  Variational methods are used to calculate structural and thermodynamical
properties of a titrating polyelectrolyte in a discrete representation. The
Coulomb interactions are emulated by harmonic repulsive forces, the force
constants being used as variational parameters to minimize the free energy. For
the titrating charges, a mean field approach is used.
  The accuracy is tested against Monte Carlo data for up to 1000 monomers. For
an unscreened chain, excellent agreement is obtained for the end-to-end
distance and the apparent dissociation constant. With screening, the
thermodynamical properties are invariably well described, although the
structural agreement deteriorates.
  A very simple rigid-rod approximation is also considered, giving surprisingly
good results for certain properties.
