The initial slope of the transient birefringence of rigid macromolecules under the action of a reversing electric pulse of arbitrary field strength

Abstract

A solution is presented for the rotational diffusion equation of rigid macromolecules in solution under the action of a reversing electric pulse. The distribution function is expanded into a functional series composed of products tiPj of the power of time (ti) and Legendre polynomial (Pj). The coefficients of the series are then easily obtained up to a higher order of time from the simple recursion formulas. The initial slope of normalized reversing birefringence at an arbitrary field strength is simply expressed by two averages of the first order Legendre polynomial and the second order Legendre polynomial, <P1≳ and <P2≳, initial slope=2Θβ2/γ (1−<P2≳)/<P2≳−6Θβ/γ <P1≳/<P2≳. Furthermore, the initial slope for pure permanent dipole orientation (γ=0) is found to be independent of the electric field. That is, initial slope=−12Θ. On the other hand, the initial slope obtained by neglecting the Brownian motion at high fields is larger by 6Θ. For example, it is equal to −6Θ for pure permanent dipole orientation. This discrepancy is also discussed.