Polyelectrolyte solutions chain ordering

In order to resolve these challenges, it is essential to account for chain connectivity, hydrodynamic interactions, electrostatic interactions, and distribution of counterions and their dynamics. It is possible to identify three distinct scenarios (a) polyelectrolyte solutions with high concentrations of added salt, (b) dilute polyelectrolyte solutions without added salt, and (c) polyelectrolyte solutions above overlap concentration and without added salt. If the salt concentration is high and if there is no macrophase separation, the polyelectrolyte solution behaves as a solution of neutral polymers in a good solvent, due to the screening of electrostatic interaction. Therefore for scenario... 

Numerous data are available on the Kerr effect in solutions of ionogenic chain molecules with secondary structures particularly of polypeptides displaying a helical conformation A high EB value in these solutions is ensured by both the polarization of ionic atmospheres and the character of the rigid secondary structure of the molecules. It is not always possible to distinguish between the effect of the structural order and the ionic state of the medium on the electro-optical properties of rigid polyelectrolyte solutions. Thus it is difficult to determine their molecular structure. 

Plestil J, Mikes J, Dusek K. Investigation of local chain ordering in polyelectrolyte solutions by small-angle X-ray scattering. Acta Polymerica 1979 30 29-32. 

The counter-ion concentrations around the polyelectrolyte chain may fluctuate, which induces an attractive interaction between the chains sharing the same clouds of counter-ions (Golestanian et al. 1999). Parallel stacking of polyelectrolyte chains favors such kind of attractions, as demonstrated in Fig. 4.11. This effect will result in the spontaneous liquid crystal ordering in polyelectrolyte solutions (Potemkin et al. 2002 Potemkin and Khokhlov 2004). Such a tendency of liquid crystal ordering acmally stabilizes the parallel rolling of DNA long chains, and squeezes them into the very limited space of cell nucleus. 

Milas M., Rinaudo M., Duplessix R., BorsaU R., Lindner P., Small angle neutron scattering from polyelectrolyte solutions From disordered to ordered xanthan chain conformation. Macromolecules, 28,1995, 3119-3124. 

It is obvious that both intra-molecular and inter-polymer phenomena in polyelectrolyte solutions are dominated by coulomb forces. Repulsive interactions would be expected to diminish aggregation. At the same time, extended chain dimensions and the long-range character of electrostatic effects can promote forms of ordering unique to polyelectrolytes. Hydrodynamic, spectroscopic and thermodynamic methods have all been brought to bear on the coupled problems of conformation, counterion distribution and inter-polymer ordering in polyion solutions. These approaches are well represented in Part III by the works on Paoletti, Berry and Jamieson. 

At this polyma concentration, the concentration of monomers within a volume occupied by a chain is on the order of the avaage monomer concentration in a solution. For strongly charged chains in salt-free solutions, the chain size is close to that of a fully stretched chain Rg bN. In this case, the chain s ovalap concentration scales with the chain s degree of polymerization as c N/Rg b N. This dependence of the solution ovalap concentration on the chain s degree of polymerization is much stronger than the one observed in solution of neutral chains for which c b N. Thus, crossova to semidilute solution regime takes place at much Iowa polyma concentrations in polyelectrolyte solutions than in solutions of... 

At length scales larger than the electrostatic interactions are screened by the other chains and counterions and the statistics of a chain is Gaussian with effective bond lengths of the order of the correlation length Thus, the chain size R in the semidilute salt-free polyelectrolyte solution is R - A /2c->/4 [26,29],... 

Our considerations qualitatively explain the results of Fig. 3.16 The dissolution of salt in addition to the polyelectrolyte suppresses the osmotic pressure contribution by the counter-ions and transforms the stiffened polyelectrol3de chain into a much more flexible quasi-neutral chain. In the absence of these polyelectrolyte characteristics, one recovers the behavior of neutral systems and, therefore, in the semidilute range the associated scaling law Eq. (3.41). Equation (3.136) correctly describes the general tendencies, but is not an accurate expression. First, in view of the complex structures in polyelectrolytes with shell formations and screening effects, equilibria have to be expressed in terms of activities rather than concentrations. Furthermore, the Donnan expression is not the only contribution to the second virial coefficient. There exists another part, AA2, which accounts as usually for excluded volume effects, the quality of the solvent and the peculiar ordering phenomena found in polyelectrolyte solutions. Therefore, in general, one has to write... 

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