Molecular dynamics simulations of a fluid near its critical point

Finite-size scaling study of dynamic critical phenomena in a vapor-liquid transition

Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the model has been obtained via the Monte Carlo simulations. The transport properties, viz., the bulk viscosity and the thermal conductivity, are calculated via the Green-Kubo relations, by taking inputs from the MD simulations in the microcanonical ensemble. The critical singularities of these quantities are estimated via the FSS method. The results thus obtained are in nice agreement with the predictions of the dynamic renormalization group and mode-coupling theories.

Finite-size scaling study of shear viscosity anomaly at liquid-liquid criticality

We study the equilibrium dynamics of a symmetrical binary Lennard-Jones fluid mixture near its consolute criticality. Molecular dynamics simulation results for the shear viscosity, η, from a microcanonical ensemble are compared with those from a canonical ensemble with various thermostats. It is observed that the Nosé-Hoover thermostat is a good candidate for this purpose, and is therefore adopted for the quantification of the critical singularity of η, to avoid the temperature fluctuations (or even drifts) that are often encountered in microcanonical simulations. Via a finite-size scaling analysis of our simulation data we have been able to confirm that the shear viscosity exhibits a weak critical singularity in agreement with the theoretical predictions.

Simulation of transport around the coexistence region of a binary fluid

We use Monte Carlo and molecular dynamics simulations to study phase behavior and transport properties in a symmetric binary fluid where particles interact via Lennard-Jones potential. Our results for the critical behavior of collective transport properties, with particular emphasis on bulk viscosity, is understood via appropriate application of finite-size scaling technique. It appears that the critical enhancements in these quantities are visible far above the critical point. This result is consistent with an earlier report from computer simulations where, however, the authors do not quantify the critical singularity.

Critical dynamics of an isothermal compressible nonideal fluid

A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible nonideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.

Simulation of static critical phenomena in nonideal fluids with the lattice Boltzmann method

A fluctuating nonideal fluid at its critical point is simulated with the lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order parameter.

Composition fluctuations, chemical exchange, and nuclear relaxation in membranes containing cholesterol

A thermodynamic model of cholesterol-phospholipid complexes is used as a starting point for calculating fluctuations in membranes containing cholesterol and phospholipids. The calculations describe fluctuations in the concentration of complexes formed between cholesterol and phospholipids with longer saturated fatty acid chains. The fluctuations in complex concentrations arise by two distinct mechanisms. In one, the chemical composition of the sample varies from point to point, and the concentration of the complexes varies according to local chemical equilibrium. In the second, the composition remains fixed, and the complexes form and dissociate according to chemical reaction kinetics. In both cases the nuclear resonance frequency of a deuterium labeled phospholipid undergoes fluctuations and line broadening as a consequence of the formation and dissociation of complexes. For a specific ternary lipid mixture at its critical composition, deuterium nuclear resonance line broadening of chain labeled phospholipids is calculated for temperatures up to 10 degrees -20 degrees above the miscibility critical temperature. This line broadening is associated with fluctuations in the degree of phospholipid chain ordering related to the formation and dissociation of complexes.

Static and dynamic critical behavior of a symmetrical binary fluid: A computer simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for T<T(c) and at the critical concentration, x(c)=12, for T>T(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.

Critical dynamics in a binary fluid: simulations and finite-size scaling

We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories provided finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.

Universal dynamic exponent at the liquid-gas transition from molecular dynamics

The liquid-gas system is expected to exhibit distinct dynamic behavior in the fluid's critical region (model H). We present molecular dynamics simulations of a Lennard-Jones fluid model starting from specially designed, near-equilibrium, initial conditions. By following the fluid's relaxation towards equilibrium, we calculate the requisite transport coefficients in the critical region. The results yield the scaling behavior of the thermal diffusion coefficient D(T) approximately xi(-1.023+/-0.018) (xi is the correlation length) and a nonconventional divergent heat conductivity, all of which are in accord with mode-coupling and renormalization group predictions, as well as some experimental data.

Demixing can occur in binary hard-sphere mixtures with negative nonadditivity

A binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma = sigma(2)/sigma(1) < 1 and a nonadditivity parameter Delta = 2 sigma(12)/(sigma(1) + sigma(2)) - 1 is considered in infinitely many dimensions. From the equation of state in the second virial approximation (which is exact in the limit d--> infinity) a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2(-d) is found, even for slightly negative nonadditivity, if Delta >-1/8 (ln gamma)(2). Arguments concerning the stability of the demixing with respect to freezing are provided.

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.

Equation of state of nonadditive d-dimensional hard-sphere mixtures

An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. Lopez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.

Cluster algorithm for nonadditive hard-core mixtures

In this paper, we present a cluster algorithm for the numerical simulations of nonadditive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than previous simulations. The phase separation for symmetric binary mixtures is studied for different nonadditivities as well as for the Widom-Rowlinson model [B. Widom and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] in two and three dimensions. The critical densities are determined from finite size scaling. The critical exponents for all the nonadditivities are consistent with the Ising universality class.