Effects of Concentration and Interactions in Star Polyelectrolyte Solutions

4 Effects of Concentration and Interactions in Star Polyelectrolyte Solutions 

A decrease in the size, R, of a PE star as a function of polymer concentration is most pronounced for polyions with a relatively small number of branches p. As discussed above, in this case the counterions are distributed most uniformly between intra- and intermolecular space. Therefore, an increase in the average concentration of counterions in the solution leads to a proportional increase in their concentration in the intramolecular volume of these branched polyions. In contrast to this, stars that have many arms have a modest response to an increase in the PE concentration. This is because at any (arbitrarily small) solution concentration, only a small fraction of the counterions is found in the intermolecular space. This behavior of PE stars should be contrasted with that of neutral star polymers. In the latter case, screening of the intramolecular excluded-volume repulsion, and the contraction of 

Star-branched polymers upon the increase in star concentration, occurs only in the semidilute regime, i.e., when the average polymer concentration in the solution exceeds the intramolecular concentration in an isolated star [24]. 

Probing forces between PE stars in a solution is a challenging experimental problem. However, advances in the technique of optical tweezers now allow direct measurement of repulsive forces between brushes of DNA [94, 95] and synthetic PE chains [96, 97] grafted onto colloidal particles of submicrometer size. 

The MD simulation study of the interaction between PE stars in a salt-free solution has been performed in [39]. The simulation results were fitted using a simplified analytical equation for repulsive force, which arises due to the decrease in translational entropy of counterions entrapped in overlapping star coronae. In this model, the repulsion starts at distances between star centers smaller than 2R, where R is the unperturbed size of an individual star. A similar approach has been applied in [40] to describe repulsion between colloidal PE brushes. 

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