A new approximate bridge function for pure fluids

The coupling parameter expansion in thermodynamic perturbation theory of simple fluids is generalized to include the derivatives of bridge function with respect to coupling parameter. We applied seventh order version of the theory to Square-Well (SW) and Lennard-Jones (LJ) fluids using Sarkisov Bridge function. In both cases, the theory reproduced the radial distribution functions obtained from integral equation theory (IET) and simulations with good accuracy. Also, the method worked inside the liquid-vapor coexistence region where the IETs are known to fail. In the case of SW fluids, the use of Carnahan-Starling expression for Helmholtz free energy density of Hard-Sphere reference system has improved the liquid-vapor phase diagram (LVPD) over that obtained from IET with the same bridge function. The derivatives of the bridge function are seen to have significant effect on the liquid part of the LVPD. For extremely narrow SW fluids, we found that the third order theory is more accurate than the higher order versions. However, considering the convergence of the perturbation series, we concluded that the accuracy of the third order version is a spurious result. We also obtained the surface tension for SW fluids of various ranges. Results of present theory and simulations are in good agreement. In the case of LJ fluids, the equation of state obtained from the present method matched with that obtained from IET with negligible deviation. We also obtained LVPD of LJ fluid from virial and energy routes and found that there is slight inconsistency between the two routes. The applications lead to the following conclusions. In cases where reference system properties are known accurately, the present method gives results which are very much improved over those obtained from the IET with the same bridge function. In cases where reference system data is not available, the method serves as an alternative way of solving the Ornstein-Zernike equation with a given closure relation with the advantage that solution can be obtained throughout the phase diagram with a proper choice of the reference system.

The integral equation theory for a model 2–2 electrolyte is studied in detail. In this model electrolyte, the ions are assumed to be the same size, and interact via a continuous potential energy which behaves as the Coulomb potential at large distances and an inverse ninth power repulsion at short distances. The ions are embedded in a dielectric continuum of fixed dielectric constant, here taken to be 78.3 ε0 in order to model water at 25 °C. The bridge function for this model is studied as a function of concentration (a) for six proposed closures, and (b) via ‘‘exact’’ inversion of data from computer simulations. A proposed closure derived from examination of the inverted bridge function yields predictions in good agreement with computer simulations. We emphasize the importance of choosing an ‘‘optimized’’ long-range potential, as opposed to the traditional Coulomb choice. A simple functional form for the bridge function results from this optimized choice of long-range potential.

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients B(j) are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d>/=5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d>/=5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].

The modified density functional theory, which is based both on the bridge density functional and the contact value theorem, has been proposed for the structural properties of penetrable sphere fluids and their mixtures near a slit hard wall. The Verlet-modified bridge function proposed by Choudhury and Ghosh [J. Chem. Phys. 119, 4827 (2003)] for one-component system has been extended for fluid mixtures. The radial distribution functions obtained from the Verlet-modified bridge function are in excellent agreement with computer simulations over a wide range of density and temperature and better than those obtained from the standard integral theories including the Percus-Yevick and hypernetted-chain closures. The calculated particle density distributions confined in a slit pore are also found to be reasonably good compared to the simulation data. Even for high density systems the accuracy of the hypernetted-chain and the mean-field approximation functionals increase with increasing temperature. However, the agreement between theory and simulation slightly deteriorates in the systems of low temperature.

We report Gibbs ensemble simulations of the coexistence region of the hard core two-Yukawa fluid with Yukawa parameters chosen to mimic the Lennard-Jones fluid. The phase envelope of the Lennard-Jones fluid is found to be well approximated by that of the Yukawa fluid. The results suggest that theoretical approaches to the hard core two-Yukawa fluid (such as integral equations and perturbation theory) could provide an analytic basis for predicting the physical properties of the Lennard-Jones fluid.

Supercritical fluids are fluids at temperature and pressure above their respective critical values. Such fluids are increasingly being used in power generation, refrigeration and chemical process industry. The objectives of the current research were to develop a fundamental understanding of the transport phenomena in near-critical supercritical fluids via high-resolution numerical simulations and careful experiments for improved design of industrial processes and applications that employ supercritical fluids. A set of synergistic experimental and numerical studies were proposed in this research. Four main focus areas under the broad spectrum of supercritical fluid transport were chosen - (a) characterization of thermoacoustic transport, (b) interaction of thermoacoustic transport with natural convection, (c) characterization of acoustically augmented transport and (d) enhancement of mass transport using acoustic waves. A numerical model to simulate thermoacoustic convection in near-critical fluids was developed. In the computational model, the conservation equations were solved along with a real-fluid equation of state for supercritical fluid and variable thermo-physical properties. Thermoacoustic waves in near-critical carbon dioxide were also investigated experimentally on acoustic time scales using a fast response measurement system. The predicted results from the calculation and the measurements provide interesting details regarding the thermal transport mechanisms at near-critical states. The numerical model was applied to investigate the interaction of buoyancy driven flows with thermoacoustic convection in near-critical supercritical fluids. This model can be extensively used for studying the steady-state thermal transport and stability behavior of near-critical fluids. Mechanically driven acoustic waves in supercritical fluid generated by a vibrating wall in a cylindrical resonator were studied both numerically and experimentally. The simulations revealed interesting steady-periodic flow patterns in the resonator filled with near-critical fluid due to the fluctuations caused by the vibrating wall. High-fidelity computational fluid dynamics models of mass transport processes in supercritical fluid extraction systems were also developed. A novel application of acoustically driven transport in supercritical fluid was demonstrated numerically for the supercritical fluid extraction process. The numerical predictions indicated major improvements in the extraction yield due to the application of acoustic waves and can be utilized in the design and optimization of supercritical fluid extraction systems.

Modeling the bridge function in the reference-hypernetted chain equation with that of a hard-sphere fluid has proven to be highly successful for simple liquids, particularly when the reference-hard-sphere diameter is treated as an adjustable parameter. In this paper, we examine the generalization of this technique to liquids of diatomic molecules, with the reference bridge function taken from that of the corresponding hard-diatomic-molecule fluid. Specifically, the diatomic molecules of the system of interest interact through an atom–atom Lennard-Jones potential while the hard-diatomic-reference model is solved in Percus–Yevick approximation. We find that variation of the sphere diameter of the hard-diatomic molecule makes possible excellent agreement with simulation results for the two-center Lennard-Jones fluid, just as it does for simple fluids.

Excess chemical potential and partial molar enthalpy of 2- iso-butoxyethanol in aqueous solution at 20 °C

Supercritical fluids in rock–H2O systems have been proposed to be important agents of mass transfer in subduction zone environments. New experimental studies were conducted on the simple model granite system NaAlSi3O8 (Ab)–H2O in order to investigate phase relations and to develop the thermodynamic mixing properties between aqueous fluid (a.k.a. vapor, V) and silicate melt (a.k.a. liquid, L) at pressures (P) and temperatures (T) approaching those of critical mixing. We established liquidus and solvus phase relations by analyzing the quenched run products from piston–cylinder experiments over a range of $$P - T - X_{{{\text{H}}_{2} {\text{O}}}}$$ conditions from 1.0 to 1.7 GPa, 630–1060 °C and 4–92 wt% H2O. Equations for the critical curve, solidus temperatures, albite solubility at the solidus, and vapor-saturated solidus H2O content were formulated as functions of $$P - T - X_{{{\text{H}}_{2} {\text{O}}}}$$ . We constructed a subregular solution model to describe the solvus curves using P and T dependent Margules coefficients ( $$W_{{{\text{H}}_{2} {\text{O}}}}$$ and $$W_{\text{Ab}}$$ ). Activities of H2O and Ab ( $$a_{{{\text{H}}_{2} {\text{O}}}}$$ and $$a_{\text{Ab}}$$ ) could be formulated using only the input at the solidus and the critical point at each pressure because of the nearly linear dependence of the parameters on T. The solvus curves were confirmed independently by means of criteria established for classification of quenched products as L, L + V, or V and are in excellent agreement with the compositions that can be calculated using the Margules coefficients. At 1.6 GPa, the H2O content at the vapor-saturated solidus is 44.5 ± 5.5 wt% and the solubility of albite at the solidus is 42.95 ± 0.99 wt%, indicating the imminent intersection of the two curves and thus a stable critical endpoint at some slightly higher pressure. We constrain the critical endpoint at 1.63 ± 0.02 GPa, 659 ± 5 °C, and a composition of ~ 44.7 wt% H2O based on the intersections of the pressure dependent solidus curves with the critical curve, the pressure dependent albite solubility curve with the vapor-saturated solidus curve. The 1.7 GPa experiments showed no evidence for liquid–vapor immiscibility across a wide range of compositions and temperatures (4–80 wt% H2O and 630–1050 °C, and furthermore, that low albite is stable in the presence of the supercritical fluid near the breakdown of albite to jadeite and quartz. These results provide a comprehensive account of the solution properties of subcritical and supercritical fluids in this model granite system at temperatures and pressures corresponding to the deep-crust regions of granite magma generation.

The structural and thermodynamic properties of the argon fluid were investigated by means of a modification of the optimised random phase approximation (ORPA) theory and the square-well (SW) potential. The results were obtained at the SW potential values 1.25 < λ < 2, and along different isotherms at a wide range of densities. The radial distribution function, g(r), was calculated, and the results obtained were extrapolated to give the appropriate contact values g(σ), g(λσ −) and g(λσ +). The results were compared with the simulation and experimental data available in the literature. The results calculated for the Helmholtz free energy (A) and internal energy (E) are in good agreement with the experimental data at the sub- and super-critical temperatures. The ORPA version considered here provided good results for the compressibility factor Z from the Virial route with the SW attractive range λ = 1.7 at high temperatures and low densities.

We report the results of the numerical estimation of statistical memory effects in diffusion for two various systems: Lennard-Jones fluids and the model of the Brownian particle in a one-dimensional harmonic lattice. We have found the relation between the diffusion coefficient and the non-Markovity parameter, which is linear for the Lennard-Jones systems in liquid state. The relation between the memory measure and the excess entropy is also discussed here.

Calculation of excess free energy from the averaged effective acceptance ratio for the Lennard-Jones fluid and the inverse twelve fluid

We present an application of Wertheim’s thermodynamic perturbation theory (TPT1) to a simple coarse grained model made of flexibly bonded Lennard-Jones monomers. We use both the reference hypernetted chain (RHNC) and mean spherical approximation (MSA) integral equation theories to describe the properties of the reference fluid. The equation of state, the density dependence of the excess chemical potential, and the critical points of the liquid–vapor transition are compared with simulation results and good agreement is found. The RHNC version is somewhat more accurate, while the MSA version has the advantage of being almost analytic. We analyze the scaling behavior of the critical point of chain fluids according to TPT1 and find it to reproduce the mean field exponents: The critical monomer density is predicted to vanish as n−1/2 upon increasing the chain length n while the critical temperature is predicted to reach an asymptotic finite temperature that is attained as n−1/2. The predicted asymptotic finite critical temperature obtained from the RHNC and MSA versions of TPT1 is found to be in good agreement with the Θ point of our polymer model as obtained from the temperature dependence of the single chain conformations.

Our implicit-solvent model for the estimation of the excess chemical potential (or, equivalently, the activity coefficient) of electrolytes is based on using a dielectric constant that depends on the thermodynamic state, namely, the temperature and concentration of the electrolyte, ε(c, T). As a consequence, the excess chemical potential is split into two terms corresponding to ion-ion (II) and ion-water (IW) interactions. The II term is obtained from computer simulation using the Primitive Model of electrolytes, while the IW term is estimated from the Born treatment. In our previous work [J. Vincze, M. Valiskó, and D. Boda, "The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion-ion correlations," J. Chem. Phys. 133, 154507 (2010)], we showed that the nonmonotonic concentration dependence of the activity coefficient can be reproduced qualitatively with this II+IW model without using any adjustable parameter. The Pauling radii were used in the calculation of the II term, while experimental solvation free energies were used in the calculation of the IW term. In this work, we analyze the effect of the parameters (dielectric constant, ionic radii, solvation free energy) on the concentration and temperature dependence of the mean activity coefficient of NaCl. We conclude that the II+IW model can explain the experimental behavior using a concentration-dependent dielectric constant and that we do not need the artificial concept of "solvated ionic radius" assumed by earlier studies.

Description of self-diffusion coefficients of gases, liquids and fluids at high pressure based on molecular simulation data