Dimeric Surfactants: A Simplified Model for the Spacer Chain

Abstract

Dimeric surfactants are composed of ordinary surfactant monomers for which the polar head groups have been chemically linked in pairs by an alkanediyl chain (“spacer”). This pairwise linking has been shown by experiments to change quite drastically the physical and chemical properties of the surfactant solution, as compared to those of the original In particular, one can mention the influence of the spacer on aggregate morphology,2 which is directly related to changes in the specific area of the surfactant molecules at interface^.^ In a recent article4 we presented a theoretical model for the interfacial behavior of dimeric surfactants and its dependence on the spacer carbon number. The model treats a saturated monolayer of soluble dimeric surfactants at an interface and considers the following major factors: (i) hydrophilic-hydrophobic interactions among the surfactant monomers, (ii) translational entropy of the dimers on the interface, (iii) exchange with the bulk solution due to surfactant solubility, and (iv) characteristics of the spacer chain. The latter is the most complicated factor to model, since the spacer chains (containing up to about 20 alkyl groups) are too short to be treated as polymer chains. Hence, we resorted to computer simulations in order to get statistical information on the spacer configurations and then combined the data with the other interactions. The model succeeds in explaining experimental findings regarding the nonmonotonic dependence of the surfactant specific area at the waterlair interface on the spacer carbon number. It also shows that the interfacial behavior is dominated by two of the factors mentioned above, namely the interactions between monomers and the characteristics of the spacers linking them. In this paper we wish to present a further simplification of our model. The main purpose is to significantly facilitate the treatment of the spacer contribution for possible applications in other models involving dimeric surfactants. Consider an aliphatic spacer chain containing n CH2 groups and connecting two surfactant monomers. Those two end monomers are restricted to lie on the flat water1 air or waterloil interface due to their amphiphilic character. On the other hand, the spacer may take various configurations, each having its o w n end-to-end distance, r . The configurations differ from those of a free chain, since the hydrophobic spacer groups favor the half-space of the nonaqueous phase, while the spacer ends are kept “pinned” to the interface. Ifwe characterize the probability distribution (‘g,) of the end-to-end distance by its mean (R,) and variance (V,) and then fit it to a Gaussian distribution (as we did in ref 4 using E, to denote the mean), the spacer contribution to the free energy per dimer can then be written as