Thermodynamic aspects, theories and computer simulations

In consideration of the thermodynamic aspects, and from the early results of Price [5] and Quintana et al. [ 135], it is now well established that the micellization of block copolymers in organic medium is an enthalpic driven process, the micellar core formation being the main contribution to the exothermic process. 

This situation is quite opposite to that reported for the micellization in aqueous medium, for low molecular weight surfactants as well as for hydrophilic-hydrophobic block copolymers in water. Typical examples are those reported by different authors for PEO-PPO-PEO block copolymers for which the micellization is an entropy driven process [ 114,135,136). According to Liu etal. [137] this phenomenon is mainly the consequence of hydrophobic interactions and changes of the water structure in vicinity of the polymer chains. 

Quite a number of theories were developed over the years in order to predict, mainly for non-polyelectrolyte systems, the structural parameters of a micelle (CMC, association number Z, core radius shell thickness L, hydrodynamic radius as a function of the copolymer characteristics, for example its molecular weight and composition. For A-B diblock copolymers which were mainly examined and where the B sequence is forming the micellar core, these characteristics are defined by the corresponding polymerization degrees and Ng. In all these theories and by using various models and mathematical approaches, the total Gibbs free energy of the micelle is expressed as the sum of several contributions, mainly those related to the core the shell and the core/shell interface 

Minimization of this equation with respect to parameters characterizing the micelle leads to correlations between the copolymer and the micellar characteristics. 

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