Intermolecular cubic phases

So what about the cubic phase In polycatenar systems, it is possible to rationalize the formation of cubic phases on the basis of surface curvature alone, which will be considered in subsequent sections. However, it can be argued that, for calamitic systems, these arguments do not hold—at least on their own—and that other factors are important. For example, if cubic-phase formation is due to surface curvature, it is not possible to explain why an Sa phase (lamellar and with no surface curvature) is seen at higher temperatures. An important factor is the presence of specific intermolecular interactions and in the case of the silver systems, these are the intermolecular electrostatic interactions resulting from the presence of formally ionic groups. This is consistent with the observation of cubic phases in the biphenylcarboxylic acids and hydrazines (Fig. 29), as well as with other materials. However, it is also evident that this is not the only factor, as no cubic phase is seen with anion chains shorter than DOS, while other studies with fluorinated alkoxystilbazoles showed that the position of fluorine substitution could determine the presence or absence of the mesophase observed in the unsubstituted derivatives (56). Thus, structural factors are clearly not negligible. 

Since the discovery of the cubic phase numerous substances of quite different chemical structure (Tables 1-4) have been found to be able to form this phase. Therefore the intermolecular interactions leading to the existence of the cubic phases must be of a different nature. In Tables 1-4 it was tried to group the substances according to their possible intermolecular interactions, which mainly determine the appearance of the cubic phase. 

The lack of complete miscibility between cubic phases of substances with different chemical structures points to the peculiarities of the intermolecular interactions in these phases. 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

Room temperatiire powder x-ray diffiracdon profiles have been obtained at hydrostadc pressures P = 0 and 1.2 gigapascals on the solid phase of cubic ( fUUerite ). Within experimental error, the linear compressibility d(ln a)ldP is the same as the interlayer compressibility d(ln c)/dP of hexagonal graphite, consistent with van der Waals intermolecular bonding. Tlie volume compressibility -square centimeter per dyne, 3 and 40 times the values for graphite and diamond, respectively. 

Effect of Unlike-Pair Interactions on Phase Behavior. No adjustment of the unlike-pair interaction parameter was necessary for this system to obtain agreement between experimental data and simulation results (this is, however, also true of the cubic equation-of-state that reproduces the properties of this system with an interaction parameter interesting question that is ideally suited for study by simulation is the relationship between observed macroscopic phase equilibrium behavior and the intermolecular interactions in a model system. Acetone and carbon dioxide are mutually miscible above a pressure of approximately 80 bar at this temperature. Many systems of interest for supercritical extraction processes are immiscible up to much higher pressures. In order to investigate the transition to an immiscible system as a function of the strength of the intermolecular forces, we performed a series of calculations with lower strengths of the unlike-pair interactions. Values of - 0.90, 0.80, 0.70 were investigated. 

Carbon dioxide molecule is the simplest form of linear molecular triatomics abundant in nature. At ambient temperatures, it crystallizes into cubic Pa-3) phase I, known as dry ice , at around 1.5 GPa and then to orthorhombic phase III Cmca) above 12 GPa (see Figs. 4 and 5). Both of these structures commonly appear in many other molecular solids [76, 77], for which stabilities have been well understood in terms of the intermolecular quadrupole-quadrupole interaction. In these phases at relatively low pressures below 15 GPa, the nearest intermolecular separation is in a range of 3.0 to 2.5 A, typically 2 - 2.5 times of the... 

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