First-principles predictor of the location of ergodic/non-ergodic transitions

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 γ 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.

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