Víctor M. Trejos

Semiclassical approach to model quantum fluids using the statistical associating fluid theory for systems with potentials of variable range

Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.

Computer simulation of liquid-vapor coexistence of confined quantum fluids

The liquid-vapor coexistence (LV) of bulk and confined quantum fluids has been studied by Monte Carlo computer simulation for particles interacting via a semiclassical effective pair potential Veff(r) = VLJ + VQ, where VLJ is the Lennard-Jones 12-6 potential (LJ) and VQ is the first-order Wigner-Kirkwood (WK-1) quantum potential, that depends on β = 1∕kT and de Boers quantumness parameter Λ=h/σ√mε, where k and h are the Boltzmanns and Plancks constants, respectively, m is the particles mass, T is the temperature of the system, and σ and ε are the LJ potential parameters. The non-conformal properties of the system of particles interacting via the effective pair potential Veff(r) are due to Λ, since the LV phase diagram is modified by varying Λ. We found that the WK-1 system gives an accurate description of the LV coexistence for bulk phases of several quantum fluids, obtained by the Gibbs Ensemble Monte Carlo method (GEMC). Confinement effects were introduced using the Canonical Ensemble (NVT) to simulate quantum fluids contained within parallel hard walls separated by a distance Lp, within the range 2σ ≤ Lp ≤ 6σ. The critical temperature of the system is reduced by decreasing Lp and increasing Λ, and the liquid-vapor transition is not longer observed for Lp∕σ < 2, in contrast to what has been observed for the classical system.

Thermodynamic properties of confined square-well fluids with multiple associating sites

In this work, a molecular simulation study of confined hard-spheres particles with square-well (SW) attractive interactions with two and four associating SW sites based on the first-order perturbation form of Wertheims theory is presented. An extended version of the Gibbs ensemble technique for inhomogeneous fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is used to predict the adsorption density profiles for associating fluids confined between opposite parallel walls. The fluid is confined in four kinds of walls: hard-wall, SW wall, Lennard-Jones (LJ) 12-6 wall potential, and LJ 10-4 wall potential. We analyze the behavior of the confined system for several supercritical temperatures as a function of variation of molecular parameters: potential range λ, bulk densities ρb*, pore width H, cutoff range interaction rc*, and range of the potential and depth of the particle-wall (λw, εw*). Additionally, we include predictions for liquid-vapor coexistence of bulk associative particles and how their critical properties are modified by the presence of associative sites in the molecule. The molecular simulation data presented in this work are of prime importance to the development of theoretical approaches for inhomogeneous fluids as classical density functional theory. The simulation results presented here are resourceful for predicting adsorption isotherms of real associating fluids such as water.

Self-diffusion coefficient of the square-well fluid from molecular dynamics simulations within the constant force approach

We present a systematic study of the self-diffusion coefficient for a fluid of particles interacting via the square-well pair potential by means of molecular dynamics simulations in the canonical (N, V, T) ensemble. The discrete nature of the interaction potential is modeled by the constant force approximation, and the self-diffusion coefficient is determined for several fluid densities at supercritical thermodynamic states. The dependence of the self-diffusion coefficient on the potential range λ is analyzed in the range of 1.1 ≤ λ ≤ 1.5. The obtained simulation results are in agreement with the self-diffusion coefficient predicted by the Enskog method. Additionally, we show that the diffusion coefficient is very sensitive to the potential range λ. Our results for the self-diffusion coefficient times density extrapolate well to the values in the zero-density limit obtained from the Chapman-Enskog theory for dilute gases. The constant force approximation used in this work to model the discrete pair potentials has shown to be an excellent scheme to compute the transport properties of square-well fluids using molecular dynamics simulations. Finally, the simulation results presented here are useful for improving theoretical approaches, such as the Enskog method.

Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory

The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the two-dimensional square-well fluid in the Barker-Henderson framework. This equation of state is based on an approximate analytical radial distribution function for d-dimensional hard-sphere fluids (1 ≤ d ≤ 3) and is validated against existing and new simulation results. The so-obtained equation of state is implemented in a discrete perturbation theory able to account for general potential shapes. The prototypical Lennard-Jones and Yukawa fluids are tested in its two-dimensional version against available and new simulation data with semiquantitative agreement.

Adsorption and phase behavior of water-like fluid models with square-well attraction and site-site association in slit-like pores: Density functional approach

The adsorption and phase behavior of two model fluids, both with square well inter-particle attraction and site-site associative interaction, in slit-like pores have been studied in the framework of a density functional theory. The mean field approach and the first-order mean spherical approximation have been applied to account for the attractive interactions. The chemical association effects are taken into account by using the first-order thermodynamic perturbation theory of Wertheim. A set of parameters for each fluid model has been chosen according to the work of [Clark et al., Mol. Phys. 104, 3561 (2006)], to describe successfully the vapor-liquid coexistence of water in the bulk phase. The influence of the slit-like pore width and of the strength of gas-solid interaction energy on the vapor-liquid coexistence envelope under confinement has been explored in detail. The theory and the results of the present work are valuable for further exploration of a wide set of models of associating fluids and of fluids with complex molecular architecture in different adsorbents, and to deal with activated carbon surfaces.