Regular solution model mixing enthalpy

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

A particularly simple approximation known as regular-solution theory was developed by Hildebrand and co-workers [J. H. Hildebrand. /. Am. Chem. Soc. 51, 66-80 (1929)]. The regular-solution model assumes that the excess enthalpy of mixing can be represented as a simple one-parameter correction... 

Strontium- and barium-containing systems do not deviate much from regular solution behavior. The relatively simple nature of these melts therefore indicates that the variation in the enthalpy of mixing with the common anion must be explainable by a model taking into account coulombic and polarization interactions between ions in a fairly simple manner. This behavior is also evidenced by the phase diagrams of the binary systems... 

The model of regular solutions is very frequently used for which the conditions expressed in Eq. (3.59) are valid. This means that the deviation from the ideal behavior is ascribed to the change in enthalpy at the interaction of the components on mixing. For the excess... 

The model of regular solutions thus ascribes deviations from the ideal solution to the non-zero enthalpy of mixing. 

Hildebrand has defined a regular solution in which deviations from ideality are attributed only to the enthalpy of mixing, the intermolecular forces being dispersion forces. The equation describing this model is... 

In a strict sense, one should model the solution at least as a regular one, but the formation enthalpy of the regular solution is much less than the driving force to form the intermetallic compound. Thus, neglecting the mixing enthalpy in the parent phase wiU not lead to any substantial error. For the intermetallic phase AI9C02, we use the quadratic approximation of the Gibbs potential... 

Assuming a regular solid solution model (Prieto 2009 Ruiz-Hernandez et al. 2010), the enthalpy of mixing at low zirconium content was fitted with a polynomial of the form ... 

Equation (5.1) includes only the ideal, combinatorial entropy of mixing and the simplest conceivable regular solution type estimate of the enthalpy of mixing based on completely random mixing of monomers mm ( ) = 1 in the liquid state language i referred to as the bare chi parameter since it ignores all aspects of polymer architecture and Interchain nonrandom correlations. For these reasons, the model blend for which Eq. (5.1) is thought to be most appropriate for is an interaction and structurally symmetric polymer mixture. The latter is defined such that the only difference between A and B chains is a v (r) tall potential, which favors phase separation at low temperatures. The closest real system to this idealized mixture is an isotopic blend, where the A and B... 

Freund and Knobel (62) have found that in addition to F-OH-F complexes, F-OH pair interactions are important. Therefore, a mixed type regular and subregular model of the solid solutions should be more appropriate. To a first approximation, the enthalpy of mixing should then have the form ... 

The term general solution was introduced by Flory to characterize polymer solutions whose enthalpy of mixing is not zero. The model of general solutions borrows the formula of excess enthalpy from regular systems and the excess entropy from athermal solutions. Thus, a treatment of non-ideal polymer solutions arises which is simpler than the conventional methods applied to real systems this allows the deduction, on the basis of the known relationships, of the expressions of functions of deviation from ideality. Thus, for the activity coefficients of components in a binary system the following relations were established ... 

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