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.

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This work introduces two expressions for the integration of the van der Waals interactions in geometries that are relevant to determining oil solubilization in micelles and the interaction among surfactants in micelles. The first integral applies to the interaction between a sphere and a spherical shell that surrounds the sphere. The second integral calculates the interaction between a truncated cone and the rest of a spherical shell that contains the cone. The new sphere-shell integration method was validated via a comparison between fully predicted and experimental surface tensions of alkanes at room temperature and reproduced the near zero surface tension values that are obtained close to the critical point. The cone-shell integration method was validated, in association with the sphere-shell expression, using a comparison between predicted and experimental cohesive energies for alkanes.

This work introduces the first of a two part thermodynamic framework to estimate the solubilization of nonpolar oils in micelles conformed by nonionic surfactants with linear alkyl tails, considering their configuration and the molecular properties of the constituents. This first part introduces a formal approach to account for the lipophilic (van der Waals) contributions to the free energy of solubilization in spherical micelles. To this end, this work uses two recently developed integration methods for sphere-shell and cone-shell VDW interactions that allow the calculation of surfactant-oil and surfactant-surfactant interactions that take place within the micelles of the solubilization process studied here. The method consists in calculating the free energy of transferring a normal alkane from its continuum, and surfactants monomers from empty micelles to produce an oil swollen micelle. The lipophilic interactions are estimated using the microscopic approach of Hamaker with Lifshitz-based Hamaker constants. The influence of n-alkane and surfactant tail length on the solubilization capacity predicted by the van der Walls free energy model (VDW-FEM) are consistent with experimental trends and it is also consistent with the lipophilic terms included in the semi-empirical Hydrophilic-Lipophilic-Difference + Net-Average-Curvature's (HLD-NAC) equation that predicts the phase behavior of microemulsions. As a result, these lipophilic terms can now be defined in terms of molecular interactions and molecular properties.

This work explores the optimum detergency conditions of alkyl ethoxylate (CXEOY) surfactants with the integrated free energy model (IFEM). IFEM is a molecular thermodynamic model that calculates the free energy of formation of oil‐swollen spherical micelles, with a core solubilization radius Ro, using surfactants from empty (oil‐free) micelles and oil molecules from a continuous oil phase. The described geometry allows for rapid calculations, using a personal laptop (3.4 GHz processor), where each solubilization energy profile (free energy vs. Ro curve) can be solved in 5 min or less. While previous work showed quantitative agreement between IFEM predictions and experimental solubilization of alkanes in CXEOY micelles, this work explores the possibility of using IFEM as a tool in surfactant selection. Experimental work has shown that detergency improved when operating near the phase inversion temperature (PIT) of the surfactant‐hexadecane system. The IFEM simulations in this work show, for the first time, that IFEM can be used to predict the PIT of surfactant‐oil systems, and that the surfactants selected via this method are consistent with the selection guided by experimental observations.