization of maximally random jammed sphere packings: Voronoi correlation functions.

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.090604], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.

Nesting of thermodynamic, structural, and dynamic anomalies in liquid silicon.

Anomalous behaviour in density, diffusivity, and structural order is investigated for silicon modeled by the Stillinger-Weber potential by performing molecular dynamics simulations. As previously reported in the case of water [J. R. Errington and P. G. Debenedetti, Nature (London) 409, 318 (2001)] and silica [M. S. Shell, P. G. Debenedetti, and A. Z. Panagiotopoulos, Phys. Rev. E 66, 011202 (2002)], a cascading of thermodynamic, dynamic, and structural anomalous regions is also observed in liquid silicon. The region of structural anomaly includes the region of diffusivity anomaly, which in turn encompasses the region of density anomaly (which is unlike water but similar to silica). In the region of structural anomaly, a tight correlation between the translational and tetrahedrality order parameter is found, but the correlation is weaker when a local orientational order parameter (q3) is used as a measure of tetrahedrality. The total excess entropy and the pair correlation entropy are computed across the phase diagram and the correlation between the excess entropy and the regions of anomalies in the phase diagram of liquid silicon is examined. Scaling relations associating the excess entropy with the diffusion coefficient show considerable deviation from the quasi-universal behaviour observed in hard-sphere and Lennard-Jones liquids and some liquid metals. Excess entropy based criteria for diffusivity and structural anomalies fail to capture the observed regions of anomaly.

An analytical expression for the direct correlation function of a hard-sphere liquid derived from the extended scaled particle theory

Integral equation methods based on the Ornstein–Zernike equation have been widely used for calculations of the radial distribution functions, g(r), of simple liquids. The closure that connects a direct correlation function, c(r), with a total correlation function, h(r), is necessary for solving the integral equation. In this work, we propose an analytical expression of the direct correlation function for a hard-sphere liquid through the solvation free energy for a pair of hard-spheres as a solute derived from the extended version of scaled particle theory (XSPT) instead of using iterative calculations with some closure. The solvation free energy has an analytical expression given by the XSPT that treats solvation of an arbitrary shaped particle into a hard-sphere liquid. In the case of a hard-sphere liquid, our new expression for the direct correlation function gives an analytical expression of the radial distribution function in Fourier Transform k-space. In addition, the radial distribution function in real-space quantitatively agrees with the Monte Carlo simulation results better than the Percus–Yevick equation method under equivalent numerical conditions. Our method with the proposed direct correlation function in this work is expected to be applied to estimation of the contributions from hydrophobic hydration in the hydration free energy of two associated molecules, which is a key to understanding the mechanism for association of proteins.

Dynamic equivalences in the hard-sphere dynamic universality class

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

Existence of a bending rigidity for a hard-sphere liquid near a curved hard wall: Validity of the Hadwiger theorem

In the context of Rosenfeld's fundamental measure theory, we show that the bending rigidity is not equal to zero for a hard-sphere fluid in contact with a curved hard wall. The implication is that the Hadwiger theorem does not hold in this case and the surface free energy is given by the Helfrich expansion instead. The value obtained for the bending rigidity (i) is an order of magnitude smaller than the bending constant associated with Gaussian curvature, (ii) changes sign as a function of the fluid volume fraction, and (iii) is independent of the choice of the location of the hard wall.

The overdamped van Hove function of atomic liquids

Using the generalized Langevin equation formalism and the process of contraction of the description we derive a general memory function equation for the thermal fluctuations of the local density of a simple atomic liquid. From the analysis of the long-time limit of this equation, a striking equivalence is suggested between the long-time dynamics of the atomic liquid and the dynamics of the corresponding Brownian liquid. This dynamic equivalence is confirmed here by comparing molecular and Brownian dynamics simulations of the self-intermediate scattering function and the long-time self-diffusion coefficient for the hard-sphere liquid.