Limitations of the stretched exponential function for describing dynamics in disordered solid materials

Around the glass transition temperature, relaxation dynamics in glass-forming materials follows a strong nonexponential behavior. It is widely accepted that an empirically based stretched exponential function, known as the Kohlrausch-Williams-Watts (KWW) function, ϕ ( t ) = e − ( t ∕ τ ) β , describes universally a broad variety of experimental data. Using intuitive pictures and ellipsometric measurements, we show that (1) in order to describe the dynamics in disordered materials such as in polymers using a KWW function, the response has to be considered over a specific region of time, (2) a single KWW function is not sufficient for correctly describing more than one relaxation processes, and (3) in certain cases, stretching exponents depending on temperature do not cover the ranges previously suggested (from 0 to 1, e.g., as a sigmoid function). As an example, we show that the temperature dependence of the stretching exponent β ( T ) depends highly on how the curve fits with the KWW function are performed.