Hopping transport in molecularly doped polymers: Joint modelling of positional and energetic disorder

Abstract

Hole transport in molecularly doped polymers (MDPs) is modelled as random walks in a bias field E over organic donors D embedded in a polymer matrix. Positional disorder for donor fraction p < 1 is represented by randomly placing donors at sites in a fcc lattice, while energetic disorder is given by a Gaussian distribution of site energies with width and spatial correlations in a sphere of radius R c . Random walks generated by Marcus or small polaron rates for steps between nearby donors yield the mobility w( E , T ). In addition to and R c , the rates depend on the parameters nand ufor the distance dependence and reorganization energy respectively. With tritolylamine (TTA) in polystyrene as the paradigm, a procedure is presented for fixing the interdependent parameters , u, nand R c that reproduce the field and temperature dependences of w( E , T ) over a wide range of p that includes dilute systems with different TTA packings enforced by saturated bonds. Positional disorder exceeds energetic disorder in dilute systems and yields constant w( E , T 0 ) near room temperature. Joint modelling of TTA and related systems accounts for the characteristic w( E , T ) of MDPs and substantially extends the picture of hopping between localized states, with nincreased by about 15% and reduced by about 25% from conventional analysis using the Gaussian disorder model. Similar parameter changes are expected in other MDPs based on the compensation temperature T 0 and on scaling TTA results.