Structure of linear polyelectrolyte chains in dilute solution

2 Structure of linear polyelectrolyte chains in dilute solution 

Consider a linear polyelectrolyte chain with m monomer units. Each monomer xmit contains a chemical moiety that is sensitive to the aqueous environment. Examples of such groups include carboxylic acids, amine bases, or generalized bases with the corresponding coxmterions such as sulfate and sodium ions. For convenience, we will restrict attention to monovalent systems, but more complicated polymers such as DNA can be treated in the same manner. If the chain in dilute aqueous solution is electrically neutral, the conformation will be determined by the persistence length of the chain, the overall chain length, and the solvent quality, just as for any linear polymer in dilute solution. However, dissociation of some of the species in 

One of the key concepts needed to carry out this calculation is the electrostatic potential, in the solution due to the charges. For a single fixed charge of magnitude at location r in a medium of dielectric constant D, the potential at location r can be expressed as  

For an actual ion characterized by a distance of closest approach, a, the potential near the ion in a salt solution of finite ionic strength is calculated to be  

The ionic strength depends on all the ions in solution. When k is very small, the potential approaches the pure Coulomb result (Equation 10.1). When the ionic strength is large, or when the dielectric constant is small, the charge is screened by the solution when xr 1. 

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