  We present a soft-potential-enhanced Poisson-Boltzmann (SPB) theory to
efficiently capture ion distributions and electrostatic potential around
rodlike charged macromolecules. The SPB model is calibrated with a
coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent
salt solutions as well as compared to a full atomistic molecular dynamics
simulations with explicit solvent. We demonstrate that our modification enables
the SPB theory to accurately predict monovalent ion distributions around a
rodlike PE in a wide range of ion and charge distribution conditions in the
weak-coupling regime. These include excess salt concentrations up to 1 M, and
ion sizes ranging from small ions, such as Na or Cl, to softer and larger ions
with size comparable to the PE diameter. The work provides a simple way to
implement an enhancement that effectively captures the influence of ion size
and species into the PB theory in the context of PEs in aqueous salt solutions.
