  Random (disordered) components in the surface anchoring of the smectic-A
liquid crystalline film in general modify the thermal pseudo-Casimir
interaction. Anchoring disorder of the quenched type is in general decoupled
from the thermal pseudo-Casimir force and gives rise to an additional
disorder-generated interaction, in distinction to the annealed disorder, whose
effect on the pseudo-Casimir force is non-additive. We consider the effects of
the surface anchoring disorder by assuming that one of the substrates of the
film is contaminated by a disorder source, resulting in a Gaussian-weighted
distribution of the preferred molecular anchoring orientation (easy axes) on
that substrate, having a finite mean and variance or, more generally, a
homogeneous in-plane, two-point correlation function. We show that the presence
of disorder, either of the quenched or annealed type, leads to a significant
reduction in the magnitude of the net thermal fluctuation force between the
confining substrates of the film. In the quenched case this is a direct
consequence of an additive free energy dependent on the variance of the
disorder, while in the annealed case, the suppression of the interaction force
can be understood based on a disorder-renormalized, effective anchoring
strength.
