Determining the Radius and the Apparent Charge of a Micelle from Electrical Conductivity Measurements by Using a Transport Theory:  Explicit Equations for Practical Use

We propose here a procedure which combines experiments and simple analytical formulas that allows us to determine good estimations of the size and charge of ionic micelles above the critical micellar concentration (cmc). First, the conductivity of n-tetradecyltrimethylammonium bromide and chloride (TTABr and TTACl, respectively) aqueous solutions was measured at 25 °C, before and above their cmc. Then, an analytical expression for the concentration dependence of the conductance of an ionic mixture with three species (monomers, micelles, and counterions) was developed and applied to the analysis of the experiments. The theoretical calculations use the mean spherical approximation (MSA) to describe equilibrium properties. Here, we propose new expressions for the electrical conductivity, adapted to the case of electrolytes that are dissymmetric in size, and applicable up to a total surfactant concentration of 0.1 mol L^-1. Moreover, we show that they are good approximations of the corresponding numerical results obtained from Brownian dynamics simulations. Since the analytical formulas given in the present paper involve a small number of unknown parameters, they allow one to derive the size and charge of macroions in solution from conductivity measurements.