Measurement of Relaxation Times of Macromolecules by the Kerr Effect

Abstract

INFORMATION on macromolecules may conveniently be found by application of the Kerr electro-optic effect. When an electric field in the form of a pulse of rectangular shape is applied to a solution the molecules will attempt to line up to a state of minimum potential energy during the rise period of the pulse. Once lined up they will remain stationery in alignment when the field amplitude is constant and then become disorientated by Brownian motion when the field ceases. If the orientation is sufficient the solution will exhibit birefringence, but since large molecules will take time to come into alignment and to return to a state of random array the rise and decay of the birefringence will lag behind that of the applied field. In general, therefore, a gradual increase of birefringence occurs, which may or may not reach a steady value according to the duration of the pulse, followed by a decay. Observations of the rise can give information on dipole moments and the steady value can be related to the Kerr constant and to molecular anisotropy. The decay for a solution of k types of molecules occurs according to the equation¹: in which Δn is the birefringence at any time t, δn_i is the maximum birefringence shown by molecules of type i and τ_i is a relaxation time which is a measure of the time the molecule takes to depart from its position of minimum potential energy. If it be assumed that the effect of the field is to produce rotation of the entire molecule then the polar or non-polar nature of the molecule is made manifest by the symmetry or asymmetry of the birefringence rise and fall, and τ_i can be related¹ to the rotary diffusion constant D_i by the equation τ_i = 1/6D_i. Values of relaxation times and diffusion constants obtained in this laboratory are reported here.