Thermodynamics of micellization of oppositely charged polymers

– The complexation of oppositely charged colloidal objects is considered in this paper as a thermodynamic micellization process where each kind of object needs the others to micellize. This requirement gives rise to quantitatively different behaviors than the so-called mixed-micellization where each specie can micellize separately. A simple model of the grand potential for micelles is proposed to corroborate the predictions of this general approach. Complexation of oppositely charged colloidal objects has been the subject of continuous and important researches since the seventies because of the numerous applications ranging from flocculants and coatings to systems mimicking biological phenomena [1]. The interest in this last field has grown in recent years as the drug carrier potential of polymer complexes has been realized [2]: most of the non-viral vectors used for gene delivery are made of complexes between negatively charged DNA and oppositely charged objects that can be either surfactants (lipoplexes) [3] or homo or co-polymers (polyplexes) [4,2]. Since a drug delivery vector has to be able to cross several biological and physical obstacles, the tailoring of a multifunction carrier challenges nowadays biologists as well as physico-chemists [5]. The common feature of these complexes is their reliance on electrostatic self-assembly. Complementary to the experimental approaches looking for various drug delivery systems based on electrostatic complexation, there is obviously a need for more thorough understanding of the underlying mechanisms of self-assembly and of the relevant parameters for controlling them [6]. In this Letter I present the general formalism required to describe the thermodynamic properties of micelles formed by complexation of oppositely charged objects and having a well defined gaussian size distribution. This allows us to address in particular the role of the mixture stoichiometry on the micelle compositions. In order to derive the most general features of the complexation viewed as a micellization process, the kind of objects considered will not be specified . The word “micellization” is used here in a generalized way: monodisperse amphiphilic molecules self-assemble forming micelles above the so-called critical micelle concentration as they are not soluble as a single specie [7]. In the case of complexation, both components of the complexes are water-soluble, but they still form aggregates that have been shown in the case of various polymer systems to exhibit a core-corona structure similar to the