Simple Dense Fluids Research Articles

Generalized Rosenfeld–Tarazona scaling and high-density specific heat of simple liquids

The original Rosenfeld–Tarazona (RT) scaling of the excess energy in simple dense fluids predicts a ∝T3/5 thermal correction to the fluid Madelung energy. This implies that the excess isochoric heat capacity scales as Cvex∝T−2/5. Careful examination performed in this paper demonstrates that the exponent −2/5 is not always optimal. For instance, in the Lennard-Jones fluid in some vicinity of the triple point, the exponent −1/3 turns out to be more appropriate. The analysis of the specific heat data in neon, argon, krypton, xenon, and liquid mercury reveals that no single value of the exponent exists, describing all the data simultaneously. Therefore, we propose a generalized RT scaling in the form Cvex∝T−α, where α is a density- and material-dependent adjustable parameter. The question concerning which material properties and parameters affect the exponent α and whether it can be predicted from general physical arguments requires further investigation.

Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids.

Since the mid-1980s, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the transition from the fluid state to the glassy state. MCT, however, is limited by the approximations used in its construction and lacks an unambiguous mechanism to institute corrections. We use recent results from a new theoretical framework--developed from first principles via a self-consistent perturbation expansion in terms of an effective two-body potential--to numerically explore the kinetics of systems of classical particles, specifically hard spheres governed by Smoluchowski dynamics. We present here a full solution for such a system to the kinetic equation governing the density-density time correlation function and show that the function exhibits the characteristic two-step decay of supercooled fluids and an ergodic-nonergodic transition to a dynamically arrested state. Unlike many previous numerical studies--and in stark contrast to experiment--we have access to the full time and wave-number range of the correlation function with great precision and are able to track the solution unprecedentedly close to the transition, covering nearly 15 decades in scaled time. Using asymptotic approximation techniques analogous to those developed for MCT, we fit the solution to predicted forms and extract critical parameters. We find complete qualitative agreement with known glassy behavior (e.g. power-law divergence of the α-relaxation time scale in the ergodic phase and square-root growth of the glass form factors in the nonergodic phase), as well as some limited quantitative agreement [e.g. the transition at packing fraction η*=0.60149761(10)], consistent with previous static solutions under this theory and with comparable colloidal suspension experiments. However, most importantly, we establish that this new theory is able to reproduce the salient features seen in other theories, experiments, and simulations but has the advantages of being derived from first principles and possessing a clear mechanism for making systematic corrections.

Universal long-time dynamics in dense simple fluids.

Dense simple fluids appear to have a long-time, very slowly evolving state which--for high-enough density--approaches a glassy, nonergodic phase. In this high-density regime, the equilibrating system decays via a three-step process as identified in mode-coupling theory (MCT). MCT, however, is an inherently phenomenological theory without prospects for improvement, and so a systematic theory has been recently developed which naturally allows one to calculate cumulants between the fundamental particle density and response fields self-consistently in a perturbation expansion in a pseudopotential. This paper details the extension of this theory and specifically addresses the universal nature of this erogodic-nonergodic transition. We find that the nonergodic state can be characterized by the associated static equilibrium state, and--nontrivially--that these states are identical regardless of whether a system is driven by Smoluchowski or Newtonian dynamics. In addition, though the specific response fields differ between Smoluchowski and Newtonian dynamics, the two share identical linear fluctuation-dissipation relations connecting the ρ-B cumulants. While we show this universality of nonergodic states within perturbation theory, we expect it to be true more generally. At leading order in the perturbation expansion, one obtains a kinetic kernel quadratic in the density analogous to the "one-loop" theory of MCT. At this one-loop level one finds vertex corrections which depend on the three-point equilibrium cumulants. Here we assume these vertex-corrections can be ignored and instead focus on computing the contributions of higher-order loops. We show that it is possible to sum up all of the loop contributions and find that these higher-order loops do not change the nonergodic state parameters substantially.

Power-law Decay and the Ergodic–Nonergodic Transition in Simple Fluids

It is well known that mode coupling theory (MCT) leads to a two-step power-law time decay in dense simple fluids. We show that much of the mathematical machinery used in the MCT analysis can be taken over to the analysis of the systematic theory developed in the Fundamental Theory of Statistical Particle Dynamics (Mazenko in Phys Rev E 81(6):061102, 2010). We show how the power-law exponents can be computed in the second-order approximation where we treat hard-sphere fluids with statics described by the Percus–Yevick solution.

Structure and interactions in fluids of prolate colloidal ellipsoids: Comparison between experiment, theory, and simulation

The microscopic structure of fluids of simple spheres is well known. However, the constituents of most real-life fluids are non-spherical, leading to a coupling between the rotational and translational degrees of freedom. The structure of simple dense fluids of spheroids - ellipsoids of revolution - was only recently determined by direct experimental techniques [A. P. Cohen, E. Janai, E. Mogilko, A. B. Schofield, and E. Sloutskin, Phys. Rev. Lett. 107, 238301 (2011)]. Using confocal microscopy, it was demonstrated that the structure of these simple fluids cannot be described by hard particle models based on the widely used Percus-Yevick approximation. In this paper, we describe a new protocol for determining the shape of the experimental spheroids, which allows us to expand our previous microscopy measurements of these fluids. To avoid the approximations in the theoretical approach, we have also used molecular dynamics simulations to reproduce the experimental radial distribution functions g(r) and estimate the contribution of charge effects to the interactions. Accounting for these charge effects within the Percus-Yevick framework leads to similar agreement with the experiment.

Nanoscale simple-fluid behavior under steady shear

In this study, we use two nonequilibrium molecular dynamics algorithms, boundary-driven shear and homogeneous shear, to explore the rheology and flow properties of a simple fluid undergoing steady simple shear. The two distinct algorithms are designed to elucidate the influences of nanoscale confinement. The results of rheological material functions, i.e., viscosity and normal pressure differences, show consistent Newtonian behaviors at low shear rates from both systems. The comparison validates that confinements of the order of 10 nm are not strong enough to deviate the simple fluid behaviors from the continuum hydrodynamics. The non-Newtonian phenomena of the simple fluid are further investigated by the homogeneous shear simulations with much higher shear rates. We observe the "string phase" at high shear rates by applying both profile-biased and profile-unbiased thermostats. Contrary to other findings where the string phase is found to be an artifact of the thermostats, we perform a thorough analysis of the fluid microstructures formed due to shear, which shows that it is possible to have a string phase and second shear thinning for dense simple fluids.

Introduction to Special Issue on Water and Associated Liquids

In the past 40 years there has been major progress in developing a quantitative as well as qualitative understanding of the structural and thermodynamic properties of dense simple fluids and fluid mixtures both in bulk and at their liquid-vapor interfaces. Relatively simple theories are possible because in bulk systems the slowly varying attractive van der Waals forces on a given molecule tends to cancel and the liquid structure is dominated by the packing of the harshly repulsive molecular cores. At interfaces and in other nonuniform environments attractive forces no longer cancel but their averaged effects can be accurately treated by a simple mean field theory. Associated liquids present new and more difficult problems that are the focus of much current research, as illustrated by work in this special issue. Here we imagine there exist a small set of very strong but directionally localized attractive interactions that can compete efficiently with the core packing forces, generally producing a smaller number of strongly bonded neighbors than are generated by core forces alone. Under appropriate conditions this can lead to fluids with fluctuating networks of nearest neighbor bonds. Workers in this area often use model potentials that incorporate this physics in the simplest possible way and try to arrive at a theoretical understanding of their consequences. Determining typical configurations even in bulk systems is highly nontrivial. Incorporating large solutes or forming an extended interface necessarily disrupts the bulk bond network and this introduces additional theoretical and practical challenges.

Anomalous nanoparticle diffusion in polymer solutions and melts: A mode-coupling theory study

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.

Phase behavior of a simple dipolar fluid under shear flow in an electric field

Nonequilibrium molecular dynamics simulations are performed on a dense simple dipolar fluid under a planar Couette shear flow. Shear generates heat, which is removed by thermostatting terms added to the equations of motion of the fluid particles. The spatial structure of simple fluids at high shear rates is known to depend strongly on the thermostatting mechanism chosen. Kinetic thermostats are either biased or unbiased: biased thermostats neglect the existence of secondary flows that appear at high shear rates superimposed upon the linear velocity profile of the fluid. Simulations that employ a biased thermostat produce a string phase where particles align in strings with hexagonal symmetry along the direction of the flow. This phase is known to be a simulation artifact of biased thermostatting, and has not been observed by experiments on colloidal suspensions under shear flow. In this paper, we investigate the possibility of using a suitably directed electric field, which is coupled to the dipole moments of the fluid particles, to stabilize the string phase. We explore several thermostatting mechanisms where either the kinetic or configurational fluid degrees of freedom are thermostated. Some of these mechanisms do not yield a string phase, but rather a shear-thickening phase; in this case, we find the influence of the dipolar interactions and external field on the packing structure, and in turn their influence on the shear viscosity at the onset of this shear-thickening regime.

Multiscale Monte Carlo Algorithm for Simple Fluids

We introduce a multiscale Monte Carlo algorithm to simulate dense simple fluids. The probability of an update follows a power law distribution in its length scale. The collective motion of clusters of particles requires generalization of the Metropolis update rule to impose detailed balance. We apply the method to the simulation of a Lennard-Jones fluid and show improvements in efficiency over conventional Monte Carlo and molecular dynamics simulations, eliminating hydrodynamic slowing down.

A stretched exponential model of collective dynamic structure factor in simple dense fluids

We propose a new stretched exponential model for the collective dynamic structure factor of simple fluids, with a scheme for obtaining the stretched exponential parameter. The present model yields numerical results in very good agreement with simulation for Lennard Jones fluids in the high density regime, where the mode coupling theory and the existing models of collective dynamic structure factor fail completely.

A consistent calculation of the chemical potential for dense simple fluids

A general method to calculate the excess chemical potential betamuex, that is based on the Kirkwood coupling parameter's dependence of the correlation functions, is presented. The expression for the one particle bridge function B(1)r is derived for simple fluids with spherical interactions. Only the knowledge of the bridge function B(2)r is required. The accuracy of our approach is illustrated for a dense hard sphere fluid. As far as B(2)r is considered as exact, B(1)r is found to be, at high densities, the normalized bridge function -B(2)rB(2)(r=0). This expression ensures a consistent calculation of the excess chemical potential by satisfying implicitly the Gibbs-Duhem constraint. Only the pressure-consistency condition is necessary to calculate the structural and thermodynamic properties of the fluid.

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.

Deriving analytical expressions for the state dependencies of the effective pair potential parameters using VIM theory

In this work, based on the variational inequality minimizing (VIM) theory of statistical thermodynamics and using the (6,12) Lennard-Jones potential function as an effective pair potential (EPP), analytical expressions for the temperature and density dependencies of the EPP parameters have been obtained. The resulting equation of state can predict thermodynamic properties such as internal energy and Helmholtz free energy for simple dense fluids such as Ar, CO, N 2, and CH 4 with differences less than 5%.

Derivation of structure factor S( Q), and direct correlation function C( Q), of liquid alkali metals and simple fluids using the LIR

Expressions for direct correlation function, C( Q), and structure factor, S( Q), of liquid alkali metals (Na, Rb, Cs) and simple dense fluids (Ar, Kr) have been derived using the linear isotherm regularity (LIR). Unlike previous models, it is shown in this work that C( Q) and, consequently, S( Q) can be obtained without employing any specific potential; only p-v-T experimental data have been used for the calculation of C( Q) and S( Q). With these expressions, it is possible to determine the height and position of the first peak of S( Q) with an acceptable accuracy. The limiting of S( Q) at Q = 0 is calculated and compared with the values obtained experimentally, and those calculated from the extended random phase approximation (ERPA) and random phase approximation (RPA) models. We have used the derived expressions for S( Q) of liquid alkali metals and simple dense fluids for prediction of the pressure and density derivatives of S( Q) in the vicinity of the first peak.

Calculation of transport properties of simple dense fluids

The transport properties of noble gases and of some other simple fluids including N 2, O 2, F 2, CO, CO 2, CH 4, CF 2Cl 2, C 2H 6, C 3H 8 and SF 6 have been calculated by the modified Enskog theory. The density dependence of the radial distribution function has been evaluated using an analytical equation of state based on the statistical–mechanical perturbation theory. The resultant transport equation of state needs three temperature-dependent parameters, which can be determined by knowing the intermolecular pair potential, plus the zero-density values of the transport coefficients. Using a simple Lennard–Jones (12-6) potential for the calculation of temperature-dependent parameters and the extrapolation of experimental low-density transport coefficient data to the zero-density limit, one can put the transport equation of state in the predictive mode. In this work the thermal conductivity and the viscosity coefficient of the helium-group gases have been calculated over a wide range of temperatures and pressures. A comparison of the calculated and experimental values of the thermal conductivity and the viscosity yields an average absolute deviation of 2.66% for the thermal conductivity and of 3.03% for the viscosity.

Role of attractive forces in self-diffusion and mutual diffusion in dense simple fluids and real substances

Diffusion is an important practical consideration in the design of processes involving mass transfer. From a theoretical standpoint, it is a relevant information when developing an understanding of dense-phase fluid structure. Recently, due to increase in computational power, the molecular dynamics (MD) technique has been applied extensively to the study of thermodynamic and transport properties. Diffusion is the most studied transport coefficient since it is an individual property, not a collective one like viscosity or thermal conductivity. This work investigates the role of attractive forces in the diffusion coefficient of pure simple fluids and their mixtures at infinite dilution. The intermolecular potential is broken down according to the ideas of Weeks, Chandler, and Andersen (WCA). It is then applied to study diffusion in idealized fluids (such as Lennard–Jones), idealized fluid mixtures, pure real substances and real substance mixtures. Molecular dynamics simulations were performed in the canonical ensemble with the Hoover–Nose thermostat for pure simple fluids and binary mixtures of simple fluids with one component and infinite dilution. These simulation results, that provide new data for pure fluids in the region of high temperature and intermediate densities, are compared to experimental results for real substances such as ethylene, sulfur hexafluoride and pure supercritical carbon dioxide (CO 2) and a CO 2/phenol mixture, where phenol is at infinite dilution. In addition, the Taylor–Aris dispersion technique was employed to measure the mutual diffusion of phenol in both liquid and supercritical CO 2. Agreement between simulation and experimental data corroborates the idea that diffusion in pure and binary simple fluid mixtures at moderate densities and high temperatures is primarily determined by repulsive forces.

Characteristics of instantaneous resonant modes in simple dense fluids with short-ranged repulsive interactions

We manifest the characteristics of the low-frequency, quasilocalized instantaneous normal modes, named as the instantaneous resonant modes (IRMs), in simple dense fluids with short-ranged repulsive interactions. The analyses include the potential energy profiles of the IRMs, and the local geometric structures and the number of the interacting neighbors of the particles at which the centers of the quasilocalization are located. We conclude that an IRM is created due to fluctuations in the local density, and has a barely-isolated center, which slightly interacts with one or two nearest neighbors, and the potential energy profile of an IRM is basically single-well with strong anharmonicity. The differences in character between the IRMs and the high-frequency localized instantaneous normal modes are also examined. Based on the barely isolated center picture, a necessary criterion for the occurrence of the IRMs is proposed. While only the imaginary-frequency IRMs are found in dense fluids with purely repulsive interactions satisfying the criterion, a tiny attractive well in the pair potential allows the occurrence of the real-frequency IRMs. The physical systems to detect the presence of the IRMs are discussed.

The linear pressure dependence of the viscosity at high densities

Over the years, experimental data of the viscosity coefficient of simple dense fluids at high pressures have been obtained both in our laboratory and elsewhere. These data show that, at high densities, i.e. roughly in the last third of the density range from vacuum to the melting transition, for constant temperature the viscosity coefficient is a linear function of the pressure in a few different but neighbouring ranges, each with different slope and intersection with the pressure axis. The slope appears to be a time of picoseconds. The intersection with the pressure axis can be considered to be a value for the internal pressure. Thus, the viscosity coefficient is directly proportional to the thermal pressure, i.e. the combination of the experimental pressure and the internal pressure, in these ranges. It is shown that such a linear pressure dependence of the viscosity occurs in large ranges of the liquid state and at high densities in the fluid state of simple molecules. We subsequently call attention to old ideas of Maxwell on the equivalence of elasticity and viscosity and the modern basis of it given by Zwanzig and Mountain. This concept leads to Maxwell’s relaxation time. On account thereof, the slope of the linear viscosity–pressure relation is interpreted as the relaxation time, i.e. the time in which a disturbance to the Maxwellian equilibrium state decreases to 1/e of its original value, and as the ideal collision interval. The similarity of the present solution and the case of electrical conductivity in an n-type semiconductor is also pointed out. This leads to a simple view on the transport mechanism and gives reason to consider the temperature dependence of the relaxation times.

Nonequilibrium grand ensemble method for dense fluids

A nonequilibrium grand ensemble method is developed for dense simple fluids by using an irreversible kinetic equation whose collision term is required to satisfy a few conditions. We show that the kinetic equation satisfying such conditions is sufficient for constructing a formal theory of irreversible processes, which is consistent with the thermodynamic laws, and an nonequilibrium extension of the Gibbs equilibrium ensemble theory. As in the equilibrium ensemble theory, nonequilibrium macroscopic (thermodynamic) variables are given in terms of the nonequilibrium partition function. This formal theory supplies the evolution equations for macroscopic observables which are consistent with the thermodynamic laws and an integral part of the nonequilibrium ensemble method. They generalize the classical hydrodynamic equations of Navier, Stokes, and Fourier to nonlinear transport processes occurring far from equilibrium. The evolution equations also include the constitutive equations for the fluid which describe transport properties of the substance when the collision term in the kinetic equation is explicitly modeled by taking into account the details of molecular collision events in the system.