Gibbs excessive

Savich W, Sun SG, Lipkowski J, Wieckowski A. 1995. Determination of the sum of Gibbs excesses of sulfate and bisulfate adsorbed at the Pt(l 11) electrode surface using chronocou-lometiy and thermodynamics of the perfectly polarized electrode. J Electroanal Chem 388 233-237. 

Sulfate adsorption on Pt(lll) was investigated by thermodynamic treatment of the Gibbs excess, which is based on the Frumkin treatment.The above cyclic voltammogram feature at Pt(lll) in sulfuric acid solution was also thought to be due to the adsorbed sulfate. ... 

The earliest equations for Gibbs excess energy, like Margules and van Laar, were largely empirical. More recent equations and NRTL and UNIQUAC are based on a semiempirical physical model, called the two-liquid theory, based on local composition. The molecules do not mix in a random way, but because of different bonding effects, the molecules prefer a certain surrounding. This results in a composition at the molecular level, the local composition, which differs from the macroscopic composition. 

The Extrapolation of the Gibbs Excess Energy to Multi-Component Systems... 

For molecules which differ in size or shape interactions between the surface of the molecules, different Gibbs excess models, such as NRTL [34] or UNIQUAC [35], are recommended, respectively. The predictive group contribution method UNIFAC [36] will fail if several polar groups compose a solvent or solute molecule. As a... 

Bosse [48] proposed a new model to predict binary Maxwell-Stefan diffusion coefficients Dij, based on Eyrings absolute reaction rate theory [49]. A correlation from Vignes [50] which was shown to be valid only for ideal systems of similar-sized molecules without energy interactions [51] was extended with a Gibbs-excess energy term... 

Fig. 2. Adsorption isotherms in all four model systems. F is the Gibbs excess adsoiption. The pressures corresponding to the three configurations shown in Figure 3 are marked with arrows. The pressure is plotted relative to the vapor pressure of the model fluid, as determined by independent Gibbs Ensemble Monte Carlo simulations. Chemical potentials were converted to pressures using a virial equation of state.

Assumption 5 In the definition of the isotherm, the convention is adopted that the solvent (if pure) or the weak solvent (in a mixed mobile phase) is not adsorbed [8]. Riedo and Kov ts [9] have given a detailed discussion of this problem. They have shown that the retention in liquid-solid i.e., adsorption) chromatography can best be described in terms of the Gibbs excess free energy of adsorption. But it is impossible to define the surface concentration of an adsorbate without defining the interface between the adsorbed layer and the bulk solvent. This in turn requires a convention regarding the adsorption equilibrium [8,9]. The most convenient convention for liquid chromatography is to decide that the mobile phase (if pure) or the weak solvent (if the mobile phase is a mixture) is not adsorbed [8]. Then, the mass balance of the weak solvent disappears. If the additive is not adsorbed itself or is weakly adsorbed, its mass balance may be omitted [30]. 

As in the previous chapter, we simplify the problem by considering the adsorption isotherm of the solute-adsorbate separately from the solvent, adopting a convention that the solvent is not adsorbed [2]. We do not consider the Gibbs excess isotherms. Admittedly, this would be more rigorous, but it would lead to a complicated presentation, and this complexity does not seem warranted in the present state of development of competitive excess isotherms and because the concentration of the solutions considered in HPLC rarely exceeds 10% (v/v). 

TABLE D.6 UNIQUAC Model for Binary Systems Dimensionless Gibbs excess energy... 

In Pitzer s model the Gibbs excess free energy of a mixed electrolyte solution and the derived properties, osmotic and mean activity coefficients, are represented by a virial expansion of terms in concentration. A number of summaries of the model are available (i,4, ). The equations for the osmotic coefficient (( )), and activity coefficients (y) of cation (M), anion (X) and neutral species (N) are given below ... 

There are several possible expressions that can be used for the Gibbs excess energy. One is the Redlich-Kister expansion... 

A number of attempts have been made to use the simple solution model to represent the solution nonidealities in binary (23,29-32) and ternary (23,33-41) III—V systems. In the simple solution model, the integral Gibbs excess energy is given in terms of an interaction energy a)( T) by the equation... 

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