  We extend the force-level ECNLE theory to treat the spatial gradients of the
alpha relaxation time and glass transition temperature, and the corresponding
film-averaged quantities, to the geometrically asymmetric case of finite
thickness supported films with variable fluid - substrate coupling. The latter
typically nonuniversally slows down motion near the solid-liquid interface as
modeled via modification of the surface dynamic free energy caging constraints
which are spatially transferred into the film, and which compete with the
accelerated relaxation gradient induced by the vapor interface. Quantitative
applications to the foundational hard sphere fluid and a polymer melt are
presented. The strength of the effective fluid-substrate coupling has very
large consequences on the dynamical gradients and film-averaged quantities in a
film thickness and thermodynamic state dependent manner. The interference of
the dynamical gradients of opposite nature emanating from the vapor and solid
interfaces is determined, including the conditions for the disappearance of a
bulk-like region in the film center. The relative importance of surface-induced
modification of local caging versus the generic truncation of the long range
collective elastic component of the activation barrier is studied. The
conditions for the accuracy and failure of a simple superposition approximation
for dynamical gradients in thin films is also determined. The emergence of near
substrate dead layers, large gradient effects on film-averaged response
functions, and a weak non-monotonic evolution of dynamic gradients in thick and
cold films, are briefly discussed. The connection of our theoretical results to
simulations and experiments is briefly discussed, as is extension to treat more
complex glass-forming systems under nanoconfinement.
