On the variational approach to Poisson–Boltzmann free energies

The variational approach to the derivation of free energies from the Poisson–Boltzmann (PB) equation is critically reviewed. It is shown that the variational principle (employing the electrostatic potential as varying function) faces several problems and therefore does not constitute a proof for the validity of the free energy expression commonly employed. The free energy functional of the system is then derived from standard thermodynamics principles. It is shown that this functional is actually minimized by the PB ionic distribution, when all physically admissible distributions are considered.