Surfactant equilibrium constants

Although anation and aquation rates of vitamin B12 are not affected appreciably by aqueous micelles, the solubilized water in reversed micelles, in contrast, influences the rate and equilibrium constants for the formation and decomposition of glycine, imidazole, and sodium azide adducts of vitamin Bl2 (Fendler et al., 1974). A vitamin B12 molecule is conceivably shielded from the apolar solvent (benzene) by some 300 surfactant molecules. 

Micelles are extremely dynamic aggregates. Ultrasonic, temperature and pressure jump techniques have been employed to study various equilibrium constants. Rates of uptake of monomers into micellar aggregates are close to diffusion-controlled306. The residence times of the individual surfactant molecules in the aggregate are typically in the order of 1-10 microseconds307, whereas the lifetime of the micellar entity is about 1-100 miliseconds307. Factors that lower the critical micelle concentration usually increase the lifetimes of the micelles as well as the residence times of the surfactant molecules in the micelle. Due to these dynamics, the size and shape of micelles are subject to appreciable structural fluctuations. 

The Menger-Portnoy model is closely related to the Berezin model employing partition coefficients instead of equilibrium constants.For the case where only two pseudophases (bulk water and micelle) are considered, the partitioning of the reactant is given by the partition coefficient P. This leads to Equation (4) describing observed rate constants as a function of surfactant concentration. 

The standard deviation has been determined as ct = j where v is the number of degrees of freedom in the fit. The parameters for the molecular interaction /3, the maximum adsorption Too, the equilibrium constant for adsorption of surfactant ions Ki, and the equilibrium constant for adsorption of counterions K2, are thus obtained. The non-linear equations for the Frumkin adsorption isotherm have been numerically solved by the bisection method. 

Mixed Admicelles. The total sur-factant adsorption o-f the two pure sur-factants and mixtures thereo-f on alumina are shown in Figure 3. The mixtures are at constant surFactant ratio in the Feed or initial solution, but not necessarily in the Final equilibrium solution. The concentration on the abscissa is the equilibrium concentration. The individual surFactant adsorption isotherms For the pure surFactants and in the mixtures are shown in Figures 4 and 5. The experiments were run at the same swamping electrolyte concentration as were the CMC data. 

The Mass Action Model The mass action model represents a very different approach to the interpretation of the thermodynamic properties of a surfactant solution than does the pseudo-phase model presented in the previous section. A chemical equilibrium is assumed to exist between the monomer and the micelle. For this reaction an equilibrium constant can be written to relate the activity (concentrations) of monomer and micelle present. The most comprehensive treatment of this process is due to Burchfield and Woolley.22 We will now describe the procedure followed, although we will not attempt to fill in all the steps of the derivation. The aggregation of an anionic surfactant MA is approximated by a simple equilibrium in which the monomeric anion and cation combine to form one aggregate species (micelle) having an aggregation number n, with a fraction of bound counterions, f3. The reaction isdd... 

Since the equilibrium constant, 07C, in equation (4.23) and the standard free energy change, AG°, for the micellisation of 1 mole of surfactant are related by... 

In what follows, one considers for illustration purposes the case in which the charge is generated on the surface of colloidal particles or droplets by the adsorption of a surfactant, namely sodium dodecyl sulfate (SDS). We selected this case because information about the adsorption of SDS on an interface is available in the literature, and as it will become clearer later the number of parameters involved is smaller than in the case of silica. A more complex calculation about the silica and the amphoteric latex particles will be presented in a forthcoming paper. It involves several kinds of surface dipoles and equilibrium constants. 

Via use of the SED technique, it is possible to determine solute solubilization equilibrium constants (activity coefficients of micellar bound solutes) as well as the surfactant concentration on both sides of the dialysis membrane among other parameters (458-460). 

Suitable absorbance changes allowed the determination of the pseudo-first order rate of attainment of the equilibrium, k (equation 35), both in the presence and the absence of the surfactants. Fro m these values and the values of (the equilibrium constant for equation (36) in the presence of surfactants), y and were obtained. The results indicated that, in the case of 19 micelles exerted a greater effect on the second-order rate constants, y, than on y (Table 13). More specifically, is in creased considerably by CTAB and decreased by NaLS, while y is decreased by both surfactants but to a much greater extent by NaLS (Table 13). For the sulfonphthalein indicators 20, sodium dodecyl sulfate has no significant effect on k whereas CTAB decreases k for the equilibrium attainment. Qualitatively the effects of micelles on the equilibria for... 

With respect to both dissociation and hydrolysis, the concentrations of the ionic species will depend highly on the pH of the solution and the ionic strength. The degree of ionization is measured by the equilibrium constant or more frequently the pK for ionization. T ical pK values of several ionizing groups used as ionic surfactants follow ... 

Mwakibete, H. Cristantino, R. Bloor, D.M. Wyn-Jones, E. Holzwarth, J.F. Reliability of the experimental methods to determine equilibrium constants for surfactant/cyclo-dextrin inclusion complexes. Langmuir 1995,11 (1), 57-60. 

Chromatographic optimizations are usually performed at a preselected pH. However, a simultaneous consideration of the three factors (i.e., surfactant, organic solvent, and pH) expands the separation capability for some problems. The retention can be predicted from (see below) where Kas, Kam, Kad, md, and sd are the equilibrium constants associated to the basic species and T has. HAM. HAD HMD, and Thsd Correspond to the acidic species. is the protonation constant in the aqueous-organic bulk solvent, and [//] is the proton concentration. 

Equation (6.20) represents the formation of a cationic micelle from N surfactant ions D+ and (N-p) firmly held counterions X. Whenever the thermodynamics of a process is under consideration, it is important to define the standard states of the species. In this example, the standard states are such that the mole fractions of the ionic species are unity and the solution properties are those of the infinitely dilute solutions. The equilibrium constant may be written in the usual way... 

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