Thermodynamics of micelle formation in water, hydrophobic processes and surfactantself-assemblies

Abstract

The critical micelle concentration (c.m.c.) for four cationic surfactants, alkyl-trimethyl-ammonium bromides, was determined as a function of temperature by conductivity measurements. The values of the standard free energy of micellisation ΔG^∘_mic at different temperatures were calculated by using a pseudo-phase transition model. Then, from the diagram (−ΔG^∘_mic/T) = f(1/T), the thermodynamic functions ΔH_app and ΔS_app were calculated. From the plots ΔH_app = f(T) and ΔS_app = f(ln T) the slopes ΔC_p = n_w(H)C_p,w and ΔC_p = n_w(S)C_p,w were calculated, with the numbers n_w(H) and n_w(S) negative and equal and therefore defined simply as n_w. The number n_w < 0, indicating condensed water molecules, depends on the reduction of cavity that takes place as a consequence of the coalescence of the cavities previously surrounding the separate aliphatic or aromatic moieties. The analysis, based on a molecular model consisting of three forms of water, namely W_I, W_II, and W_III, respectively, was extended to several other types of surfactants for which c.m.c. data had been published by other authors. The results of this analysis form a coherent scheme consistent with the proposed molecular model. The enthalpy for all the types of surfactant is described by ΔH_app = −3.6 + 23.1ξ_w − ξ_wC_p,wT and the entropy by ΔS_app = +10.2 + 428ξ_w − ξ_wC_p,w ln T where ξ_w = |n_w| represents the number of molecules W_III involved in the reaction. The term Δh_w = +23.1 kJ mol⁻¹ξ_w⁻¹ indicates an unfavourable endothermic contribution to enthalpy for reduction of the cavity whereas the term Δs_w = +428 J K⁻¹ mol⁻¹ξ_w⁻¹ represents a positive entropy contribution for reduction of the cavity, what is the driving force of hydrophobic association. The processes of non polar gas dissolution in water and of micelle formation were found to be strictly related: they are, however, exactly the opposite of one another. In micelle formation no intermolecular electronic short bond is formed. We propose, therefore, to substitute the term “hydrophobic bond” with that of “hydrophobic association”.