Liquid crystals thermodynamic properties

New glycolipids have to be synthesized to get further insights into liquid crystal properties (mainly lyotropic liquid crystals), surfactant properties (useful in the extraction of membrane proteins), and factors that govern vesicle formation, stability and tightness. New techniques have to be perfected in order to allow to make precise measurements of thermodynamic and kinetic parameters of binding in 3D-systems and to refine those already avalaible with 2D-arrays. Furthermore, molecular mechanics calculations should also be improved to afford a better modeling of the conformations of carbohydrates at interfaces, in relation with physical measurements such as NMR. 

Liquid crystals have properties intermediate between those of true liquids and crystals. Unlike glasses, they are thermodynamically stable. 

Liquid crystals represent a state of matter with physical properties normally associated with both soHds and Hquids. Liquid crystals are fluid in that the molecules are free to diffuse about, endowing the substance with the flow properties of a fluid. As the molecules diffuse, however, a small degree of long-range orientational and sometimes positional order is maintained, causing the substance to be anisotropic as is typical of soflds. Therefore, Hquid crystals are anisotropic fluids and thus a fourth phase of matter. There are many Hquid crystal phases, each exhibiting different forms of orientational and positional order, but in most cases these phases are thermodynamically stable for temperature ranges between the soHd and isotropic Hquid phases. Liquid crystallinity is also referred to as mesomorphism. 

General reviews of the structure and properties of liquid crystals can be found in the following G. H. Brown, J. W. Doane, and V. D. Neff. "A Review of the Structure and Physical Properties of Liquid Crystals." CRC Press, Cleveland, Ohio, 1971 P. J. Collings and M. Hind, Introduction to Liquid Crystals. Nature s Delicate Phase of Matter," Taylor and Francis, Inc., Bristol. Pennsylvania, 1997 P. J. Collins, "Liquid Crystals. Nature s Delicate Phase of Matter," Princeton University Press. Princeton. New Jersey, 1990. A thermodynamic description of the phase properties of liquid crystals can be found in S. Kumar, editor, "Liquid Crystals in the Nineties and Beyond, World Scientific, Riven Edge, New Jersey, 1995. 

Jorgensen et al. has developed a series of united atom intermolecular potential functions based on multiple Monte Carlo simulations of small molecules [10-23]. Careful optimisation of these functions has been possible by fitting to the thermodynamic properties of the materials studied. Combining these OPLS functions (Optimised Potentials for Liquid Simulation) with the AMBER intramolecular force field provides a powerful united-atom force field [24] which has been used in bulk simulations of liquid crystals [25-27],... 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Liquid crystals are thermodynamic phases composed of a great many molecules. These molecules, termed mesogens, possess a free energy of formation, of course. LCs (their structure, properties, everything that gives them their unique identity), however, are not defined at the level of the constituent molecules any more than a molecule is defined at the level of its constituent atoms. LCs are supermolecules. How do they differ from supramolecular... 

The distinct properties of liquid-crystalline polymer solutions arise mainly from extended conformations of the polymers. Thus it is reasonable to start theoretical considerations of liquid-crystalline polymers from those of straight rods. Long ago, Onsager [2] and Flory [3] worked out statistical thermodynamic theories for rodlike polymer solutions, which aimed at explaining the isotropic-liquid crystal phase behavior of liquid-crystalline polymer solutions. Dynamical properties of these systems have often been discussed by using the tube model theory for rodlike polymer solutions due originally to Doi and Edwards [4], This theory, the counterpart of Doi and Edward s tube model theory for flexible polymers, can intuitively explain the dynamic difference between rodlike and flexible polymers in concentrated systems [4]. 

Liquid crystals, as the name implies, are condensed phases in which molecules are neither isotropically oriented with respect to one another nor packed with as high a degree of order as crystals they can be made to flow like liquids but retain some of the intermolecular and intramolecular order of crystals (i.e., they are mesomorphic). Two basic types of liquid crystals are known lyotropic, which are usually formed by surfactants in the presence of a second component, frequently water, and thermotropic, which are formed by organic molecules. The thermotropic liquid-crystalline phases are emphasized here they exist within well-defined ranges of temperature, pressure, and composition. Outside these bounds, the phase may be isotropic (at higher temperatures), crystalline (at lower temperatures), or another type of liquid crystal. Liquid-crystalline phases may be thermodynamically stable (enantiotropic) or unstable (monotropic). Because of their thermodynamic instability, the period during which monotropic phases retain their mesomorphic properties cannot be predicted accurately. For this reason it is advantageous to perform photochemical reactions in enantiotropic liquid crystals. 

In Chapter 3 we described the structure of interfaces and in the previous section we described their thermodynamic properties. In the following, we will discuss the kinetics of interfaces. However, kinetic effects due to interface energies (eg., Ostwald ripening) are treated in Chapter 12 on phase transformations, whereas Chapter 14 is devoted to the influence of elasticity on the kinetics. As such, we will concentrate here on the basic kinetics of interface reactions. Stationary, immobile phase boundaries in solids (e.g., A/B, A/AX, AX/AY, etc.) may be compared to two-phase heterogeneous systems of which one phase is a liquid. Their kinetics have been extensively studied in electrochemistry and we shall make use of the concepts developed in that subject. For electrodes in dynamic equilibrium, we know that charged atomic particles are continuously crossing the boundary in both directions. This transfer is thermally activated. At the stationary equilibrium boundary, the opposite fluxes of both electrons and ions are necessarily equal. Figure 10-7 shows this situation schematically for two different crystals bounded by the (b) interface. This was already presented in Section 4.5 and we continue that preliminary discussion now in more detail. 

Molecular properties can be classified according to their end-poinl observables, such as chemical I reactivity. solubility, acid-basel. physical (a function of physical state gas. liquid, solid thermodynamic), or biological (ligand or enzyme agonist or antagonist). These properties reflect macroscopic, or bulk, properties, which exist only for the bulk material, e.g.. heat of crystallization, ur microscopic properties, which exist for an ensemble of the molecule. As use of CAMM methods... 

Modem scaling theory is a quite powerful theoretical tool (applicable to liquid crystals, magnets, etc) that has been well established for several decades and has proven to be particularly useful for multiphase microemulsion systems (46). It describes not just interfacial tensions, but virtually any thermodynamic or physical property of a microemulsion system that is reasonably dose to a critical point. For example, the compositions of a microemulsion and its conjugate phase are described by equations of the following form ... 

Lipid-water gel phases were previously regarded as metastable structures that are formed before separation of water and lipid crystals when the corresponding lamellar liquid crystal is cooled. New information on gel phases (see below) reveals that they can form thermodynamically stable phases with very special structural properties. This characteristic makes them as interesting as the lamellar liquid crystals from a biological point of view. 

The electrostatic part, Wg(ft), can be evaluated with the reaction field model. The short-range term, i/r(Tl), could in principle be derived from the pair interactions between molecules [21-23], This kind of approach, which can be very cumbersome, may be necessary in some cases, e.g. for a thorough analysis of the thermodynamic properties of liquid crystals. However, a lower level of detail can be sufficient to predict orientational order parameters. Very effective approaches have been developed, in the sense that they are capable of providing a good account of the anisotropy of short-range intermolecular interactions, at low computational cost [6,22], These are phenomenological models, essentially in the spirit of the popular Maier-Saupe theory [24], wherein the mean-field potential is parameterized in terms of the anisometry of the molecular surface. They rely on the physical insight that the anisotropy of steric and dispersion interactions reflects the molecular shape. 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

We have carried out detailed Monte Carlo (MC) calculations in the isothermal-isobaric ensemble employing the intermolecular potentials of Williams and Cox [19] and Kitaigorodskii [20] along with the intramolecular potentials of Haigh [14], Bartell [21], and BHS [16]. In addition, we have used the potentials of Williams and Kitaigorodskii for the intramolecular contributions. We report thermodynamic properties as well as the crystal and the molecular structures of biphenyl based on these calculations. We also examine the structural aspects of this fascinating molecule in the crystalline (monoclinic) phase at 300 K and 110 K and in the liquid state. 

Indeed, a direct relationship between the lifetimes of films and foams and the mechanical properties of the adsorption layers has been proven to exist [e.g. 13,39,61-63], A decrease in stability with the increase in surface viscosity and layer strength has been reported in some earlier works. The structural-mechanical factor in the various systems, for instance, in multilayer stratified films, protein systems, liquid crystals, could act in either directions it might stabilise or destabilise them. Hence, quantitative data about the effect of this factor on the kinetics of thinning, ability (or inability) to form equilibrium films, especially black films, response to the external local disturbances, etc. could be derived only when it is considered along with the other stabilising (kinetic and thermodynamic) factors. Similar quantitative relations have not been established yet. Evidence on this influence can be found in [e.g. 2,13,39,44,63-65]. 

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