The HLD–NAC equation of state for microemulsions formulated with nonionic alcohol ethoxylate and alkylphenol ethoxylate surfactants

The net–average curvature (NAC) model (Langmuir, 19, 186, 2003) is a simple, yet powerful, equation of state to fit and predict the phase behavior of microemulsions (μEs) formulated with ionic surfactants. However, its use for nonionic surfactants systems has not been evaluated until now. The objective of this work is to use the NAC equation of state to model the phase behavior of μEs formulated with pure alcohol ethoxylate (CiEj) and commercial nonylphenol ethoxylate (NPEj) surfactants with a range of alkanes (Cn). The NAC model requires three basic parameters: the characteristic curvature of the nonionic surfactant (Ccn), the characteristic length (ξ), and the scaling length parameter (L). The first part of this contribution presents a brief review of the NAC model and other thermodynamic models of μEs. Later, five example applications of the NAC model are presented and discussed: (I) fit/prediction of phase inversion temperature (PIT) values, (II) prediction of phase transition temperatures and characteristic lengths, (III) fit/prediction of interfacial tensions, (IV) prediction of “fish” phase diagrams, and (V) prediction of the composition of bicontinuous systems. The NAC model was able to fit the phase behavior observed in all the experimental scenarios, and predict within 30% the value of phase volumes and transition temperatures for CiEj systems. The largest deviations can be attributed to a poor estimation of ξ obtained through empirical correlations. It was also noted that for commercial NPEj surfactants, the NAC model can also fit and predict the phase behavior of these systems, only that more complex empirical correlations are needed for ξ and Ccn due to the partition of different surfactant n-mers into the excess oil and aqueous phases. In all cases, a good agreement was found when the length parameter (L) was estimated as 1.4 times the extended length of the surfactant tail.