Entropy and droplet size distributions of Winsor I and II microemulsions

A review is presented of some general notions underlying the current theory of Winsor I and II microemulsions where the exposition is based on a comparison between the droplet kind of approach and the corresponding multiple equilibrium treatment. We show that the droplet size distributions derived earlier, although put in different mathematical forms in the respective treatments, are in effect the same, of the type S(R) exp(−4πR2σ/kT) where the preexponential factor, S(R), is due to the fluctuations in size and shape of the droplets, and the droplet surface tension, σ is curvature-dependent in accordance with the Helfrich expression. Full consistency is demonstrated among the two approaches, at least in sofar as surfactant density fluctuations are not explicitly taken into account. Moreover, on the basis of the multiple equilibrium model, we can actually estimate the length scale parameter l introduced earlier in the droplet kind of treatment to fully account for the entropy of dispersion, to be about 1 nm, in fair agreement with previous estimates.