Effect of the Polydispersity of Molecular Length on the Decay Process of Transient Electric Birefringence of Rodlike Macromolecules in Dilute Solution

Abstract

Abstract The effect of polydispersity on transient electric birefringence (EB) was examined for a dilute solution which contains like macromolecules of varying lengths. The molecules were assumed to be rigid rods of cylindrical symmetry, so that the molecular weight is linearly proportional to length. Polydispersity was expressed by the ratio of the weight-average to the number-average lengths lw/ln. A logarithmic-normal type continuous length distribution was generally used. Calculations were performed for the birefringence-average relaxation time 〈τ〉EB and initial slope 〈S〉EB as a function of the electric field strength E, which is applied prior to the start of the decay process, with the electric parameter (βw)2/2γw, which is related to the weight-average permanent dipole moment (the βw-term) and polarizability anisotropy (the γw-term). Both 〈τ〉EB and 〈S〉EB are very sensitive to E, lw/ln, and (βw)2/2γw. A convenient method was devised for determining the polydispersity parameters (lw/ln and lw) from the weight-averages of relaxation time and initial slope, which are free from the mechanism of field orientation. Examples are given for a polydisperse, rigid rodlike sonicated DNA sample in aqueous solution.