Thermodynamics of droplet clustering in percolating AOT water-in-oil microemulsions

The conductivity of water-in-oil microemulsions formulated with AOT (dioctyl sulfosuccinate) in hexane, isooctane, decane, and dodecane was investigated for a wide composition and temperature range (W₀ = [water]/ [AOT] = 0-50; S₀ = [oil]/[AOT] = 20, 13, 5; and T = 10-62°C). A sharp increase in electrical conductivity with increasing temperature was exhibited for W₀ > 15, indicative of a percolation phenomenon. The temperature at which the percolation occurred decreased with increasing W₀ (and corresponding microemulsion droplet size) and with decreasing S₀. An increase in the molecular weight of the alkane solvent shifted the percolation threshold to lower temperatures and dispersed volume fraction values. The free energy, enthalpy, and entropy associated with the formation of droplet clusters in percolating water-in-oil microemulsions were estimated utilizing as association model, similar to that used in describing the micellization of amphiphiles. The enthalpy of cluster formation, ΔH°_cl, was found to be positive (on the order of 100 kJ/mol), indicating that the transfer of microemulsion droplets from solution to the percolating cluster was an enthalpically-disfavored endothermic process. The deformation of the surfactant monolayers upon droplet clustering and the activation energy barrier for the movement of ions and/or water through the droplet-surfactant interface and the apolar solvent during percolation were identified as probable causes of this enthalpic resistance; the microemulsion droplets were subject to "enthalpic stabilization" against clustering. A positive entropie contribution, ΔS°_cl, was the driving force for clustering. The positive entropy was attributed to free volume dissimilarities between the surfactant tail and the oil and could be related to the attractive interactions known to exist between microemulsion droplets. Both ΔH°_cl and ΔS°_cl increased with increasing droplet size and molecular weight of the apolar solvent that constituted the continuous phase.