Direct Method of Measuring Molecular Quadrupole Moments

Abstract

An experiment whose object is the determination of permanent molecular quadrupole moments is suggested. It is analogous to those used in measurements of electro‐optical Kerr constants, but the uniform electric field proportional to the applied voltage V is replaced by the field gradient of a square four‐wire condenser. If the wires at x=±a are at a potential V relative to those at y=±a, then the field gradient on the z axis will tend to orient quadrupolar molecules so that a fluid in the condenser will become doubly refracting. The induced anisotropy in the refractive index of a gas is shown to be first order in the applied voltage and of the form n_x—n_y=[B+(A/T)]V, while in the Kerr effect it is second order in V, and is given by n_x—n_y=[C+(D/T)+(E/T ²)]V². The constant A is proportional to the molecular quadrupole moment and to the anisotropy in the polarizability, while B is proportional to the quadrupole moment induced in a molecule by a uniform field. In spherical molecules A, D, and E are zero. Calculations indicate that measurements of n_x—n_y, leading to accurate molecular quadrupole moments, should be practicable with present‐day equipment. The theory of the effect in dense media is also developed.