A law of corresponding states for hopping transport in disordered materials

A law of corresponding states (LCS) is derived for hopping transport in materials with energetic and geometrical disorder. Under certain conditions, two materials that differ only in the size of the energetic disorder should have identical transport properties, provided that one material at one temperature and electric field strength is compared with the other at suitably scaled temperature and field strength. Under certain special conditions, one can also compare materials with different concentrations of transport sites. When applied to the Gaussian disorder model (GDM) of Bässler and co-workers, the temperature and field dependence inferred from the simulations is found to require modification. Although the modification appears innocuous, it substantially reduces the agreement previously found (but evidently fortuitous) between the GDM and experiment. The use of the LCS to compare closely related materials is illustrated with data on amorphous molecular solids from the literature.