Gibbs adsorption equation, definition

In line with the Gibbs adsorption equation (equation 3.33 in chapter 3), the presence of thermodynamically unfavourable interactions causes an increase in protein surface activity at the planar oil-water interface (or air-water interface). As illustrated in Figure 7.5 for the case of legumin adsorption at the n-decane-water interface (Antipova et al., 1997), there is observed to be an increase in the rate of protein adsorption, and also in the value of the steady-state interfacial pressure n. (For the definition of this latter quantity, the reader is referred to the footnote on p. 96.)... 

Both problems, changes of the equilibrium adsorption with micellar concentration and the influence of micelles on the adsorption rate, are the subjects of this review. Various definitions of the CMC are represented at the outset. Nowadays the thermodynamics of micellisation is the most developed part of modem theories of micellar systems. Two main approaches ("quasichemical and "pseudophase") are discussed in the second section of this chapter. In section 3 the thermodynamic equations for the Gibbs adsorption of surfactants in the micellar region are considered together with corresponding experimental data. The subsequent sections are devoted to non-equilibrium micellar systems. First, section 4 delineates briefly the theory of... 

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 material in this chapter is organized broadly in two segments. The topics on monolayers (e.g., basic definitions, experimental techniques for measurement of surface tension and sur-face-pressure-versus-area isotherms, phase equilibria and morphology of the monolayers, formulation of equation of state, interfacial viscosity, and some standard applications of mono-layers) are presented first in Sections 7.2-7.6. This is followed by the theories and experimental aspects of adsorption (adsorption from solution and Gibbs equation for the relation between... 

The definition of Gibbs elasticity given by Eq. (19) corresponds to an instantaneous (Aft t ) dilatation of the adsorption layer (that contributes to o ) without affecting the diffuse layer and o. The dependence of o on Ty for nonionic surfactants is the same as the dependence of o on Ty for ionic surfactants, cf Eqs (7) and (19). Equations (8) and (20) then show that the expressions for Eq in Table 2 are valid for both nonionic and ionic siufactants. The effect of the surface electric potential on the Gibbs elasticity Eq of an ionic adsorption monolayer is implicit, through the equilibrium siufactant adsorption T y which depends on the electric properties of the interface. To illustrate this let us consider the case of Langmuir adsorption isotherm for an ionic surfactant (17) ... 

The excesses of the system can be represented by three-parameter quantities. For the existence of the equation of definition, the value of the factors can be chosen arbitrarily. The choice = 0 is permitted. When the values of the factors (v = l v = l / = 0) are chosen, the excess adsorption of a multicomponent system is equal to the adsorption capacity of the surface layer, i.e. to the real amount in the layer (Guggenheim excess if the factors are previously given, the relative Gibbs excess or the Findenegg excess, etc., can also be defined). In an inverse procedure the value of belonging to a given excess can be obtained. Thus, relationships of quantities that are inaccessible in the traditional set of tools can be derived. 

The second equation in Eq. (105) represents a form of the Laplace equation of capillarity. For the so-called surface of tension, P = 0 by definition [143,208] then, 7 = 0 and Eq. (105) coincides with Eq. (95). On the other hand, if the Gibbs dividing surface is defined as the equimolecular dividing surface (the surface for which the adsorption of solvent is equal to zero see Refs. 8 and 207), then B is not zero and the generalized Laplace equation should be used. It is interesting to note that for a flat intermolecular dividing surface, B... 

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