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 led to renaming the HLD surfactant parameter, sigma (sigma), 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 degrees 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 center dot ln(S)-k(bi)center dot EACN+Cc(bi) -a(Tbi)center dot(T-25 degrees C), could now be interpreted as a curvature expression, and it was demonstrated that Cc could be obtained from curvature using the expression Cc = Cc(bi)/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.

Automated summary

This study tested the validity of the curvature interpretation of the HLD and the Cc concept for single ionic surfactants and proposed a method to assess Cc without the use of reference surfactants or alcohols.