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

The Thermodynamical Instability Induced by Pressure Ionization in Fluid Helium