Absolute Rate of Charge Separation and Recombination in a Molecular Model of the P3HT/PCBM Interface

Abstract

A simplified model system is used to compute the rates of interfacial charge separation (CS) and recombination (CS) in the P3HT/PCBM blend (poly(3-hexylthiophene) and [6,6]-phenyl-C 61 -butyric acid methyl ester) used in bulk heterojunction solar cells. The absolute charge-transfer rates of CS ( k CS ) and CR ( k CR ) processes were calculated to be 1.50 × 10 11 and 1.93 × 10 9 s −1, respectively, from the Marcus−Levich−Jortner rate equation, in reasonable agreement with the range of available experimental values for a model containing a six thiophene rings chain and a single PCBM molecule. A detailed discussion of the inaccuracy intrinsic in the evaluation of all quantities entering the rate expression (equilibrium energy, electronic coupling, and internal and external reorganization energies) is provided together with a discussion of the sensitivity of the computed rate to these quantities. A variety of DFT methods is used to evaluate the states energy of the system (TDDFT, calculation with background charges, and unrestricted DFT), and it was found that unrestricted calculations of the lowest triplet state can describe with good accuracy the equilibrium energy and geometry of the charge-transfer states. A physically plausible range for the external reorganization energy is computed with a continuum model, and it is shown that a more accurate evaluation of this quantity is not essential.