Numerical solution of the hypernetted chain equation for a solute of arbitrary geometry in three dimensionsThreepoint extension hypernetted chain, conventional hypernetted chain, and superposition approximations: Numerical results for the force between two plates Equilibrium properties of a harddisk fluid via the hypernetted chain integral equation theoryIn a previous paper [M. Lozada-Cassou, J. Chem. Phys. 80, 3344 (1984)], we have proposed a three point extension for integral equation theories. Here we apply our formalism to the interaction of two charged plates of infinite extension, immersed in an electrolyte, and solve the three point extension to the hypernetted chain/mean spherical theory. We calculate the ionic profile around the plates and the pressure between the plates, as a function of distance between them, for a 1:1 and 2:2 electrolyte for different concentrations and potentials on the plates. We compare our results with the Verwey-Overbeek (VO) theory. We find excellent agreement with the VO theory for low potentials and concentrations. However, there is qualitative disagreement for higher potentials and/or concentrations. The interaction force between the plates becomes attractive at a sufficiently high potential and/or concentration. Since the VO force is always repulsive, in our theory the attraction is a consequence of the ionic size. As one would expect from an electrostatically correct theory, the charge on the plates depends on the distance between the plates.

The conventional hypernetted chain/mean spherical (HNC/MS) equation and a superposition approximation to the Born–Green–Yvon (BGY) equation are derived and numerically solved for the force between two charged plates immersed in a primitive model electrolyte or a point-ion electrolyte. The results are compared to the force calculated through the three-point extension to the HNC/MS approximation. The force between two hard plates, immersed in a hard-sphere fluid, is also calculated with these three theories. Excellent agreement is found among the three theories for the force between two hard uncharged plates. For charged plates, the agreement goes from good to total disagreement, depending on the plate potential and/or electrolyte concentration. While the three theories predict attractions between the plates, the conventional HNC/MS and BGY equations predict a nonexistent attraction at low electrolyte concentration. The corresponding conventional method and superposition approximation method calculations of the force between two plates immersed in a point-ion solution are in surprisingly good agreement with the Verwey–Overbeek results, when the potential on the plates is low,and/or the electrolyte concentration is high.

Articles you may be interested inOn the phase and interface behavior along the three-phase line of ternary Lennard-Jones mixtures: A collaborative approach based on square gradient theory and molecular dynamics simulations Phase and interfacial behavior of partially miscible symmetric Lennard-Jones binary mixtures By means of extensive equilibrium molecular dynamics simulations we have investigated the behavior of the interfacial tension ␥ of two immiscible symmetrical Lennard-Jones fluids. This quantity is studied as function of reduced temperature T*ϭk B T/⑀ in the range 0.6рT*р3.0. We find that, unlike the monotonic decay obtained for the liquid-vapor interfacial tension, for the liquid-liquid interface, ␥(T) has a maximum at a specific temperature. We also investigate the effect that surfactantlike particles have on the thermodynamic as well as the structural properties of the liquid-liquid interface. It is found that ␥ decays monotonically as the concentration of the surfactantlike particles increases.

The diffusivity of a nanoparticle suspended in a liquid crystal is investigated in the limit of nematic ordering and under isotropic conditions. Molecular simulations are performed with the liquidcrystalline solvent represented at the level of Gay-Berne mesogens in the canonical (N,V,T) ensemble. The mesogen-colloid interaction strength is varied to induce anchoring that ranges from parallel to perpendicular. Mean square displacements, orientational correlation functions, and relative colloidal diffusivities are reported for different types of mesogenic anchoring on the nanoparticle. The Gay-Berne parametrization is contextualized with respect to experimental observations, and a specific set of parameters is found to reproduce the characteristic ratio of mesogenic diffusivities observed in recent experiments. The results presented in this work provide a means to determine anchoring strength at small length scales, and the parameterizations provided in this work could serve as a starting point to interpret experimental data for nanoparticle suspensions in liquid-crystals at a molecular level.

Binary fluid mixtures of 1:1 concentration can demix in a phase transition of first order or of second order. We analyze the two scenarios in density-concentration space and relate them to the structure of the line at which the demixing coexistence surface cuts the liquid-vapor coexistence surface. These scenarios help us to decide between first and second order for a model of a symmetric Lennard-Jones mixture. An optimized reference hypernetted chain integral equation method is employed for calculating the correlation functions and from there the pressure and chemical potentials. We conclude that demixing of a 1:1 mixture is of first order in the whole range of parameters that we have investigated. We did not find a critical point in the 1:1 concentration plane.