  The experimental results presented in this paper show the influence of the
elastic deformation of porous solids on the adsorption process. With p+-type
porous silicon formed on highly boron doped (100) Si single crystal, we can
make identical porous layers, either supported by or detached from the
substrate. The pores are perpendicular to the substrate. The adsorption
isotherms corresponding to these two layers are distinct. In the region
preceding capillary condensation, the adsorbed amount is lower for the membrane
than for the supported layer and the hysteresis loop is observed at higher
pressure. We attribute this phenomenon to different elastic strains undergone
by the two layers during the adsorption process. For the supported layer, the
planes perpendicular to the substrate are constrained to have the same
interatomic spacing as that of the substrate so that the elastic deformation is
unilateral, at an atomic scale, and along the pore axis. When the substrate is
removed, tridimensional deformations occur and the porous system can find a new
configuration for the solid atoms which decreases the free energy of the system
adsorbate-solid. This results in a decrease of the adsorbed amount and in an
increase of the condensation pressure. The isotherms for the supported porous
layers shift toward that of the membrane when the layer thickness is increased
from 30 to 100 microns. This is due to the relaxation of the stress exerted by
the substrate as a result of the breaking of Si-Si bonds at the interface
between the substrate and the porous layer. The membrane is the relaxed state
of the supported layer.
