Rotational Relaxation in Polar Gases

Abstract

Rotational collision numbers for pure polar gases have been calculated by classical mechanics. For the purposes of the calculation, a polar molecule was taken to be a point dipole imbedded in a hard core and the interaction between molecules was confined to a plane. A perturbation calculation correct through third order gave the result $$\frac{Z_{\mathrm{rot}}\text{(1,\hspace{0.17em}T)}}{Z_{\mathrm{rot}}{\text{(2,\hspace{0.17em}T}}_0)}=\frac{{\gamma }_1}{{\gamma }_2}{\left(\frac{{\mu }_2}{{\mu }_1}\right)}^4\left(\frac{M_1}{M_2}\right){\left(\frac{T}{T_0}\right)}^3{\left[\frac{{\eta }_2{\mathrm{(T}}_0)}{{\eta }_1\mathrm{(T)}}\right]}^2\frac{h_{11}{\text{(2,\hspace{0.17em}T}}_0)}{h_{11}\text{(1,\hspace{0.17em}T)}},$$ where the numbers 1 and 2 label chemical species, γ is the number of rotational degrees of freedom, M the molecular mass, μ the dipole moment, T the absolute temperature, T₀ a reference temperature, and η the viscosity. The function θ₁₁ has as its argument ${\text{(16π/5)(I/M)η(πMkT)}}^{\text{−1/2}}$ , where I is an average moment of inertia. The theoretical results show that the rotational collision number increases for increasing temperature and decreasing dipole moments and moments of inertia. The dipole moment and moment of inertia dependence is in qualitative agreement with experiment. Since the experimental temperature dependence is somewhat in doubt, no conclusion can be made concerning the correctness of the theoretical temperature dependence.