The characteristic curvature (Cc) definition and its use in assessing Cc for single ionic surfactants

The Hydrophilic-Lipophilic-Difference (HLD) is a set of empirical equations that correlate the formulation conditions at phase inversion (HLD=0). Based on partition studies for nonionic surfactants, the HLD can be interpreted as a normalized chemical potential difference between the surfactant dissolved in water and oil. The Net-Average Curvature (NAC) model extrapolates this interpretation into a curvature form that has been used to fit and predict the phase behavior of surfactant-oil-water (SOW) systems. The curvature interpretation of HLD led to the renaming of the HLD surfactant parameter, sigma (σ), as the characteristic curvature (Cc). This work addresses two concerns around this interpretation; first, for ionic surfactants, an HLD≠0 value for one surfactant might not mean the same for another (breaking the chemical potential interpretation), and second, the Cc interpretation has not been demonstrated. To this end, the net curvature (Hn) of six anionic and two cationic surfactants was evaluated (individually) from solubilization data at the characteristic condition of 25°C, no added cosolvent, in the presence of an oil mixture with equivalent alkane carbon number (EACN) of zero, and as a function of salinity. These studies showed that, indeed, the original HLD equation for ionic surfactant could not be interpreted as chemical potential or curvature because a salinity prefactor "bi" was missing. The revised equation, HLDbi = bi∙ln(S)-kbi∙EACN+Ccbi -aTbi∙(T-25°C), could now be interpreted as a curvature expression, and it was demonstrated that Cc could be obtained from curvature at characteristic conditions, only that the proper expression is Cc = Ccbi/bi.