The solution of b
By substituting the solutions about fi (Tc ) of Eqs. (A1) - (A5) into Eq. (20) at the critical point, b can be solved based on Eq. (12) as the following equation:
\(\mathrm{b=}\mathrm{V}_{\mathrm{c}}\mathrm{-}\frac{\mathrm{R}\mathrm{T}_{\mathrm{c}}}{{\mathrm{5}\mathrm{P}}_{\mathrm{c}}\mathrm{h}}\)(A6)
It also can be expressed in the form of the critical compression factor:
\(\mathrm{b=}\mathrm{V}_{\mathrm{c}}\mathrm{-}\frac{\mathrm{R}\mathrm{V}_{\mathrm{c}}}{{\mathrm{5}\mathrm{Z}}_{\mathrm{c}}\mathrm{h}}\)(A7)
Similar to the treatment in the original M-H EOS, the coefficient is introduced into Eq. (A7)9. In order to verify whether the new coefficient β was valid, a large number of calculations have been carried out rigorously and the final data presented in the support information have verified its feasibility. The new formula ofb is expressed as follows:
\(\mathrm{b=}\mathrm{V}_{\mathrm{c}}\mathrm{-}\frac{\beta V_{c}}{15Z_{c}h}\)(A8)
β is a constant for a given substance that depends uponZ c, the value of β is between 3.0 and 4.09. Figure A1 shows the relationship between β and β /Z c, it also can be expressed as the following formula: