Evaluation of the counterion distribution around spherical micelles in solution by small-angle neutron scattering

The counterion distribution around tetramethylammonium dodecyl sulfate micelles has been evaluated by small-angle neutron scattering (SANS) using the contrast variation technique. The scattering from the counterions and the hydrated shell was isolated by matching the scattering length densities of the core and aqueous medium by adjusting the ${\mathrm{H}}_2$O-to-${\mathrm{D}}_2$O ratio. Thus the core component of the scattering was ‘‘erased,’’ due to zero contrast with the solvent. The counterion distribution was estimated by fitting the SANS data to a model of an isolated particle consisting of a core, shell, and counterion atmosphere, with only three adjustable parameters. For a micellar concentration of 6 vol %, the aggregation number, core radius, shell thickness, and charge number were estimated as 77, 18.6 Å, 4.6 Å, and 44, respectively. Similar values were obtained for a concentration of 3 vol %. In addition, the electrostatic potential and the dissociation equilibrium at the micellar surface were also evaluated. The estimated value of the surface potential of micelles (-4.7kT) indicated the validity of using the numerical solution of nonlinear Poisson-Boltzmann equation for the calculation of the counterion distribution. © 1996 The American Physical Society.