Single-Chain Conformation in Polyelectrolyte Solutions

In a polar solvent, a polyelectrolyte chain can dissociate the counter-ions on the side groups, and becomes a macro-ion or a charged polymer, as demonstrated in Fig. 4.10. The macro-ion chain is surrounded by small counter-ions. If the charge valence of the counter-ions is larger than mie, they can effectively cross-link the macro-ions to form polyelectrolyte gels. 

Bio-macromolecules such as DNA, RNA and proteins exhibit the properties of polyelectrolytes in aqueous solutions. The migration of fragments hydrolyzed from bio-macromolecules in the aqueous gel can be oriented by the weak electric field. Long chains drift slowly, short chains drift fast, and their difference in the speed results in a characteristic spectmm. This is the principle of gel electrophoresis. As a fundamental method in gene engineering, gel electrophoresis has been widely applied in the identification and analysis of DNA and protein characteristic sequences. 

The fraction of charged monomers p on the polyelectrolyte backbone is highly sensitive to the environmental factors such as temperature, strength of the electric field, ion concentration and pH value (Barrat and Joanny 1996). In the polyelectrolyte solutions, the Coulomb force on the polymer chain plays an important role in determining the chain conformation. The Coulomb energy between two charge units is 

This length scale characterizes the distance between two charges of the same species allowed by the thermal fluctuations. In other words, when the charge density p on the polymer chain becomes too high, for instance, p e//, the counter-ions will accumulate around the chain to maintain the effective charge density at constant e//. Such a phenomenon is called Manning condensation of counter-ions (Manning 1969). 

The fraction of charged monomers on the chain determines the Coulomb energy of single chain, as given by 

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