A technique to study the statistical distribution and collision rates of additive molecules in compartmentalized liquids is developed and applied to C O ( H~O )~~+ in SDS micelles. The physical model employs a dilute solution of a nitroxide free radical, the indicator, in the presence and absence of a varying concentration of paramagnetic molecules, the broadeners, which are C O ( H~O )~~+ in this case. The EPR spectra of the indicator vary nonlinearly with the concentration of the broadener in a manner consistent with a hypothesis that the resident time of a CO(H~O)~*+ ion on one micelle is long compared with lO-'s but inconsistent with a random distribution of the added divalent cations among the micelles. A simple theory is developed which takes into account interactions between broadeners residing in the same compartment and ignores such interactions if they reside in different compartments. Assuming a small electrostatic repulsion between the cations brings the experimental results into agreement with theory and allows the collision rate of the broadener with the indicator to be estimated.
For C O ( H~O )~~+ ,this collision rate decreases linearly as a function of the inverse volume of the micelle as predicted by a simple random walk model. The polarity of SDS micelles, as estimated by the I4N hyperfine coupling constant of the indicator, decreases linearly with micelle size, while the microviscosity, as estimated from the rotational correlation time of the indicator, increases linearly with this size.