Gibbs elasticity modulus

Another indirect method for the estimation of Gibbs elasticity modulus is based on the determination of the surface dilatation modulus E in experiments in which the surfaces of the surfactant solutions undergo small amplitude deformations of oscillatory nature [100-102], It is shown [100, see also Chapter 7] that the concentration dependence of a Gibbs elasticity modulus at constant film thickness should be nearly the same as the concentration dependence of (twice) the surface elastic modulus E when film thickness and frequency are related by... 

The reorientation of molecules in the adsorption layer should have a strong effect on the surface elasticity modules (cf paragraph 4.5 of Chapter 4). The Gibbs elasticity modulus (, =-(dy/dlnT), =(dy/dln A)p can be calculated from the equation of state (2.84) together with the relationships (2.85)-(2.88). Therefore, this value should reflect the processes involved in the equilibrium transition between the adsorption states. ... 

Fig.2.10. Dependence of the Gibbs elasticity modulus CioEOg solutions on surface pressure reorientation model water/air interface (1) reorientation model water/hexane interface (2) von Szyszkowski-Langmuir equation for both interfaces (3).

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

The elasticity depends on the rate of film expansion. Under quasistatic equilibrium conditions its values are very low and in such a case it is called Gibbs elasticity. When there is no equilibrium it is called Maiangoni elasticity. The largest value of the elasticity modulus, acquired when the adsorption layer behaves as insoluble one, is called Marangoni dilatation modulus Em). 

Bianko and Marmur [99] have developed a new technique for the measurement of Gibbs elasticity of foam films. In order to exclude the effect of the mass transfer of the surfactant, the stretching of an isolated soap bubble is used. The surface tension needed for the calculation of the elasticity modulus is determined by the pressure in the bubble and the radius of curvature. The modulus obtained are considerably lower than those derived by the technique of Prins et al. [95]. 

Two types of elasticity could be distinguished equilibrium (Gibbs elasticity) and dynamic (Marangoni elasticity). According to Gibbs the modulus of elasticity of the film is... 

The second case concerns a thin film. Here the change in 77 is governed by the limited amount of surfactant in the bulk liquid in the film, since by far most of the surfactant will be in the adsorbed layers. The time for diffusional transport (normal to the surfaces) is taken to be negligible in the thin film it would nearly always be < 0.1s. The modulus then is purely elastic. Rather than the modulus, the Gibbs elasticity of the film is given, by... 

Lucassen-Reynders EH, Cagna A, Lucassen J (2001) Gibbs elasticity, surface dilational modulus and diffusional relaxation in nonionic surfactant monolayers. Colloid Surf A 186(l-2) 63-72... 

Dilational moduli play an important part in a number of practical processes involving interfaclal area changes, where K° is a measure of the resistance a monolayer has against creating an interfaclal tension gradient Vy upon extension or compression. Emulsification and foam formation are representatives of such processes. On the other hand, once Vy has been created, the modulus controls the rate of relaxation. Historically, only static values have been considered. Recall that for elasticities of the Gibbs type, expressions for K° can be formulated on the basis of two-dimensional equations of state, see 13.4.30 and 30a]. In more modem developments the modulus is also studied under dynamic, or non-equilibrium... 

Film Elasticity The differential change in surface tension of a surface film with relative change in area. Also termed surface elasticity, dilata-tional elasticity, areal elasticity, compressional modulus, surface dilata-tional modulus, or modulus of surface elasticity. For fluid films, the surface tension of one surface is used. The Gibbs film (surface) elasticity is the equilibrium value. If the surface tension is dynamic (time-dependent) in character, then for nonequilibrium values, the term Marangoni film... 

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