Theoretical solar-to-electrical energy-conversion efficiencies of perylene-porphyrin light-harvesting arrays

The efficiencies of organic solar cells that incorporate light-harvesting arrays of organic pigments were calculated under 1 sun of air mass 1.5 solar irradiation. In one set of calculations, photocurrent efficiencies were evaluated for porphyrin, phthalocyanine, chlorin, bacteriochlorin, and porphyrin-bis(perylene) pigment arrays of different length and packing densities under the assumption that each solar photon absorbed quantitatively yielded one electron in the external circuit. In another more realistic set of calculations, solar conversion efficiencies were evaluated for arrays comprising porphyrins or porphyrin-(perylene)₂ units taking into account competitive excited-state relaxation pathways. A system of coupled differential equations for all reactions in the arrays was solved on the basis of previously published rate constants for (1) energy transfer between the perylene and porphyrin pigments, (2) excited-state relaxation of the perylene and porphyrin pigments, and (3) excited-state electron injection into the semiconductor. This formal analysis enables determination of the optimal number of pigments in an array for solar-to-electrical energy conversion. The optimal number of pigments depends on the molar absorption coefficient and the density at which the arrays can be packed on an electrode surface. Taken together, the ability to employ fundamental photophysical, kinetic, and structural parameters of modular molecular architectures in assessments of the efficiency of solar-to-electrical energy conversion should facilitate the design of molecular-based solar cells.