Multicomponent free enthalpy

Crystallization is bypassed. We speak of a frozen-in, supercooled, liquid-like structure. This type of quasistatic solid structure is thermodynamically controlled but not in thermal equilibrium and thus is not absolutely stable it tends to relax and slowly approach an equilibrium structure (whatever this may be in a complex multicomponent composition, it represents a minimum of the Gibbs free enthalpy). This also means that all... 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

The quantities Xa, Xb, etc, are called the partial molar quantities. The partial molar free enthalpy is also called the chemical potential and given the letter jx. In general, the partial molar quantities are not additive, but the following relationship can be derived between two different components (easily generalized for multicomponent systems)... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

The Universal Quasi-chemical Theory or UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts. The dominant entropic contribution is described by a combinatorial part ( ). Intermolecular forces responsible for the enthalpy of mixing are described by a residual part ( ). The sizes and shapes of the molecule determine the combinatorial part, which is thus dependent on the compositions and requires only pure component data. Since the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. As the UNIQUAC equations are about as simple for multi-component solutions as for binary solutions, the UNIQUAC equations for multicomponent solutions are given below. Species are identified by subscript i, subscript j is a dummy index. Here, is a relative molecular surface area and r, is a relative molecular volume. Both of these quantities are pure-species parameters. 

Various aspects of materials chemistry of the R,Ba cuprates have been approached in the literature firom a thermodynamic point of view. These reports are either general (MacManus-Driscoll 1997) or specialized to selective synthesis methods, either carbon-free (powders, Heintz and Dardant 1997 thin films by CVD, Ottosson et al. 1991 sputtering. Raven et al. 1992) or carbon-based (CVD, Vahlas and Besmann 1992). Also for these multicomponent cuprates, thermodynamics reflects well the underlying chemical properties. As an example, calorimetric data show clearly that the enthalpies of formation... 

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