Degree of micellisation

Fig. 29 Dependence of the degree of micellisation on the molar fraction of acrylic acid and topology (o) AA20 side chains, ( ) AA37 side chains, (A) AA85 side chains, ( ) block copolymers...

Let us suppose that K i and ni are constant. Then, using the material balance condition (5.19) and the degree of micellisation in the form ai = n CM/Cioti we obtain [12]... 

Since this point corresponds to a maximum rate of increase of the micellisation degree with the total surfactant concentration, the corresponding concentration may be taken as the CMC. This fact allows to introduce in Eq. (5.43) the degree of micellisation acMC at the CMC. 

When the CMC is eonsidered to be an inflection point of the dependence ai(lnctoti) the corresponding degree of micellisation at the CMC becomes... 

Numerous theories, models and mathematical approaches have been developed over the years in order to describe the micellisation process and the dependence of fundamental structural parameters of the micelles, like cmc, aggregation number (Nagg), overall size (Rm), core radius (Rc) and corona thickness (L), on the molecular characteristics of the block copolymer, with respect to the degrees of polymerisation of the constituent blocks (Na and N ), as well as the Flory-Huggins interaction parameters x between the blocks and between the blocks and the solvent. Some of these approaches use the minimisation of the total free energy of the micellar system so as to extract relations between the copolymer and micelle features, while others are based on the scaling concept of Alexander-de Gennes and... 

Amphiphilic block copolymers with one ionic block constitute an intriguing class of macromolecules, since their self-assembly in aqueous solution usually leads to the formation of spherical micelles with a hydrophobic core and a polyelectrolyte corona. These micelles are particularly interesting because the intrinsic properties of their polyelectrolyte corona are strongly influenced by many parameters like pH, salt concentration, degree of dissociation, polar interactions and so on. Moreover, they can be considered as a model to spherical polyelectrolyte brushes and thus provide a unique opportunity to study polyelectrolyte properties in high concentration conditions. The micellisation behaviour of ionic amphiphilic copolymers has been reviewed by Riess [1], Gohy [2], Eisenberg et al. [112, 113], Forster et al. [138] and Cohen Stuart et al. [139]. 

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