Crystallinity equilibrium

The analysis of hydrotropic action is conveniently divided into two parts (1) The isotropic llquld/llquld crystalline equilibrium between essential phases and (2) The molecular mechanism for the Influence of the hydrotrope on the equilibrium. 

Crystalline equilibrium, which is characteristic for polymer solutes separating into phases when transferring into the temperature and concentration zone of confined compatibility of components (i) crystalline polymer and (ii) non-saturated (low-concentration) polymer solution in a solvent. 

Liquid-crystalline equilibrium is typical of solutions decomposing into two phases with increasing polymer content, i.e. isotropic (low-concentration) and anisotropic (highly concentrated) polymer solutions converting further into a single-phase liquid-crystalline system. 

Shadowspeaker, L., Shah, M., and Busch, R. (2004) On the crystalline equilibrium phases of the Zr57Cui5.4Nii2.6AlioNb5 bulk metallic glass-forming alloy, Scripta Mater., 50, 1035-1038. 

In Fig. 4.3 we also plot the (equilibrium) binodals using FVT outlined in Chap. 3 for hard spheres plus penetrable hard spheres with diameters of 2Rg. Qualitatively, the phase diagram topology is quite well predicted. For q = 0.08, only equilibrium fluid, crystal and fluid + crystal regions are found and predicted. Both for q = 0.57 and 1 the phase diagram contains fluid, gas, liquid and crystalline (equilibrium) phases. In the different unmixing regions one now finds gas-liquid coexistence with a critical point, three-phase gas-liquid-crystal and... 

Although examples of the successive passage to crystalline equilibrium through the stage of liquid equilibrium are relatively well known from general considerations, they were established by a direct experiment in [51] for some systems with an intermediate phase of liquid-crystalline equilibrium, and this should be discussed in more detail. 

Oligomer systems are typically described by phase diagrams of an amorphous equilibrium according to classification by S.P. Papkov [168,206]. Sometimes amorphous-crystalline equilibrium [134,165] is observed [134,165]. The majority of oligomer system phase diagrams is asymmetric and has upper critical solubility temperature (UCST). 

By saccharic acid is usually meant D-gluco-saccharic acid, m.p. 125-126°C, obtained by the oxidation of glucose or starch. This exists in water solution in equilibrium with its two y lactones, both of which can be obtained crystalline, though the acid itself does not crystallize readily. 

The surface tensions for a certain cubic crystalline substance are 7100 = 160 ergs/cm, 7110 = 140 eigs/cm, and 7210 = 7120 = 140 ergs/cm. Make a Wulff construction and determine the equilibrium shape of the crystal in the xy plane. (If the plane of the paper is the xy plane, then all the ones given are perpendicular to the paper, and the Wulff plot reduces to a two-dimensional one. Also, 7100 = 7010. etc.)... 

Broadening of spots can result from themial diffuse scattering and island fomiation, among other causes. The themial effects arise from the disorder in atomic positions as they vibrate around their equilibrium sites the sites themselves may be perfectly crystalline. 

From the standpoint of thermodynamics, the dissolving process is the estabHsh-ment of an equilibrium between the phase of the solute and its saturated aqueous solution. Aqueous solubility is almost exclusively dependent on the intermolecular forces that exist between the solute molecules and the water molecules. The solute-solute, solute-water, and water-water adhesive interactions determine the amount of compound dissolving in water. Additional solute-solute interactions are associated with the lattice energy in the crystalline state. 

Solvent Resistance. At temperatures below the melting of the crystallites, the parylenes resist all attempts to dissolve them. Although the solvents permeate the continuous amorphous phase, they are virtually excluded from the crystalline domains. Consequently, when a parylene film is exposed to a solvent a slight swelling is observed as the solvent invades the amorphous phase. In the thin films commonly encountered, equilibrium is reached fairly quickly, within minutes to hours. The change in thickness is conveniently and precisely measured by an interference technique. As indicated in Table 6, the best solvents, specifically those chemically most like the polymer (eg, aromatics such as xylene), cause a swelling of no more than 3%. 

One of the simplest cases of phase behavior modeling is that of soHd—fluid equilibria for crystalline soHds, in which the solubility of the fluid in the sohd phase is negligible. Thermodynamic models are based on the principle that the fugacities (escaping tendencies) of component are equal for all phases at equilibrium under constant temperature and pressure (51). The soHd-phase fugacity,, can be represented by the following expression at temperature T ... 

Table 3. Mass Ratio of Crystalline Chloride and Chlorate Salts in Equilibrium with an Aqueous Solution...

The existence of the nitronium ion in sulfuric-nitric acid mixtures was demonstrated both by cryoscopic measurements and by spectroscopy. An increase in the strong acid concentration increases the rate of reaction by shifting the equilibrium of step 1 to the right. Addition of a nitrate salt has the opposite effect by suppressing the preequilibrium dissociation of nitric acid. It is possible to prepare crystalline salts of nitronium ions, such as nitronium tetrafluoroborate. Solutions of these salts in organic solvents rapidly nitrate aromatic compounds. ... 

For a substance to dissolve in a liquid, it must be capable of disrupting the solvent structure and permit the bonding of solvent molecules to the solute or its component ions. The forces binding the ions, atoms or molecules in the lattice oppose the tendency of a crystalline solid to enter solution. The solubility of a solid is thus determined by the resultant of these opposing effects. The solubility of a solute in a given solvent is defined as the concentration of that solute in its saturated solution. A saturated solution is one that is in equilibrium with excess solute present. The solution is still referred to as saturated, even... 

Phosphorus (like C and S) exists in many allotropic modifications which reflect the variety of ways of achieving catenation. At least five crystalline polymorphs are known and there are also several amorphous or vitreous forms (see Fig. 12.3). All forms, however, melt to give the same liquid which consists of symmetrical P4 tetrahedral molecules, P-P 225 pm. The same molecular form exists in the gas phase (P-P 221pm), but at high temperatures (above 800°C) and low pressures P4 is in equilibrium with the diatomic form P=P (189.5 pm). At atmospheric pressure, dissociation of P4 into 2P2 reaches 50% at 1800°C and dissociation of P2 into 2P reaches 50% at 2800°. 

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