Effect of Molecular Fluctuations on Hole Diffusion within Dye Monolayers

Measured hole diffusion coefficients in dye monolayers are larger than can be explained by a charge hopping model with a static distribution of parameters describing intermolecular hole transfer. We show that large amplitude fluctuations of the tethered dye configurations on the surface could explain the observed diffusion rates by enabling charges trapped in particular configurations to escape as the dye orientation changes. We present a multiscale model of hole transport that includes the effect of dynamic rearrangement of the monolayer of anchored dyes. Conformations of pairs of indolene dye molecules (both D102 and D149) were generated by a rigid molecular packing algorithm and Car–Parrinello molecular dynamics to mimic the conformational and configurational disorder of a dye monolayer adsorbed to an anatase (101) titanium dioxide surface. The electronic coupling ( J ij ) for each pair of neighboring dyes was calculated to build distributions representing the disorder in a real system. These values were used as inputs to Marcus’ non-adiabatic equation for charge transfer to calculate the rate of hole hopping for each pair. Hole diffusion was simulated with a continuous time random walk, accounting for different time scales of molecular rearrangement (changes in the dye geometry). The dynamic nature of configurational disorder was captured by reassigning the values of J ij, drawn from the aforementioned distributions, after a fixed renewal time. We found hole diffusion coefficients of 3.3 × 10 –8 and 9.2 × 10 –8 cm 2 s –1 for D102 and D149, respectively, for a renewal time of 10 –7 s. This is in good agreement with the corresponding measured coefficients for D102 and D149 of 9.6 × 10 –8 and 2.5 × 10 –7 cm 2 s –1, whereas the diffusion coefficients are underestimated by at least a factor of 15 if the dynamics are ignored. Fast rearrangement of dye monolayer configuration may explain the high lateral hole diffusion coefficients determined experimentally. Our results indicate that both chemical structure and the availability of different packing configurations must be considered when designing conductive molecular monolayers.