Quantum chemical calculation of hole transport properties in crystalline polyethylene

Hole mobility in crystalline polyethylene (PE) is evaluated from an atomistic point of view, with the combination of quantum chemical calculation and kinetic Monte Carlo simulations. Hole hopping rate between PE chains are computed by Fermi's golden rule and Marcus rate expression. It turns out that hole transfer in PE occurs in a hopping regime rather than in a band regime even for crystalline structure without any inherent structural disorders. The results indicate that in crystalline PE, hole hops between localized states that are created by polaronic effect. The hole mobility is strongly dependent on the chain length, and increases with increasing chain-length. When the chain length was comparable to the thickness of lamellar crystals, i.e., the characteristic length scale of crystal in the direction of c axis, hole mobility and activation energy for hole transfer were in reasonable agreement with experimental values. Simulated results support the experimental prediction that fast and slow mobility are due to charge transfer in the crystalline region and amorphous region, respectively. Our findings show that high hole mobility observed in crystalline PE, regardless of the small inter-molecular electronic couplings, is due to the small reorganization energy, which is realized through the intra-molecular hole delocalization, and due to quantum tunneling effects owing to the small energetic disorder and high-frequency intra-molecular phonon modes.