  A systematic study of pressure ionization is carried out in the chemical
picture by the example of fluid helium. By comparing the variants of the
chemical model, it is demonstrated that the behavior of pressure ionization
depends on the construction of the free energy function. In the chemical model
with the Coulomb free energy described by the Pad\'e interpolation formula,
thermodynamical instability induced by pressure ionization is found to be
manifested by a discontinuous drop or a continuous fall and rise along the
pressure-density curve as well as the pressure-temperature curve, which is very
much like the first order liquid-liquid phase transition of fluid hydrogen from
the first principles simulations. In contrast, in the variant chemical model
with the Coulomb free energy term empirically weakened, no thermodynamical
instability is induced when pressure ionization occurs, and the resulting
equation of state achieves good agreement with the first principles simulations
of fluid helium.
