0000000000174351
AUTHOR
Nigel B. Wilding
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.
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 wit…
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.
Concentration and energy fluctuations in a critical polymer mixture
A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the concentration distribution, the coexistence curve separating the A-rich and B-rich phases is identified as a function of temperature and chemical potential. To locate the critical point of the model, the cumulant intersection method is used. The accuracy of this approach for determining the critical parameters of fluids is assessed. Attention is then focused on the joint distribution function of the critical concentration and energy, which is analysed usi…
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, particula…
Polymeric alloys: Model materials for the understanding of the statistical thermodynamics of mixtures
Polymeric materials find industrial applications that are comparable to those of metals and ceramics.1 In addition to the great variability via the synthesis of various monomers and the choice of the degree of polymerization (N), alloying of polymers finds increasing attention for combining favorable materials properties.1,2 But polymeric (binary) alloys (A,B) of flexible polymers with chain lengths NA, NB are also most interesting for testing theoretical concepts: changing NA, NB one controls the entropy of mixing, keeping intermolecular forces invariant. Variation of these control parameters thus allows stringent tests of the theories on miscibility, unmixing etc. Furthermore, the large s…
Liquid-vapour phase behaviour of a symmetrical binary fluid mixture
Using Monte-Carlo simulation and mean field calculations, we study the liquid-vapour phase diagram of a square well binary fluid mixture as a function of a parameter $\delta$ measuring the relative strength of interactions between particles of dissimilar and similar species. The results reveal a rich variety of liquid-vapour coexistence behaviour as $\delta$ is tuned. Specifically, we uncover critical end point behaviour, a triple point involving a vapour and two liquids of different density, and tricritical behaviour. For a certain range of $\delta$, the mean field calculations also predict a `hidden' (metastable) liquid-vapour binodal.
Tricritical universality in a two-dimensional spin fluid
Monte Carlo simulations are used to investigate the tricritical point properties of a 2d spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2d Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point properties are also compared with the simulation measurements.
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 $n\ensuremath{-}1$ to $n\ensuremath{-}2$, etc.) and are accompanied by an almost periodic strain pattern, due to ``soliton staircases'' …
Errors in Monte Carlo simulations using shift register random number generators
We report large systematic errors in Monte Carlo simulations of the tricritical Blume-Capel model using single spin Metropolis updating. The error, manifest as a $20\%$ asymmetry in the magnetisation distribution, is traced to the interplay between strong triplet correlations in the shift register random number generator and the large tricritical clusters. The effect of these correlations is visible only when the system volume is a multiple of the random number generator lag parameter. No such effects are observed in related models.
Simulation studies of fluid critical behaviour
We review and discuss recent advances in the simulation of bulk critical phenomena in model fluids. In particular we emphasise the extensions to finite-size scaling theory needed to cope with the lack of symmetry between coexisting fluid phases. The consequences of this asymmetry for simulation measurements of quantities such as the particle density and the heat capacity are pointed out and the relationship to experiment is discussed. A general simulation strategy based on the finite-size scaling theory is described and its utility illustrated via Monte-Carlo studies of the Lennard-Jones fluid and a two-dimensional spin fluid model. Recent applications to critical polymer blends and solutio…