Magdaleno Medina-Noyola

Time-dependent self-diffusion in model suspensions of highly charged Brownian particles

A quantitative comparison is reported between the predictions of two theories of the time-dependent self-diffusion properties of suspensions of highly charged Brownian particles. The first theory, based on the overdamped N-body Fokker-Planck dynamics, involves a mode-mode coupling approximation for the time-dependent self-friction function, whereas the second one makes use of short-time conditions derived from the N-body Smoluchowski equation. In both cases, the relevant dynamic properties can be expressed in terms solely of the radial distribution function g(r). This quantity is first calculated using the rescaled mean spherical approximation (RMSA). By comparing with computer simulation results for g(r), it is found that the RMSA becomes increasingly inaccurate as the freezing transition is approached. We observe, however, that the RMSA itself provides a device to fit the simulation results for g(r). Using this procedure, the time-dependent self-diffusion coefficient, calculated from both theories, is in good agreement with Brownian dynamics simulations.

Rescaled mean spherical approximation for colloidal mixtures

In this work, the rescaled mean spherical approximation (RMSA) for colloidal mixtures interacting via a DLVO-type potential is developed, and its application to suspensions of highly charged macroions is illustrated. For this purpose we introduce a simple scheme to solve the mean spherical approximation (MSA) for Yukawa mixtures with factorized coupling parameters. This scheme consists of the mapping of the Yukawa system onto a corresponding primitive model system. Such a correspondence is used as a device for the calculation of the static structure functions of the original Yukawa mixture. Within this scheme, a straightforward implementation of the rescaling procedure is performed, which allows for the calculation of partial structure factors in strongly interacting mixtures. The rescaling procedure we use is an extension of that introduced by Hansen and Hayter for monodisperse suspensions. The structure factors obtained with the rescaled mean spherical approximation compare well with computer simulation results. The advantages and limitations of the RMSA are also discussed in some detail.

Structural properties of solutions of spherical micelles: Effect of finite size of small ions

The effects of a finite size of the small ions (counterions and ions of 1–1 electrolytes added to the supporting solution) on the structural properties of solutions of spherical micelles are studied. This study is based on the primitive model of the solution and the mean spherical approximation. The structure obtained using the primitive model is contrasted with that of the one component macrofluid model for these systems. At high ionic strengths, interesting effects are observed in the short‐range correlations between the macroparticles, directly related with the finite size of the small ions. Similar effects are also observed on the structure of the electrical double layer around each macroparticle. The consequences of these results for the interpretation of recent neutron scattering experiments from ionic micellar systems are briefly discussed. It is found that for small amounts of added salt a given experimental structure factor can be reproduced with a smaller effective charge on a micelle in the pre...

Statics and tracer-diffusion in binary suspensions of polystyrene spheres: experiment vs. theory

Extensive measurements of the static and dynamic field autocorrelation function of dilute bidisperse suspensions of charged polystyrene spheres, obtained by static and dynamic light scattering experiments, are discussed in terms of the two-component macroion fluid model. The suspensions under study consist of a small amount of large spheres immersed in a system of small spheres. For these suspensions the self-scattering function at short and intermediate times can be determined by dynamic light scattering (DLS), performed at large wavenumbers. The self-scattering function contains information on the tracer-diffusion of both small and large spheres. The experimentally observed self-scattering functions of the binary mixtures are compared with theoretical calculations based on the so-called single exponential approximation (SEXP). The SEXP is based on the exact short-time behavior of the single particle dynamics and within it the dynamic properties are entirely expressed in terms of the partial static structure functions. The latter are calculated using the extended rescaled mean spherical approximation (RMSA) for colloidal mixtures. Good agreement between experimental data and the SEXP theory has been found.

Aging of a homogeneously quenched colloidal glass-forming liquid.

The nonequilibrium self-consistent generalized Langevin equation theory of colloid dynamics is used to describe the nonstationary aging processes occurring in a suddenly quenched model colloidal liquid with hard-sphere plus short-ranged attractive interactions, whose static structure factor and van Hove function evolve irreversibly from the initial conditions before the quench to a final dynamically arrested state. The comparison of our numerical results with available simulation data are highly encouraging.

STRUCTURE AND SELF-DIFFUSION IN A MODEL TWO-DIMENSIONAL BROWNIAN LIQUID

The static structure and the time‐dependent self‐diffusion motion of interacting Brownian particles in a model two‐dimensional suspension are discussed. For the static structure we report Brownian dynamics results assuming a hard disk plus Yukawa pair potential. The self‐diffusion properties of this model system are calculated from two independent theoretical approaches. In order to assess the accuracy of the predictions of these two theories, we also performed Brownian dynamics calculations of the time‐dependent self‐diffusion coefficient for a wide range of values of both the particle concentration and the pair potential coupling constant. We find that both theories reproduce very well the main features exhibited by the Brownian dynamics data. Quantitatively, there are some discrepancies between both theoretical predictions and the Brownian dynamics results, which are negligible at moderate couplings, but become larger for strongly coupled systems and long times.

Spatial correlations between charged colloidal particles: The mean spherical (dense point limit) approximation

The static structure factor of a suspension of charged polystyrene spheres is calculated within a Debye–Huckel level of approximation. This is based on the mean spherical closure of the Ornstein–Zernike integral equation of the primitive model of the ionic solution constituted by the macroparticles and their counterions, in the limit negligible size of the latter. The explicit calculations in the dense point limit (charge of the counterions/charge of the macroparticles→0) are compared with the experimental results and it is found that this extremely simple theory reproduces the main features of the liquidlike structure of the suspension. Further quantitative refinements of the theory are naturally suggested by the method employed here, in which this Debye–Huckel approximation is the simplest nontrivial application.

Theory of self-diffusion of highly charged spherical Brownian particles

Starting from the N-particle Smoluchowski equation without hydrodynamic interactions the authors derived an expression for the mean square displacement by modelling the memory function entered in the equation for the incoherent scattering function. The numerical evaluation of that expression is done for the case of spherical particles interacting via a screened Coulombic potential. The results of this theory compare favourably with computer simulation results.

Dynamic equivalence between atomic and colloidal liquids

We show that the kinetic-theoretical self-diffusion coefficient of an atomic fluid plays the same role as the short-time self-diffusion coefficient DS in a colloidal liquid, in the sense that the dynamic properties of the former, at times much longer than the mean free time, and properly scaled with DS, will be indistinguishable from those of a colloidal liquid with the same interaction potential. One important consequence of such dynamic equivalence is that the ratio DL/DS of the long-time to the short-time self-diffusion coefficients must then be the same for both an atomic and a colloidal system characterized by the same inter-particle interactions. This naturally extends to atomic fluids a well-known dynamic criterion for freezing of colloidal liquids (L?wen H. et al., Phys. Rev. Lett., 70 (1993) 1557). We corroborate these predictions by comparing molecular and Brownian dynamics simulations on the hard-sphere system and on other soft-sphere model systems, representative of the ?hard-sphere?dynamic universality class.

Electrolyte friction on non-spherical polyions

Abstract In this Letter we present theoretical results for the electrolyte friction effects on the translational Brownian motion of non-spherical polyions. We show that electrolyte friction effects may become comparatively much larger for a needle-like macroion than for a sphere of similar charge and size.