Lucassen—Reynders equation

Ionic surfactants are electrolytes dissociated in water, forming an electrical double layer consisting of counterions and co-ions at the interface. The Gouy-Chapman theory is used to model the double layer. In conjunction with the Gibbs adsorption equation and the equations of state, the theory allows the surfactant adsorption and the related interfacial properties to be determined [9,10] (The Gibbs adsorption model is certainly simpler than the Butler-Lucassen-Reynders model for this case.). 

The modern resurgence in interest in capillary wave hydrodynamics, which started in the early 1950s, centers around the damping effects and the presence of a viscoelastic film between two fluids [37,49-56]. All are more or less similar, in the assumptions invoked and the hydrodynamic theory used. The Lucassen-Reynders-Lucassen [55] and Kramer s [56] dispersion equations are essentially identical except Kramer ignores the gravity wave at the outset which is consistent with the wave vector range often used experimentally, and this is seen in Fig. 3. 

Lucassen-Reynders and Benjamins -2) derived an equation for protein mono-layers, considered to be purely two-dimensional. The protein molecules are treated as discs of molecular area, floating in a solvent (water) of molecular area. Lateral interaction is accounted for in terms of a partial molar heat of mixing, related to w in the FFG equation 13.4.37] or x in the Flory Huggins picture. Their equation reads... 

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.)... 

A convenient method of analyzing the relation of adsorption to equilibrium wetting has been developed by Lucassen-Reynders (1963). Combination of the Gibbs adsorption equation (2.19) with Young s equation (6.3) yields... 

Lucassen-Reynders (1981) derived the electrostatic term of the film pressure. Her model is that of a surface charge by long chain ions, without taking into consideration inorganic counterions. Starting from the equation of Davies (1951) for the electrostatic repulsion in surface films... 

Lucassen (1968) and Lucassen-Reynders (1969) worked out the theory for longitudinal surface waves, which appear at elasticity modules higher than 30 mN/m and behaves like a stretched membrane. The related dispersion equation has the form... 

For the description of mixed monolayers, the choice of the dividing surface proposed by Lucassen-Reynders (see Eqs. 2.18, 2.19) is superior [58, 59]. The results obtained using the Butler equation (2.7) and Lucassen-Reynders dividing surface model for the description of mixed monolayers of non-ionic or ionic surfactants, and proteins assuming reorientation or aggregation of adsorbed molecules were presented and discussed in overviews [58, 59]. In this chapter, these concepts are discussed and further developed. 

Lucassen-Reynders). For non-ideal surface layers the following equation of state is obtained... 

All systems shown in these figures can be perfectly described by the model defined by Eqs. (3.28)-(3.31) which supports this theoretical model based on Butler s equation for the chemical potentials of the surface layer, and the regular solution theory. In addition, this agreement is due to the certain choice of the dividing surface after Lucassen-Reynders, and to the fact that Eq. (3.31) was used to calculate the mean molar area of the surfactants mixture. It is important to note that in some cases (for mixtures of normal alcohols. Fig. 3.62, and mixtures of sodium dodecyl sulphate (Ci2S04Na) with 1-butanol and 1-nonanol, Figs. 3.63 and... 

Equations defining an average molecular area demand for all siufactant components of a mixture, taking into account different cOj have been proposed by Lucassen-Reynders (38, 39) and Joos and coworkers (33,41). An example in which the contribution of each component to coj is determined by its adsorption relative to the other adsorptions (31, 38) is... 

Lucassen-Reynders and Lucassen (Lucassen 1968, Lucassen-Reynders and Lucassen 1969) have derived the dispersion relation for a liquid surface in the presence of a surface film. They showed that periodic disturbance of such a film-covered surface results in a surface tension that varies from point to point on the surface because of the fluctuations in surface concentration. Consequently, in addition to a transverse stress being developed, a finite tangential surface stress is also present. The solution to this dispersion equation has two roots, one of which corresponds to the capillary waves (transverse motion) and one of which corresponds to longitudinal or dilational waves derived from the transverse stress. The dispersion relation (D( o)) obtained for a film at the interface between two media is... 

Interfacial pressures below 2 inN/m increased linearly with surfactant concentration (activity) (Fig. 4.39). The linear relationship is in agreement with a thermodynamic model of adsorption developed by Lucassen-Reynders [105] and others [106-108]. For surfactants which are strong 1 1 electrolytes, the model suggests the limiting form of the equation of state ... 

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