Sub-Arrhenius diffusion in a classical system: Binary colloidal mixture in an external potential

Abstract

In the transport processes in many physical systems, the temperature dependence of diffusivity is assumed to be exhibit Arrhenius behavior, i.e., a linear relationship log(D)∝1∕T . When extended to lower temperatures, deviations are observed in many physical systems. The phenomenological description of these deviations identifies them as sub-Arrhenius and super-Arrhenius regimes based on the concave or convex nature of log(D)∝1∕T curve and the activation energy becomes temperature dependent. In general, super-Arrhenius behavior is observed in classical systems such as supercooled liquids where correlated motions play an important role in the dynamical behavior of the system, whereas sub-Arrhenius behavior is proposed to be intimately related to quantum tunneling effect of penetration of an energy barrier along the reaction path as in the case of chemical reactions. In this article, we show that a purely classical system, such as binary colloidal mixture under an external repulsive potential, can undergo sub-Arrhenius diffusion. The depletion interactions between the repulsive potential barrier and larger particles in the presence of the smaller particles contribute to the temperature dependence of activation energy which in turn lead to the sub-Arrhenius diffusion of larger particles in the mixture.