F. de J. Guevara-Rodríguez

The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: An integral equation study

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation for a totally asymmetric primitive model electrolyte around a spherical macroparticle is obtained and solved numerically in the case of size-asymmetric systems. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular-dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential versus charge relationship, radial distribution functions, mean electrostatic potential, and cumulative reduced charge for representative examples of 1:1 and 2:2 salts with a size-asymmetry ratio of 2. Our results are collated with those of the modified Gouy-Chapman (MGC) and unequal radius modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size-asymmetry effects. One of the most striking characteristics found is that, contrary to the general belief, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e., counterions do not always dominate. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features cannot be described by traditional mean-field theories such as MGC, URMGC, or even by enhanced formalisms, such as HNC/MSA, if they are based on the RPM.

Communication: Equation of state of hard oblate ellipsoids by replica exchange Monte Carlo

We implemented the replica exchange Monte Carlo technique to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. For this purpose, we considered the analytical approximation of the overlap distance given by Bern and Pechukas and the exact numerical solution given by Perram and Wertheim. For both cases we capture the expected isotropic-nematic transition at low densities and a nematic-crystal transition at larger densities. For the exact case, these transitions occur at the volume fraction 0.341, and in the interval 0.584-0.605, respectively.

Hard ellipsoids: Analytically approaching the exact overlap distance

Following previous work [G. Odriozola and F. de J. Guevara-Rodríguez, J. Chem. Phys. 134, 201103 (2011)], the replica exchange Monte Carlo technique is used to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. Here, in addition to the analytical approximation of the overlap distance given by Berne and Pechukas (BP) and the exact numerical solution of Perram and Wertheim, we tested a simple modification of the original BP approximation (MBP) which corrects the known T-shape mismatch of BP for all aspect ratios. We found that the MBP equation of state shows a very good quantitative agreement with the exact solution. The MBP analytical expression allowed us to study size effects on the previously reported results. For the thermodynamic limit, we estimated the exact 1:5 hard ellipsoid isotropic-nematic transition at the volume fraction 0.343 ± 0.003, and the nematic-solid transition in the volume fraction interval (0.592 ± 0.006)-(0.634 ± 0.008).

A simple model of tracer-diffusion of nonspherical Brownian particles

We present a Brownian dynamic simulation of the translational and rotational motion of an interacting nonspherical Brownian particle. This simulation experiment involves an idealized model system of a suspension of spherical colloidal particles with which the nonspherical particle interacts. The latter is represented as a rigid linear array of (two or three) spherical particles. The direct pair interactions between all the spheres in the system (including those of the tracer particle) are modeled by a repulsive Yukawa potential. For simplicity, the two-dimensional version of this simulation experiment is considered, and hydrodynamic interactions are ignored. From the simulation experiment, we determine the translational and rotational mean-square-displacement of the nonspherical tracer particle. Here we focus only on the early deviations, due to the direct interactions, from the short-time, free-diffusion regime. In the analysis of these results, use is made of the recently developed Generalized Langevin ...

INTERMEDIATE-TIME TRACER-DIFFUSION OF NONSPHERICAL BROWNIAN PARTICLES

The time-dependent tracer-diffusion properties of a nonspherical Brownian particle that interacts with a suspension of spherical particles are studied in terms of an idealized but nontrivial model system for which the predictions of the generalized Langevin equation approach to tracer diffusion can be calculated, and compared with the results of a computer simulation experiment. In the model, the nonspherical particle is represented by a linear array of NT (=2 or 3) spherical particles with nearest-neighbor separation ΔL. For this model, we calculate the rotational and the (transversal and longitudinal) translational mean squared displacements, both, directly from the computer simulation, and approximately using the generalized Langevin equation approach. The theory is found to reproduce qualitatively and quantitatively the main features of the results of the simulation experiment for these properties.

Glass–liquid–glass reentrance in mono-component colloidal dispersions

The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics is employed to describe the ergodic-non-ergodic transition in model mono-disperse colloidal dispersions whose particles interact through hard-sphere plus short-ranged attractive forces. The ergodic-non-ergodic phase diagram in the temperature-concentration state space is determined for the hard-sphere plus attractive Yukawa model within the mean spherical approximation for the static structure factor by solving a remarkably simple equation for the localization length of the colloidal particles. Finite real values of this property signals non-ergodicity and determines the non-ergodic parameters f(k) and f(s)(k). The resulting phase diagram for this system, which involves the existence of reentrant (repulsive and attractive) glass states, is compared with the corresponding prediction of mode coupling theory. Although both theories coincide in the general features of this phase diagram, there are also clear qualitative differences. One of the most relevant is the SCGLE prediction that the ergodic-attractive glass transition does not preempt the gas-liquid phase transition, but always intersects the corresponding spinodal curve on its high-concentration side. We also calculate the ergodic-non-ergodic phase diagram for the sticky hard-sphere model to illustrate the dependence of the predicted SCGLE dynamic phase diagram on the choice of one important constituent element of the SCGLE theory.