A New Theory of Dynamic Arrest in Colloidal Mixtures

We present a new first-principles theory of dynamic arrest in colloidal mixtures based on the multi-component self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E {\bf 72}, 031107 (2005); ibid {\bf 76}, 039902 (2007)]. We illustrate its application with the description of dynamic arrest in two simple model colloidal mixtures, namely, the hard-sphere and the repulsive Yukawa binary mixtures. Our results include the observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested, and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the ("fixed point") equations for the non-ergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic--non-ergodic phase diagram of the binary hard-sphere mixture.