Precision relative aggregation number determinations of SDS micelles using a spin probe. A model of micelle surface hydration

A spin-probe method is described that can detect changes in the relative aggregation numbers in SDS micelles with a precision of about one molecule. The method is based on the fact that the N-14 hyperfine coupling constant is sensitive to the average fraction of the volume occupied by water in the region of the nitroxide moiety that is located on average near the micelle surface. Defining A(0)(N-A) to be the N-14 hyperfine coupling constant at an aggregation number N-A, We find A(0)(N-A) = A(0)(0) + (partial derivative A(0)/partial derivative N-A)N-A, where N-A is controlled by varying either the SDS or the NaCl concentrations. For the spin probe 5-doxylstearic acid ester(5DSE), by combination of the results of experiments in which the SDS and/or the NaCl concentrations were varied, linear least-squares fits gave A(0)(0) = (15.498 +/- 0.009) G and partial derivative A(0)/partial derivative N-A = - 3.99 +/- 0.02 mG/molecule (constant). A(0)(N-A) depends only on the aggregation number despite the fact that a given value of N-A may be prepared by choosing different combinations of NaCl and SDS concentrations. This means that, for a given micelle size, neither interactions between micelles nor the ionic strength of the solution influence the value of A(0). A geometric model, based on a simple model in which a spherical hydrocarbon core is surrounded by a concentric spherical polar shell, is developed to predict the volume fraction of the polar shell occupied by water as a function of N-A. This water fraction is written in terms of a hydration number per surfactant molecule, N(H2O). A(0)(N-A) is related to N(H2O) by employing the nonempirical polarity index introduced by Mukerjee et al. (Mukerjee, P.; Ramachandran, C.; Pyter, R. A. J. Phys. Chem. 1982, 86, 3189). The value of N(H2O) decreases as the micelle grows because the volume per surfactant molecule in the polar shell decreases. Once N(H2O) is specified at a particular value of N-A, no further adjustable parameters enter into the model. The variation with micelle size of the theoretical polarity is in excellent agreement with experiment for values of N(H2O) that are comparable to those found from transport properties. The sphere-rod transition is observed as a rather sharp transition in which the detected water volume fraction becomes constant. Detailed future tests of the model are outlined.