A consideration of the accuracy and application of the Brather approximation for the transformation of dielectric relaxation data from the time domain to the frequency domain

The methodology for conversion of transient current data in the time domain into dielectric loss data in the frequency domain using the Brather approximation is described. A test of the accuracy of the approximation is made using the 'stretched exponential' relaxation function (Kohlrausch-Williams-Watts function) for which the Fourier transform has been previously tabulated for a range of exponent \ ̄gb(0 < \ ̄gb ≤ 1). As an example of the application of the Brather approximation we report ultra-low frequency dielectric loss data (10^-3.5 to 10^-0.4) for a liquid-crystalline side-chain polymer as derived from transient current data.