Expected influence of spatial confinement on glass transitions

Abstract
The rate of diffusive molecular motions, which are arrested at a glass transition, is expected to depend on system size for sufficiently small systems as a result of the cooperative nature of these motions. Two concrete pictures of such cooperativity are discussed : Sequences of coupled particle jumps as occur in kinetically constrained lattice-gas models, and fluctuations of collective flow as are apparent in MD simulations of simple liquids of high density. Collective flow quantitatively explains the size dependence of the velocity-autocorrelation functions (VAFs) at intermediate and long times in a very dense binary liquid of hard spheres. A substantial size dependence of the VAFs is also found at short times t < 7τ , where τ is the mean time of free flight, which so far is unexplained. The size dependence of the self-diffusion coefficients of the mixture depends sensitively on this short-time behaviour.