The distribution of relaxation frequencies from photon correlation spectroscopy near the glass transition

The relaxation function obtained by photon correlation spectroscopy of a liquid near the glass transition has a highly nonexponential decay. This nonexponential behavior can be represented by a distribution of exponential relaxation processes. Using a real-time, 4-bit, 4-sample time, 256-channel correlator we have obtained very high quality depolarized spectra of polystyrene over seven decades in time. The relaxation function was calculated from the data and a least squares fit to the weighting factors of a sum of exponentials was performed using techniques described by Ostrowsky et al. A least squares fit was obtained using a powerful program in the port© mathematical subroutine library called IQP which finds a minimum for the quadratic programming problem subject to certain constraints. This yields the distribution of relaxation frequencies characteristic of a liquid near the glass transition. The shape of the distribution is very similar to the distribution of relaxation frequencies obtained from the empirical Williams–Watts function.