Relationship between Mobility and Diffusion Coefficient in Molecularly Doped Polymers

A theoretical photocurrent transient equation for a thin or thick sample was derived from the charge transport equation. This equation has been fitted to measured photocurrent transients of molecularly doped polymers in order to obtain the actual relationship between the mobility (µ) and the diffusion coefficient (D). The relationship between the mobility and the diffusion coefficient has been derived from the Langevin equation which takes into account the random electric field resulting from the randomly located and the randomly oriented electric dipoles. A time correlation function of the fluctuating electric field necessary for calculating the diffusion coefficient is assumed to be 2σE2exp (-|t|/τ), where σE is the dispersion of the fluctuating electric field, which is proportional to the electric dipole moment, and τ is the correlation time of the electric field fluctuation. The result, D=τσE2 µ2, was consistent with the actual relation, D∝µ2.