Melts phase equilibria

In this chapter the mineral-melt phase equilibria that control the compositions of partial melts are examined on the basis of experimental and thermodynamic databases, and this information is used to predict the effects of partial melt extraction from fertile upper mantle on residual mineralogy and major-element chemistry. 

The fusion free energy of both chain ends can be calculated from the equilibrium condition Z = 1 in Eq. 4 by setting the chain length r = 2 in the melt phase. The additional contribution is thus given by... 

Esterification is the first step in PET synthesis but also occurs during melt-phase polycondensation, SSP, and extrusion processes due to the significant formation of carboxyl end groups by polymer degradation. As an equilibrium reaction, esterification is always accompanied by the reverse reaction being hydrolysis. In industrial esterification reactors, esterification and transesterification proceed simultaneously, and thus a complex reaction scheme with parallel and serial equilibrium reactions has to be considered. In addition, the esterification process involves three phases, i.e. solid TPA, a homogeneous liquid phase and the gas phase. The respective phase equilibria will be discussed below in Section 3.1. 

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

Let us call the melt phase a and the solid phase with complete immiscibility of components y. P is constant and fluids are absent. The Gibbs free energy relationships at the various T for the two phases at equilibrium are those shown in figure 7.2, with T decreasing downward from Ty to Tg. The G-X relationships observed at the various T are then translated into a T-X stability diagram in the lower part of the figure. 

Figure 9,13 Relationship between activity of H2O in gaseous phase and molar amount of H2O in melt at equilibrium. Experimental data from Burnham and Davis (1974) ( ) Fraser (1975b) ( ) Kurkjian and Russel (1958) ( ). Reprinted from B. J. Wood and D. G. Fraser, Elementary Thermodynamics for Geologists, 1976, by permission of Oxford University Press.

The preparation of fully aromatic polyesters is mostly performed by melt condensation. Complex phase equilibriums and states of aggregation are formed in... 

During mantle partial melting, the partition coefficients of Th, Pa, and Ra are different from that of U. Assuming the melt and the mantle residue as a whole maintains secular equilibrium, if the melting process is slow, there is chemical equilibrium between the phases, which means each phase (such as the melt phase) is out of secular equilibrium because of different partition coefficients (McKenzie, 1985). 

Fig. 2. PT diagram for a pure substance that expands on melting (not to scale). For a substance that contracts on melting, eg, water, the fusion curve, A, has a negative slope point /is a triple state point is the gas—liquid critical state (—) are phase boundaries representing states of two-phase equilibrium ...

A number of reviews have appeared covering the various aspects of borate glasses. The structure, physical properties, thermochemistry, reactions, phase equilibria, and electrical properties of alkali borate melts and glasses have been presented (73). The application of x-ray diffraction, nmr, Raman scattering, ir spectroscopy, and esr to structural analysis is available (26). Phase-equilibrium diagrams for a large number of anhydrous borate systems are included in a compilation (145), and thermochemical data on the anhydrous alkali metal borates have been compiled (17). 

In the developed process it is important to know the influence of the pressure on the melting point of the substance in the presence of the gas s-l-transition and the phase-equilibrium 1-v-data of the system. 

Transamidation is an important process in the melt phase for polyamides because it is usually the process by which an equilibrium molecular weight distribution is reestablished and, in the case of the melt blending of two or more polyamides to form a copolymer, it is the process by which randomization of the individual monomers along the chain is effected. In the solid phase, chain mobility is restricted and equilibrium in either case often is not achieved. 

The solution of Eq. (26) for the phase equilibrium condition gives P(T) (e.g., vapor pressure as a function of temperature) or T(P) (e.g., melting point as a function of pressure). A single point on one of these curves can be obtained by measurement or calculation.1 We will now show how thermodynamics can be used to obtain the slope of these curves. Equation (26), pa = pp, holds at phase equilibrium. If we change either P or T and the system remains at equilibrium, Eq. (26) must still hold ... 

Condensed-phase equilibria are treated by Eq. (40), the Clapeyron equation. The most important type of condensed-phase equilibrium is that between solid and liquid. For melting, Ais always positive, because the solid is the lowest-energy (and enthalpy) arrangement of molecules. The direction of change of the melting temperature with pressure,... 

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