Finite-size thermomechanical effects in smectic liquid crystals: The vapor pressure paradox as an anharmonic phenomenon.

We pursue a systematic statistical mechanics study of finite smectic stacks of semiflexible manifolds bounded by interfaces under tension. We address, by analytic calculations and Monte Carlo simulations, the effects of the surface tension on smectic interlayer distances. We use our theoretical results to elucidate the so called vapor pressure paradox (VPP) in multilamellar membrane phases and explain the experiments of Katsaras [Biophys. J. 73, 2924 (1997); 75, 2157 (1998)]. We show that the effects of the interfacial tension are substantially weaker than suggested by the previous theoretical discussion of the VPP effects [R. Podgornik and V. A. Parsegian, Biophys. J. 72, 942 (1997)]. By consistently taking into account the discrete, layered character of smectic liquid crystals, and anharmonic phonon effects, we show that the essence of VPP effects is in spatially nonuniform thermal expansion of smectic interlayer separations. We find that the average period of the whole finite stack can be both smaller (ordinary VPP effect at high enough interfacial tensions) or bigger (a reverse VPP effect at low interfacial tensions, overlooked in previous studies), relative to the average period of the corresponding infinite smectic stack. Looking at stacks from outside, these two effects show up as if there is an attractive (for the ordinary VPP effect), or repulsive (for the reverse VPP effect) pseudo-Casimir force acting between the two stack interfaces. We show however that the physics of VPP effects is obscured by schematically invoking Casimir-like forces. Rather, the ordinary and the reverse VPP effects are to be both characterized as thermomechanical anharmonic effects caused by a spatially nonuniform thermal expansion of smectic interlayer distances. Interlayer distances close to stack surfaces expand less (more) for the ordinary (reverse) VPP effect than those deep in the stack. The reverse VPP prevails at low interfacial tensions, simply because the membrane at the top of the stack is more free to fluctuate than membranes in the bulk. By increasing interfacial tension above a threshold value, fluctuations of the membrane at the stack top become suppressed, and the ordinary VPP effect prevails. In this study, we demonstrate that finite-size VPP effects in a strongly entropic system, such as the sterically stabilized lamellar phases, can be described quantitatively well by a simple analytic approach.