Critical evaluation of models for self-assembly of short and medium chain-length surfactants in aqueous solutions

During numerous visits to our Laboratory professor Johannes (Hans) Lyklema emphasized the importance of a holistic view on thermodynamics. In order to fulfill this aim he assembled the monumental Fundamentals of Interface and Colloid Science series. The basic state functions (internal energy, enthalpy and free energies) are interrelated by Gibbs and Helmholtz relationships. First-order phase transitions are characterized by first-order state variables (temperature, pressure, entropy, volume). Interactions are, however best expressed by second-order partial derivatives (compressibility, heat capacity and expansivity). They are related to the first-order state variables by relaxation contributions quantifying the degree of cooperativity of self-assembly processes leading to phase separation. In particular they exhibit the limit when phase transitions are changed to second-order processes. This was the focus of my first review dedicated to the memory of professor Lyklema, "Characterization of van der Waals type bimodal,- lambda,- meta- and spinodal phase transitions in liquid mixtures, solid suspensions and thin films" (ACIS 253 (2018) 66). In the present review the attention is placed on short and medium chain-length surfactant self-assembly in aqueous solutions without additives (salts or solubilizates). The dependence of state functions described above on concentration, temperature and pressure is compared to corresponding dynamic molecular processes occurring on different time, frequency and length scales including structure analysis. It is convincingly shown that Hartley-Tanford space filled spherical anhydrous micelle core - polar shell model designed for long chain-length surfactants (cmc < 0.01 mol/dm³, N > 50) cannot be enforced on short and medium chain-length surfactant non-sperical micelles (cmc close to unity, N < 20). Moreover, it is shown that a proper validity evaluation of proposed models for micelle formation is seriously undermined by their application to only a narrow concentration range near critical micelle concentration (cmc). When successful each model should characterize all self-assembly processes occurring (also at limiting association concentration, lac, at second critical concentration, 2cc and at third critical concen-tration, 3cc) within the entire concentration range of thermodynamically stable surfactant solutions. All other self-assembly processes except micelle formation are rarely considered. The pre-micelle formation at lac is, for example omitted as deviations from presented models. The reviewed reports are therefore selected on the basis of maximum investigated concentration range and of largest possible number of homologues.