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

Abstract

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 Characteristic Curvature (Cc) of Ionic Surfactants Assessed via Small-Angle X-ray Scattering

“…Figure presents the HLD curvature values obtained with ξ TS (squares), ξ TR (circles), and ξ EL (triangles) as a function of salinity. The HLD curvature from solubilization (crosses) in Figure was obtained from our previous work on Cc determination from TEtB solubilization . The HLD curvature from solubilization values and the ellipsoidal model values are consistent, except for the low salinity value ( S added = 0.5% NaCl).…”

“… b Value of EACN reported by Choi . The table was reproduced with permission from Leng and Acosta (ref ). Copyright 2023 Wiley. …”

“…The oil phase was added to the test tubes, introducing 1.5 mL of toluene and 1.5 mL of ethyl benzoate (3 mL of TEtB). The 50/50 volume ratio of these oils is known to produce an EACN of zero . Paraffin-lined caps were used to seal the test tubes to mitigate evaporation.…”

“…The solubilization studies of Leng and Acosta considered various salinities (not only S = 1 w/v % NaCl), setting T = 25 °C and EACN = 0. The researchers plotted − L · H n curvature = − L ·(1/ R o – 1/ R w ) vs ln­( S ), where S is the total salinity of the system (added salt plus unbound electrolyte) . This plot resulted in lines where the slope represented “bi” and the intercept represented “Cc bi ”, whereby Cc was assessed as Cc bi /bi.…”

Review: Implementing the hydrophilic–lipophilic deviation model when formulating detergents and other surfactant‐related applications

“…It should be noted that the term characteristic curvature is also referred to as the surfactant contribution parameter (SCP) or denoted by the symbol σ in prior literature (Salager, 2021;Schirone et al, 2021). With a disclaimer that the physical interpretation of the Cc or SCP term has been the subject of intense discussion reported elsewhere (Acosta et al, 2003b(Acosta et al, , 2008Ghayour & Acosta, 2019;Leng & Acosta, 2022). For nonionic surfactants:…”