Forced extension of a wormlike chain in the Gibbs and Helmholtz ensembles.

A semiflexible polymer can be stretched by either applying a force to it or by fixing the positions of its endpoints. The two approaches generally yield different results and correspond to experiments performed in either the Gibbs or Helmholtz statistical ensembles. Here, we derive the Helmholtz force-extension relationship for the commonly used wormlike-chain model in the strongly stretched regime. By analyzing it in comparison with the Gibbs ensemble result, we show that equivalence between the two relationships is achieved only in the long-chain thermodynamic limit.

Mixed Lead Halide Passivation of Quantum Dots.

Infrared-absorbing colloidal quantum dots (IR CQDs) are materials of interest in tandem solar cells to augment perovskite and cSi photovoltaics (PV). Today's best IR CQD solar cells rely on the use of passivation strategies based on lead iodide; however, these fail to passivate the entire surface of IR CQDs. Lead chloride passivated CQDs show improved passivation, but worse charge transport. Lead bromide passivated CQDs have higher charge mobilities, but worse passivation. Here a mixed lead-halide (MPbX) ligand exchange is introduced that enables thorough surface passivation without compromising transport. MPbX-PbS CQDs exhibit properties that exceed the best features of single lead-halide PbS CQDs: they show improved passivation (43 ± 5 meV vs 44 ± 4 meV in Stokes shift) together with higher charge transport (4 × 10-2 ± 3 × 10-3 cm2 V-1 s-1 vs 3 × 10-2 ± 3 × 10-3 cm2 V-1 s-1 in mobility). This translates into PV devices having a record IR open-circuit voltage (IR Voc ) of 0.46 ± 0.01 V while simultaneously having an external quantum efficiency of 81 ± 1%. They provide a 1.7× improvement in the power conversion efficiency of IR photons (>1.1 µm) relative to the single lead-halide controls reported herein.