  The relaxation dynamics of glass forming liquids and their structure are
influenced in the vicinity of confining walls. In view of the great potential
of this effect for applications in those fields of science and industry, where
liquids occur under strong confinement (e.g., nano-technology), the number of
researchers studying various aspects and consequences of this non-monotonic
behaviour has been rapidly growing. This review aims at providing an overview
of the research activity in this newly emerging field. We first briefly discuss
how competing mechanisms such as packing effects and short-range attraction may
lead to a non-monotonic glass transition scenario in the bulk. We then analyse
confinement effects on the dynamics of fluids using a thermodynamic route which
relates the single particle dynamics to the excess entropy. Moreover, relating
the diffusive dynamics to the Widom's insertion probability, the oscillations
of the local dynamics with density at moderate densities are fairly well
described. At high densities belonging to the supercooled regime, however, this
approach breaks down signaling the onset of strongly collective effects.
Indeed, confinement introduces a new length scale which in the limit of high
densities and small pore sizes competes with the short-range local order of the
fluid. This gives rise to a non-monotonic dependence of the packing structure
on confinement, with a corresponding effect on the dynamics of structural
relaxation. This non-monotonic effect occurs also in the case of a cone-plate
type channel, where the degree of confinement varies with distance from the
apex. This is a very promising issue for future research with the possibility
of uncovering the existence of alternating glassy and liquid-like domains.
