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In this paper we present a theoretical model which describes the kinetics of adsorption and desorption from a micellar solution of nonionic surfactants at a silica surface. Numerical calculations based on this model have been compared with experimental results of C n E m surfactant adsorption, obtained by ellipsometry, and show good agreement. The aim of this work was to develop a model for adsorption through a stagnant layer onto a solid, hydrophilic surface. The surface is considered to be planar and homogeneous. Outside the surface there is a micellar solution of a pure nonionic surfactant. Both monomers and micelles are considered to be able to adsorb. To facilitate the evaluation of the model, a computer program was written which solves the mathematical equations numerically. The course of adsorption and desorption of a number of short-chain C n E m surfactants has been simulated with this program. The results obtained, in terms of amounts adsorbed as a function of time, were compared with experimental data determined by time-resolved null ellipsometry. The same program was used to calculate concentration profiles outside the silica surface. Not only has this model made it possible for us to explain and better understand experimental results, but it has also allowed us to gain an understanding of how the course of adsorption and desorption is affected by parameters which are difficult to vary experimentally in a controlled way. Two examples of this, which will be discussed in this paper, are the effects of stagnant layer thickness and the relation between critical surface aggregation concentration (csac) and critical micelle concentration (cmc).

This paper is the second of two dealing with the adsorption and desorption kinetics of nonionic surfactants at a solid−liquid interface. The first paper described a model of the kinetics of single nonionic surfactant adsorption. This work is now being completed by extending the theoretical model to cover binary surfactant systems. The evolution of the total surface excess during the adsorption and desorption has been modeled and compared with experimental results obtained by in situ null ellipsometry. In this comparison, the surface behavior of the two nonionic surfactant pairs C14E6−C10E6 and C12E5−C12E8 at a planar silica−water interface was studied. These binary systems represent two different types of polydispersity:  different lengths of the hydrocarbon chains and unequal numbers of ethylene oxide groups in the hydrophilic headgroups. The critical micelle concentrations (cmcs) of the surfactants in the former pair therefore differ a great deal, whereas those of the surfactants in the latter pair are similar. A comparison between experiments and simulations showed good agreement. In an attempt to further analyze the experimental results, individual amounts adsorbed and concentration profiles were calculated. The results of these simulations showed that each surfactant in a given pair has a characteristic adsorption and desorption path. According to the model, this path is determined mainly by the mutual relationship between their cmcs.

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The adsorption of surfactant-alcohol mixtures at the silica-water interface was studied by means of ellipsometry. The results show that addition of even small amounts of alcohol can have large effects on the characteristics of the adsorbed layer. For example, a 20% replacement of the octa(ethylene glycol) dodecyl (C12E8) surfactants by dodecanol results in an increase in the total surface excess of 80%. The thickness of the adsorbed layer, on the other hand, is virtually unaffected by the alcohol being added. Hence, as the alcohol content increases, the adsorbed surfactant aggregates at the silica-water interface mainly grow in the surface plane. A surfactant such as C12E5, which forms relatively large surface aggregates from the start, can only solubilize a small fraction of the long-chain alcohols before the system phase separates. This fraction was found not to result in any major structural changes in the surface layer. These findings are discussed in terms of surfactant packing and in relation to observations in bulk solutions reported earlier. Our study also includes measurements of adsorption and desorption kinetics for both the surfactant and the surfactant-alcohol systems. The main finding is that the effect of alcohol is most obvious in the desorption kinetics. We conclude that the effects observed are due to differences between the surfactant and the alcohol in monomer solubility.