Simple models of junction multiplicity

The multiplicity of the junctions is in principle determined automatically by the equilibrium requirement for a given associative interaction. In the case of hydrophobic interaction, the chain length of a hydrophobe, the strength of water-hydrophobe interaction, the geometric form of an aggregate, and other factors determine the association constant X(T) and the junction multiplicity k. For practical treatment, we avoid complexity in finding the precise form of the coefficients yt, but instead, we introduce model junctions [26]. 

In one of the practical models in commmon use, multiplicities lying in a certain range covering from k = koio k are equally allowed (mini-max junction). In such cases we have 

Such assumption of limited range can be, to some extent, justified in the case of micelles of hydrophobic chains [27]. 

When only a single value is allowed, i.e ko = k =k, we call the model the fixed multiplicity model. Thus, for k = 2, the fixed multiplicity model reduces to the pairwise association. The normalization relation (7.98) for the fixed multiplicity model of monodisperse polymers (/ and n definite) is given by 

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