Direct assessment of the characteristic curvature (Cc) of surfactants via small angle scattering

Abstract: The characteristic curvature (Cc), or sigma as it is used in the original hydrophilic-lipophilic-difference (HLD) equations, is an indicator of the normalized curvature (by the surfactant tail length "L") that a surfactant would acquire under a set of characteristic conditions: an oil with an equivalent alkane carbon number (EACN) of zero, at 25 Celsius, in the absence of co-solvents or co-surfactants, and for the case of ionic surfactants, at a total salinity that is equivalent to 1 w/v% NaCl. Previously, this definition of Cc has been used to calculate this parameter based on solubilization data at the characteristic condition and the estimated surfactant volume to interfacial area (v_s/a_s) ratio. While this previous method has provided a methodology to assess Cc without the need for a reference co-surfactant, it is still an indirect assessment of curvature. In this work, we use small angle X-ray scattering (SAXS) studies to assess curvatures and the Cc value directly. To this end, SAXS profiles were obtained for various surfactants at the characteristic condition, except that the salinity scan was conducted to plot the normalized net curvature -L*Hn vs. the logarithm of total salinity (ln(S)). The -L*Hn vs. ln(s) curves were largely linear, as predicted by the net-average curvature (NAC) model, with a slope "bi" and intercept "Cc_bi" such that the Cc is assessed as Cc_bi/bi. The SAXS-assessed Cc values were compared to those obtained via solubilization and phase behavior with references surfactants (the conventional method), finding that the solubilization and SAXS-assessed Cc were very similar, and their deviation from the phase behavior-assessed Cc was within the expected uncertainties for these measurements. Several methodological recommendations are provided to avoid some of the potential artifacts in the measurement. Although the measurement requires access to a benchtop SAXS system, the direct assessment of Cc via SAXS is a fast and reliable method, provided that the proper controls and checks are used.