RESUMO
The Integrated Free Energy Model (IFEM) is a platform used to predict the solubilization of nonpolar oils in nonionic alkyl-polyethylene oxide (C(X)EO(Y)) micelles starting from a free energy balance of costs and gains when surfactants from empty micelles and oil from a continuous oil phase assemble to form an oil-swollen micelle. IFEM considers lipophilic interactions between surfactant tails and oil solubilized in the core of micelles, and the interaction between surfactant tails and the oil solubilized in the surfactant tail domain, as well as oil-oil and surfactant-surfactant tail interactions. Expressions to calculate these lipophilic interactions from van der Waals (VDW) interaction potential were introduced in a previous publication. In this article, two new surfactant-water interactions are considered, surfactant headgroup dehydration during solubilization, and surfactant tail group dehydration. These six interaction terms, in addition to two entropy of mixing contributions (in the lipophilic and in the hydrophilic domains) make up the eight terms of the IFEM platform. Of these terms, only the headgroup dehydration requires a calibrated parameter. After calibrating this parameter, the model is capable of predicting experimental solubilization data, and the experimental trends reflected by a semi-empirical model, the Hydrophilic-Lipophilic-Difference+Net-Average-Curvature (HLD-NAC). Although there are numerous approaches to predict the surfactant-oil-water (SOW) phase behavior, the IFEM platform is the only one, to the knowledge of the authors that produces an explicit connection between molecular interactions and experimental data for real SOW systems. The IFEM platform can be programmed in a personal computer using relatively inexpensive software and its explicit nature opens the possibility to introduce additional interaction terms for more complex SOW systems.
RESUMO
The hydrophobicity of surfactants has been described through different concepts used to guide the formulation of surfactant-water (SW) and surfactant-oil-water (SOW) systems. An integrated framework of hydrophobicity indicators could provide a complete tool for surfactant characterization, and insights on how their relationship may influence the overall phase behavior of the system. The hydrophilic-lipophilic difference (HLD) and the characteristic curvature (Cc) parameter, included in the HLD, have been shown to correlate with different hydrophobicity indicators including the hydrophilic-lipophilic balance (HLB), packing factor (Pf), phase inversion temperature (PIT), spontaneous curvature (Ho), surfactant partition (K(o-w)), and the critical micelle concentration (CMC). This work aims to investigate whether the HLD can further describe a concomitant hydrophobicity parameter, the cloud point (CP) of alkyl ethoxylates. After applying group contribution models to calculate the Cc of monodisperse (pure) nonionic alkyl ethoxylates, a linear correlation between the calculated Cc and the CP was observed for pure surfactants with 8 ethylene oxide (EO) units or less. Furthermore, using an apparent equivalent alkane carbon number (EACN) to represent the hydrophobicity of the micelle core, the HLD equation was capable of predicting cloud point temperatures of pure alkyl ethoxylates, typically within 5 °C. Polydisperse surfactants did not follow the linear CP-Cc correlation found for pure surfactants. After treating polydisperse samples using a liquid-liquid extraction procedure used to remove the most hydrophobic components in the mixture, the resulting treated surfactants fell in the correlation line of pure alkyl ethoxylates. A closer look at the partition behavior of these treated surfactants showed that their partition, Cc and cloud point are dominated by the most abundant ethoxymers in the treated surfactant. The HLD also predicted the cloud point depression of treated surfactants with increasing sodium chloride concentration. This work shows how the HLD framework could be extended to predict the behavior of SW systems.
