Effect of nonideal statistics on electron diffusion in sensitized nanocrystalline TiO2

Charge-extraction and time-resolved photocurrent measurements on sensitized electrolyte-infused porous nanocrystalline TiO2 films show that the actual electronic charge in the films is significantly larger than that estimated from small perturbation methods by a constant, light-intensity independent factor (T-n). This result, combined with continuous time random-walk simulations, confirms the theoretical prediction [J. Bisquert, J. Phys. Chem. B 108, 2323 (2004)] that small perturbation techniques measure the chemical diffusion coefficient of electrons instead of the normally assumed tracer diffusion coefficient of electrons; the ratio of the chemical diffusion coefficient to the tracer diffusion coefficient defines the thermodynamic factor (T-n). The difference between the two diffusion coefficients is attributed to nonideal statistics, owing to the presence of an exponential density of states. The ratio of the chemical diffusion coefficient to the tracer diffusion coefficient and therefore the ratio of the actual photoinjected charge in the nanoparticle film to the charge estimated from small perturbation methods is shown to equal the inverse of the disorder parameter alpha (T-n=1/alpha), which relates to the slope of the exponential density of states. Typically, the 1/alpha factor ranges from 2 to 4.