Triplet exciton transport in isotopic mixed naphthalene crystals. II. Master equation analysis

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Abstract
The experimental data on triplet exciton transport in isotopically mixed crystals of naphthalene/perdeuteronaphthalene (paper I) are contrasted with singlet exciton transport in the same samples (20%–100%) and analyzed in terms of incoherent hopping models. The master equation approach is emphasized and extended. We modify the conventional continuum master equations via a physically plausible cutoff of the high‐frequency transfer rates. This results in an experimentally acceptable functional form (transport linear with high power of concentration) and nearest‐neighbor transfer time (100 ps). We also developed a lattice master equation (numerically soluble), using an experimentally tested exciton superexchange formula. The somewhat surprising result is that the lattice master equations do not fit the experimental functional form. The success of the continuum models and the failure of the lattice models are attributed to the latter’s neglect of the spread in transfer rates for a given intersite distance. We claim that clusterization as well as diagonal homogeneous and/or inhomogeneous disorder cause the above spread. On the other hand, these energy mismatches are small with respect to the thermal energy, in contrast to the singlet exciton transport case, where, due to larger energy mismatches, a percolation‐like critical concentration is observed. Thus for the given concentration and temperature regimes, the triplet exciton transport is diffusive while the singlet exciton transport is percolative. Lower temperatures and/or concentrations are required for percolative triplet energy transport in these systems