Multiple-time-scale motion in molecularly linked nanoparticle arrays.

We explore the transport of electrons between electrodes that encase a two-dimensional array of metallic quantum dots linked by molecular bridges (such as α,ω alkaline dithiols). Because the molecules can move at finite temperatures, the entire transport structure comprising the quantum dots and the molecules is in dynamical motion while the charge is being transported. There are then several physical processes (physical excursions of molecules and quantum dots, electronic migration, ordinary vibrations), all of which influence electronic transport. Each can occur on a different time scale. It is therefore not appropriate to use standard approaches to this sort of electron transfer problem. Instead, we present a treatment in which three different theoretical approaches-kinetic Monte Carlo, classical molecular dynamics, and quantum transport-are all employed. In certain limits, some of the dynamical effects are unimportant. But in general, the transport seems to follow a sort of dynamic bond percolation picture, an approach originally introduced as formal models and later applied to polymer electrolytes. Different rate-determining steps occur in different limits. This approach offers a powerful scheme for dealing with multiple time scale transport problems, as will exist in many situations with several pathways through molecular arrays or even individual molecules that are dynamically disordered.