Supercritical Lennard-Jones Fluid Research Articles

Molecular hydrodynamic theory of the velocity autocorrelation function.

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes and tagged-particle self-motion are modeled by linear hydrodynamic equations; the fluid's spatial velocity power spectrum is identified as a necessary initial condition for the momentum current correlation. This formulation leads to a natural physical interpretation of the VACF as a superposition of products of quasinormal hydrodynamic modes weighted commensurately with the spatial velocity power spectrum, the latter of which appears to physically bridge continuum hydrodynamical behavior and discrete-particle kinetics. The methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals. Furthermore, we obtain a new, hydrodynamic form of the self-intermediate scattering function whose description has been extended to low densities where the Schmidt number is of order unity; various calculations are performed for gaseous and supercritical argon to support the general validity of the theory. Excellent quantitative agreement is obtained with recent MD calculations for a dense supercritical Lennard-Jones fluid.

Local density dynamics in a supercritical Lennard-Jones fluid

The collective particle dynamics of supercritical Lennard-Jones fluid is investigated on the basis of molecular dynamic modeling data. The intermediate scattering functions and dynamic structure factor spectra for the wavenumber range k ∈ [0.18; 3.26] σ−1 were calculated. The characteristics of dynamic structure factor spectra such as the thermal diffusivity and the sound velocity were estimated.

Mean force kinetic theory applied to self-diffusion in supercritical Lennard-Jones fluids.

A new kinetic-theory-based calculation of the self-diffusion coefficient for dense supercritical Lennard-Jones fluids is presented. The mean force kinetic theory, which was recently developed for transport in dense plasmas, is applied for the calculation of diffusion in dense neutral fluids. The calculation only requires the pair distribution function, a quantity that is readily calculable from equilibrium statistical mechanics for many systems, including the Lennard-Jones fluid. The self-diffusion coefficients are compared with calculations from molecular dynamics simulations, and good agreement at high density is demonstrated, even in the vicinity of the solid-fluid coexistence line. A comparison of different kinetic models with molecular dynamics simulations demonstrates that the transport coefficients have important contributions due to particle interaction via a potential of mean force and local correlations, which increase the collision rate. The new calculations compare well to those from free-volume theory and overcome a limitation of this theory that prevents its use in systems that interact via long range monotonic potentials. It is expected that this approach will also apply to other systems, including neutral-plasma and neutral-electrolyte mixtures.

Mesoscopic coarse-grained representations of fluids rigorously derived from atomistic models.

Mesoscopic models are widely used to study complex organization and transport phenomena in chemical and biological systems. Defining a rigorous procedure by which a mesoscopic coarse-grained (CG) representation for a fluid can be constructed from an atomistic fine-grained (FG) model is a long-standing question in the field. The connection of these CG models with the FG level of description, which might be built by CG mappings from the FG model, is often unclear. The present paper introduces a new CG mapping scheme that uses dynamically self-consistent smooth centroidal Voronoi tessellation to address this challenging problem. The new mapping scheme is applied to the coarse-graining of supercritical Lennard-Jones fluid systems at different CG resolutions under both quiescent conditions and non-equilibrium shear flow. The method generates continuous, stable, and ergodic CG trajectories and quantitatively captures the slow collective motions of the underlying FG fluids. A parameterization of the CG models from the mapped CG trajectory is then developed based on the Mori-Zwanzig formalism. The Generalized Langevin Equation describes the dynamics of CG variables, and the parameterized result is shown to reproduce the structural and dynamical correlations of the CG system. The new dynamical mapping scheme and the parameterization protocol open up an avenue for direct bottom-up construction of mesoscopic models of fluids in a Lagrangian description.

Probabilistic characterization of the Widom delta in supercritical region.

We present a probabilistic classification algorithm to understand the structural transition of supercritical Lennard-Jones (LJ) fluid. The classification algorithm is designed based on the exploratory data analysis on the nearest Voronoi neighbors of subcritical vapor and liquid. The algorithm is tested and applied to LJ type fluids modeled with the truncated and shifted potential and the Weeks-Chandler-Andersen potential. The algorithm makes it available to locate the Widom delta, which encloses the supercritical gas-liquid boundary and the percolation transition loci in a geometrical manner, and to conjecture the role of attractive interactions on the structural transition of supercritical fluids. Thus, the designed algorithm offers an efficient and comprehensible method to understand the phase behavior of a supercritical mesophase.

Adsorption behaviors of supercritical Lennard-Jones fluid in slit-like pores

Understanding the adsorption behaviors of supercritical fluid in confined space is pivotal for coupling the supercritical technology and the membrane separation technology. Based on grand canonical Monte Carlo simulations, the adsorption behaviors of a Lennard-Jones (LJ) fluid in slit-like pores at reduced temperatures over the critical temperature, Tc* = 1.312, are investigated; and impacts of the wall-fluid interactions, the pore width, and the temperature are taken into account. It is found that even if under supercritical conditions, the LJ fluid can undergo a “vapor-liquid phase transition” in confined space, i.e., the adsorption density undergoes a sudden increase with the bulk density. A greater wall-fluid attractive potential, a smaller pore width, and a lower temperature will bring about a stronger confinement effect. Besides, the adsorption pressure reaches a local minimum when the bulk density equals to a certain value, independent of the wall-fluid potential or pore width. The insights in this work have both practical and theoretical significances.

Extension of Kirkwood-Buff theory to the canonical ensemble.

Kirkwood-Buff (KB) integrals are notoriously difficult to converge from a canonical simulation because they require estimating the grand-canonical radial distribution. The same essential difficulty is encountered when attempting to estimate the direct correlation function of Ornstein-Zernike theory by inverting the pair correlation functions. We present a new theory that applies to the entire, finite, simulation volume, so that no cutoff issues arise at all. The theory gives the direct correlation function for closed systems, while smoothness of the direct correlation function in reciprocal space allows calculating canonical KB integrals via a well-posed extrapolation to the origin. The present analysis method represents an improvement over previous work because it makes use of the entire simulation volume and its convergence can be accelerated using known properties of the direct correlation function. Using known interaction energy functions can make this extrapolation near perfect accuracy in the low-density case. Because finite size effects are stronger in the canonical than in the grand-canonical ensemble, we state ensemble correction formulas for the chemical potential and the KB coefficients. The new theory is illustrated with both analytical and simulation results on the 1D Ising model and a supercritical Lennard-Jones fluid. For the latter, the finite-size corrections are shown to be small.

Time dependence of the velocity autocorrelation function of a fluid: An eigenmode analysis of dynamical processes.

The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.

Intermolecular interactions and the thermodynamic properties of supercritical fluids

The role of different contributions to intermolecular interactions on the thermodynamic properties of supercritical fluids is investigated. Molecular dynamics simulation results are reported for the energy, pressure, thermal pressure coefficient, thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound of fluids interacting via both the Lennard-Jones and Weeks-Chandler-Andersen potentials. These properties were obtained for a wide range of temperatures, pressures, and densities. For each thermodynamic property, an excess value is determined to distinguish between attraction and repulsion. It is found that the contributions of intermolecular interactions have varying effects depending on the thermodynamic property. The maxima exhibited by the isochoric and isobaric heat capacities, isothermal compressibilities, and thermal expansion coefficient are attributed to interactions in the Lennard-Jones well. Repulsion is required to obtain physically realistic speeds of sound and both repulsion and attraction are necessary to observe a Joule-Thomson inversion curve. Significantly, both maxima and minima are observed for the isobaric and isochoric heat capacities of the supercritical Lennard-Jones fluid. It is postulated that the loci of these maxima and minima converge to a common point via the same power law relationship as the phase coexistence curve with an exponent of β = 0.32. This provides an explanation for the terminal isobaric heat capacity maximum in supercritical fluids.

Generalized model of thermal boundary conductance between SWNT and surrounding supercritical Lennard-Jones fluid – derivation from molecular dynamics simulations

Using classical molecular dynamics simulations, we have studied thermal boundary conductance (TBC) between a single-walled carbon nanotube (SWNT) and surrounding Lennard-Jones (LJ) fluids. With an aim to identify a general model that expresses the TBC for various surrounding materials, TBC was calculated for three different surrounding LJ fluids, hydrogen, nitrogen, and argon in supercritical phase. The results show that the TBC between an SWNT and surrounding LJ fluid is approximately proportional to local density (ρL) formed on the outer surface of SWNT and energy parameter (ε) of LJ potential, and inverse proportional to mass (m) of surrounding LJ fluid. In addition, the influence of the molecular mass of fluid on TBC is far more than other inter-molecular potential parameters in realistic range of molecular parameters. Through these parametric studies, we obtained a phenomenological model of the TBC between an SWNT and surrounding LJ fluid.

Anomalous change in the dynamics of a supercritical fluid

We perform molecular dynamics simulations to investigate dynamical properties of a supercritical Lennard-Jones fluid. We find that in the supercritical region there is a short-ranged deviation in dynamic character. We further find that this anomalous change is associated with the presence of the Widom line, the locus of specific heat maxima, of the liquid-vapor phase transition. The salient change in dynamics is consistent with a crossover in the correlation of the diffusion coefficient with the excess entropy. Our results lead to an interpretation that, even though a supercritical fluid excludes a singularity, its dynamical properties can be significantly affected by the existence of thermodynamic response maxima.

Collective excitations in supercritical fluids: Analytical and molecular dynamics study of “positive” and “negative” dispersion

The approach of generalized collective modes is applied to the study of dispersion curves of collective excitations along isothermal lines of supercritical pure Lennard-Jones fluid. An effect of structural relaxation and other nonhydrodynamic relaxation processes on the dispersion law is discussed. A simple analytical expression for the dispersion law in the long-wavelength region of acoustic excitations is obtained within a three-variable viscoelastic model of generalized hydrodynamics. It is shown that the deviation from the linear dependence in the long-wavelength region can be either "positive" or "negative" depending on the ratio between the high-frequency (elastic) and isothermal speed of sound. An effect of thermal fluctuations on positive and negative dispersion is estimated from the analytical solution of a five-variable thermoviscoelastic model that generalizes the results of the viscoelastic treatment. Numerical results are reported for a Lennard-Jones supercritical fluid along two isothermal lines T(*)=1.71,4.78 with different densities and discussed along the theoretical expressions derived.

A transferable coarse-grained potential to study the structure of confined, supercritical Lennard-Jones fluids

In this paper, we develop a transferable coarse-grained interatomic potential to study the structure of simple (spherical and nonpolar) Lennard-Jones (LJ) fluids confined at supercritical temperatures. The potential is used in empirical potential based quasicontinuum theory, [A. V. Raghunathan et al., J. Chem. Phys. 127, 174701 (2007)] to study the structure of three simple LJ fluids (oxygen, methane, and argon) confined in slitlike geometries. The results obtained using the coarse-grained interatomic potential are found to be in good agreement with those predicted by equilibrium molecular dynamics simulations.

Nonmonotonic crossover from adsorption to desorption in supercritical fluid near a weakly attractive surface

The density profiles of a supercritical Lennard-Jones fluid near a weakly attractive surface are used to study the excess adsorption Gamma of supercritical fluid in a wide density range. We report the observation of two extrema of Gamma along the isotherm as a function of density. The attractive fluid-wall interaction potential tends to make Gamma positive, whereas the missing neighbor effect tends to make Gamma negative. The latter effect enhances with increasing fluid density due to the growth of the fluid-fluid attraction that results in the crossover from adsorption to depletion (Gamma=0) at some particular fluid density. With approaching the critical point, Gamma decreases as the bulk correlation length and passes through a minimum when the average density of confined fluid is close to the bulk critical density. Variation of Gamma with temperature and density is determined by the monotonic trend from adsorption to desorption upon increasing fluid density and by the increase of the absolute value of Gamma when approaching the critical point. Interplay of these trends results in two extrema of Gamma in the temperature-density plane. This effect may be responsible for the crossover from adsorption to desorption with approaching the critical temperature observed experimentally along the isotherms and along the critical isochore. The density profiles of a supercritical fluid are found to be exponential and the power law behavior predicted theoretically was not detected even when the bulk correlation length xi achieves 11 molecular diameters.

Direct and indirect correlations in low density supercritical Lennard-Jones fluids

We have carried out a detailed comparison of the direct and indirect correlation functions obtained from canonical molecular dynamics (NVT-MD) simulation of supercritical Lennard-Jones fluids to the results obtained by solving the Ornstein–Zernike equation with the approximate Duh–Henderson (DH) closure. The variations of equilibrium correlations are studied as functions of density at two supercritical isotherms near and away from the critical point. The direct and indirect correlations predicted using the DH closure provides a very good agreement with our simulation results at low densities. However, a marked deviation is observed at higher densities. These results are correlated to the discrepancies between the density and temperature dependence of the underlying bridge function. The implication of these results on the calculation of chemical potential and the Krichevskii parameter is also presented.

Application of Fokker-Planck-Kramers equation treatment for short-time dynamics of diffusion-controlled reaction in supercritical Lennard-Jones fluids over a wide density range

The validity of a Fokker-Planck-Kramers equation (FPKE) treatment of the rate of diffusion-controlled reaction at short times [K. Ibuki and M. Ueno, J. Chem. Phys. 119, 7054 (2003)] is tested in a supercritical Lennard-Jones fluid over a wide density range by comparing it with the Langevin dynamics and molecular dynamics simulations and other theories. The density n range studied is 0.323n(c)< or =n< or =2.58n(c) and the temperature 1.52T(c), where n(c) and T(c) are the critical density and temperature, respectively. For the rate of bimolecular reactions, the transition between the collision-limited and diffusion-limited regimes is expected to take place in this density range. The simulations show that the rate constant decays with time extensively at high densities, and that the magnitude of decay decreases gradually with decreasing density. The decay profiles of the rate constants obtained by the simulations are reproduced reasonably well by the FPKE treatment in the whole density range studied if a continuous velocity distribution is used in solving the FPKE approximately. If a discontinuous velocity distribution is used instead of the continuous one, the FPKE treatment leads to a rate constant much larger than the simulation results at medium and low densities. The rate constants calculated from the Smoluchowski-Collins-Kimball (SCK) theory based on the diffusion equation are somewhat smaller than the simulation results in medium and low densities when the intrinsic rate constant is chosen to adjust the steady state rate constant in the low density limit to that derived by the kinetic collision theory. The discrepancy is relatively small, so that the SCK theory provides a useful guideline for a qualitative discussion of the density effect on the rate constant.

Molecular dynamics study of the density and temperature dependence of bridge functions in normal and supercritical Lennard-Jones fluids

A systematic study of the density and temperature dependence of bridge functions has been carried out using molecular dynamics simulation studies in one-component Lennard-Jones fluids. In deriving the liquid structure, approximate closures are generally used in integral equation theories of liquids to obtain static density correlations. In the present work, we have directly compared the simulated bridge function to two such commonly used closures, viz., hybrid mean spherical approximation (HMSA) [J. Chem. Phys. 84, 2336 (1986)] and Duh-Henderson [J. Chem. Phys. 104, 6742 (1996)] closures with thermodynamic parameters varying from the normal liquid to the supercritical fluid phase far from and near the critical point. In the normal liquid region, both closures show a qualitative agreement with the simulated bridge function, although the extent of correlation at distances sigma < r < or = 2.5sigma is generally underestimated. A similar behavior is obtained in supercritical fluids far from the critical point where critical fluctuations are no longer important. In contrast, significant deviations are observed in the bridge functions in supercritical fluids near the critical point even at densities as small as 25% or 50% of the critical density. Such behavior appears to have resulted from competing contributions to the bridge function from decreasing indirect correlations and small yet significant cavity correlations persistent even at very low densities.

A new approximate bridge function for pure fluids

The integral equation theory is used to investigate the structural and thermodynamic properties of the Lennard-Jones fluid with a new approximate bridge function, which is based on the modification of its expansion in powers of the thermal potential. The thermodynamic consistency is achieved via the virial and compressibility routes. The problem of the renormalization of the indirect correlation function is also considered with an original prescription for partitioning the pair potential. The bridge function as well as the excess chemical potential and the excess entropy, which are calculated by means of standard formulas of statistical mechanics, are compared to simulation data. The thermodynamic properties of the supercritical Lennard-Jones fluid calculated with the present closure relation are in excellent agreement with those obtained from computer simulation.

A self-consistent integral equation: Bridge function and thermodynamic properties for the Lennard-Jones fluid

A new approximate bridge function is proposed as an expansion in powers of the thermal potential, which ensures the thermodynamic consistency with the classical pressure-compressibility condition. The bridge function compares very well the simulation data at large separation as well as in the most important region of the core. The thermodynamic properties of the supercritical Lennard-Jones fluid calculated by means of standard formulas of statistical mechanics involving correlation functions and bridge function are in excellent agreement with those obtained from computer simulation.

Local density augmentation in attractive supercritical solutions. III. How important is the solute–solvent interaction range?

We study the local solute–solvent structure in dilute supercritical solutions, using as a model system a dilute Yukawa solute in a supercritical Lennard-Jones fluid. Our primary interest is in the effect of the solute–solvent interaction range on the local solvent density around the solute. We employ the integral equation theory for inhomogeneous fluids to calculate the solute–solvent structural properties. The theory is shown to be in excellent agreement with Monte Carlo simulations and to provide a substantial improvement over the integral equation theory formulated for homogeneous fluids. In particular, it is demonstrated that the homogeneous theory greatly overestimates the local density enhancement for long-ranged solute–solvent interactions in the highly compressible supercritical regime.