Yang-Xin Yu

Structures of hard-sphere fluids from a modified fundamental-measure theory

We reformulate Rosenfeld’s fundamental-measure theory using the excess Helmholtz energy density from the Boublik–Mansoori–Carnahan–Starling–Leland equation of state instead of that from the scaled-particle theory. The new density functional theory yields improved density distributions, especially the contact densities, of inhomogeneous hard-sphere fluids as well as more accurate direct and pair correlation functions of homogeneous hard spheres including those of highly asymmetric mixtures. This new density functional theory will provide an accurate reference for the further development of a statistical-thermodynamic theory of complex fluids at uniform and at inhomogeneous conditions.

Density functional theory for inhomogeneous mixtures of polymeric fluids

A new density functional theory is developed for inhomogeneous mixtures of polymeric fluids by combining Rosenfeld’s fundamental-measure theory for excluded volume effects with Wertheim’s first-order thermodynamic perturbation theory for chain connectivity. With no adjustable parameters, theoretical predictions are in excellent agreement with Monte Carlo simulation data for the density distributions and for the adsorption isotherms of hard-sphere chains near hard walls or in slit-like pores. This theory is applied to calculate the force between two parallel hard walls separated by hard-sphere chains at different densities. Calculated results indicate that the chain-mediated force is attractive and decays monotonically with separation at low chain densities, it oscillates at high chain densities and in between, it is attractive at small separation and repulsive at large separation. This new density functional theory is simpler than similar theories in the literature and is directly applicable to mixtures.

Density-functional theory of spherical electric double layers and ζ potentials of colloidal particles in restricted-primitive-model electrolyte solutions

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.

A fundamental-measure theory for inhomogeneous associating fluids

The fundamental-measure theory (FMT) of Rosenfeld for hard spheres is extended to inhomogeneous associating fluids on the basis of Wertheim’s first-order thermodynamic perturbation theory (TPT1). The excess intrinsic Helmholtz energy, which includes contributions from hard-sphere repulsion and from intermolecular bonding, is represented as a functional of three weighted densities that are related to the geometry of spherical particles. In the absence of association, this theory is the same as the original FMT, and at bulk conditions it reduces to TPT1. In comparison with Monte Carlo simulation results, the extended fundamental-measure theory provides good descriptions of the density profiles and adsorption isotherms of associating hard spheres near a hard wall. Calculated results indicate that the critical temperatures for the vapor–liquid equilibria of associating fluids in hard slit pores are suppressed compared with that for the bulk fluid and the confinement has more significant impact on the liquid side than the vapor side of the coexistence curve. Unlike nonpolar fluids at similar conditions, saturated associating liquids in hard slit pores do not exhibit strong layering near the solid surface.

MODIFICATION AND APPLICATION OF THE MEAN SPHERICAL APPROXIMATION METHOD

Abstract Lu, J.-F., Yu, Y.-X. and Li, Y.-G., 1993. Modification and application of the mean spherical approximation method. Fluid Phase Equilibria, 85: 81-100. The mean spherical approximation (MSA) method is improved by the introduction of the effective diameter of the cation. The dependence of the ionic strength on the effective diameters is mainly attributed to the solvation effect. This modified model has been used to correlate the mean ionic activity coefficients for 85 single-electrolyte solutions. The results show that the modified MSA gives smaller deviations than the original MSA and Pitzer models. The modified MSA was also applied to calculate 32 mixed-electrolyte solutions without any mixing parameters. The calculated results indicate that the modified MSA can be used to calculate the mixture properties in terms of the parameters of single-electrolyte solutions. Furthermore, the mean ionic activity coefficients of some single-electrolyte solutions can be calculated for other temperatures by using the parameters obtained at 298.15 K.

Simulation study of hydrogen storage in single walled carbon nanotubes

Abstract Hydrogen storage in single-walled carbon nanotubes (SWNTs) is studied by grand canonical Monte Carlo (GCMC) simulation. Hydrogen–hydrogen and hydrogen–carbon interactions are both modeled with Lennard–Jones potential. Hydrogen–carbon interactions are integrated over the whole nanotube to get molecule–tube interactions. Three adsorption isotherms of different diameters at 293.15 K , one adsorption isostatics at 2.66 MPa with radius of 0.587 nm , the amount of adsorption as a function of van der Waals (VDW) distance of nanotubes with the three diameters at 3 MPa (where the VDW distance is defined as the distance between the walls of the nearest neighbor tubes in the bundle, as measured from the carbon centers) and the adsorption as function of continuously changing diameter are displayed. Finally, the influences of pressures, temperatures, the diameters and VDW distances of SWNTs on adsorption are discussed.

Extended test-particle method for predicting the inter- and intramolecular correlation functions of polymeric fluids

The Percus’ test-particle method is extended to predict the inter- and intramolecular correlation functions of polymeric fluids using a density functional theory developed earlier [J. Chem. Phys. 117, 2368 (2002)]. The calculated inter- and intramolecular distribution functions as well as the site–site correlation functions agree well with the results from Monte Carlo simulation for freely jointed hard-sphere chains. Compared with the integral-equation approaches and alternative density functional theories, the present method is free of molecular simulations as input and has the advantage of self-consistency among inter- and intramolecular correlation functions and thermodynamic properties.

A Density Functional Theory for Lennard-Jones Fluids in Cylindrical Pores and Its Applications to Adsorption of Nitrogen on MCM-41 Materials

A density functional theory (DFT) constructed from the modified fundamental-measure theory and the modified Benedict-Webb-Rubin equation of state is presented. The Helmholtz free energy functional due to attractive interaction is expressed as a functional of attractive weighted-density in which the weight function is a mean-field-like type. An obvious advantage of the present theory is that it reproduces accurate bulk properties such as chemical potential, bulk pressure, vapor-liquid interfacial tension, and so forth when compared with molecular simulations and experiments with the same set of molecular parameters. Capabilities of the present DFT are demonstrated by its applicability to adsorption of argon and nitrogen on, respectively, a model cylindrical pore and mesoporous MCM-41 materials. Comparison of the theoretical results of argon in the model cylindrical pore with those from the newly published molecular simulations indicates that the present DFT predicts accurate average densities in the pore, slightly overestimates the pore pressure, and correctly describes the effect of the fluid-pore wall interaction on average densities and pressures in the pore. Application to adsorption of nitrogen on MCM-41 at 77.4 K shows that the present DFT predicts density profiles and adsorption isotherms in good agreement with those from molecular simulations and experiments. In contrast, the hysteresis loop of adsorption calculated from the mean-field theory shifts toward the low pressure region because a low bulk saturated pressure is produced from the mean-field equation of state. The present DFT offers a good way to describe the adsorption isotherms of porous materials as a function of temperature and pressure.

Surface tension for aqueous electrolyte solutions by the modified mean spherical approximation

Abstract The concentration dependence of the surface tension of single and mixed electrolyte aqueous solutions is studied, based on the assumption that the surface layer can be treated as a separate phase located between vapor and bulk liquid phases. The mean spherical approximation modified by Lu et al. [J.-F. Lu, Y.-X. Yu, Y.-G. Li, Fluid Phase Equilibria 85 (1993) 81–100] is used to calculate the activity coefficients of water in the surface and bulk liquid phases. The relation between the electrolyte concentration in the surface and bulk liquid phases is established and only one parameter needs to be determined. The surface tensions for 31 single electrolyte aqueous solutions are correlated and the overall average absolute deviation is 0.70%. The surface tensions at different temperatures are predicted with the parameters obtained at one fixed temperature. By introducing the proper mixing rules, the surface tensions for 14 mixed electrolyte aqueous solutions are predicted without any mixing parameters, and the total average absolute deviation is 0.63%. All the calculated results are compared with that of the surface tension model for aqueous electrolyte solutions proposed by Li et al. [Z.-B. Li, Y.-G. Li, J.-F. Lu, Ind. Eng. Chem. Res. 38 (1999) 1133–1139].

Structures and correlation functions of multicomponent and polydisperse hard-sphere mixtures from a density functional theory

The structures of nonuniform binary hard-sphere mixtures and the correlation functions of uniform ternary hard-sphere mixtures were studied using a modified fundamental-measure theory based on the weight functions of Rosenfeld [Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)] and Boublik-Mansoori-Carnahan-Starling-Leland equation of state [Boublik, J. Chem. Phys. 53, 471 (1970); Mansoori et al., J. Chem. Phys. 54, 1523 (1971)]. The theoretical predictions agreed very well with the molecular simulations for the overall density profiles, the local compositions, and the radial distribution functions of uniform as well as inhomogeneous hard-sphere mixtures. The density functional theory was further extended to represent the structure of a polydisperse hard-sphere fluid near a hard wall. Excellent agreement was also achieved between theory and Monte Carlo simulations. The density functional theory predicted oscillatory size segregations near a hard wall for a polydisperse hard-sphere fluid of a uniform size distribution.