Studies of phase transitions and critical phenomena: I. Origin of broken particle-hole symmetry in critical fluids. II. Phase transitions of interacting membranes

The longstanding problem of the precise correspondence between critical phenomena in fluids and ferromagnets is resolved in Part I through a synthesis of mean field theory, exact results for lattice models, field-theoretic techniques, and by extensive quantitative comparison with experiment. Emphasis is placed on the origin of broken particle-hole symmetry in fluids as reflected in the form of the critical point scaling fields and in systematic variations in certain nonuniversal critical amplitudes with molecular polarizability. Those trends and the degree to which the scaling axes are linearly mixed versions of the bare "thermal" and "magnetic" fields in particle-hole symmetric systems are shown both for lattice models and real fluids to be intimately related to the presence of many-body interactions of the Axilrod-Teller type. A quantitatively accurate microscopic expression for the field-mixing operator of fluids is derived on the basis of an exact Hubbard-Stratonovich transformation relating the fluid Hamiltonian to that of a Landau-Ginzburg-Wilson model.; A phenomenological theory of the phase behavior of multilamellar liquid crystals of hydrated phospholipid bilayers is developed in Part II, and its predictions tested by extensive comparison with experiment. A Ginzburg-Landau free energy functional based on the elastic properties of two coupled monolayers is proposed to describe intrabilayer ordering, and the phenomenon of structural phase transitions driven by membrane interactions is described by incorporating in addition the attractive dispersion interactions and repulsive "hydration" forces acting between membranes. The theory indicates and experiments support a connection between the pseudocriticality of the bilayer transitions and the large susceptibility of the in-plane order to membrane interactions. The pseudocriticality in turn is suggested to arise from the analog of a capillary critical point accessible by finite-size effects. Theoretical phase diagrams involving planar ({dollar}Lsb{lcub}alpha{rcub}{dollar} and {dollar}Lsb{lcub}beta{rcub}{dollar}) and modulated ({dollar}Psb{lcub}beta{rcub}{dollar}) lamellar phases are in semiquantitative agreement with experiment, as are such predicted characteristics of the modulated structure as the variation of the ripple wavelength and stability of the phase with chainlength and water content. Experiments support the predicted existence of a Lifshitz point accessible by varying chainlength and hydration.