Heat Capacity of Transfer of (Ethylene oxide)13-(propylene oxide)30-(ethylene oxide)13 from Water to the Aqueous Anionic Surfactant Solutions at 298 K. A Quantitative Treatment

Heat capacities of transfer (ACpt) of unimeric (ethylene oxide)(13)-(propylene oxide)(30)-(ethylene oxide)(13) from water to the aqueous surfactant solutions as functions of the surfactant concentrations (m(S)) were determined at 298 K. The surfactants investigated are sodium hexanoate, sodium heptanoate, sodium octanoate, sodium undecanoate, and sodium dodecanoate. For short alkyl chain surfactants, the profiles of the DeltaCp(t) versus ms curves show maxima and minima; for long alkyl chain surfactants, the maximum becomes sharper and moved to lower ms values whereas the minimum tends to disappear. These experimental trends are different from those of the enthalpy in agreement with the fact that heat capacity, being the derivative of enthalpy with respect to temperature, reflects additional terms generated by temperature change on the equilibria in solution. On the basis of a thermodynamic model recently proposed by us for properties first derivatives of Gibbs free energy, a quantitative treatment of the experimental data was done. Such an approach assumes that even in the dilute surfactant region monomers of surfactant associate with unimeric copolymer generating surfactant-copolymer aggregation complexes and, whenever the surfactant achieves the conditions for the micellization, the formation of copolymer-micelle mixed aggregates takes place. The equation derived for the heat capacity of transfer is more complex than that for the enthalpy because it contains five additional terms due to the shift of the equilibria induced by the temperature change. It turned out that these contributions, evaluated by using the equilibrium constants and the associated enthalpies, cannot be neglected for a quantitative treatment of the experimental data. The minimizing procedure provided the heat capacity changes for the formation of the surfactant-copolymer aggregation complexes and the copolymer-micelle mixed aggregates