Incoherent charge hopping and conduction in DNA and long molecular chains

We establish some relations between the kinetics of incoherent, hopping charge transport in bridged large scale chemical systems or in a single-component duplex DNA, and the electrical properties (electric current (j) and conductance (g)) of these systems connected by two electrodes. We considered two distinct voltage distributions across the equienergetic chain (with N bridge elements, and an intersite hopping rate k), which involve the voltage being biased only across the edge bridge elements (case (i)), and the voltage being equally distributed across the bridge (case (ii)). For sufficiently long chains in the low voltage (Φ) domain, we find that j = (ek/N)G(κ₁,κ_-1)(eΦ/k_BT), where G() is a function of charge injection rates κ₁(κ _-1) to (from) the electrode. The low field (constant) conductance is g = 1.6 × 10^-19(k/N)G Ω^-1. At high voltages we established the existence of a maximal, constant, Φ independent current (j_max), where g → 0. For case (i) j_max = ek/N, being determined by the intersite hopping rate and by N^-1, as appropriate for diffusional charge transport. For case (ii) j_max = eκ₁, being independent of the chain length, and determined by the rate of charge injection from the electrode. Finally, we applied our kinetic model for the description of incoherent charge transport in and the electronic properties of a donor-acceptor pair connected by two electrodes.