Abstract
The solubilization of hydrophobic components by surfactants that form microemulsion droplets has been investigated from a theoretical point of view. By means of combining thermodynamics of self-assembly to form small systems with bending elasticity theory, we have been able to demonstrate a strong correlation between the second critical micelle concentration (CMC2) of surfactant micelles and their solubilization capacity (σ). The correlation may be rationalized as a consequence of all three bending elasticity constants spontaneous curvature (H0), bending rigidity (kc) and saddle-splay constant (k¯c) showing similar trends with respect to the two quantities, i.e. σ increases and CMC2 decreases with decreasing values of kcH0 and increasing values of kc and k¯c, respectively. As a result, we demonstrate that the solubilization capacity is predicted to always be higher for a gemini surfactant with CMC2 = 11 mM as compared with a gemini surfactant with CMC2 = 18 mM. The predicted correlation between solubilization capacity and CMC2 agrees with experimental observations showing that surfactants forming larger micelles in general have better solubilization capacity than surfactants forming smaller micelles. The theory also demonstrates, in agreement with experiments, that σ is raised in the entire range of surfactant concentrations, below as well as above CMC2, regardless of micelle size. Consequently, our theory predicts that small micelles formed below CMC2 increase in size, whereas large rodlike or wormlike micelles formed above CMC2 decrease in size, as a hydrophobic solubilizate is added to a micellar solution.
Highlights
Surfactant molecules self-assemble in an aqueous solvent above the critical micelle concentration (CMC1) and form micelles
In this way bending elasticity constants were estimated for two cationic surfactants (12, 6- Br and 12, 8-Br) previously studied with time-resolved fluorescence quenching (TRFQ),[31,32] mixed hexadecyltrimethyl ammonium bromide (CTAB)/sodium octyl sulfate (SOS) micelles studied with small-angle neutron scattering (SANS)[16] and two gemini esterquat surfactants (9E2Q-3-Q2E9 and 11E2Q-3-Q2E11) studied with SANS.[24]
Experimental observations have shown that small globular micelles increase slightly in size, whereas long rodlike or wormlike micelles dramatically decrease in size, as a long-chained aliphatic hydrocarbon is added to an aqueous surfactant solution.[7,9,10]
Summary
Surfactant molecules self-assemble in an aqueous solvent above the (first) critical micelle concentration (CMC1) and form micelles. The formation of swollen micelles, due to the addition of a third hydrophobic component, eliminates the geometrical restrictions that are the basis for the CPP theory It is not possible with this approach to predict the transformation in size and shape of micelles as a long-chained aliphatic solubilizate is added to the surfactant solution. A more fruitful approach for the theoretical understanding of surfactant self-assembly is based on the consideration of bending properties of the surfactant monolayer making up micelles and bilayers.[14] In accordance, we have recently developed a novel theory (the general micelle model) from which it is possible to rationalize the growth behavior of surfactant micelles, including the rapid growth above a certain concentration usually referred to as the second critical micelle concentration (CMC2).[15,16] According to the general micelle model, size, shape and growth behavior of micelles are primarily determined by the three bending elasticity constants spontaneous curvature, bending rigidity and saddle-splay constant. Our present model is restricted to the case where the hydrophobic solibilizate is entirely solubilized into the interior core of the microemulsion droplets and not mixed into the surfactant layer
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