Mechanics of Supercooled Liquids

Abstract

Pure substances can often be cooled below their melting points and still remain in the liquid state. For some supercooled liquids, a further cooling slows down viscous flow greatly, but does not slow down selfdiffusion as much. We formulate a continuum theory that regards viscous flow and selfdiffusion as concurrent, but distinct, processes. We generalize Newton's law of viscosity to relate stress, rate of deformation, and chemical potential. The selfdiffusion flux is taken to be proportional to the gradient of chemical potential. The relative rate of viscous flow and selfdiffusion defines a length, which, for some supercooled liquids, is much larger than the molecular dimension. A thermodynamic consideration leads to boundary conditions for a surface of liquid under the influence of applied traction and surface energy. We apply the theory to a cavity in a supercooled liquid and identify a transition. A large cavity shrinks by viscous flow, and a small cavity shrinks by selfdiffusion.