Small Gibbs adsorption equation

Primarily, this approach was based on the formal analogy between a first order phase transition and the micellisation. When a new phase of a pure substance is formed the chemical potential of this substance and its concentration in the initial phase do not change with the total content of this substance in the system. A similar situation is observed above the CMC, where the adsorption and the surface tension become approximately constant. In reality variations of these properties are relatively small to be observed by conventional experimental methods. The application of the Gibbs adsorption equation shows that the constancy of the surfactant activity above the CMC follows from the constancy of the surfactant adsorption T2 [13]... 

As mentioned in the discussion around Eqs. (21)-(24), we need values of the five parameters listed in Eqs. (53) and of the surfactant concentration, Csa, to be able to calculate values of various properties of microemulsions (O/W + O or W/O-fW). Of these five parameters the area per surfactant molecule, (t.,., can be determined accurately from the Gibbs adsorption equation, Eq. (1), and there is only a small uncertainty regarding the values of / and c. 

In deriving the Gibbs adsorption equation we need to define an interface or interfacial area. As the interface in real systems is an area of small but non-zero... 

New technique for the experimental measurement of the amount adsorbed is described by McBain, G. F. Mills, and T. F. Ford.1 The surface is reduced to a small fraction of its original area, the adsorbed material being displaced into the interior, and its amount estimated interferometrically. The results with hydrocinnamic and dodecyl sulphonic acids confirm Gibbs s equation fairly well, but the method does not yet appear consistent enough to give more than the order of magnitude of the adsorption. 

This form of the Gibbs fundamental equation demonstrates the importance of surface and interfacial tension measurements of interfacial layers out of the adsorption equilibrium. These methods are the most frequently used techniques to follow the time-dependence of the adsorption process. However, for very slow processes, which occurs in systems with extremely small amounts of surfactants, other methods such as the radio-tracer technique and ellipsometry, or the very recently developed technique of neutron reflectivity, can be used to directly follow the change of surface concentration with time. 

Marangoni and Gibbs elasticity. The mechanism of elastic action of the adsorption layer can be represented as follows. Any deformation of the surface accompanying, for example, an increase in its area decreases the quantity of adsorbed surfactants per unit area. This decreases the surface pressure of surfactant molecules and hence increases the surface tension that counteracts further elongation of the surface. If the concentration of surfactants in the adsorption layer is small, then the two-dimensional gas of surfactant molecules is governed by the equation of state... 

Here, is the so called foam parameter, and t is the viscosity m the surfactant-containing phase (Liquid 1 in Fig. 15) the influence of the transition zone film - bulk liquid is not accounted for in Eq. (76). Note that the bulk and surface diffusion fluxes (see the terms with and Z) in the latter equation), which tend to damp the surface tension gradients and to restore the uniformity of the adsorption monolayers, accelerate the film thinning (Fig. 1). Moreover, since Din Eq. (76) is divided by the film thickness h, the effect of surface diflhsion dominates that of bulk diffusion for small values of the film thickness. On the other hand, the Gibbs elasticity Eq (the Marangoni effect) decelerates the thinning. Equation (76) predicts that the rate of... 

The Gibbs equation serves as a basis for studying the adsorption thermodynamics [11, 24,44]. For the strongly adsorbed surfactants with a small molar fraction in the solution compared to the molar fraction of the solvent (the solvents are mutually insoluble) the Gibbs equation is written as [45] ... 

When a solid is involved, the Kelvin equation cannot be used, because the surface tension cannot be readily measured, the nanoparticles of metals are usually not spherical. Moreover, mechanical strain or stress that may occur in very small particles could influence the Gibbs energy of adsorption. Nevertheless, the physical rules are the same and the excess surface Gibbs energy has been observed as a lowering of the melting point of the metal. 

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