Persistence length of flexible polyelectrolyte chains

We calculate the dependence of the electrostatic persistence length, le, of weakly charged flexible polyelectrolyte chains using a self-consistent variational theory. The variation of le with κ, the inverse Debye screening length, is controlled by the parameter l0lB/A2 where l0 is the bare persistence length, lB is the Bjerrum length, and A is the mean distance between charges along the chain. Several distinct regimes for the dependence of le on κ emerge depending on the value of l0lB/A2. We show that when l0lB/A2≪1 we recover the classical result, le∝κ−2. For intermediate values of l0lB/A2, le∝κ−1. In this regime one can also get le∝κ−y with y<1 depending on the strength of the Coulomb interaction. When l0lB/A2≫1 we find le∝κ−2. Qualitative comparisons between our theory and simulations as well as other theories are presented.