On a possible microscopic mechanism underlying the vapor pressure paradox

We investigate the free energy and the profile of the displacement field in a stack of sterically interacting smectic multilayers bounded by surfaces under tension. We show that this tension can lead to a significant change in the multilayer free energy. It creates an additional long-range attraction (a pseudo-Casimir attraction) of the van der Waals type and leads to a perturbation in the spatial profile of the displacement field fluctuations. This perturbation can extend to macroscopic distances into the multilayer, away from the perturbing surfaces. The lowering of the free energy of the layers varies explicitly as an inverse power of the thickness of the stack, but also depends implicitly on the bare interactions between the smectic layers. One may regard this lowered energy as being due to a kind of mechanical van der Waals force. We investigate in detail the characteristics and magnitude of the free energy as well as the fluctuations in the displacement field for some typical situations of underlying interlamellar interactions.