Rotational relaxation of spherical-top molecules by atoms

A theoretical study of rotational relaxation of spherical-top molecules in an inert gas is presented. Under the assumption that the molecules and atoms collide as rough spheres, two previous theoretical methods obtained apparently conflicting results. These two methods are shown to be in agreement, the discrepancy being related to the definition of a fundamental relaxation time. When applied to the recent ultrasonic-absorption experiments, the relevant relaxation time is equal to that first reported by Widom. Throughout, the modified rough-sphere collision theory developed by Offerhaus is used. If ℵα is a reduced moment of inertia, defined by ℵα = I/μσ2αβ, where I is the moment of inertia of the rotating molecule, μ is the reduced mass of the atom-molecule pair, and σαβ is the sum of the atomic and molecular radii, then Nrot, the number of collisions suffered by each molecule in a time equal to the relaxation time, is Nrot = 34(1 + ℵα)2/ℵα(1 − cos φ). Here φ is a parameter related to the rotation of a particular relative velocity vector, and ranges from zero (smooth spheres) to л (rough spheres). A correction to this result related to the attractive potential between atoms and molecules is obtained by multiplying Nrot by the factor exp (−ε/kBT), in which ε is the depth of the attractive potential well, kB is Boltsmann's constant and T is the temperature. Values for Nrot are tabulated for a variety of spherical-top molecule-inert gas systems.