Theory of fluids of non-axial quadrupolar molecules

Abstract

Thermodynamic perturbation theory is used to derive expressions for thermodynamic quantities for a fluid composed of non-axial quadrupolar molecules. These expressions have the same form as the corresponding ones for axial molecules, but with the single axial dipole and quadrupole moments (μ, Q) replaced by effective moments which are rotationally invariant combinations of the components of the multipole moments μ and Q. If the quadrupole moment is weak, so that the perturbation expansion can be terminated at the second order term, a single effective axial quadrupole moment used in the axial expressions correctly reproduces the free energy and pressure second virial coefficient. For stronger quadrupole moments, where third and higher order terms are needed, this ‘effective axial’ approximation is generally poor, and one must use the correct non-axial expressions. For pure ethylene it is shown that the effective axial approximation gives accurate results for the third order free energy term A ₃, and hence for the thermodynamic properties, because the two invariant combinations of Q _αα (α = x, y, z) that arise in A ₃ have the same magnitude in this case. For mixtures of ethylene with an axial quadrupolar molecule the effective axial approximation usually gives poor results, however, since it predicts the wrong sign for part of the unlike-pair contribution to the free energy. These conclusions are supported by numerical calculations for ethylene and ethylene mixtures (C₂H₄/Xe, C₂H₄/NO₂).