A simple model for the collapse of polyelectrolyte macromolecules

A simple theory for the conformational properties of highly charged flexible chains is presented. The scaling exponent γ describing the end-to-end distance R≡b(Z−1)γ is obtained, where b is the distance between monomers and Z is the number of monomers of a single chain. We find that at high temperatures, γ≈35. In this limit the electrostatic interactions are negligible, entropy dominates, and the chain behaves as a neutral polymer. As the temperature, is lowered, electrostatic repulsion between charged monomers becomes more important and the chain begins to stretch, with 35<γ<1. If the temperature is lowered even further, the condensation of counterions starts, complexes are formed, and the net charge of the chain is reduced. The repulsion between monomers decreases, and the chain starts to contract. At this temperature the chain is in a collapsed state due to dipole–ion interactions, with γ≈0.3. The fraction of associated ions mc to a given chain is also obtained for various interaction strengths. The results are in good agreement with molecular dynamics simulation studies.