Theory of the Role of Attractive Forces in the Dynamics of Supercooled Liquids under Isochoric and Isobaric Conditions

Microscopic, force-level, dynamical theories of supercooled liquids (e.g., mode-coupling, elastically cooperative nonlinear Langevin equation (ECNLE)) employ a projection approximation that replaces the real forces by a single effective force determined by the equilibrium pair structure. Recent isochoric simulations by Berthier and Tarjus suggest that under isochoric conditions such theories fail to capture the effect of attractions which might not change structure but can strongly slow relaxation. We propose a hybrid dynamical theory where the ECNLE approach with effective forces is employed for repulsions, but for attractions a new projection-less description is developed where the attractive forces directly enter. The theory is applied to the Lennard-Jones and repulsive WCA fluids in the supercooled regime. Under isochoric conditions, we find qualitative agreement with the recent simulations, where attractive forces are important depending on the specific density. Under isobaric conditions, attractive forces are found to be unimportant due to the combined effect of thermal contraction and increasing effective particle size upon cooling. The new theory exhibits density scaling, and realistically predicts the relaxation time of molecular liquids over 14 decades in time.