arXiv subjects

Nigel B. Wilding

Publications and source records attributed to Nigel B. Wilding.

70 records · Page 4Linked to original sources

arXiv2005

Finite-size scaling and particle size cutoff effects in phase separating polydisperse fluids

We study the liquid-vapor phase behaviour of a polydisperse fluid using grand canonical simulations and moment free energy calculations. The strongly nonlinear variation of the fractional volume of liquid across the coexistence region prevents naive extrapolation to detect the cloud point. We describe a finite-size scaling method which nevertheless permits accurate determination of cloud points and spinodals from simulations of a single system size. By varying a particle size cutoff we find that the cloud point density is highly sensitive to the presence of rare large particles; this could affect the reproducibility of experimentally measured phase behavior in colloids and polymers.

cond-mat.stat-mech↗

arXiv2005

Liquid-vapor interface of a polydisperse fluid

We report a Grand Canonical Monte Carlo simulation study of the liquid-vapor interface of a model fluid exhibiting polydispersity in terms of the particle size $σ$. The bulk density distribution, $ρ^0(σ)$, of the system is controlled by the imposed chemical potential distribution $μ(σ)$. We choose the latter such that $ρ^0(σ)$ assumes a Schulz form with associated degree of polydispersity $\approx 14%$. By introducing a smooth attractive wall, a planar liquid-vapor interface is formed for bulk state points within the region of liquid-vapor coexistence. Owing to fractionation, the pure liquid phase is enriched in large particles, with respect to the coexisting vapor. We investigate how the spatial non-uniformity of the density near the liquid-vapor interface affects the evolution of the local distribution of particle sizes between the limiting pure phase forms. We find (as previously predicted by density functional theory, Bellier-Castella {\em et al}, Phys. Rev. {\bf E65}, 021503 (2002)) a segregation of smaller particles to the interface. The magnitude of this effect is quantified for various $σ$ via measurements of the relative adsorption. Additionally, we consider the utility of various estimators for the interfacial width and highlight the difficulties of isolating the intrinsic contribution of polydispersity to this width.

cond-mat.soft↗

arXiv2004

Polydisperse hard spheres at a hard wall

The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focussed on the local density distribution $ρ(σ,z)$, measuring the number density of particles of diameter $σ$ at a distance $z$ from the wall. The form of $ρ(σ,z)$ is obtained for bulk volume fractions $η_b=0.2$ and $η_b=0.4$ for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity $δ=11.5%$ and $δ=40.4%$, and a truncated Schulz form having $δ=40.7%$. Excellent overall agreement is found between the DFT and simulation results, particularly at $η_b=0.2$. A detailed analysis of $ρ(σ,z)$ confirms the presence of oscillatory size segregation effects observed in a previous DFT study (Pagonabarraga {\em et al.}, Phys. Rev. Lett. {\bf 84}, 911 (2000)). For large $δ$, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive $σ$-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity $δ(z)$ is suppressed in this region, while further from the wall it exhibits oscillations.

cond-mat.soft↗

arXiv2004

Liquid-gas coexistence and critical point shifts in size-disperse fluids

Specialized Monte Carlo simulations and the moment free energy (MFE) method are employed to study liquid-gas phase equilibria in size-disperse fluids. The investigation is made subject to the constraint of fixed polydispersity, i.e. the form of the `parent' density distribution $ρ^0(σ)$ of the particle diameters $σ$, is prescribed. This is the experimentally realistic scenario for e.g. colloidal dispersions. The simulations are used to obtain the cloud and shadow curve properties of a Lennard-Jones fluid having diameters distributed according to a Schulz form with a large (40%) degree of polydispersity. Good qualitative accord is found with the results from a MFE method study of a corresponding van der Waals model that incorporates size-dispersity both in the hard core reference and the attractive parts of the free energy. The results show that polydispersity engenders considerable broadening of the coexistence region between the cloud curves. The principal effect of fractionation in this region is a common overall scaling of the particle sizes and typical inter-particle distances, and we discuss why this effect is rather specific to systems with Schulz diameter distributions. Next, by studying a family of such systems with distributions of various widths, we estimate the dependence of the critical point parameters on $δ$. In contrast to a previous theoretical prediction, size-dispersity is found to raise the critical temperature above its monodisperse value. Unusually for a polydisperse system, the critical point is found to lie at or very close to the extremum of the coexistence region in all cases. We outline an argument showing that such behaviour will occur whenever size polydispersity affects only the range, rather than the strength of the inter-particle interactions.

cond-mat.soft↗

arXiv2004

Phase equilibria and fractionation in a polydisperse fluid

We describe how Monte Carlo simulation within the grand canonical ensemble can be applied to the study of phase behaviour in polydisperse fluids. Attention is focused on the case of fixed polydispersity in which the form of the `parent' density distribution $ρ^\circ(σ)$ of the polydisperse attribute $σ$ is prescribed. Recently proposed computational methods facilitate determination of the chemical potential distribution conjugate to $ρ^\circ(σ)$. By additionally incorporating extended sampling techniques within this approach, the compositions of coexisting (`daughter') phases can be obtained and fractionation effects quantified. As a case study, we investigate the liquid-vapor phase equilibria of a size-disperse Lennard-Jones fluid exhibiting a large ($δ=40%$) degree of polydispersity. Cloud and shadow curves are obtained, the latter of which exhibit a high degree of fractionation with respect to the parent. Additionally, we observe considerable broadening of the coexistence region relative to the monodisperse limit.

cond-mat.stat-mech↗

arXiv2003

Continuous demixing at liquid-vapor coexistence in a symmetrical binary fluid mixture

We report a Monte Carlo finite-size scaling study of the demixing transition of a symmetrical Lennard-Jones binary fluid mixture. For equal concentration of species, and for a choice of the unlike-to-like interaction ratio delta=0.7, this transition is found to be continuous at liquid-vapor coexistence. The associated critical end point exhibits Ising-like universality. These findings confirm those of earlier smaller scale simulation studies of the same model, but contradict the findings of recent integral equation and hierarchical reference theory investigations.

cond-mat.stat-mech↗

arXiv2002

Phase behaviour and thermodynamic anomalies of core-softened fluids

We report extensive simulation studies of phase behaviour in single component systems of particles interacting via a core-softened interparticle potential. Two recently proposed examples of such potentials are considered; one in which the hard core exhibits a shoulder, (Sadr-Lahijany et al, Phys. Rev. Lett. 81, 4895 (1998)) and the other in which the softening takes the form of a linear ramp (Jagla, Phys. Rev. E63, 061501 (2001)). Using a combination of state-of-the-art Monte Carlo methods, we obtain the gas, liquid and solid phase behaviour of the shoulder model in two dimensions. We then focus on the thermodynamic anomalies of the liquid phase, namely maxima in the density and compressibility as a function of temperature. Analysis of the finite-size behaviour of these maxima suggests that, rather than stemming from a metastable liquid-liquid critical point, as previously supposed, they are actually induced by the quasi-continuous nature of the two dimensional freezing transition. For the ramp model in three dimensions, we confirm the existence of a stable liquid-liquid ("second") critical point occurring at higher pressure and lower temperature than the liquid-gas critical point. Both these critical points and portions of their associated coexistence curves are located to high precision. In contrast to the shoulder model, the observed thermodynamic anomalies of this model are found to be authentic, i.e. they are not engendered by an incipient new phase. We trace the locus of density and compressibility maxima, the former of which appears to converge on the second critical point.

cond-mat.stat-mech↗

arXiv2001

Grand canonical ensemble simulation studies of polydisperse fluids

We describe a Monte Carlo scheme for simulating polydisperse fluids within the grand canonical ensemble. Given some polydisperse attribute $σ$, the state of the system is described by a density distribution $ρ(σ)$ whose form is controlled by the imposed chemical potential distribution $μ(σ)$. We detail how histogram extrapolation techniques can be employed to tune $μ(σ)$ such as to traverse some particular desired path in the space of $ρ(σ)$. The method is applied in simulations of size-disperse hard spheres with densities distributed according to Schulz and log-normal forms. In each case, the equation of state is obtained along the dilution line, i.e. the path along which the scale of $ρ(σ)$ changes but not its shape. The results are compared with the moment-based expressions of Boublik et al (J. Chem. Phys. {\bf 54}, 1523 (1971)) and Salacuse and Stell (J. Chem. Phys. {\bf 77}, 3714 (1982)). It is found that for high degrees of polydispersity, both expressions fail to give a quantitatively accurate description of the equation of state when the overall volume fraction is large.

cond-mat.stat-mech↗

arXiv2001

The Lennard-Jones-Devonshire cell model revisited

We reanalyse the cell theory of Lennard-Jones and Devonshire and find that in addition to the critical point originally reported for the 12-6 potential (and widely quoted in standard textbooks), the model exhibits a further critical point. We show that the latter is actually a more appropriate candidate for liquid-gas criticality than the original critical point.

cond-mat.soft↗

arXiv1999

Monte Carlo investigations of phase transitions: status and perspectives

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.

cond-mat.stat-mech↗

arXiv1999

Absence of simulation evidence for critical depletion in slit-pores

Recent Monte Carlo simulation studies of a Lennard-Jones fluid confined to a mesoscopic slit-pore have reported evidence for ``critical depletion'' in the pore local number density near the liquid-vapour critical point. In this note we demonstrate that the observed depletion effect is in fact a simulation artifact arising from small systematic errors associated with the use of long range corrections for the potential truncation. Owing to the large near-critical compressibility, these errors lead to significant changes in the pore local number density. We suggest ways of avoiding similar problems in future studies of confined fluids.

cond-mat.stat-mech↗

arXiv1997

Critical end point behaviour in a binary fluid mixture

We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particularly that in the coexistence diameter, should also be detectable experimentally.

cond-mat.stat-mech↗

arXiv1997

Coexistence Curve Singularities at Critical End Points

We report an extensive Monte Carlo study of critical end point behaviour in a symmetrical binary fluid mixture. On the basis of general scaling arguments, singular behaviour is predicted in the diameter of the liquid-gas coexistence curve as the critical end point is approached. The simulation results show clear evidence for this singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential. Both singularities should be detectable experimentally.

cond-mat.stat-mech↗

arXiv1995

Critical point and coexistence curve properties of the Lennard-Jones fluid: A finite-size scaling study

Monte Carlo simulations within the grand canonical ensemble are used to explore the liquid-vapour coexistence curve and critical point properties of the Lennard-Jones fluid. Attention is focused on the joint distribution of density and energy fluctuations at coexistence. In the vicinity of the critical point, this distribution is analysed using mixed-field finite-size scaling techniques aided by histogram reweighting methods. The analysis yields highly accurate estimates of the critical point parameters, as well as exposing the size and character of corrections to scaling. In the sub-critical coexistence region the density distribution is obtained by combining multicanonical simulations with histogram reweighting techniques. It is demonstrated that this procedure permits an efficient and accurate mapping of the coexistence curve, even deep within the two phase region.

cond-mat↗

arXiv1994

Liquid-vapour asymmetry in pure fluids: A Monte Carlo simulation study

Monte Carlo simulations within the grand canonical ensemble are used to obtain the joint distribution of density and energy fluctuations $p_L(ρ,u)$ for two model fluids: a decorated lattice gas and a polymer system. In the near critical region the form of $p_L(ρ,u)$ is analysed using a mixed field finite-size-scaling theory that takes account of liquid-vapour asymmetry. Field mixing transformations are performed that map $p_L(ρ,u)$ onto the joint distribution of critical scaling operators \ptMEstar\ appropriate to the Ising fixed point. Carrying out this procedure permits a very accurate determination of the critical point parameters. By forming various projections of \ptMEstar , the full universal finite-size spectrum of the critical density and energy distributions of fluids is also obtained. In the sub-critical coexistence region, an examination is made of the influence of field mixing on the asymmetry of the density distribution.

cond-mat↗

arXiv1994

Accurate Measurements of the Chemical Potential of Polymeric Systems by Monte-Carlo Simulation

We present a new Monte-Carlo method for estimating the chemical potential of model polymer systems. The method is based upon the gradual insertion of a penetrable `ghost' polymer into the system and is effective for large chain lengths and at high densities. Insertion of the ghost chain is facilitated by use of an expanded ensemble in which weighted transitions are permitted between states characterising the strength of the excluded volume and thermal interactions experienced by the ghost chain. We discuss the implementation and optimisation of the method within the framework of the bond fluctuation model, and demonstrate its precision by a calculation of the finite-size corrections to the chemical potential.

cond-mat↗