Electronic transport in a model tetraphenylbenzidine main-chain polymer: Direct comparison of time-of-flight hole drift mobility and electrochemical determinations of hole diffusion

Abstract

Electronic transport behavior is analyzed in a model polytetraphenylbenzidine (PTPB) hole transport polymer in which electroactive tetraphenylbenzidine sites are covalently bonded within the polymer main chain. Time-of-flight (TOF) techniques are used to measure the hole drift mobility as a function of electric field and temperature. The TOF data are parametrized using the phenomenological model originally proposed by Gill. For comparative purposes, the disorder model developed by the Marburg group is also used to analyze the data. Transport of holes in PTPB is demonstrated to occur via hopping among the TPB functional units. A pattern of convoluted field and temperature-dependent features, now known to be shared by a broad class of disordered molecular materials, is revealed by the TOF data. Thin solid film electrochemical techniques are applied in parallel with the TOF technique to independently obtain hole diffusion coefficients (${\mathit{D}}_{\mathit{h}}$) in thin films of PTPB. As a unique consequence of this comparison, it is established that mobilities, computed from solid-state hole diffusion data using the Einstein relation, converge with zero-field extrapolated TOF mobilities over a wide temperature range when the extrapolation is computed from log μ vs ${\mathit{E}}^{1/2}$ plots. Therefore, the functional dependence of the logarithm of the drift mobility on the square root of field, a much discussed general feature of electronic transport in disordered molecular materials, is demonstrated to persist through the critical low-field limit. At the same time it is demonstrated that the contribution of thermally driven diffusive broadening, which can now be calculated directly from the independently determined electrochemical hole diffusion coefficients, makes an insignificant contribution to the experimentally observed width of the time-of-flight transit pulse. A comparison of the PTPB data with analogous TOF data on solid solutions of TPD (the functional unit in PTPB) dispersed in polycarbonate is described. The observation that hole drift mobilities in PTPB are an order of magnitude smaller than those in the corresponding TPD-polycarbonate solid solution is discussed in terms of disorder and steric constraints.