A numerical method of obtaining the relaxation distribution function from decay curves and its application to the decay process of electric birefringence of concentrated poly-γ-benzyl-l-glutamate solutions

Abstract

In (I), we describe a numerical method for determining the relaxation distribution function from decay curves. The distribution function is expanded in a series of appropriate polynomials and the best values of the coefficients are determined by the method of least squares. In order to examine its applicability and limit, we apply it to some artificial decay curves constructed with different types of distribution functions. According to the results, our method is more adequate for the continuous distribution than for the discrete one. Accurate calculation is very effective so long as the original decay data are accurate, while rough calculation is good when the original decay data are rough or include some noise. Therefore, rough calculation is practical for analysis of experimental decay data which are not free from errors.

In (II), we apply our method to the decay process of electric birefringence of several concentrated poly-γ-benzyl-L-glutamate solutions. It is sometimes necessary to modify the experimental data because of improper selection of the base line. The semi-logarithmic plot is effective for modification. In order to make our physical image clearer, the length distribution function is introduced. Field strength dependence, time dependence and concentration dependence of the length distribution curve have been obtained. Our method is powerful for investigating a systematic change of the distribution function with changes of external or internal conditions.