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 led to renaming the HLD surfactant parameter, sigma (σ), as the characteristic curvature (Cc). This work tests the validity of the curvature interpretation of the HLD, and the Cc concept, for single ionic surfactants and the use of this concept as a method to assess the Cc without the use of reference surfactants or alcohols. To this end, the net curvature of six anionic and two cationic surfactants was evaluated 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 the original HLD equation for ionic surfactant could not be interpreted as chemical potential or curvature because a salinity prefactor (coefficient) “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 using the expression Cc = Ccbi/bi. This single surfactant method produces uncertainties that, for most surfactants, ranged from 0.2 to 1 Cc units, similar to the uncertainty obtained with the conventional method of Cc determination using mixtures of test and reference 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.

The characteristic curvature (Cc), within the Hydrophilic-Lipophilic Difference + Net (Hn) -Average (Ha) Curvature (HLD-NAC) framework, is the dimensionless net curvature, Hn∙L (L is the surfactant’s tail length parameter), that a surfactant acquires at the characteristic condition (T=25°C, no added cosurfactants, oil with an equivalent alkane carbon number (EACN) of zero, and for ionic surfactants, a total salinity (S) of 1 g NaCl/100 mL). A recent article demonstrated the validity of the Cc concept, where Hn was assessed via oil and water solubilization radii. Here, we assess Hn from the characteristic length (ξ) obtained from the analysis of SAXS profiles of microemulsions produced at semi-characteristic conditions (characteristic condition, but varying S). The predicted relationship, -L∙Hnsemi-characteristic = Ccbi + bi∙ln(S), was confirmed with the five ionic surfactants explored. The SAXS-assessed Cc (Cc = Ccbi/bi) values are consistent with those obtained from solubilization studies and phase inversion scans. The Cc-SAXS method provides a way to assess the hydrophobicity of ionic surfactants directly, avoiding the bias that could be introduced by cosurfactants in phase inversion studies; and minimizing the impact of potential uncertainties in the surfactant volume-to-area ratio (vs/as) required to calculate the solubilization radii in the solubilization method.