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.

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.

We report that Eq. ͑25͒ of this paper contains a mistake deriving from the accidental mixing of two conventions for the normalization of the intermediate scattering functions and other related properties. The correct form of this equation is ͑25͒This equation is one important element of the self-consistent generalized Langevin equation ͑SCGLE͒ theory for colloidal mixtures presented in that paper, which also illustrates the predictive power of this theory by means of its application to a model binary mixture. For this, a systematic quantitative comparison of the numerical results of the theory with Brownian dynamics simulations was performed, which is illustrated in Figs. 1-3. The results of the SCGLE reported in those figures were calculated using the mistaken expression. As it happens, however, in the particular case of binary mixtures, both expressions for ⌬ ␣ * ͑t͒ ͑Eq. ͑25͒ and the corrected equation above͒ coincide when either n 1 or n 2 vanish or when n 1 = n 2 ; these were the conditions for which the specific illustrative calculations were presented in the paper, except for the first and third columns of Fig. 3. Thus, the reported mistake only propagated to the numerical results of the SCGLE theory reported in the this figure.We have re-calculated all the results of the SCGLE theory employing the corrected expression above for ⌬ ␣ * ͑t͒ for the cases in which the correction applies, i.e., n 1 and n 2 different from 0 and different between them. We find that all the conclusions of the paper remain valid, and are even reinforced. As an illustration, here we present a modified version of Fig. 3, in which we have deleted the results of the SEXP approximation ͑dashed lines in the original Fig. 3͒, and have added the corrected SCGLE results ͑lines with black squares͒. For systems with low concentrations ͑left column͒ the changes are imperceptible, whereas for the more concentrated system in the third column, the corrected results are in much better agreement with the simulation data. Thus, the comment in the paper stating that "In contrast, in the right column of Fig. 3, we 0 2 4 6 0.5 0.75 1 D(t)/D 0 φ 1 =.0000725 0 2 4 6 t/t 0 φ 1 =.00022 0 2 4 6 φ 1 =.00066 0 0.5 1 F 11 (k,t) 0 0.5 1 1.5 0 0.5 1 1.5 F 22 (k,t) 0 0.5 1 1.5 kσ 0 0.5 1 1.5 FIG. 3. Corrected version of Fig. 3, in which we have deleted the results of the SEXP approximation ͑dashed lines in the original Fig. 3͒, and have added the corrected SCGLE results ͑lines with black squares͒.

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