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

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 G°mic at different temperatures were calculated by using a pseudo-phase transition model. Then, from the diagram (-G°mic /T) = f(1/T), the thermodynamic functions Happ and Sapp were calculated. From the plots Happ = f(T) and Sapp = f(lnT) the slopes Cp = nw(H)Cp,w and Cp = nw(S)Cp,w were calculated, with the numbers nw(H) and nw(S) negative and equal and therefore defined simply as nw. The number nw<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 WI, WII, and WIII, 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 Happ = -3.6 + 23.1w - wCp,wT and the entropy by Sapp = +10.2 + 428w - wCp,w ln T where w = |nw| represents the number of molecules WIII involved in the reaction. The term hw = +23.1 kJ mol-1 w-1 indicates an unfavourable endothermic contribution to enthalpy for reduction of the cavity whereas the term sw = +428 J K-1 mol-1 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’’.