Photoconductor Discharge Curves, the Stretched Exponential, and Exponential Decay Functions

Exponential decay, bi-exponential decay, and related decay processes are common in the physical world. Stretched exponential time dependence of the form e−(kt)c has been observed in connection with the discharge of electrophotographic photoconductors, luminescence in porous silicon, dielectric relaxation in glassy and polymeric materials, as well as in other systems. Exponential decay, the stretched exponential, the Kohlrausch-Williams-Watts function KWW, and the Buettner function satisfy a differential equation that depends on the exponent c and the entropy of the system. The form of the decay function determined by the exponent c can be shown to be consistent with cooperative events occurring during relaxation and can be related to the chemical potential of the system. This indicates that probabilistic, cooperative events may play a role in the dynamics of stretched exponential decay processes in addition to distributions of relaxation times and relaxation paths.