Lianghui Gao

Date of Graduation

2004

Document Type

Dissertation/Thesis

Abstract

In this dissertation, I pursue the constant pressure ensemble approach to elucidate the statistical mechanics of smectic phases of semi-flexible manifolds. I use this approach to consider in detail sterically stabilized phases of semi-flexible polymers in two-dimensional smectic systems. For the first time, the universal constants characterizing the entropic repulsion between semi-flexible polymers are obtained. The thermodynamic limit is quickly approached within this constant pressure ensemble. Then I elucidate the classical problem of the elastic free energy of semi-infinite smectic A that fills the semi-space above an interface (a boundary smectic layer) of a given shape. I obtain an effective interface Hamiltonian that takes into account the system discreteness introduced by the layered character of Smectics A. I use this interface Hamiltonian to develop an efficient novel approach to the statistical mechanics of stacks of infinite semi-flexible manifolds. Within this approach, doing the practically thermodynamic limit is reduced to considering a small stack, with just a few interacting manifolds, representing a subsystem of an infinite smectic. This dramatic reduction in the number of degrees of freedom is achieved by treating the first (the last) manifold of the small stack as an interface with the semi-infinite smectic medium below (above) the small stack. I also study the finite smectic stacks of semiflexible manifolds bounded by interfaces under tension. I address, by analytic calculations and Monte-Carlo simulations, the effects of the surface tension on smectic interlayer distances. These theoretical results are used to elucidate the so-called vapor pressure paradox (VPP) in multi-lamellar membrane phases and explain the experiments. The effects of the interfacial tension are substantially weaker than suggested by the previous theory. By consistently taking into account the discrete, layered character of Smectics, and enharmonic phonon effects, the essence of VPP effects is in spatially non-uniform thermal expansion of smectic interlayer separations. I find 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.

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