Distance-Dependence of Interparticle Energy Transfer in the Near-Infrared within Electrostatic Assemblies of PbS Quantum Dots

This paper describes control of the rate constant for near-infrared excitonic energy transfer (EnT) within soluble aqueous assemblies of PbS quantum dots, cross-linked by Zn²⁺, by changing the length of the mercapto-alkanoic acid (MAA) that serves as the cross-linking ligand. Sequestration of Zn²⁺ by a chelating agent or zinc hydroxide species results in deaggregation of the assemblies with EnT turned "off". Upon decreasing the number of methylene groups in MAAs from 16 to 3, the interparticle separation decreases from 5.8 nm to 3.7 nm and the average observed EnT rate increases from ∼(150 ns)^-1 to ∼(2 ns)^-1. A master equation translates intrinsic (single-donor-single-acceptor) EnT rate constants predicted for each ligand length using Förster theory to observed average rate constants. For interparticle distances greater than ∼4 nm, the point dipole approximation (PDA) implementation of Förster theory agrees with experimentally measured rates. At shorter interparticle distances, the PDA drastically underestimates the observed EnT rate. The prediction of the rates of these short-distance EnT processes is improved by ∼20% by replacing the PDA with a transition density cube calculation of the interparticle Coulombic coupling.