Volumes and heat capacities of the aqueous sodium dodecanoate/sodium perfluorooctanoate mixtures in the presence of β-cyclodextrin

Abstract

Apparent molar volumes (V_Φ) and heat capacities (C_Φ) of the sodium dodecanoate (NaL)/sodium perfluorooctanoate (NaPFO) mixtures in the water/β-cyclodextrin (β-CD) solvent as functions of the surfactant total molality (m_t) were determined at 25 °C. For a given surfactant mixture, V_Φ decreases with m_t to ca. 0.05 mol kg⁻¹ thereafter it increases tending to a constant value. C_Φ displays a behaviour opposite to V_Φ. The m_t values where the apparent molar properties exhibit extrema are nearly coincident with the critical micellar concentrations determined by conductivity. An equation correlating V_Φ to m_t was derived by assuming that the equilibria for the 1∶1 surfactant/cyclodextrin complex formation and the micellization were simultaneously present. A mass action model described the aggregation process of each pure surfactant. The V_Φ quantitative analysis of the NaL/β-CD and NaPFO/β-CD mixtures provided the volume changes for the complex formation. It was impossible to extend an analogous treatment to V_Φ of the NaL/NaPFO mixtures. Therefore, simulations were done based on the following points: (1) the pseudo-phase transition model for micellization was employed; (2) the composition of the mixed micelles was set equal to the stoichiometric NaL/NaPFO ratio and (3) the properties of the β-CD/NaL and β-CD/NaPFO complex formation in water were used. As concerns the heat capacity, the equation correlating C_Φ to m_t contained also the terms due to the presence of the contributions for the shift of the equilibria of micellization and the surfactant/cyclodextrin inclusion complex formation with temperature. The heat capacity changes for the β-CD/NaL and β-CD/NaPFO complex formation were evaluated from data of pure surfactants. Then, according to the approach used for the volume, C_Φ of the NaL/NaPFO mixtures were computed. As a general result, the simulations of both the volume and the heat capacity were rather satisfactory. The relevance of this study is due to the ability in predicting the thermodynamic properties of the surfactant–surfactant–cyclodextrin–water quaternary systems based on the acquaintance of the thermodynamics of micellization of the surfactant mixtures in water and the complex formation between each surfactant and cyclodextrin in water.