Deconstructing charge transport in complex materials III

Previously I have written posts about the important issue of understanding (and enhancing) the charge mobility of molecular materials. Key questions include:

What determines the relative magnitude of electron and hole mobilities?

How does mobility depend on the intermolecular separation and relative orientation?

I have tried to emphasize the charge transport is largely incoherent and that consequently a quantitative and qualitative understanding can be achieved via Marcus-Hush electron transfer theory [which is essentially equivalent to Holstein's small polaron theory]. I really don't think these points are appreciated enough (or at all) by people working on these materials.

This week at the conference I was delighted to become aware of the nice work of the group of Swapan Pati (one of the organisers) on this problem. [Their work precedes my rantings on this blog].

In this 2007 J. Chem. Phys. paper they take such approach and perform electronic structure calculations to calculate the two key physical quantities H_DA, (the matrix element for charge transfer = the Huckel parameter t) and the reorganisation energy for both electron and hole transport in different single crystal polymorphs of benzene and napthalene. H_DA falls off rapidly with distance and can vary significantly with the relative orientation and position of aromatic rings. The relative mobility of electrons and holes is determined by the relative magnitude of both H_DA and the reorganisation energy. Contrary to the standard dogma there are situations where the electron mobility is larger than the hole mobility.

Mohakud and Pati also have a J. Materials Chemistry paper applying a similar approach to octathio[8]circulene.

To me, important open questions include:

• How will these results be modified by the screening and polarisation associated with bulk crystal? [I suspect H_DA may not change much but the reorganisation energy may increase significantly].
• How does the experimental activation energy for the mobility compare to 1/4 of the reorganisation energy?
• Can this approach be extended to describe the observed field-dependent mobility? [see for example this 2008 PRL by Emin].