Interactions and Phase Transitions

In principle, if the electronic stracture of a liquid crystal molecule is known, one can deduce the various thermodynamical properties. This is a monumental task in quantum statistical chemistry that has seldom, if ever, been attempted in a quantitative or conclusive way. There are some fairly rehable guidelines, usually obtained empirically, that relate molecular stmctures with the existence of the liquid crystal mesophases and, less rehably, the corresponding transition temperatures. 

One simple observation is that to generate liquid crystals, one should use elongated molecules. This is best illrrstratedby the CB homolog n = 1,2,3.). For u 4, the material does not exhibit a nematic phase. For n = 5-7, the material possesses a nematic range. For 8, smectic phases begin to appear. 

Another reliable observation is that the nematic isotropic phase transition tem- 

Such molecrrlar-stmcture-based approaches are clearly extremely complex and often tend to yield contradictory predictions, because of the wide variation in the molecrrlar electronic stmctures and intermolecirlar interactions present. In order to explain the phase transition and the behavior of the order parameter in the vicinity of the phase transition temperature, some simpler physical models have been employed. For the nematic phase, a simple but qirite successful approach was introduced by Maier and Saupe. The liquid crystal molecirles are treated as rigid rods, which are correlated (described by a long-range order parameter) with one another by Corrlomb interactions. For the isotropic phase, deGennes introduced a Landau type of phase transition theory, which is based on a short-range order parameter. 

The theoretical formalism for describing the nematic isotropic phase transition and some of the results and consequences are given in the next section This is followed by a surrrmary of some of the basic concepts irrtroduced for the isotropic phase. 

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Di Salvo, F. J. (1977) in Electron-Phonon Interactions and Phase Transitions (ed. Riste, T.) Plenum Press, New York, p. 107. 

A variety of publications are dealing with T1 relaxation measurements in combination with NOE experiments to investigate the reorientational dynamics of ionic liquids in solution (and sometimes also in the solid state) [17-22], The data can then be interpreted concerning inter-ionic interactions and phase transitions. 

Thomas, H. Theory of Jahn-Teller Transitions. In Riste, T. (ed.) Electron-Phonon Interactions and Phase Transitions, p. 245. New Yoik-London Plenum Press 1977... 

Herbut, I. (2006). Interactions and phase transitions on graphene s honeycomb Lattice. Phys. Rev. Lett. 97,146401. 

H. Lowen, E. Allahyarov, J. Dzubiella, C. von Ferber, A. Jusufi, C. N. Likos, and M. Heni, Interactions and phase transitions of colloidal dispersions in bulk and at interfaces, Phil Trans. R. Soc. London A 359, 909-920 (2000). 

Carri, G.A. and Muthukumar, M., 1999. Attractive interactions and phase transitions in solutions of similarly charged rod-Uke polyelectrolytes, J. Chem. Phys., Ill, 1765-1777. 

G. A. Carri and M. Muthukumar,/. Chem. Phys., Ill, 1765 (1999). Attractive Interactions and Phase Transitions in Solutions of Similarly Charged Rod-Like Polyelectrolytes. 

The theory of quenched-annealed fluids is a rapidly developing area. In this chapter we have attempted to present some of the issues already solved and to discuss only some of the problems that need further study. Undoubtedly there remains much room for theoretical developments. On the other hand, accumulation of the theoretical and simulation results is required for further progress. Of particular importance are the data for thermodynamics and phase transitions in partly quenched, even quite simple systems. The studies of the models with more sophisticated interactions and model complex fluids, closer to the systems of experimental focus and of practical interest, are of much interest and seem likely to be developed in future. 

Then, there are model Hamiltonians. Effectively a model Hamiltonian includes only some effects, in order to focus on those effects. It is generally simpler than the true full Coulomb Hamiltonian, but is made that way to focus on a particular aspect, be it magnetization, Coulomb interaction, diffusion, phase transitions, etc. A good example is the set of model Hamiltonians used to describe the IETS experiment and (more generally) vibronic and vibrational effects in transport junctions. Special models are also used to deal with chirality in molecular transport junctions [42, 43], as well as optical excitation, Raman excitation [44], spin dynamics, and other aspects that go well beyond the simple transport phenomena associated with these systems. 

The book thus embraces an extended study on a variety of issues within the theory of orientational ordering and phase transitions in two-dimensional systems as well as the theory of anharmonic vibrations in low-dimensional crystals and dynamic subsystems interacting with a phonon thermostat. For the sake of readability, the main theoretical approaches involved are either presented in separate sections of the corresponding chapters or thoroughly scrutinized in appendices. The latter contain the basic formulae of the theory of local and resonance states for a system of bound harmonic oscillators (Appendix 1), the theory of thermally activated reorientations and tunnel relaxation of orientational... 

The book covers a variety of questions related to orientational mobility of polar and nonpolar molecules in condensed phases, including orientational states and phase transitions in low-dimensional lattice systems and the theory of molecular vibrations interacting both with each other and with a solid-state heat bath. Special attention is given to simple models which permit analytical solutions and provide a qualitative insight into physical phenomena. 

This review describes experimental techniques, then gives some selected results of H, and NMR studies of pressure effects on the structure, dynamics and phase transitions of phospholipid bilayers. Other examples deal with 2D-NOESY experiments on lipid vesicles and pressure effects on the interaction of anaesthetics with phospholipid bilayers. Furthermore, we discuss... 

We note that earlier research focused on the similarities of defect interaction and their motion in block copolymers and thermotropic nematics or smectics [181, 182], Thermotropic liquid crystals, however, are one-component homogeneous systems and are characterized by a non-conserved orientational order parameter. In contrast, in block copolymers the local concentration difference between two components is essentially conserved. In this respect, the microphase-separated structures in block copolymers are anticipated to have close similarities to lyotropic systems, which are composed of a polar medium (water) and a non-polar medium (surfactant structure). The phases of the lyotropic systems (such as lamella, cylinder, or micellar phases) are determined by the surfactant concentration. Similarly to lyotropic phases, the morphology in block copolymers is ascertained by the volume fraction of the components and their interaction. Therefore, in lyotropic systems and in block copolymers, the dynamics and annihilation of structural defects require a change in the local concentration difference between components as well as a change in the orientational order. Consequently, if single defect transformations could be monitored in real time and space, block copolymers could be considered as suitable model systems for studying transport mechanisms and phase transitions in 2D fluid materials such as membranes [183], lyotropic liquid crystals [184], and microemulsions [185],... 

An interesting case of SB is presented by enantiomer formation. In recent papers [15] it was shown that enantiomers can be presented as the low symmetry, PJT distorted configurations of a hypothetical high-symmetry structure, and as such their interaction in the liquid phase via collisions under special conditions may lead to some kind of cooperativity and phase transition (SB) resulting in singleenantiomer broken symmetry configuration. 

This chapter reviews recent studies on energy levels and excited state dynamics of lanthanides (R) in nano-structures, which include R-doped dielectric nano-crystals, implanted nano-particles of semiconductors, coated core-shell nano-particles, nano-tubes and nano-balls stuffed with R ions. New phenomena such as the action of confinement on ion-phonon interaction and its consequences for electronic transitions, energy transfer, and phase transitions are discussed in the light of experimental and theoretical studies reported in the literature. Although the review aims at being comprehensive and covers all the important aspects in the field, emphasis is given to identification and theoretical analysis of various mechanisms for... 

D. Y. Yoon, Polym. Prepr. ACS, Div. Polym. Chem., 30(2j, 71 (1989). Chain Packing and Phase Transition of Cubic-Lattice Polymer Systems with Orientation-Dependent Interactions. 

This model is based on quasimolecular dynamics, in which the medium is assumed to be composed of an assembly of meso-scale discrete particles (i.e., finite elements). Tlie movement and deformation of the material system and its evolution are described by the aggregate movements of these elements. Two types of basic characteristics, geometrical and physical, are considered. In tlie geometrical aspect, sliapes and sizes of elements and tlie manner of their initial aggregation and arrangement are the important factors. In the physical aspect, mechanical, physical, and chemical characteristics, such as the interaction potential, phase transition, and chemical reactivity may be tlie important ones. To construct this model, many physical factors, including interaction potential, friction of particles, shear resistance force, energy dissipation and temperature increase, stress and strain at the meso- and macro-levels, phase transition, and chemical reaction are considered. In fact, simulation of chemical reactions is one of the most difficult tasks, but it is the most important aspect in shock-wave chemistiy. 

Solid hydrate research of the last fifteen years is critically evaluated with regard to bonding and structure of water molecules. This review focusses on new results of structure determination and infrared and Raman studies in terms of hydrogen bonding and other intermolecular bonding interactions, distortion and disorder of water molecules, intermolecular and intramolecular coupling and anharmonicity of water bands, isotopic effects, and phase transitions. The techniques used for structure determination and spectroscopic measurements of solid hydrates are discussed. 

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