Theoretical unification between Quenched-Annealed and Equilibrated-Mixture Systems

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.