Dynamics of disorder in mixed ionic-electronic transport in cross-linked non-conjugated redox polymers

The coupled electronic and ionic transport mechanisms in organic mixed ionic-electronic conductors (OMIECs) remain elusive to rationalize. We introduce here an approach to model the entangled hole and ion transport in linear and cross-linked triphenylamine-based (TPA) non-conjugated polymers, studied as redox active materials for organic electrodes. The polymers are created via a heuristic method based on molecular dynamics (MD) simulations. Remarkable energetic disorder effects (up to 1.6 eV) are computed in the static limit, for both pristine and doped polymer films, seemingly hindering hole transport. The explicit inclusion of dynamic effects in modelling the energetic disorder leads instead to strong and rapid oscillations of the site-energies, thus enabling a dynamic opening of hole transport channels. To go beyond the static limit for the calculation of the hole transfer rates, encompassing the time-dependence of disorder effects, effective Marcus residence times are introduced for the first time. Distributions of charge escape times are derived for both linear and cross-linked polymers, in their pristine and doped states. Linear polymers show hole escape networks denser than cross-linked ones, suggesting a more efficient hole de-trapping developing as a function of time and disorder effects. Our approach shows that electronic transport in non-conjugated organic electrodes is a highly interdependent phenomenon connected to the bulk morphologies, polymer chain mobility and ion dynamics. A multiscale modelling that captures the dynamics of disorder is therefore indispensable.