Effect of dispersion on the relaxation-retardation time scale ratio

A simple relation between relaxation (modulus) and retardation (permittivity and compliance) times is determined for cases of dispersive instead of purely exponential response functions. An analytical solution for the Cole-Cole case and numerical treatments of the Cole-Davidson function reveal that the ratio of the relaxation- to retardation time constant is given by the ratio of the high- to low-frequency dielectric constant raised to the power of 1x, where x is the exponent that gauges the deviation from exponentiality.