Gibbs elastic properties

It is based on equilibrium properties and is directly related to the Gibbs elasticity (17.). In the present context a gauges how strongly the surface tension depends on the surfactant distribution along the bubble interface. Second, captures the kinetics of the adsorption process and is defined by... 

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) ... 

Surfactants play a crucial role in emulsification and emulsion stability. A first step in any quantitative study on emulsions should be to determine the equilibrium and dynamic properties of the oil-water interface, such as interfacial tension, Gibbs elasticity, sinfactant adsorption, counterion binding, siuface electric potential, adsorption relaxation time, etc. Useful theoretical concepts and expressions, which are applicable to ionic, nonionic, and micellar surfac-... 

It is proved that the role of surface viscosity on the drainage velocity is small (Ivanov and Dimitrov 1988, Singh et al. 1996 and Danov et al. 1999a). In fact, in the dimensionless form of Eq. (20) the surface viscosity term is scaled with the Marangoni term, which is proportional to the Gibbs elasticity. The interfacial properties of all liquids in the presence of surfactants show that if the surface viscosity is not small then the Gibbs elasticity is extremely large and the... 

We find then that it is possible to generate a surface tension gradient in a foam film by stretching various elements of the film to different extents. The increase in surface tension due to stretching imparts an elasticity to the film. This property of foam films was first recognized by Gibbs [34] and is usually referred to as the Gibbs elasticity Cq. It is defined as... 

FIGURE 1.5 Gibbs elasticities of submicellar SDS solutions at two different film thicknesses. (After Lucassen, J. Dynamic properties of free liquid films and foams, in Anionic Surfactants, Physical Chemistry of Surfactant Action (Lucassen-Reynders, E.H., ed.), Marcel Dekker, New York, Surfactant Sci. Series, Vol. 11, Chapter 6, p. 217, 1981.)... 

As a rule, dynamic processes with fluid interfaces are accompanied by interfacial dilatation, compression, and/or two-dimensional flows in the surfactant adsorption mono-layer. These processes are affected by the interfacial rheological properties, such as surface (Gibbs) elasticity, dilatational, and shear-surface viscosity, and adsorption relaxation time see Sec. III.F. The interfacial rheological properties are especially important for the foaminess of surfactant solutions and the emulsion preparation by homogenization. 

It is important to note that it is often difficult to accurately measure and that of AT and AS cannot be measured. As a result, is usually calculated based on the elastic properties of the polymer gel using Eq. (19). Both AT and AS have to be calculated based on Eqs. (39) and (41), this is usually possible as long as appropriate expressions exist for the Gibbs energy of the fluid mixture that forms the gel phase and A of the polymer network. 

Because the Gibbs elasticity eo involves a derivative of the surface tension with respect to the surface concentration and the surface concentration is itself a derivative of the surface tension with respect to the bulk concentration, Sc is proportional to d y/dc. The Gibbs elasticity is, therefore, sensitive to very small differences in surface tension variation with surfactant bulk concentration, more sensitive than the surface coverage itself. Both r and e cannot be evaluated by the preceding two equations when the bulk concentration is above the cmc. However, in general, the surface coverage does not change appreciably above the cmc, and the surface properties determined at this concentration can be used as a first approximation for the more concentrated solutions. 

A notable characteristic of stable films is their resistance to mechanical disturbance. Gibbs [178] considered the important property to be the elasticity of the film E ... 

The subscript G specifies elasticity determined from isothermal equilibrium measurements, such as for the spreading pressure-area method, which is a thermodynamic property and is termed the Gibbs surface elasticity, EG. EG occurs in very thin films where the number of molecules is so low that the surfactant cannot restore the equilibrium surface concentration after deformation. 

An important thermodynamic property of a surfactant adsorption monolayer is its Gibbs (surface) elasticity ... 

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