Thermodynamics Gibbs adsorption isotherm

Thermodynamically Consistent Isotherm Models. These models include both the statistical thermodynamic models and the models that can be derived from an assumed equation of state for the adsorbed phase plus the thermodynamics of the adsorbed phase, ie, the Gibbs adsorption isotherm,... 

This equation has been criticized on thermodynamic grounds because it does not satisfy the Gibbs adsorption isotherm unless all monolayer capacities n] are equal. 

Adsorbed-Solution Theory The common thermodynamic approach to multicomponent adsorption treats adsorption equilibrium in a way analogous to fluid-fluid equilibrium. The theory has as its basis the Gibbs adsorption isotherm [Young and Crowell, gen. refs.], which is... 

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

The correct thermodynamic treatment of adsorption processes is possible only on liquid-gas and liquid-liquid interfaces, where the surface energy or the surface tension of the liquid can precisely be determined. For these systems, the Gibbs adsorption isotherm can be applied. For example on a liquid-liquid interface,... 

The thermodynamics of 2D Meads overlayers on ideally polarizable foreign substrates can be relatively simply described following the interphase concept proposed by Guggenheim [3.212, 3.213] and later applied on Me UPD systems by Schmidt [3.54] as shown in Section 8.2. A phase scheme of the electrode-electrolyte interface is given in Fig. 8.1. Thermodynamically, the chemical potential of Meads is given by eq. (8.14) as a result of a formal equilibrium between Meads and its ionized form Me in the interphase (IP). The interphase equilibrium is quantitatively described by the Gibbs adsorption isotherm, eq. (8.18). In the presence of an excess of supporting electrolyte KX, i.e., c , the chemical potential is constant and... 

The classical theory of the Gibbs adsorption isotherm is based on the use of an equation of state for the adsorbed phase hence it assumes that this adsorbed phase is a mobile fluid layer covering the adsorbent surface. By contrast, in the statistical thermod)mamic theory of adsorption, developed mainly by Hill [15] and by Fowler and Guggenheim [12], the adsorbed molecules are supposed to be localized and are represented in terms of simplified physical models for which the appropriate partition function may be derived. The classical thermodynamic fimctions are then derived from these partition fimctions, using the usual relationships of statistical thermodynamics. 

The use of an equation of state to derive isotherms is based on the assumption that the adsorbed layer can be treated as a two-dimensional phase. In this case, the fimdamental equations in classical thermodynamics can be applied. Thus, at constant temperature, the Gibbs adsorption isotherm becomes... 

Under these circumstances the distribution coefficient for MiXi is zero, and that for M2X2, infinity. It follows that the Galvani potential difference is not defined for this interface. However, the thermodynamics of the interface can be derived on the basis of the Gibbs adsorption isotherm. 

The basic thermodynamic equation describing the properties of the polarizable interface is the Gibbs adsorption isotherm (GAI, equation (8.3.17)), that is,... 

An important principle from thermodynamics is the well-known Gibbs adsorption isotherm, which provides a relationship among the bulk-phase concentration c, the interfacial concentration T, and the interfacial tension (essentially the surface free energy per unit area) ... 

So far the Gibbs adsorption isotherm represents the best foimded theoretical backgroimd for the calculation of the adsorption excess densities of surfactants. Statistical thermodynamics may enable us in future to calculate adsorption densities by accounting for the chemical structure of a surfactant. Beside the direct calculation of excess adsorption densities F with the help of r - log c-plots, relationships of F and the interfacial tension y as functions of the surfactant bulk concentration are very helpful. 

This is called the Gibbs adsorption isotherm. The equation represents the most general and pure thermodynamic description of enrichment of a substance on a surface. The description of the surface concentration of ions on the electrode is also possible by special... 

It would appear from this analysis of Vernon and Lopatkin s paper that although they are correct in pointing out that the conventional definition (12) of Fi ignores the change in volume of the system accompanying adsorption, when employing the measured adsorptions in thermodynamic equations (e.g. the Gibbs adsorption isotherm) the effect of this discrepancy cancels out in the calculation of the relative adsorption. Any one of the equations (10), (11), (12), or (13) may thus be used in thermodynamic calculations, by substitution in the appropriate equality in (20). 

The thermodynamics of adsorption is particularly important for analyzing the catalytic reactions as weU as the surface characterization of the catalysts. In this section, first, we will derive the Gibbs adsorption isotherm, and then we will use the Gibbs adsorption isotherm to derive the more useful isotherms such as Langmuir s and Fowler Guggenheim isotherms. 

Concerning the behaviour of ions near the air-water interface (and in principle at all interfaces), the Gibbs adsorption isotherm suggests that an increase in surface tension is an indication for a depletion of ions at this interface. In contrast, as in the case of surfactants, the surface tension decreases, when ions are adsorbed or when they have at least a certain propensity to the interface. While this is rigorously correct in the thermodynamic limit (provided that the activity coefficients are taken into account correctly), caution must be taken if molecular interpretation is attempted. It is one of the great merits of Jungwirth and Tobias work to show... 

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