Expected influence of spatial confinement on glass transitions

The rate of diffusive molecular motions, which are arrested at a glass tran sition, is expected to depend on system size for sufficiently small systems as a result of the cooperative nature of these motions. Two concrete pictu res of such cooperativity are discussed: Sequences of coupled particle jump s as occur in kinetically constrained lattice-gas models, and fluctuations of collective flow as are apparent in MD simulations of simple liquids of h igh density. Collective flow quantitatively explains the size dependence of the velocity-autocorrelation functions (VAFs) at intermediate and long tim es in a very dense binary liquid of hard spheres. A substantial size depend ence of the VAFs is also found at short times t < 7 tau, where tau is the m ean time of free flight, which so far is unexplained. The size dependence o f the self-diffusion coefficients of the mixture depends sensitively on thi s short-time behaviour.