Role of Counterion Concentration in Determining Micelle Aggregation: Evaluation of the Combination of Constraints from Small-Angle Neutron Scattering, Electron Paramagnetic Resonance, and Time-Resolved Fluorescence Quenching P. C. Griffiths* and A. Paul School of Chemistry, Cardiff UniVersity, P.O. Box 912, Cardiff CF10 3TB, Wales, U.K. R. K. Heenan and J. Penfold Neutron DiVision, Rutherford and Appleton Laboratory, Chilton Didcot OX11 0QX, Oxon, U.K. Radha Ranganathan and Barney L. Bales Department of Physics and Astronomy and the Center for Supramolecular Studies, California State UniVersity, Northridge, California 91330-8268 ReceiVed: October 17, 2003; In Final Form: January 22, 2004 Small-angle neutron scattering (SANS) has been used to study a series of aqueous solutions of (i) the anionic surfactant sodium dodecyl sulfate and the simple electrolyte sodium chloride and (ii) the cationic surfactants dodecyltrimethylammonium bromide and dodecyltrimethylammonium chloride, in the presence of sodium bromide and sodium chloride, respectively. For all three systems, the surfactant spans a wide concentration range, and by suitable choices of electrolyte concentration, it is possible to engineer these solutions to have the same concentration of counterions in the aqueous phase. According to a recent hypothesis by Bales et al. (J. Phys. Chem. B 2001, 105, 6798), such a series is expected to produce micelles having the same aggregation number (N agg ), a point verified by time-resolved fluorescence quenching (TRFQ) and electron paramagnetic resonance (EPR). The SANS results presented here are in good agreement with the TRFQ and EPR studies. We therefore show unequivocally that the sizes and shapes of these surfactant micelles depend only on the free counterion concentration, a conclusion supported by conventional theories of micellization. Subsequently, for the SDS data, a comparison is made between fitting the SANS data to a model in which the aggregation number and degree of hydration are constrained and fitting them to a model in which these features are fittable parameters. In essence, both approaches yield the same conclusion. Such an approach is not possible with the cationic surfactants, as the contrast between the hydrated shell and the core is minimal. Introduction Small-angle neutron scattering (SANS) has evolved into a very powerful technique for studying the morphology of micelles formed in aqueous solution by surfactants, as well as the interaction between them. 1,2 These properties are usually quanti- fied within the context of a particular model describing the micelle morphology, as embodied by the form factor, and combined with some model taken from liquid theory to describe the intermicelle interactions via the structure factor. The surfactant number or molecular packing parameter 3 (N s ) is a remarkably simple and insightful parameter to consider when discussing the morphology of the structures formed by surfactants. Defined as the ratio of the volume (V) of the surfactant tail to the area per headgroup (a 0 ) and the length of the surfactant tail (l), N s )V/a 0 l, this dimensionless quantity can be translated into a specific micelle shape; that is, spherical micelles are predicted when 0 < N s < 1 / 3 , whereas, for cylindrical micelles, 1 / 3 < N s < 1 / 2 . Within the context of this study and established theories of micellization, an increase in the ionic strength of the solution will screen the interheadgroup repulsion, and thus, a 0 decreases. Given that V and l are constant, N s increases and the micelle becomes more elongated. This simple approach suggests that there is a correlation between the ionic strength of the solution and the micelle morphology and, inter alia, the aggregation number. The effective area per surfactant headgroup (a 0 ) of an ionic surfactant micelle is a rather difficult quantity to calculate due to the tendency of the surfactant counterions to dissociate from the micelle surface. However, the dressed micelle model 4,5 allows the degree of counterion dissociation (R Na + ) to be calculated by solving the nonlinear Poisson-Boltzmann equa- tion describing the ion distribution around a charged spherical structure. Typical values for SDS solutions (16 mM < [SDS] < 600 mM in the presence of 0 mM < [NaCl] < 200 mM salt) are 0.20 <R Na + < 0.30, in excellent agreement with the same quantity measured by SANS. 6,23 Recently, the hypothesis was advanced 7 that the aggregation numbers of ionic micelles, at a constant temperature, depend only on the concentration of counterions in the aqueous phase (C aq ): Ionic micelles grow in response to increases in the value of C aq whether the counterions are provided by the surfactant alone or by the surfactant plus any added electrolyte. 7 Taking SDS and NaCl as an example, the micellized surfactant provides a counterion concentration equal to R Na + S m , where S m is the concentration of surfactant forming the micelles and R Na + is the degree of dissociation of the (sodium) counterions from the micelle surface. The concentration of counterions added via salt N agg ) N agg (C aq ) (1) 3810 J. Phys. Chem. B 2004, 108, 3810-3816 10.1021/jp0371478 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/03/2004