Analytical evaluation of distribution of relaxation time

The complex dielectric constant of a material in the condensed phase provides important information with regard to its microscopic properties. The real and imaginary properties of the dielectric constant are usually studied as a function of frequency at various constant temperatures or alternatively, as a function of temperature at various constant frequencies. Time domain measurements may also be employed instead of frequency domain measurements as an alternative technique. Using transformation techniques the time domain data are transformed into the frequency domain. A complex plane plot of the dielectric data in the frequency domain can be described by several functions such as Cole-Cole, Davidson-Cole or Havriliak Negami expressions. From these expressions the distribution of relaxation times G(tau) may be derived analytical methods. Each of the distribution functions has distinct characteristics that may be used to gain insight into the macroscopic properties. The author has evaluated the distribution functions for several polymers. In this paper the calculations for poly(methyl methacralate) PMMA and poly(vinyl acetate) are presented. In PVAc the influence of the glass transition temperature on the distribution is clearly evident.