István Szalai

Diffusivity and conductivity of a primitive model electrolyte in a nanopore

Equilibrium and non-equilibrium molecular dynamics simulations are applied to obtain the diffusion coefficient and electric conductivity of ions in dilute electrolytes confined in neutral cylindrical pores. The electrolyte is described with the restricted primitive model and the wall of the pore is modelled as a soft wall. The equilibrium molecular dynamics simulations show that the axial diffusion coefficient of ions decreases with increasing confinement. For a fixed pore radius the diffusion coefficient decreases with increasing number density of the ions. The current response of the system to an applied electric field is maintained at constant temperature by Gaussian isokinetic equations of motion, and at constant concentration by periodic boundary conditions with recycling of ions in the axial direction. The electric conductivity is calculated from the current density and the electric field applied for different pore sizes. In contrast to the trend in diffusivity, conductivity increases slightly in smaller pores. For a very small pore, however, conductivity is lower than the bulk, because oppositely charged ions moving in opposite directions under the electric field cannot avoid collisions with each other in a narrow channel.

The mean spherical approximation for a dipolar Yukawa fluid

The dipolar hard sphere fluid (DHSF) is a useful model of a polar fluid. However, the DHSF lacks a vapor–liquid transition due to the formation of chain-like structures. Such chains are not characteristic of real polar fluids. A more realistic model of a polar fluid is obtained by adding a Lennard–Jones potential to the intermolecular potential. Very similar results are obtained by adding a Yukawa potential, instead of the Lennard–Jones potential. We call this fluid the dipolar Yukawa fluid (DYF). We show that an analytical solution of the mean spherical approximation (MSA) can be obtained for the DYF. Thus, the DYF has many of the attractive features of the DHSF. We find that, within the MSA, the Yukawa potential modifies only the spherically averaged distribution function. Thus, although the thermodynamic properties of the DYF differ from those of the DHSF, the MSA dielectric constant of the DYF is the same as that of the DHSF. This result, and some other predictions, are tested by simulations and are found to be good approximations.

Thermodynamics and structural properties of the dipolar Yukawa fluid

We report computer simulations and a theoretical study of the thermodynamics and structure of a dipolar Yukawa system. A comparison between the analytical mean spherical approximation (MSA) solution, perturbation theory and Monte Carlo simulation data of pressure, internal energy and dielectric constant is given. In the perturbation theory, the MSA solution of hard core Yukawa fluid is used as a reference system. It was found that the MSA solution is reasonable only at lower dipole moments, while the perturbation theory gives good results at low and high values of dipole moment. Liquid–vapor coexistence data of dipolar Yukawa fluid are also obtained by Monte Carlo simulation and by both MSA and perturbation theory. It was found that at high dipole moments the liquid–vapor equilibrium disappears while chain-like structures appear in the low density fluid phase. The appearance of chain-like structures of dipolar Yukawa fluid is discussed in comparison with the Stockmayer fluid.

A study of orientational ordering in a fluid of dipolar Gay-Berne molecules using density-functional theory

We present a density-functional approach to describe the orientational ordering of nonpolar and dipolar Gay–Berne fluids. The first-order perturbation theory developed by Velasco et al. [J. Chem. Phys. 102, 8107 (1995)] for a Gay–Berne fluid is simplified and tested for molecules with a length to breath ratio of κ=3 and energy anisotropies of κ′=1, 1.25, 2.5, and 5. The theory is found to be in fair agreement with existing simulation data for the location of the isotopic–nematic phase transition, but it overestimates the vapor–liquid critical point of the fluid due to a description of the free energy at the mean-field level. The effect on the phase behavior of including a central longitudinal point dipole within the Gay–Berne molecule is studied using a correct treatment of the long-range dipolar contribution at the level of a second-order virial theory [B. Groh and S. Dietrich, Phys. Rev. E 50, 3814 (1994)]. For a given energy anisotropy of κ′=5 and reduced dipole moment μ*=0.5 we search for a stable fer...

DETERMINATION OF VAPOUR-LIQUID EQUILIBRIUM USING CAVITY-BIASED GRAND CANONICAL MONTE CARLO METHOD

In a previous paper a new simulation method was introduced for the determination of vapour–liquid equilibrium (VLE) of pure fluids in the grand canonical ensemble (Boda, D., Liszi, J., and Szalai, I., 1996, Chem. Phys. Lett., 256, 474). Its basic idea is the extrapolation of the pressure in the directions of reciprocal temperature and configurational chemical potential via third-order Taylor series expansion: p(β, μ). The coefficients of the series can be obtained from fluctuation formulae by performing grand canonical Monte Carlo (GC MC) simulations on both vapour and liquid sides. It was found that the main shortcoming of the method originates from the inaccurate calculation of the pressure on liquid side because of the slow convergence of the original GC MC simulation used. It is now shown that the application of the cavitybiased GC MC method of Mezei on the liquid side can overcome this difficulty. The linked-cell method to fasten the cavity-searching algorithm is proposed. The results of test calcula...

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.

Non-equilibrium molecular dynamics simulation study of the frequency dependent conductivity of a primitive model electrolyte in a nanopore

The frequency dependence of electrical conductivity in a 0.1 molar univalent restricted primitive model electrolyte confined in cylindrical pores is studied by non-equilibrium molecular dynamics simulations. At high frequencies, conductivity is independent of pore size and approaches the zero value limit. The phase lag is independent of pore size and approaches the value π/2 at high frequency. At low frequencies, the conductivity is relatively constant and approaches the zero frequency (dc) conductivity value. For pores with radius smaller than 3 times the ion diameter, severe confinement effects lead to different low frequency behaviour. In these very small pores, axial collisions increase at low frequency and lead to much lower conductivity and a negative phase shift. The current response in severely confined electrolytes can be analogous to an LRC circuit with resonance at a characteristic frequency.

Ion transport in simple nanopores

Equilibrium and non-equilibrium molecular dynamics (EMD and NEMD) simulations are reported for the study of ion transport in an infinite long cylindrical nanopore. Results are compared for 3 models of electrolytes including the restricted primitive model (RPM), the solvent primitive model (SPM), and the extended simple point charge model (SPC/E). In EMD simulations, the mean square displacements are used to yield diffusion coefficients. Conductivity can be obtained through the Nernst–Einstein relation. Current and conductivity are calculated directly in NEMD simulations in which an external field is present along the pore axis. The effects of confinement on the ion transport are studied for the 3 model electrolytes. Comparing the EMD results and the NEMD results show that the Nernst–Einstein relation fails for the 3 models of electrolytes in very narrow nanopores. In addition to direct current NEMD simulations, alternate current (AC) NEMD simulations are performed to investigate the frequency dependence of ion transport. Towards high frequencies, a pore-size independent behavior is observed with vanishing conductivity and a phase lag approaching 90°. The effect of confinement is more evident at low frequencies and an electrical capacitor like behavior is observed in the narrowest pores, as indicated by the conductivity, the phase lag and the Cole–Cole plot. The narrowest pores show a combined reactance–resistance–capacitance (LRC) character and a maximum conductivity can be seen at the resonance frequency.

Influence of static electric field on the vapour–liquid coexistence of dipolar soft-sphere fluids

The influence of a static homogeneous electric field on the vapour–liquid equilibrium of dipolar soft-sphere fluids has been studied by the Gubbins–Pople–Stell perturbation theory. The thermodynamic properties of the fluid as functions of the field strength were derived from the Helmholtz energy containing the field-dependent relative permittivity. The dielectric saturation was studied by a perturbation theoretical treatment of the Kirk-wood equation. Our calculations can yield a weak negative saturation. It was found that the critical quantities increase, while the temperature range of the phase coexistence narrows with the field strength. A comparison between our electrostriction results and simulation data shows reasonable agreement at low field strengths.