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We generalize the force-level Nonlinear Langevin Equation theory of singleparticle hopping to include collective effects associated with long rangeelastic distortion of the liquid. The activated alpha relaxation event is of amixed spatial character, involving two distinct, but inter-related, local andcollective barriers. There are no divergences at volume fractions below jammingor temperatures above zero Kelvin. The ideas are first developed andimplemented analytically and numerically in the context of hard sphere fluids.In an intermediate volume fraction crossover regime, the local cage process isdominant in a manner consistent with an apparent Arrhenius behavior. Thesuper-Arrhenius collective barrier is more strongly dependent on volumefraction, dominates the highly viscous regime, and is well described by anonsingular law below jamming. The increase of the collective barrier isdetermined by the amplitude of thermal density fluctuations, shear modulus ortransient localization length, and a growing microscopic jump length. Alpharelaxation time calculations are in good agreement with recent experiments andsimulations on dense fluids and suspensions of hard spheres. Comparisons of thetheory with elastic models and entropy crisis ideas are explored. The presentwork provides a foundation for constructing a quasi-universal,fit-parameter-free theory for relaxation in thermal molecular liquids over 14orders of magnitude in time.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Elastically Cooperative Activated Barrier Hopping Theory of Relaxation  in Viscous Fluids. I. General Formulation and Application to Hard Sphere  Fluids