Numerical Calculation of the Relaxation Spectrum from the Correlation Function

摘要

It has been shown that the distribution of relaxation times, H(ln τ), in semi-logarithmic time scale can easily be calculated numerically from the derivative of the relaxation function in semilogarithmic scale. In that, ln τ, the abscissa, is divided into N different segments of equal size, then H is considered to be a linear function of ln τ within each segment. The technique has been applied to a Williams-Watts function as well as to the relaxation function obtained by photon correlation spectroscopy from atactic polystyrene glass. It has been demonstrated that the relaxation functions can be precisely reproduced from the calculated distribution functions.