James S. Walker

Theory of multiple phase separations in binary mixtures: Phase diagrams, thermodynamic properties, and comparisons with experiments

The lattice‐gas models of phase separating binary liquid mixtures, introduced by Walker and Vause, are studied in detail and generalized within a high‐temperature series expansion. This approximation allows for a straightforward study of rather complex, orientationally specific pair interactions, like those found in real systems. These theories can predict much of the complex miscibility phenomena often found in these mixtures, which are characterized by hydrogen‐bonding interactions. Such phenomena include up to five critical solution points as a function of temperature. By comparisons with experiments, we determine the model parameters, thus mapping these experiments onto the global phase diagrams. These experiments include studies of the dependence of liquid/liquid miscibility on temperature, pressure, concentration of electrolytes, and addition of a dilute third component. Specifically, we make direct comparison with various experiments on the binary systems 2‐butanol+H2O, 3‐methyl pyridine+H2O(D2O), ...

Lattice theory of binary fluid mixtures: Phase diagrams with upper and lower critical solution points from a renormalization‐group calculation

A generalized lattice model representing the interaction between two molecular species in a binary liquid mixture is introduced. The model interaction potential consists of a highly directionally‐dependent orientational part, due to hydrogen bonding, coupled to the configurational van der Waals interaction. Closed‐loop temperature vs concentration solubility phase diagrams are produced in good agreement with experimental systems. These diagrams are obtained using renormalization‐group methods. The possible types of phase diagrams predicted by the phenomenological Landau theory are also discussed.

Effects of orientational degrees of freedom in closed-loop solubility phase diagrams

Abstract It is shown, within a lattice-gas model calculation, how fluctuating orientational degrees of freedom are responsible for closed-loop phase diagrams observed in many binary liquid mixtures. Quantitative agreement with experiment is obtained, and qualitative features, such as the shape of the closed-loops, are related to molecular properties of the liquids in the mixture.

Renormalization group theory in solution thermodynamics

Abstract Renormalization group theory is a powerful technique from condensed matter physics that has many potential applications in applied molecular thermodynamics, although it has not yet been widely used by chemical engineers. In this review the fundamental ideas of the method are described in the language of solution thermodynamics. A detailed description of a representative renormalization technique—the Migdal-Kadanoff method—is given. Applications both to simple liquid mixtures and to complex hydrogen-bonding mixtures are described.

Reentrant transitions in liquid crystals: theoretical predictions of new phenomena

Abstract A new mechanism is proposed for the reentrant nematic-smectic A-nematic transitions seen in several liquid crystals. The mechanism applies in particular to systems with strong dipolar head-group interactions, and involves a subtle interplay between these forces and the Lennard-Jones interactions of the tails. A simple model which embodies the mechanism is developed, and solved exactly. In addition to providing an understanding of the experiments to date, our model makes definite predictions for new types of reentrant phase diagrams.

Deuteron tunneling at electron-volt energies

We speculate on a new mechanism for deuteron-deuteron fusion reactions at electron-volt energies. Appealing to conservation principles, it is shown that deuteron tunneling leading to fusion is very unlikely to take place between two isolated deuterons. It is argued that in solids, however, tunneling may lead to fusion via a new reaction mechanism which populates energy levels of4He, with simultaneous energy transfer to an electron. Predictions of this theory are that d+d+e− fusion at electron-volt energies in solids should lead to copious production of tritium, protium, energetic electrons, and small quantities of4He.

Lattice Theory for Helix-Coil Induced Reentrant Isotropic-Nematic Transitions

Abstract A lattice model is proposed to study reentrant isotropic-nematic phase transitions mediated by helix-coil transformations within individual liquid crystal molecules. The system consists of a racemic mixture of molecules in solution with a solvent capable of hydrogen bonding. We first introduce a model to describe helix-coil transformations in the presence of such a solvent. This model displays not only normal helix-coil transformations, but also inverted transformations (i.e. reentrant), as well as reversion to the coiled state at high temperatures. Secondly, we develop a model for the isotropic-nematic phase transition which incorporates intermolecular interactions on the same footing with the intramolecular interactions. Reentrance of the isotropic phase is driven by the inverted helix-coil transformation. Within the nematic phase the effect of induced rigidity is observed. In addition, when solvent-solvent bonding is important in the system, doubly reentrant phase diagrams are predicted. We st...

INTERACTION-DRIVEN ASYMMETRIC COEXISTENCE CURVES AND THE SINGULAR DIAMETER

Abstract The interplay of asymmetric interactions and density fluctuations in binary liquid mixtures is shown to produce a breakdown of the law of rectilinear diameter. We find that this singularity and the overall phase diagram asymmetry are suppressed with increasing pressure. These considerations suggest the systems in which the diameter anomaly should be most readily observed.

Multiple reentrance and fractal phase boundaries in the Barker–Fock model

The Barker–Fock model, which addresses the issue of closed-loop phase diagrams in binary liquid mixtures, is shown to exhibit a wealth of interesting and rather unexpected physical phenomena. For example, renormalization-group studies indicate that in addition to the standard closed-loop diagrams seen in many binary liquid mixtures, the Barker–Fock model also yields multiple reentrance – perhaps of unlimited degree. In addition, one of the “phase boundaries” in the model is actually many separate phases mixed together to form a “fractal foam”. Behavior of this kind is interesting in its own right, and particularly so when the underlying model has direct physical relevance.

An infinity of phase transitions as a function of temperature: exact results for a model with fixed-point imaging

Position-space renormalization-group methods are used to derive exact results for an Ising model on a fractal lattice. The model incorporates both nearest-neighbor and long-range interactions. The long-range interactions, which span all length scales on the lattice, can be thought of as resulting from fractal periodic boundary conditions. We present exact phase diagrams and specific heats in terms of these two interactions, and show that a “hall of mirrors” fixed-point imaging mechanism leads to an infinite number of phase transitions.