ABSTRACT: In this paper we apply the self-consistent generalized Langevin equation
theory (SCGLE) of dynamic arrest for colloidal mixtures to predict the glass
transition of a colloidal fluid permeating a porous matrix of obstacles with
random distribution. We obtained the transition diagrams for different size
asymmetries and so we give an asserted description of recent simulations
results [K. Kim, K. Miyazaki, and S. Saito, Europhys. Lett. 88, 36002 (2009)]
of Quenched-Annealed and Equilibrated-Mixture systems which reveal very
different qualitative scenarios which are in apparent contradiction with
theoretical predictions of Mode Coupling Theory (MCT) [V. Krakoviack. Phys.
Rev. E 75, 031503 (2007)]. We show that SCGLE theory predicts the existence of
a reentrant region in EM systems as predicted using MC theory. However,
opposite to MCT predictions, we show that it is practically impossible to
distinguish a rentrant region in QA systems if it would exist. Qualitative
comparisons are in good agreement with simulation results and thus, we propose
SCGLE theory as a useful tool for the interpretation of the arrest transition
in ideal porous systems.
ABSTRACT: The diffusive relaxation of a colloidal fluid adsorbed in a porous medium depends on many factors, including the concentration and composition of the adsorbed colloidal fluid, the average structure of the porous matrix, and the nature of the colloid-colloid and colloid-substrate interactions. A simple manner to describe these effects is to model the porous medium as a set of spherical particles fixed in space at random positions with prescribed statistical structural properties. Within this model one may describe the relaxation of concentration fluctuations of the adsorbed fluid by simply setting to zero the short-time mobility of one species (the porous matrix) in a theory of the dynamics of equilibrium colloidal mixtures, or by extending such dynamic theory to explicitly consider the porous matrix as a random external field, as recently done in the framework of mode coupling theory [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)]. Here we consider the first approach and employ the self-consistent generalized Langevin equation (SCGLE) theory of the dynamics of equilibrium colloidal mixtures, to describe the dynamics of the mobile component. We focus on the short- and intermediate-time regimes, which we compare with Brownian dynamics simulations involving a binary mixture with screened Coulomb interactions for two models of the average static structure of the matrix: a porous matrix constructed by quenching configurations of an equilibrium mixture in which both species were first equilibrated together, and a preexisting matrix with prescribed average structure, in which we later add the mobile species. We conclude that in both cases, if the correct static structure factors are provided as input, the SCGLE theory correctly predicts the main features of the dynamics of the permeating fluid.
Physical Review E 04/2008; 77(4 Pt 1):040401. · 2.26 Impact Factor
ABSTRACT: One of the main elements of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E 62, 3382 (2000); 72, 031107 (2005)] is the introduction of exact short-time moment conditions in its formulation. The need to previously calculate these exact short-time properties constitutes a practical barrier for its application. In this Brief Report, we report that a simplified version of this theory, in which this short-time information is eliminated, leads to the same results in the intermediate and long-time regimes. Deviations are only observed at short times, and are not qualitatively or quantitatively important. This is illustrated by comparing the two versions of the theory for representative model systems.
Physical Review E 01/2008; 76(6 Pt 1):062502. · 2.26 Impact Factor
ABSTRACT: This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.
Physical Review E 11/2007; 76(4 Pt 1):041504. · 2.26 Impact Factor
ABSTRACT: This letter presents a remarkably simple approach to the first-principles determination of the ergodic/non-ergodic transition in monodisperse colloidal suspensions. It consists of an equation for the long-time asymptotic value ° of the mean squared displacement of the colloidal particles, whose finite real solutions signal the non-ergodic state, and determines the non-ergodic parameter f(k). We illustrate its concrete application to three simple model colloidal systems, namely, hard-spheres, hard-spheres plus repulsive (screened Coulomb) Yukawa interaction, and hard-sphere plus attractive Yukawa tail. The results indicate that this is quite a competitive theory, similar in spirit to, but conceptually independent from, the well-known mode coupling theory.
Revista Mexicana de Física. 01/2007;