Lucassen-Reynders dividing surface

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

The average To of the partial molar area for all components or all possible states at the interface is often used in conjunction with the Lucassen-Reynders dividing surface, which can be equivalently described as... 

The choice of the Lucassen-Reynders dividing surface has a number of advantages, including the fact that the contribution of non-ideahty of entropy... 

In the following, the Lucassen-Reynders dividing surface is used to obtain a number of significant adsorption models. 

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 approach regards the surface as a two-dimensional solution described by Eq. (2.7) applied to an electroneutral dividing surface which contains only electroneutral... 

Clearly, Gibbs dividing surface is used in Eq. (2.54), where Eo = 0. The adsorption isotherm Eq. (2.53) involves another definition of the dividing surface (Lucassen-Reynders surface with Eo 5 0), which inevitably introduces some deficiency when the two Eqs. (2.53) and (2.54) are used simultaneously. The difference between the positions of these surfaces is of the order of the dimensions of an inorganic ion. 

The thickness of the S-H layer is of the order of the dimension of ions, therefore the ehoiee of the location of the dividing surface according to Lucassen-Reynders condition 0 + [(1 +r, j +r =rRx, almost does not vary the location of the surface upon increasing... 

The bulk concentration is usually denoted by Cj and expressed in mol/1. The molar portion of surfactant at the surface is equal to the monolayer coverage Oj, if the dividing surface is chosen according to Lucassen-Reynders (see Eq. 2.18). Therefore, instead of expression (2.175) one obtains... 

Here 6, = FitOi is the monolayer coverage, Fi is the adsorption, n = yo - y is the surface pressure, yo is the surface tension of solvent, n, = coj/too, and coo are the partial molar surface areas of the surfactant and solvent, respectively, bi is the adsorption constant, Cj is the surfactants concentration in the solution bulk. The Frumkin parameters ai and a2 represent the interactions of components 1 and 2 with the solvent, while the parameter ai2 accounts for interactions between the two surfactants 1 and 2 in the ternary regular mixture (see Eq. 2.32) a,=HJ,/RT aj=HJ2/RT a,2=(Ho,+Ho2-HJj)/2RT, where Hy=A,jRT. Choosing the dividing surface after Lucassen-Reynders (cf. Chapter 2), one can eliminate the contributions from the entropic non-ideality of the solvent, thus reducing Eq. (3.27) to a much simpler form... 

Note that, while the choice of the dividing surface after Lucassen-Reynders does not affect the form of the adsorption isotherm, Eqs. (3.28) and (3.29), the values of nj are now given by... 

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... 

In the presented work different ways of describing the adsorption layers of the ionic surfactants are considered, assuming an electro-neutral double layer. Additionally, the definition of the dividing surface was used as proposed by Lucassen-Reynders [33] a specific compressibility of the adsorption layer was taken into account [23], The new theoretical model based on a competitive... 

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