  Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged
soft matter problems, we work out the Coulombic grand potential of a long
cylindrical charged polyion in a binary electrolyte solution of arbitrary
valency and for low salt concentration. We obtain the exact analytical low-salt
asymptotic expression for the grand potential, derived from known properties of
the exact solutions to the cylindrical PB equation. These results are relevant
for understanding nucleic acid processes. In practice, our expressions are
accurate for arbitrary polyion charges, provided their radius is smaller than
the Debye length defined by the electrolyte.
