Flexible polyelectrolytes in salt-free solutions

We present a simple model for a flexible polyelectrolyte in salt-free solution. The molecule is assumed to be a helix with height H and fixed radius R, and its net charge is determined by the fraction of associated counterions, m. The Helmholtz free energy is constructed using the main ideas of Debye, Huckel and Bjerrum on electrolyte solutions. The treatment closely resembles that of Manning, but the molecule here is finite and the geometry is non-trivial. The equilibrium configuration is determined by the values of H and m that minimize the free energy. We found that at low temperatures the chain is in a state of minimum height H and maximum associated ion fraction m. The results are then compared with simulations