Exciton Dynamics in Disordered Poly(p-phenylenevinylene). 2. Exciton Diffusion

We present a first principles theory of exciton diffusion in conformationally disordered conjugated polymers. Central to our theory is that exciton transfer occurs from vibrationally relaxed states (VRSs) to local exciton ground states (LEGSs). LEGSs are determined by the diagonal and off-diagonal disorder induced by static density and torsional fluctuations, and VRSs are further localized by exciton-phonon coupling. The theory is implemented using the Frenkel-Holstein model to calculate the wave functions and energies of the LEGSs and VRSs. The coupling of VRSs and LEGSs via long-range dipole-dipole interactions leads to the familiar line-dipole approximation for the exciton transfer integral. The exciton transfer rates are derived from the Fermi Golden rule. The theory is applied to an ensemble of conformationally disordered poly(p-phenylenevinylene) chains using a kinetic Monte Carlo algorithm. The following are shown: (i) Torsional disorder and trans-cis defects reduce the exciton diffusion length. (ii) Radiative recombination occurs from VRSs in the tail of their density of states. (iii) Torsional disorder increases the band gap, the line width of the density of states, and the Stokes shift. As a consequence, it causes a blue shift in the vertical absorption, but a red shift in the emission. (iv) The energy of the radiated photon decreases as -log t, with a gradient that increases with torsional disorder. The predicted exciton diffusion lengths of ~8-11 nm are in good agreement with experimental values.