Enrique Díaz-Herrera

Three point extension for hypernetted chain and other integral equation theories: Numerical results

In 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. A...

Three‐point extension hypernetted chain, conventional hypernetted chain, and superposition approximations: Numerical results for the force between two 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...

Interfacial tension behavior of binary and ternary mixtures of partially miscible Lennard-Jones fluids: A molecular dynamics simulation

By means of extensive equilibrium molecular dynamics simulations we have investigated the behavior of the interfacial tension γ of two immiscible symmetrical Lennard-Jones fluids. This quantity is studied as function of reduced temperature T*=kBT/e in the range 0.6⩽T*⩽3.0. We find that, unlike the monotonic decay obtained for the liquid-vapor interfacial tension, for the liquid–liquid interface, γ(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 γ decays monotonically as the concentration of the surfactantlike particles increases.

Effects of anchoring strength on the diffusivity of nanoparticles in model liquid-crystalline fluids

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 liquid-crystalline 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.

Liquid crystal nanodroplets, and the balance between bulk and interfacial interactions

Molecular dynamics simulations of a coarse grain model are used to explore the morphology of thermotropic liquid crystal nanodroplets. The characteristic length of the droplets is such that different contributions to the energy, including interfacial and bulk-like terms, have comparable magnitudes. Depending on the relative strength of such contributions, a wide variety of mesophases can be identified. These range from a completely disordered isotropic phase at elevated temperatures, to ordered radial and smectic phases at low temperatures. Bipolar, uniaxial and axial phases are also observed. Our results suggest that according to the ratio between perpendicular and planar anchoring strengths, an isotropic–radial transition may occur through several intermediate phases. In contrast, a direct bipolar–radial transition is never observed. Our results are summarized in the form of a generic phase diagram for spherical nanodroplets as a function of anchoring strength. The diagram exhibits a number of common features with phase transitions that have been observed in experiments with larger, micron-sized droplets. Perhaps more importantly, it serves to emphasize the balance that exists in nanodroplets between surface and bulk interactions, droplet size and temperature, and how that balance influences the behavior of the system.

Phase and interfacial behavior of partially miscible symmetric Lennard-Jones binary mixtures

We have carried out extensive equilibrium molecular-dynamics simulations to study quantitatively the topology of the temperature versus density phase diagrams and related interfacial phenomena in a partially miscible symmetric Lennard-Jones binary mixture. The topological features are studied as a function of miscibility parameter, alpha = epsilonAB/epsilonAA. Here epsilonAA = epsilonBB and epsilonAB stand for the parameters related to the attractive part of the intermolecular interactions for similar and dissimilar particles, respectively. When the miscibility varies in the range 0 < alpha < 1, a continuous critical line of consolute points Tcons(rho)--critical demixing transition line--appears. This line intersects the liquid-vapor coexistence curve at different positions depending on the values of alpha, yielding mainly three different topologies for the phase diagrams. These results are in qualitative agreement to those found previously for square-well and hard-core Yukawa binary mixtures. The main contributions of the present paper are (i) a quantitative analysis of the phase behavior and (ii) a detailed study of the liquid-liquid interfacial and liquid-vapor surface tensions, as function of temperature and miscibility as well as its relationship to the topological features of the phase diagrams.

Wetting phenomenon in the liquid-vapor phase coexistence of a partially miscible Lennard-Jones binary mixture.

We have carried out extensive equilibrium molecular dynamics simulations to study the structure and the interfacial properties in the liquid-vapor phase coexistence of partially miscible binary Lennard-Jones mixtures. By analyzing the structural properties as a function of the miscibility parameter, alpha, we found that at relatively low temperatures the system separates forming a liquid A-liquid B interface in coexistence with the vapor phase. At higher temperatures and, 0< alpha < or =0.5 , we found a temperature range, T*w (alpha) < or =T*< T*Cons (alpha) , where the liquid phases are wet by the vapor phase. Here, T*w (alpha) represents the wetting transition temperature and T*Cons (alpha) is the consolute temperature of the mixture. However, for 0.5< alpha <1 , no wetting phenomenon occurs. For the particular value, alpha=0.25 , we analyzed quantitatively the T* versus rho* , and P* versus T* phase diagrams and found, T*c approximately 1.25 , and T*Cons approximately 1.25 . We also studied quantitatively, as a function of temperature, the surface tension and the adsorption of molecules at the liquid-liquid interface. It was found that the adsorption shows a jump from a finite negative value up to minus infinity, when the vapor wets the liquid phases, suggesting that the wetting transition is of first order. The calculated phase diagram, together with the wetting phenomenon, strongly suggests the existence of a tricritical point. These results agree well with some experiments carried out in fluid binary mixtures.

Analytical equation of state with three-body forces: Application to noble gases

We developed an explicit equation of state (EOS) for small non polar molecules by means of an effective two-body potential. The average effect of three-body forces was incorporated as a perturbation, which results in rescaled values for the parameters of the two-body potential. These values replace the original ones in the EOS corresponding to the two-body interaction. We applied this procedure to the heavier noble gases and used a modified Kihara function with an effective Axilrod-Teller-Muto (ATM) term to represent the two- and three-body forces. We also performed molecular dynamics simulations with two- and three-body forces. There was good agreement between predicted, simulated, and experimental thermodynamic properties of neon, argon, krypton, and xenon, up to twice the critical density and up to five times the critical temperature. In order to achieve 1% accuracy of the pressure at liquid densities, the EOS must incorporate the effect of ATM forces. The ATM factor in the rescaled two-body energy is most important at temperatures around and lower than the critical one. Nonetheless, the rescaling of two-body diameter cannot be neglected at liquid-like densities even at high temperature. This methodology can be extended straightforwardly to deal with other two- and three-body potentials. It could also be used for other nonpolar substances where a spherical two-body potential is still a reasonable coarse-grain approximation.

Effect of flexibility on liquid-vapor coexistence and surface properties of tangent linear vibrating square well chains in two and three dimensions

The effect of flexibility on liquid-vapor and interfacial properties of tangent linear vibrating square well chains is studied. Surface tension, orthobaric densities, vapor pressures, and interfacial thicknesses are reported and analyzed using corresponding states principles. Discontinuous molecular dynamics simulations in two and three dimensions are performed on rigid tangent linear vibrating square well chains of different lengths. In the case of two dimensions, simulation results of completely flexible tangent linear vibrating square well chains are also reported. Properties are calculated for chains of 2-12 monomers. Rigidity is controlled by trapping the first and last monomer in the chain in a vibrating well at half of the distance of the whole chain. Critical property values are reported as obtained from orthobaric densities, surface tensions, and vapor pressures. For the fully flexible chains, the critical temperatures increase with chain length but the effect saturates. In contrast, the critical temperatures increase for the rigid chains until no more critical point is found.

Metastable liquid lamellar structures in binary and ternary mixtures of Lennard-Jones fluids.

We have carried out extensive equilibrium molecular dynamics simulations to investigate the liquid-vapor coexistence in partially miscible binary and ternary mixtures of Lennard-Jones fluids. We have studied in detail the time evolution of the density profiles and the interfacial properties in a temperature region of the phase diagram where the condensed phase is demixed. The composition of the mixtures is fixed, 50% for the binary mixture and 33.33% for the ternary mixture. The results of the simulations clearly indicate that in the range of temperatures 78<T<102 K-in the scale of argon-the system evolves towards a metastable alternated liquid-liquid lamellar state in coexistence with its vapor phase. These states can be achieved if the initial configuration is fully disordered-that is, when the particles of the fluids are randomly placed on the sites of an fcc crystal or the system is completely mixed. As temperature decreases these states become very well defined and more stables in time. We find that below 90 K, the alternated liquid-liquid lamellar state remains alive for 80 ns, in the scale of argon, the longest simulation we have carried out. Nonetheless, we believe that in this temperature region these states will be alive for even much longer times.