arXiv subjects

Nigel B. Wilding

Publications and source records attributed to Nigel B. Wilding.

At least 55 records · Page 3Linked to original sources

arXiv2011

Polydispersity induced solid-solid transitions in model colloids

Specialized Monte Carlo simulation techniques and moment free energy method calculations, capable of treating fractionation exactly, are deployed to study the crystalline phase behaviour of an assembly of spherical particles described by a top-hat "parent" distribution of particle sizes. An increase in either the overall density or the degree of polydispersity is shown to generate a succession of phase transitions in which the system demixes into an ever greater number of face-centred cubic "daughter" phases. Each of these phases is strongly fractionated: it contains a much narrower distribution of particle sizes than is present in the system overall. Certain of the demixing transitions are found to be nearly continuous, accompanied by fluctuations in local particle size correlated over many lattice spacings. We explore possible factors controlling the stability of the phases and the character of the demixing transitions.

cond-mat.stat-mech↗

arXiv2010

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

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.

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arXiv2010

Monte Carlo cluster algorithm for fluid phase transitions in highly size-asymmetrical binary mixtures

Highly size-asymmetrical fluid mixtures arise in a variety of physical contexts, notably in suspensions of colloidal particles to which much smaller particles have been added in the form of polymers or nanoparticles. Conventional schemes for simulating models of such systems are hamstrung by the difficulty of relaxing the large species in the presence of the small one. Here we describe how the rejection-free geometrical cluster algorithm (GCA) of Liu and Luijten [Phys. Rev. Lett 92, 035504 (2004)] can be embedded within a restricted Gibbs ensemble to facilitate efficient and accurate studies of fluid phase behavior of highly size-asymmetrical mixtures. After providing a detailed description of the algorithm, we summarize the bespoke analysis techniques of Ashton et al. [J. Chem. Phys. 132, 074111 (2010)] that permit accurate estimates of coexisting densities and critical-point parameters. We apply our methods to study the liquid--vapor phase diagram of a particular mixture of Lennard-Jones particles having a 10:1 size ratio. As the reservoir volume fraction of small particles is increased in the range 0--5%, the critical temperature decreases by approximately 50%, while the critical density drops by some 30%. These trends imply that in our system, adding small particles decreases the net attraction between large particles, a situation that contrasts with hard-sphere mixtures where an attractive depletion force occurs.

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arXiv2010

Crystalline phases of polydisperse spheres

We use specialized Monte Carlo simulation methods and moment free energy calculations to provide conclusive evidence that dense polydisperse spheres at equilibrium demix into coexisting fcc phases, with more phases appearing as the spread of diameters increases. We manage to track up to four coexisting phases. Each of these is fractionated: it contains a narrower distribution of particle sizes than is present in the system overall. We also demonstrate that, surprisingly, demixing transitions can be nearly continuous, accompanied by fluctuations in local particle size correlated over many lattice spacings.

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arXiv2010

Grand canonical simulation of phase behaviour in highly size-asymmetrical binary fluids

We describe a Monte Carlo scheme for the grand canonical simulation study of fluid phase equilibria in highly size-asymmetrical binary mixtures. The method utilizes an expanded ensemble in which the insertion and deletion of large particles is accomplished {\em gradually} by traversing a series of states in which a large particle interacts only partially with the environment of small particles. Free energy barriers arising from interfacial coexistence states are surmounted with the aid of multicanonical preweighting, the associated weights being determined from the transition matrix. As an illustration, we present results for the liquid-vapour coexistence properties of a Lennard-Jones binary mixture having a 10:1 size ratio.

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arXiv2009

Fluid phase coexistence and critical behaviour from simulations in the restricted Gibbs ensemble

The symmetrical restricted Gibbs ensemble (RGE) is a version of the Gibbs ensemble in which particles are exchanged between two boxes of fixed equal volumes. It has recently come to prominence because -- when combined with specialized algorithms -- it provides for the study of near-coexistence density fluctuations in highly size-asymmetric binary mixtures. Hitherto, however, a detailed framework for extracting accurate estimates of critical point and coexistence curve parameters from RGE density fluctuations has been lacking. Here we address this problem by exploiting an exact link between the RGE density fluctuations and those of the grand canonical ensemble. In the sub-critical region we propose and test a simple method for obtaining accurate estimates of coexistence densities. In the critical region we identify an observable that serves as a finite system size estimator for the critical point parameters, and present a finite-size scaling theory that allows extrapolation to the thermodynamic limit.

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arXiv2008

Solid-liquid coexistence of polydisperse fluids via simulation

We describe a simulation method for the accurate study of the equilibrium freezing properties of polydisperse fluids under the experimentally relevant condition of fixed polydispersity. The approach is based on the phase switch Monte Carlo method of Wilding and Bruce [Phys. Rev. Lett. {\bf 85}, 5138 (2000)]. This we have generalized to deal with particle size polydispersity by incorporating updates which alter the diameter $σ$ of a particle, under the control of a distribution of chemical potential differences $\tildeμ(σ)$. Within the resulting isobaric semi-grand canonical ensemble, we detail how to adapt $\tildeμ(σ)$ and the applied pressure such as to study coexistence, whilst ensuring that the ensemble averaged density distribution $ρ(σ)$ matches a fixed functional form. Results are presented for the effects of small degrees of polydispersity on the solid-liquid transition of soft spheres.

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arXiv2007

A polydisperse lattice-gas model

We describe a lattice-gas model suitable for studying the generic effects of polydispersity on liquid-vapor phase equilibria. Using Monte Carlo simulation methods tailored for the accurate determination of phase behaviour under conditions of fixed polydispersity, we trace the cloud and shadow curves for a particular Schulz distribution of the polydisperse attribute. Although polydispersity enters the model solely in terms of the strengths of the interparticle interactions, this is sufficient to induce the broad separation of cloud and shadow curves seen both in more realistic models and experiments.

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arXiv2007

Phase behavior of a fluid with competing attractive and repulsive interactions

Fluids in which the interparticle potential has a hard core, is attractive at moderate separations, and repulsive at greater separations are known to exhibit novel phase behavior, including stable inhomogeneous phases. Here we report a joint simulation and theoretical study of such a fluid, focusing on the relationship between the liquid-vapor transition line and any new phases. The phase diagram is studied as a function of the amplitude of the attraction for a certain fixed amplitude of the long ranged repulsion. We find that the effect of the repulsion is to substitute the liquid-vapor critical point and a portion of the associated liquid-vapor transition line, by two first order transitions. One of these transitions separates the vapor from a fluid of spherical liquidlike clusters; the other separates the liquid from a fluid of spherical voids. At low temperature, the two transition lines intersect one another and a vapor-liquid transition line at a triple point. While most integral equation theories are unable to describe the new phase transitions, the Percus Yevick approximation does succeed in capturing the vapor-cluster transition, as well as aspects of the structure of the cluster fluid, in reasonable agreement with the simulation results.

cond-mat.soft↗

arXiv2006

Phase behaviour of a symmetrical binary fluid mixture

We have investigated the phase behaviour of a symmetrical binary fluid mixture for the situation where the chemical potentials $μ_1$ and $μ_2$ of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when $μ_1=μ_2$, the phase diagram exhibits both a liquid-vapor critical point and a tricritical point. The corresponding phase behaviour for the case $μ_1\neμ_2$ is investigated via integral-equation theory calculations within the mean spherical approximation (MSA), and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behaviour can occur, these being distinguished by the relationship between the critical lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other, is also studied, revealing interesting features.

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arXiv2006

Wetting transitions in polydisperse fluids

The properties of the coexisting bulk gas and liquid phases of a polydisperse fluid depend not only on the prevailing temperature, but also on the overall parent density. As a result, a polydisperse fluid near a wall will exhibit density-driven wetting transitions inside the coexistence region. We propose a likely topology for the wetting phase diagram, which we test using Monte Carlo simulations of a model polydisperse fluid at an attractive wall, tracing the wetting line inside the cloud curve and identifying the relationship to prewetting.

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arXiv2006

Simulation of phase transitions in highly asymmetric fluid mixtures

We present a novel method for the accurate numerical determination of the phase behavior of fluid mixtures having large particle size asymmetries. By incorporating the recently developed geometric cluster algorithm within a restricted Gibbs ensemble, we are able to probe directly the density and concentration fluctuations that drive phase transitions, but that are inaccessible to conventional simulation algorithms. We develop a finite-size scaling theory that relates these density fluctuations to those of the grand-canonical ensemble, thereby enabling accurate location of critical points and coexistence curves of multicomponent fluids. Several illustrative examples are presented.

cond-mat.soft↗

arXiv2006

Phase behaviour and particle-size cutoff effects in polydisperse fluids

We report a joint simulation and theoretical study of the liquid-vapor phase behaviour of a fluid in which polydispersity in the particle size couples to the strength of the interparticle interactions. Attention is focussed on the case in which the particles diameters are distributed according to a fixed Schulz form with degree of polydispersity $δ=14%$. The coexistence properties of this model are studied using grand canonical ensemble Monte Carlo simulations and moment free energy calculations. We obtain the cloud and shadow curves as well as the daughter phase density distributions and fractional volumes along selected isothermal dilution lines. In contrast to the case of size-{\em independent} interaction strengths (N.B. Wilding, M. Fasolo and P. Sollich, J. Chem. Phys. {\bf 121}, 6887 (2004)), the cloud and shadow curves are found to be well separated, with the critical point lying significantly below the cloud curve maximum. For densities below the critical value, we observe that the phase behaviour is highly sensitive to the choice of upper cutoff on the particle size distribution. We elucidate the origins of this effect in terms of extremely pronounced fractionation effects and discuss the likely appearance of new phases in the limit of very large values of the cutoff.

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arXiv2006

Phase behaviour of a symmetrical binary fluid mixture in a field

Integral equation theory calculations within the mean spherical approximation (MSA) and grand canonical Monte Carlo (MC) simulations are employed to study the phase behaviour of a symmetrical binary fluid mixture in the presence of a field arising from unequal chemical potentials of the two particle species. Attention is focused on the case for which, in the absence of a field, the phase diagram exhibits a first order liquid-liquid transition in addition to the liquid-vapor transition. We find that in the presence of a field, two possible subtypes of phase behaviour can occur, these being distinguished by the relationship between the critical lines in the full phase diagram of temperature, density, and concentration. We present the detailed form of the respective phase diagrams as calculated from MSA and compare with results from the MC simulations, finding good overall agreement.

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arXiv2006

Accurate simulation estimates of cloud points of polydisperse fluids

We describe two distinct approaches to obtaining cloud point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand canonical ensemble. The first method determines the chemical potential distribution $μ(σ)$ (with $σ$ the polydisperse attribute) under the constraint that the ensemble average of the particle density distribution $ρ(σ)$ matches a prescribed parent form. Within the region of phase coexistence (delineated by the cloud curve) this leads to a distribution of the fluctuating overall particle density n, p(n), that necessarily has unequal peak weights in order to satisfy a generalized lever rule. A theoretical analysis shows that as a consequence, finite-size corrections to estimates of coexistence properties are power laws in the system size. The second method assigns $μ(σ)$ such that an equal peak weight criterion is satisfied for p(n)$ for all points within the coexistence region. However, since equal volumes of the coexisting phases cannot satisfy the lever rule for the prescribed parent, their relative contributions must be weighted appropriately when determining $μ(σ)$. We show how to ascertain the requisite weight factor operationally. A theoretical analysis of the second method suggests that it leads to finite-size corrections to estimates of coexistence properties which are {\em exponentially small} in the system size. The scaling predictions for both methods are tested via Monte Carlo simulations of a novel polydisperse lattice gas model near its cloud curve, the results showing excellent quantitative agreement with the theory.

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arXiv2006

Metastable liquid-liquid coexistence and density anomalies in a core-softened fluid

Linearly-sloped or `ramp' potentials belong to a class of core-softened models which possess a liquid-liquid critical point (LLCP) in addition to the usual liquid-gas critical point. Furthermore they exhibit thermodynamic anomalies in the density and compressibility, the nature of which may be akin to those occurring in water. Previous simulation studies of ramp potentials have focused on just one functional form, for which the LLCP is thermodynamically stable. In this work we construct a series of ramp potentials, which interpolate between this previously studied form and a ramp-based approximation to the Lennard-Jones (LJ) potential. By means of Monte Carlo simulation, we locate the LLCP, the first order high density liquid (HDL)-low density liquid (LDL) coexistence line, and the line of density maxima for a selection of potentials in the series. We observe that as the LJ limit is approached, the LLCP becomes metastable with respect to freezing into a hexagonal close packed crystalline solid. The qualitative nature of the phase behaviour in this regime shows a remarkable resemblance to that seen in simulation studies of accurate water models. Specifically, the density of the liquid phase exceeds that of the solid; the gradient of the metastable LDL-HDL line is negative in the pressure (p)-temperature (T) plane; while the line of density maxima in the p-T plane has a shape similar to that seen in water and extends well into the {\em stable} liquid region of the phase diagram. As such, our results lend weight to the `second critical point' hypothesis as an explanation for the anomalous behaviour of water.

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arXiv2006

Influence of polydispersity on the critical parameters of an effective potential model for asymmetric hard sphere mixtures

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential (R. Roth {\em et al}, Phys. Rev. E{\bf 62} 5360 (2000)) designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: $q\equivσ_s/\barσ_b=0.1$ and $q=0.05$. We find that inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.

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arXiv2005

Freezing line of the Lennard-Jones fluid: a Phase Switch Monte Carlo study

We report a Phase Switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard sphere freezing, and builds on a previous PSMC study of the LJ system by Errington (J. Chem. Phys. {\bf 120}, 3130 (2004)). The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results for which we compare to a previous Gibbs-Duhem integration study. Additionally we provide new background regarding the statistical mechanical basis of the PSMC method and extensive implementation details.

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