Condensed crystal phases

In contrast to solid state crystallization, crystallization from vapor, solution, and melt phases, which correspond to ambient phases having random structures, may be further classified into condensed and dilute phases. Vapor and solution phases are dilute phases, in which the condensation process of mass transfer plays an essential role in crystal growth. In the condensed melt phase, however, heat transfer plays the essential role. In addition to heat and mass transfer, an additional factor, solute-solvent interaction, should be taken into account. 

The temperatures and pressures for the sH system are very similar to those found in si and sll diagrams. If ahydrate forms in a pipeline with both gas and condensate/oil phases present, examining the pressure-temperature conditions may be insufficient to determine the hydrate crystal structure. 

In Attard s approach, tetramethylorthosilicate (TMOS) was hydrolyzed and condensed in the aqneons domain of the liqnid crystal phase at pH of abont 2, leading to mesostmctured hexagonal, cubic, or lamellar sihca. Methanol from the hydrolysis of TMOS destroys the long-range order of the liquid crystal however, upon the removal of methanol, the lyotropic liquid crystal is restored and serves as the template phase for the further condensation of silicates. The resnlting pore system replicates the shape of the lyotropic mesophase, so this process is also termed nanocasting . 

J is the number of nuclei formed per unit time per unit volume, No is the number of molecules of the crystallizing phase in a unit volume, v is the frequency of atomic or molecular transport at the nucleus-liquid interface, and AG is the maximum in the Gibbs free energy change for the formation of clusters at a certain critical size, 1. The nucleation rate was initially derived for condensation in vapors, where the preexponential factor is related to the gas kinetic collision frequency. In the case of nucleation from condensed phases, the frequency factor is related to the diffusion process. The value of 1 can be obtained by minimizing the free energy function with respect to the characteristic length. 

Keneshea et al. ( ) measured the saturation enthalpy increments above 298.15 K for the condensed phases of NbClg in a drop calorimeter up to the critical point (804 3 K). A figure presented by Keneshea et al. (5) indicated roughly 30 data points, the lowest occurring at approximately 360 K. The differences between the saturation and standard enthalpy increments for the crystal phase are negligible, so that the heat capacity values which we adopt are those which are derived from the reported enthalpy equation, H (T) - H (298.15 K) - [-10.53 + 3.535 x 10 S] 0.07 kcal mol". This equation is reported to apply to the teraerature region 298.15 - 478.9 K. 

Crystal nucleation from the melt is but one type of nucleation in the condensed phase. Other processes of interest include the nucleation of salt crystals from aqueous solution, of one crystalline phase from another or from a glass, and of liquid crystal phases from one another or from the isotropic liquid. In this review we discuss only the nucleation of crystals from the melt. The major emphasis will be on single-component systems, although crystallization of alloys and binary mixtures will also be considered. 

The typical synthesis of mesoporous material can be divided into two main stages (i) Formation of the organic-inorganic liquid-crystal phase (mesophases or mesostructure) results from the self-assembly of surfactant molecules and inorganic species which are polymerizable (or condensable) under synthesis conditions. Moreover, this mesostructure has a crystal lattice with the cell length in the nanometer range, (ii) Removal of surfactant from the mesostructure by calcination at high temperatures or other physical or chemical treatments results in the formation of mesopores (the space occupied by surfactant molecules) in the mesostructure. 

Mesostructure syntheses can be carried out under conditions in which the silicate alone would not condense to solid (at pH 12 14 and low silicate concentration) and the surfactant CTAB (concentration < 2%) alone would not form a lyotropic liquid-crystal phase. The rapid formation of MCM-41 when surfactant solution and silicate solution are combined indicates that there is strong interaction between the cationic surfactant and anionic silicate species in the formation of mesophases. 

Careful control of the surfactant-water content and the rate of condensation of silica at high alkalinity resulted in hollow tubules 0.3 to 3 pm in diameter.[292] The wall of the tubules consisted of coaxial cylindrical pores, nanometers in size, that are characteristic of those of MCM-41. The formation of this higher-order structure may take place through a liquid-crystal-phase transformation mechanism involving an anisotropic membrane-to-tubule phase change. 

The requirement of non-centrosymmetry is not restricted to the molecular level, but also applies to the macroscopic nonlinear susceptibility, which means that the NLO molecules have to be organized in a non-centrosymmetric alignment. The first measurements of the macroscopic second-order susceptibility, have been performed on crystals without centrosymmetry [5]. However, many organic molecules crystallize in a centrosymmetric way. Other condensed oriented phases such as Langmuir-Blodgett (LB) films and poled polymers therefore seem to be the most promising bulk systems for NLO applications. 

Finally, we note that the model itself is not accurate in the ionic crystal phase. The condensed counterions sit on the rods in our model, whereas they really should sit in between the rods. In other words, the structure of the ionic crystal is not captured correctly by the model. Recent calculations argue that multiple moments perpendicular to the rod axis that arise when counterions lie between rods are important to the low-temperature behavior [23], This is probably a source of greater quantitative error at low temperatures than is the Gaussian approximation. 

PEIs were synthesised from pyromellitic anhydride and CO-aminoacids, condensed first to form a di-acid (13) and subsequently reacted with a range of mes-ogen forming diols, e.g. 4,4 -biphenyldiol, 2,6-dihydroxynaphthalene, methyl-, chloro- and phenylhydroquinone. None of the polymers were found to contain a liquid crystal phase [27]. 

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