arXiv subjects

Nigel B. Wilding

Publications and source records attributed to Nigel B. Wilding.

At least 37 records · Page 2Linked to original sources

arXiv2018

DL_MONTE: A multipurpose code for Monte Carlo simulation

DL_MONTE is an open source, general-purpose software package for performing Monte Carlo simulations. It includes a wide variety of force fields and MC techniques, and thus is applicable to a broad range of problems in molecular simulation. Here we provide an overview of DL_MONTE, focusing on key features recently added to the package. These include the ability to treat systems confined to a planar pore (i.e. `slit' or `slab' boundary conditions); the lattice-switch Monte Carlo (LSMC) method for evaluating precise free energy differences between competing polymorphs; various commonly-used methods for evaluating free energy profiles along transition pathways (including umbrella sampling, Wang-Landau and transition matrix); and a supplementary Python toolkit for simulation management and application of the histogram reweighting analysis method. We provide two `real world' examples to elucidate the use of these methods in DL_MONTE. In particular, we apply umbrella sampling to calculate the free energy profile associated with the translocation of a lipid through a bilayer. Moreover we employ LSMC to examine the thermodynamic stability of two plastic crystal phases of water at high pressure. Beyond this, we provide instructions on how to access DL_MONTE, and point to additional information valuable to existing and prospective users.

physics.comp-ph↗

arXiv2018

Composition inversion in mixtures of binary colloids and polymer

Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered "simple". Here we consider a very simple mixture of two colloidal and one non-adsorbing polymer species which can be simplified even further to a size-asymmetrical binary mixture, in which the effective colloid-colloid interactions depend on the polymer concentration. We show that this basic system exhibits surprisingly rich phase behaviour. In particular, we enquire whether such a system features only a liquid-vapor phase separation (as in one-component colloid-polymer mixtures) or whether, additionally, liquid-liquid demixing of two colloidal phases can occur. Particle-resolved experiments show demixing-like behaviour, but when combined with bespoke Monte Carlo simulations, this proves illusory, and we reveal that only a single liquid-vapor transition occurs. Progressive migration of the small particles to the liquid phase as the polymer concentration increases gives rise to composition inversion - a maximum in the large particle concentration in the liquid phase. Near criticality the density fluctuations are found to be dominated by the larger colloids.

cond-mat.soft↗

arXiv2017

Disappearance of the hexatic phase in a binary mixture of hard disks

Recent studies of melting in hard disks have confirmed the existence of a hexatic phase occurring in a narrow window of density which is separated from the isotropic liquid phase by a first-order transition, and from the solid phase by a continuous transition. However, little is known concerning the melting scenario in mixtures of hard disks. Here we employ specialized Monte Carlo simulations to elucidate the phase behavior of a system of large ($l$) and small ($s$) disks with diameter ratio $σ_l/σ_s=1.4$. We find that as small disks are added to a system of large ones, the stability window of the hexatic phase shrinks progressively until the line of continuous transitions terminates at an end point beyond which melting becomes a first-order liquid-solid transition. This occurs at surprisingly low concentrations of the small disks, $c\lesssim 1\%$, emphasizing the fragility of the hexatic phase. We speculate that the change to the melting scenario is a consequence of strong fractionation effects, the nature of which we elucidate.

cond-mat.stat-mech↗

arXiv2017

Drying and Wetting Transitions of a Lennard-Jones Fluid: Simulations and Density Functional Theory

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay, or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, ie. in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent $ν_\parallel$ which controls the parallel correlation length, i.e. the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. We suggest reasons for this discrepancy.

cond-mat.stat-mech↗

arXiv2016

Critical Drying of Liquids

We report a detailed simulation and classical density functional theory study of the drying transition in a realistic model fluid at a smooth substrate. This transition (in which the contact angle $θ\to 180^\circ$) is shown to be critical for both short ranged and long-ranged substrate-fluid interaction potentials. In the latter case critical drying occurs at exactly zero attractive substrate strength. This observation permits the accurate elucidation of the character of the transition via a finite-size scaling analysis of the density probability function. We find that the critical exponent $ν_\parallel$ that controls the parallel correlation length, i.e. the extent of vapor bubbles at the wall, is over twice as large as predicted by mean field and renormalization group calculations. We suggest a reason for the discrepancy. Our findings shed new light on fluctuation phenomena in fluids near hydrophobic and solvophobic interfaces.

cond-mat.stat-mech↗

arXiv2016

Coarse-grained depletion potentials for anisotropic colloids: application to lock-and-key systems

When a colloid is mixed with a depletant such as a non-adsorbing polymer, one observes attractive effective interactions between the colloidal particles. If these particles are anisotropic, analysis of these effective interactions is challenging in general. We present a method for inference of approximate (coarse-grained) effective interaction potentials between such anisotropic particles. Using the example of indented (lock-and-key) colloids, we show how numerical solutions can be used to integrate out the (hard sphere) depletant, leading to a depletion potential that accurately characterises the effective interactions. The accuracy of the method is based on matching of contributions to the second virial coefficient of the colloids. The simplest version of our method yields a piecewise-constant effective potential; we also show how this scheme can be generalised to other functional forms, where appropriate.

cond-mat.soft↗

arXiv2015

Improved grand canonical sampling of vapour-liquid transitions

Simulation within the grand canonical ensemble is the method of choice for accurate studies of first order vapour-liquid phase transitions in model fluids. Such simulations typically employ sampling that is biased with respect to the overall number density in order to overcome the free energy barrier associated with mixed phase states. However, at low temperature and for large system size, this approach suffers a drastic slowing down in sampling efficiency. The culprits are geometrically induced transitions (stemming from the periodic boundary conditions) which involve changes in droplet shape from sphere to cylinder and cylinder to slab. Since the overall number density doesn't discriminate sufficiently between these shapes, it fails as an order parameter for biasing through the transitions. Here we report two approaches to ameliorating these difficulties. The first introduces a droplet shape based order parameter that generates a transition path from vapour to slab states for which spherical and cylindrical droplet are suppressed. The second simply biases with respect to the number density in a tetragonal subvolume of the system. Compared to the standard approach, both methods offer improved sampling, allowing estimates of coexistence parameters and vapor-liquid surface tension for larger system sizes and lower temperatures.

cond-mat.stat-mech↗

arXiv2015

Quantifying density fluctuations in water at a hydrophobic surface: evidence for critical drying

Employing smart Monte Carlo sampling techniques within the grand canonical ensemble, we investigate the properties of water at a model hydrophobic substrate. By reducing the strength of substrate-water attraction we find that fluctuations in the local number density, quantified by a rigorous definition of the local compressibility $χ(z)$, increase rapidly for distances $z$ within $1$ or $2$ molecular diameters from the substrate as the degree of hydrophobicity, measured by the macroscopic contact angle $θ$, increases. Our simulations provide evidence for a continuous (critical) drying transition as the substrate-water interaction becomes very weak: $\cos(θ)\to -1$. We speculate that the existence of such a transition might account for earlier simulation observations of strongly enhanced density fluctuations.

cond-mat.stat-mech↗

arXiv2015

Unusual liquid phases for indented colloids with depletion interactions

We study indented spherical colloids, interacting via depletion forces. These systems exhibit liquid-vapor phase transitions whose properties are determined by a combination of strong "lock-and-key" bonds and weaker non-specific interactions. As the propensity for lock-and-key binding increases, the critical point moves to significantly lower density, and the coexisting phases change their structure. In particular, the liquid phase is "porous", exhibiting large percolating voids. The properties of this system depend strongly on the topological structure of an underlying bond network: we comment on the implications of this fact for the assembly of equilibrium states with controlled porous structures.

cond-mat.soft↗

arXiv2014

Self-assembly and crystallisation of indented colloids at a planar wall

We report experimental and simulation studies of the structure of a monolayer of indented ("lock and key") colloids, on a planar surface. On adding a non-absorbing polymer with prescribed radius and volume fraction, depletion interactions are induced between the colloids, with controlled range and strength. For spherical particles, this leads to crystallisation, but the indented colloids crystallise less easily than spheres, in both simulation and experiment. Nevertheless, simulations show that indented colloids do form plastic (rotator) crystals. We discuss the conditions under which this occurs, and the possibilities of lower-symmetry crystal states. We also comment on the kinetic accessibility of these states.

cond-mat.soft↗

arXiv2014

Demixing cascades in cluster crystals

In a cluster crystal, each lattice site is occupied by multiple soft-core particles. As the number density is increased at zero temperature, a `cascade' of isostructural phase transitions can occur between states whose site occupancy differs by unity. For low but finite temperature, each of these transitions terminates in a critical point. Using tailored Monte Carlo simulation techniques we have studied such demixing cascades in systems of soft particles interacting via potentials of the generalized exponential form $u(r)=ε\exp[-(r/σ)^n]$. We have estimated the critical parameters of the first few transitions in the cascade as a function of the softness parameter $n$. The critical temperature and pressure exhibit non-monotonic behaviour as $n$ is varied, although the critical chemical potential remains monotonic. The trends for the pressure and chemical potential are confirmed by cell model calculations at zero temperature. As $n\to 2^+$, all the transitions that we have observed are preempted by melting although we cannot rule out that clustering transitions survive at high density.

cond-mat.soft↗

arXiv2014

Three-body interactions in complex fluids: virial coefficients from simulation finite-size effects

A simulation technique is described for quantifying the contribution of three-body interactions to the thermodynamical properties of coarse-grained representations of complex fluids. The method is based on comparing the third virial coefficient $B_3$ for a complex fluid with that of an approximate coarse-grained model described by a pair potential. To obtain $B_3$ we introduce a new technique which expresses its value in terms of the measured volume-dependent asymptote of a certain structural function. The strategy is applicable to both Molecular Dynamics and Monte Carlo simulation. Its utility is illustrated via measurements of three-body effects in models of star polymer and highly size-asymmetrical colloid-polymer mixtures.

cond-mat.soft↗

arXiv2014

Self-assembly of colloidal polymers via depletion-mediated lock and key binding

We study the depletion-induced self-assembly of indented colloids. Using state-of-the-art Monte Carlo simulation techniques that treat the depletant particles explicitly, we demonstrate that colloids assemble by a lock-and-key mechanism, leading to colloidal polymerization. The morphology of the chains that are formed depends sensitively on the size of the colloidal indentation, with smaller values additionally permitting chain branching. In contrast to the case of spheres with attractive patches, Wertheim's thermodynamic perturbation theory fails to provide a fully quantitative description of the polymerization transition. We trace this failure to a neglect of packing effects and we introduce a modified theory that accounts better for the shape of the colloids, yielding improved agreement with simulation.

cond-mat.soft↗

arXiv2014

Quantifying the effects of neglecting many-body interactions in coarse-grained models of complex fluids

We describe a general simulation scheme for assessing the thermodynamic consequences of neglecting many-body effects in coarse-grained models of complex fluids. The method exploits the fact that the asymptote of a simple-to-measure structural function provides direct estimates of virial coefficients. Comparing the virial coefficients of an atomistically detailed system with those of a coarse-grained version described by pair potentials, permits the role of many-body effects to be quantified. The approach is applied to two models: (i) a size-asymmetrical colloid-polymer mixture, and (ii) a solution of star polymers. In the latter case, coarse-graining to an effective fluid described by pair potentials is found to neglect important aspects of the true behaviour.

cond-mat.soft↗

arXiv2012

A Monte Carlo method for chemical potential determination in single and multiple occupancy crystals

We describe a Monte Carlo scheme which, in a single simulation, yields a measurement of the chemical potential of a crystalline solid. Within the isobaric ensemble, this immediately provides an estimate of the system free energy, with statistical uncertainties that are determined precisely and transparently. An extension to multiple occupancy ("cluster") solids permits the direct determination of the cluster chemical potential and hence the equilibrium conditions. We apply the method to a model exhibiting cluster crystalline phases, where we find evidence for an infinite cascade of critical points terminating coexistence between crystals of differing site occupancies.

cond-mat.stat-mech↗

arXiv2012

Transitions between imperfectly ordered crystalline structures: A phase switch Monte Carlo study

A model for two-dimensional colloids confined laterally by "structured boundaries" (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance D between the confining walls is reduced at constant particle number from an initial value D_0, for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from n to n-1 to n-2 etc.) and are accompanied by an almost periodic strain pattern, due to "soliton staircases" along the boundaries. Since standard simulation studies of such transitions are hampered by huge hysteresis effects, we apply the phase switch Monte Carlo method to estimate the free energy difference between the structures as a function of the misfit between D and D_0, thereby locating where the transitions occurs in equilibrium. For comparison, we also obtain this free energy difference from a thermodynamic integration method: the results agree, but the effort required to obtain the same accuracy as provided by phase switch Monte Carlo would be at least three orders of magnitude larger. We also show for a situation where several "candidate structures" exist for a phase, that phase switch Monte Carlo can clearly distinguish the metastable structures from the stable one. Finally, applying the method in the conjugate statistical ensemble (where the normal pressure conjugate to D is taken as an independent control variable) we show that the standard equivalence between the conjugate ensembles of statistical mechanics is violated.

cond-mat.stat-mech↗

arXiv2011

Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of accurate simulation results with theory

We report a detailed study, using state-of-the-art simulation and theoretical methods, of the depletion potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q=σ_s/σ_b. Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir, η_s^r. Two specialized Monte Carlo simulation schemes --the geometrical cluster algorithm, and staged particle insertion-- are deployed to obtain accurate depletion potentials for a number of combinations of q\leq 0.1 and η_s^r. After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely η_s^r=0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this η_s^r. The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small sphere packing fractions that we consider. The effective potentials from simulation, DFT and the morphometric approximation were used to compute the second virial coefficient B_2 as a function of η_s^r. Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity towards fluid fluid phase separation in additive binary hard sphere mixtures with q\leq 0.1.

cond-mat.stat-mech↗

arXiv2011

Accurate simulation estimates of phase behaviour in ternary mixtures with prescribed composition

This paper describes an isobaric semi-grand canonical ensemble Monte Carlo scheme for the accurate study of phase behaviour in ternary fluid mixtures under the experimentally relevant conditions of prescribed pressure, temperature and overall composition. It is shown how to tune the relative chemical potentials of the individual components to target some requisite overall composition and how, in regions of phase coexistence, to extract accurate estimates for the compositions and phase fractions of individual coexisting phases. The method is illustrated by tracking a path through the composition space of a model ternary Lennard-Jones mixture.

cond-mat.stat-mech↗