Gibbs equation surfactant application

When a surfactant is injected into the liquid beneath an insoluble monolayer, surfactant molecules may adsorb at the surface, penetrating between the monolayer molecules. However it is difficult to determine the extent of this penetration. In principle, equilibrium penetration is described by the Gibbs equation, but the practical application of this equation is complicated by the need to evaluate the dependence of the activity of monolayer substance on surface pressure. There have been several approaches to this problem. In this paper, previously published surface pressure-area Isotherms for cholesterol monolayers on solutions of hexadecy1-trimethyl-ammonium bromide have been analysed by three different methods and the results compared. For this system there is no significant difference between the adsorption calculated by the equation of Pethica and that from the procedure of Alexander and Barnes, but analysis by the method of Motomura, et al. gives results which differ considerably. These differences indicate that an independent experimental measurement of the adsorption should be capable of discriminating between the Motomura method and the other two. 

Equation 9 states that the surface excess of solute, T, is proportional to the concentration of solute, C, multiplied by the rate of change of surface tension, with respect to solute concentration, d m,/dCThe concentration of a surfactant in a G—L interface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration in an L—L interface from a plot of interfacial tension. In typical applications, the approximate form of the Gibbs equation was employed to calculate the area occupied by a series of sulfosuccinic ester molecules at the air—water interface (8) and the energies of adsorption at the air-water interface for a series of commercial nonionic surfactants (9). 

Reversibility of Adsorption. Apparently, the data in Figure 10.13 imply that the Gibbs equation (10.2) does not hold for the protein. As we have seen, it is valid for the amphiphile. However, the slopes dll/d In c given in the figure differ only by a factor 2 between the two surfactants, whereas the values of Fm differ by two orders of magnitude. The explanation is not fully clear. Application of the Gibbs equation to polymers is anyway questionable, because it is generally not known what the relation is between concentration (c) and activity (a) of the surfactant. Moreover, proteins and other polymers are virtually always mixtures. 

Application of the Gibbs equation under the assumption that the change of the surfactant activity in the monomeric form is negligible near the CMC yields... 

The form of the Gibbs equation applicable to anionic surfactants in the presence of less than swamping amounts of added electrolyte has been considered by several workers. On the assumption of negligible adsorption of Cl" ion, Matijevic and Pethica [26] proposed the following equation... 

Adsorption can be measured by direct or indirect methods. Direct methods include surface microtome method [46], foam generation method [47] and radio-labelled surfactant adsorption method [48]. These direct methods have several disadvantages. Hence, the amount of surfactant adsorbed per unit area of interface (T) at surface saturation is mostly determined by indirect methods namely surface and interfacial tension measurements along with the application of Gibbs adsorption equations (see Section 2.2.3 and Figure 2.1). Surfactant structure, presence of electrolyte, nature of non-polar liquid and temperature significantly affect the T value. The T values and the area occupied per surfactant molecule at water-air and water-hydrocarbon interfaces for several anionic, cationic, non-ionic and amphoteric surfactants can be found in Chapter 2 of [2]. 

Primarily, this approach was based on the formal analogy between a first order phase transition and the micellisation. When a new phase of a pure substance is formed the chemical potential of this substance and its concentration in the initial phase do not change with the total content of this substance in the system. A similar situation is observed above the CMC, where the adsorption and the surface tension become approximately constant. In reality variations of these properties are relatively small to be observed by conventional experimental methods. The application of the Gibbs adsorption equation shows that the constancy of the surfactant activity above the CMC follows from the constancy of the surfactant adsorption T2 [13]... 

Motomura et al. proposed a method of evaluation of various thermodynamic properties of micellar solutions from the surface tension data in the framework of the pseudophase treatment of micellisation [50, 52-55]. According to these authors, the micellar composition at the CMC can be found from the functional dependence of the CMC on the overall surfactant mole fraction using an analogy to the method proposed by Nguyen et al. [49], The approach of Motomura et al. [50] gives also a possibility to determine the relation between the composition of the surface layer and the micelles. Application of the Gibbs-Duhem equation to the whole... 

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