Liquid crystalline state thermodynamics

In addition to this thermotropic mesomorphism, a lysotropic mesomorphism is observed [98]. The phase transition temperature, Tt, for the transition from the crystalline to the liquid crystalline state decreases as a function of water content. The decrease in Ttis due to destabilization of the crystal lattice in the head group region by water molecules. This, in turn, decreases the interaction between the fatty acid chains. When the water content reaches a certain level, the phospholipids assume a thermodynamically optimal arrangements whereby the fatty acids are directed to the... 

Abstract. Free-volume structure in the lanthanum salt of laurinic acid in crystalline and liquid-crystalline states and an effect of dissolved Cgo molecules on the mean nanovoid radius and concentration were studied by means of the positron annihilation technique. La(Ci2H25COO)3 clathrate compound with dissolved C6o molecules was obtained, which is thermodynamically more stable than a simple mixture of components. Increased mean nanovoid radius (from 0.28 to 0.39 nm) after the inclusion of C6o molecules and concomitant decrease of the positronium annihilation rate by a factor of 2.7 indicate the decrease of the smallest nanovoid concentration. 

It was found that when a certain concentration is attained, the solutions of these polymers acquire thermodynamically stable properties of anisotropy, still retaining relatively high mobility, i.e. they exhibit the properties typical of the liquid crystalline state. 

The liquid crystal state for low molecular weight compounds such as cholesterol esters has been known for more than 75 years. This is a mesomorphic state of matter, intermediate between the crystal state and the liquid state. In the liquid crystalline state the molecules retain preferential orientations relative to one another over large distances—a property normally associated with the crystalline state yet liquid crystals from low molecular weight substances are highly fluid in their thermodynamically stable condition. 

Objects with L D and L D are regarded as rods and discs respectively, and the theory applies for both rods and discs. At a larger aspect ratio and high particle concentration, if the particles partially stop thermodynamical free rotation and lose orientational entropy, the loss of entropy is compensated and outweighed by the gain in excluded volume entropy. Thus an anisotropic colloid transits from isotropic to liquid crystalline state. 

Nowadays a wealth of experimental and theoretical methods are available to investigate the mesomorphic behavior of liquid crystals. For a detailed description of the liquid crystalline state the reader is referred to textbooks,review articles," and to proceedings of recent confer-ences. " We mention only briefly examples of mesogenic compounds with some thermodynamic properties, especially for those which have been studied dielectrically at elevated pressures (see below). 

A broader thermodynamic examination of the phase equilibria involving the liquid-crystalline phase should also include consideration of the effect of pressure, although a change in the pressure within moderate limits should not strongly affect the position of the phase equilibrium regions for condensed systems. Application of an external deforming field should first be expressed by a shift in the boundaries of the transition to the liquid-crystalline state, since pressure results in a decrease in the free volume of the system and limitation of... 

Precipitation of the polymer on addition of a nonsolvent or with any changes in the thermodynamic parameters in solutions whose conc tration is below the critical point of the transition to the liquid-crystalline state is the most typical case of the intermediate phase equilibrium in rigid-chain polymer-solvent systems. Instead of the anticipated establishment of isotropic-anisotrqric phase equilibrium, equilibrium of two amorphous (isotropic) phases initially arises if the parameter x attains values greater than +0.5. 

Some of the distinctions that we shall have to examine in more detail before proceeding much further are the considerations of order versus disorder, solid versus liquid, and thermodynamics versus kinetics. These dualities are taken up in the next section. With those distinctions as background, we shall examine both the glassy and crystalline states from both the experimental and modelistic viewpoint. 

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. 

This condition means that for f < 0.63 the disordered arrangement of molecules is thermodynamically unstable and the system is spontaneously reorganized into an ordered liquid crystalline phase of a nematic type (Flory called this state crystalline ). This result has been obtained only as a consequence of limited chain flexibility without taking into account intermolecular interactions. 

The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. 

In the present article, we focus on the scaled particle theory as the theoretical basis for interpreting the static solution properties of liquid-crystalline polymers. It is a statistical mechanical theory originally proposed to formulate the equation of state of hard sphere fluids [11], and has been applied to obtain approximate analytical expressions for the thermodynamic quantities of solutions of hard (sphero)cylinders [12-16] or wormlike hard spherocylinders [17, 18]. Its superiority to the Onsager theory lies in that it takes higher virial terms into account, and it is distinctive from the Flory theory in that it uses no artificial lattice model. We survey this theory for wormlike hard spherocylinders in Sect. 2, and compare its predictions with typical data of various static solution properties of liquid-crystalline polymers in Sects. 3-5. As is well known, the wormlike chain (or wormlike cylinder) is a simple yet adequate model for describing dilute solution properties of stiff or semiflexible polymers. 

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