Box-Like Cell Model of a Polyelectrolyte Star

The box-like cell model of a PE star can be considered as a generalization of a classical mean-field Flory approach, which was first suggested to describe the swelling of a polymer chain in a good solvent [90], The Flory approach estimates the equilibrium dimensions of a macromolecule, as a function of its parameters, by balancing the free energy of intramolecular (repulsive) interactions with the conformational entropy loss of a swollen chain. Within the box-like approximation, the star is characterized by the radius of its corona, R (end-to-end distanee of the arms), or by the average intramolecular concentration of its monomers  

Provided that the arms remain stretehed with respeet to their Gaussian size, R the conformational free energy of p uniformly stretched Gaussian chains (arms) is  

The free energy of non-electrostatie interactions is, within the virial expansion, given by  

In the absence of charges, or at a low degree of ionization of the arms, the star conformation is controlled by a balance between two first terms in (7) (i.e., the short-range interarm repulsions and the conformational entropy of stretched arms). As a result, the star size is given by (4). That is, the power law dependencies, obtained on the basis of the blob model, are recovered. The physical reasons why there is a match of the star size as obtained by the scaling and in the mean field approximations are discussed in details in [23]. 

2 Poly electrolyte Star Conformation in a Dilute Salt-Free Solution 

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