Abstract
The exciton transmission characteristics of a linear molecular crystal containing a nondilute concentration of substitutional impurities are studied theoretically. This model also simulates energy transport in certain long polymers. In the event of exciton scattering by the impurities, we determine exactly the energy flux resulting from the ultimate evolution of an initial nonstationary electronic state. The result is exact for an arbitrary number of impurities located at arbitrary lattice positions within the crystals. We focus attention on two cases, the randomly and the periodically substituted crystals. In the randomly alloyed crystal, we show that the exciton transport is not diffusive; the steady state exciton flux decreases exponentially as the length of the disordered region increases and does not satisfy the ordinary diffusion equation. For the special case of periodic substitution, we are able to present very simple expressions for the exciton transmission probability and flux and to show that the transport is coherent. Similarities and differences between this problem and the one of phonon transport in an isotopically substituted harmonic lattice are noted.
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