Gibbs surface elasticity

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 ... 

As mentioned in the Sec. 1, an important thermo-dynamic parameter of a surfactant adsorption monolayer is its Gibbs (surface) elasticity. The physical concept of surface elasticity is the most transparent for monolayers of insoluble surfactants, for which it was initially introduced by Gibbs (18, 19). The increments A a and AT in the definition of Gibbs elasticity ... 

Chapters 26—29 all discuss hydrodynamic aspects of emulsified systems. The contribution by Danov, Kralchevsky, and Ivanov presents a very fundamental and thorough survey of different phenomena in emulsions related to dynamic and hydrodynamic motions, such as the dynamics of surfactant adsorption mono-layers, which include the Gibbs surface elasticity, and characteristic time of adsorption, mechanisms of droplet-droplet coalescence, hydrodynamic interactions and drop coalescence, interpretation of the Bancroft rule with regard to droplet symmetry, and, finally, kinetics of... 

J or mN m ), is defined by the Gibbs surface elasticity, where A is the film surface area (see, for example, Wang and Yoon, 2008) ... 

Second, the new surface can be created without increasing the number of surface atoms by purely elastic strain of the solid (Figure 1.1.b). The extra stress due to the surface, called by Gibbs surface tension or by other authors surface stress (Mullins 1963, Cahn 1989), is denoted as ysv and expressed as a force per unit length. 

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... 

E.H. Lucassen-Reynders, Surface Elasticity and Viscosity in Compression/ Dilation, in Anionic Surfactants Physical Chemistry and Surfactant Action E.H. Lucassen-Reynders, Ed., Marcel Dekker (1981). (Review of dllatlonal rheology mode, emphasis on Gibbs monolayers includes discussion on 2D equations of state.)... 

In the presence of liquid flow, the situation becomes more complicated due to the creation of surface tension gradients [17]. These gradients, described by the Gibbs dilational elasticity [17], e, initiate a flow of mass along the interface in direction of a higher surface or interfacial tension (the Marangoni effect), e is given by the... 

The Gibbs effect can be evaluated quantitatively. Gibbs defined a coefficient of surface elasticity E as the stress divided by the strain per unit area, E = [2dy/(dA/A). The greater the value of E, the greater the ability of the film to withstand shocks on thinning. 

Many surfactant solutions show dynamic surface tension behavior. That is, some time is required to establish the equilibrium surface tension. If the surface area of the solution is suddenly increased or decreased (locally), then the adsorbed surfactant layer at the interface would require some time to restore its equilibrium surface concentration by diffusion of surfactant from or to the bulk liquid. In the meantime, the original adsorbed surfactant layer is either expanded or contracted because surface tension gradients are now in effect, Gibbs—Marangoni forces arise and act in opposition to the initial disturbance. The dissipation of surface tension gradients to achieve equilibrium embodies the interface with a finite elasticity. This fact explains why some substances that lower surface tension do not stabilize foams (6) They do not have the required rate of approach to equilibrium after a surface expansion or contraction. In other words, they do not have the requisite surface elasticity. 

The first surface elasticity measurements appear to have been the Gibbs elasticity measurements made by Mysels et al. (25) for thin-films that are supported by glass frames. Their results indicated that for a number of surfactant systems EG (film) 10 mN/m, but the rigid films produced by the addition of a suitable alcohol could increase the elasticity of dodecyl sulfate to EQ (film) 100 mN/m. Lucassen-Reynders (23) reported a similar range of values of EM, from near-zero to about 70 mN/m, and suggested that adding simple electrolyte into an anionic surfactant solution could increase the elasticity by factors of 2 to 3. 

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... 

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. ... 

Gibbs/Maragoni effect, surface elasticity and viscosity... 

The Gibbs coefficient of surface elasticity E) was introduced as a variable resistance to surface deformation... 

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