Miscibility-temperature relationship

Kejrwords equation of state, free volume, bulk modulus, isothermal compressibility, isobaric expansivity, surface tension, pressure-volume-temperature relationship (P-V-T), pol)mner miscibility, injection molding. 

By combining Eqs. (8.42), (8.49), and (8.60), show that Vi°(52 - 5i) = (l/2)RTj., where T. is the critical temperature for phase separation. For polystyrene with M = 3 X 10, Shultz and Floryf observed T. values of 68 and 84°C, respectively, for cyclohexanone and cyclohexanol. Values of Vi° for these solvents are abut 108 and 106 cm mol", respectively, and 5i values are listed in Table 8.2. Use each of these T. values to form separate estimates of 62 for polystyrene and compare the calculated values with each other and with the value for 62 from Table 8.2. Briefly comment on the agreement or lack thereof for the calculated and accepted 5 s in terms of the assumptions inherent in this method. Criticize or defend the following proposition for systems where use of the above relationship is justified Polymer will be miscible in all proportions in low molecular weight solvents from which they differ in 5 value by about 3 or less. 

Formic, acetic, propionic, and butyric acids are miscible with water at room temperature. SolubiUty in water decreases rapidly for the higher alkanoic acids as the chain length increases (Table 8) (19). The solubiUty in water at pH 2—3 for unionized acids is given by the following relationship ... 

Also, hydrates are more soluble in water-miscible solvents than are the corresponding anhydrous forms. For example, the solubility of caffeine hydrate is lower than that of anhydrous caffeine in water but higher in ethanol. The maximum concentration seen may be due to the solubility of the anhydrous crystalline phase or due to a temporary steady state in which the rate of dissolution of the metastable anhydrous form and the rate of crystallization of the stable hydrate are equal. The decreasing concentration represents crystallization of the stable hydrate from a solution supersaturated with respect to it. If the maximum concentration of the solute in the dissolution experiment corresponds to the solubility, then the initial increase in concentration follows the Noyes-Whitney equation [15]. Van t Hoff plots of log solubility versus the reciprocal of temperature give linear relationships (Fig. 16). 

At this point, you re usually given the temperature versus mole fraction diagram for two miscible liquids (Fig. 140), and you re told it s a consequence of Raoult s Law. Well, yes. But not directly. Raoult s Law is a relationship of pressure, not temperature, versus mole fraction and Raoult s Law is pretty much a straight line. You don t need all your orbitals filled to see that you ve been presented with a temperature versus mole fraction diagram, there are two lines (not one), and neither of them are very straight. 

Figure 2.6 A temperature-composition diagram showing the relationship of temperature and solvent miscibility for two partially miscible liquids...

To understand the mechanism of polyblending, experiments have been carried out with polymeric solution. W. Borchard and G. Rehage mixed two partially miscible polymer solutions, measured the temperature dependence of the viscosity, and determined the critical point of precipitation. When two incompatible polymers, dissolved in a common solvent, are intimately mixed, a polymeric oil-in-oil emulsion is formed. Droplet size of the dispersed phase and its surface chemistry, along with viscosity of the continuous phase, determine the stability of the emulsion. Droplet deformation arising from agitation has been measured on a dispersion of a polyurethane solution with a polyacrylonitrile solution by H. L. Doppert and W. S. Overdiep, who calculated the relationship between viscosity and composition. 

Equation (3.6) illustrates that the solubility of a solid in a liquid depends on the enthalpy change at Tm and the melting temperature of the solid. Equation (3.6) is a valid one when T > Tm because the liquid solute in an ideal solution is completely miscible in all proportions. Table 3.1 shows the ideal solubilities of compounds and their heat of fusion. Equation (3.6) is the equation for ideal solubility. The relationship of In x2 (ideal or nonideal solubility) vs. 1/T is shown in Figure 3.1. 

Most food biopolymers have limited miscibility on a molecular level and form multicomponent, heterophase and nonequilibrium dispersed systems. A thermodynamic approach is applicable for studying structure-property relationships in formulated foods since their structures are based on nonspecific interactions between components and such thermodynamically based operations as mixing of components, changing temperature and/or pH, underlies processing conditions. 

The temperature-composition phase diagram constructed from thermal arrests observed in the MoFe-UFa system is characteristic of a binary system forming solid solutions, a minimum-melting mixture (22 mole % UFe at 13.7°C.), and a solid-miscibility gap. The maximum solid solubility of MoFq in the UFe lattice is about 30 mole % MoFe, whereas the maximum solid solubility of UFe in the MoFe lattice is 12 to 18 mole % UFe- The temperature of the solid-state transformation of MoFe increases from ——lO C. in pure MoFe to 5°C. in mixtures with UFe, indicating that the solid solubility of UFe is greater in the low temperature form of MoFe than in the high temperature form of MoFe- This solid-solubility relationship is consistent with the crystal structures of the pure components The low temperature form of MoFe has an orthorhombic structure similar to that of UFe. 

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. 

An alternative criterion of energy content is the aniline gravity product (AGP), which is related to calorific value (ASTM D-1405, IP 193). The aniline gravity product is the product of the API gravity (ASTM D-287, ASTM D-1298) and the anifine point of the fuel (ASTM D-611, IP 2). The aniline point is the lowest temperature at which the fuel is miscible with an equal volume of aniline and is inversely proportional to the aromatic content. The relationship between the aniline gravity product and calorific value is given in the method. In another method (ASTM D-3338), the heat of combustion is calculated from the fuel density, the 10%, 50%, and 90% distillation temperatures, and the aromatic content. However, neither method is legally acceptable, and other methods (ASTM D-240, ASTM D-1655, ASTM D-4809) are preferred. 

Return now to the point c. At this point there exists the invariant system solid nitrile, two liquid phases, vapour. If heat be added, the solid nitrile will disappear, and there will be left the univariant system consisting of two liquid phases and vapour. Such a system will exhibit relationships similar to those already studied in the previous chapter. As the temperature rises, the mutual solubility of the two fused components becomes greater, until at d (55 5 ) the critical solution temperature is reached, and the fused components become miscible in all proportions. 

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