Structure and Optical Bandgap Relationship of π-Conjugated Systems

<div><p>In bulk heterojunction photovoltaic systems both the open-circuit voltage as well as the short-circuit current, and hence the power conversion efficiency, are dependent on the optical bandgap of the electron-donor material. While first-principles methods are computationally intensive, simpler model Hamiltonian approaches typically suffer from one or more flaws: inability to optimize the geometries for their own input; absence of general, transferable parameters; and poor performance for non-planar systems. We introduce a set of new and revised parameters for the adapted Su-Schrieffer-Heeger (aSSH) Hamiltonian, which is capable of optimizing geometries, along with rules for applying them to any -conjugated system containing C, N, O, or S, including non-planar systems. The predicted optical bandgaps show excellent agreement to UV-vis spectroscopy data points from literature, with a coefficient of determination , a mean error of −0.05 eV, and a mean absolute deviation of 0.16 eV. We use the model to gain insights from PEDOT, fused thiophene polymers, poly-isothianaphthene, copolymers, and pentacene as sources of design rules in the search for low bandgap materials. Using the model as an in-silico design tool, a copolymer of benzodithiophenes along with a small-molecule derivative of pentacene are proposed as optimal donor materials for organic photovoltaics.</p></div

Synthesis of π‑Bridged Dually-Dopable Conjugated Polymers from Benzimidazole and Fluorene: Separating Sterics from Electronics

We describe the synthesis and characterization of three new alternating copolymers containing fluorene and a dually dopable benzimidazole moiety. Poly­(2-<i>n</i>-heptyl-benzimidazole-<i>alt</i>-9,9-di-<i>n</i>-octylfluorene) (<b>PBIF</b>), poly­(2-<i>n</i>-heptyl-benzimidazole-vinylene-9,9-di-<i>n</i>-octylfluorene) (<b>PBIF-VL</b>), and poly­(2-<i>n</i>-heptyl-benzimidazole-ethynylene-9,9-di-<i>n</i>-octylfluorene) (<b>PBIF-EL</b>) were synthesized from Suzuki, Heck, and Sonogashira cross-coupling reactions in reasonable yield. The materials were characterized through ultraviolet–visible spectroscopy, photoluminescence, and cyclic voltammetry. The vinyl and ethynyl bridges in <b>PBIF-VL</b> and <b>PBIF-EL</b> were incorporated to separate benzimidazole and fluorene units while retaining conjugation. This allowed us to differentiate between steric and electronic contributions to the band gap (<i>E</i>_g) changes that occur upon acid/base doping of these materials. We demonstrate that the blue shift arising from acid doping <b>PBIF</b> is due to steric torsion, while the red shift found upon base doping <b>PBIF</b> is due to both sterics and possibly an electronic effect. These findings are supported through the use of molecular modeling

Bandgaps of copolymers and their parent regioregular polymers, including BDT of parallel fused rings (gray diamonds), Tt (green squares), BBTD (red circles), and BBT (blue squares).

<p> is the number of carbon atoms in the conjugated pathway. The yellow up-triangles, magenta left-triangles, and cyan right-triangles are copolymers of BDT with Tt, BBTD, and BBT, respectively. Copolymers show steep bandgap reductions via polymerization. (e) Excitons in copolymers do not show spontaneous charge separations, where the electron and hole states extend over both the BDT and Tt units. (f) In contrast, spontaneous charge separations occur at the bulk heterojunction interfaces, leaving behind a hole polaron state in the polymer phase and an electron state in the phase.</p

Density of states (DOS) and wavefunctions of all the -bands of PTh and PEDOT, both containing 20 monomer units.

<p>In addition to the ring (R), localized (L), valence (V), conduction (C), and other bands of higher energies (wavefunctions not shown) of PTh, the two low-lying oxygen (O) bands that are formed in PEDOT push the remaining bands, which have nodes between the O and -C sites, upwards in energy. The HOMO level (top of the V band) increases in energy more than the LUMO level (bottom of the C band) because the former has larger wavefunction components on the -C sites. This effectively lowers the optical bandgap of PEDOT, as compared to PTh.</p

PTh (b), PT32bT (c), and PTA (d) share the identical conjugated carbon backbone (a) with an equal amount of carbon atoms along the conjugated path, for instance = 120 as shown.

<p>The computed optical band gap (e) and energies of LUMO (f) and HOMO (g) as a function of the number of fused rings in their oligomers, where for PTh, 2 for PT32bT, and for PTA. Unfavorable electron hopping between S and -C are plotted as orange diamonds in (f) on the right y-axis.</p

Predicted aSSH optical bandgaps are compared with experimental ones for 198 independent -conjugated systems.

<p>Subgroups include simple rings (Gray squares), parallel fused rings (red circles), perpendicular fused rings (blue diamonds), copolymers (yellow down-triangles), PAHs (violet up-triangles), and - stacking systems (gray crosses). Dashed and solid lines are and deviations from experimental values, respectively. The coefficient of determination of , mean error −0.05 eV, and mean absolute deviation 0.16 eV.</p

aSSH parameters.

<p>Dots over elements specify the number of -electrons contributed to the conjugated system. C-C bonds in six-membered aromatic rings and the bridge bonds between perpendicular fused rings require .</p>a<p>Reference: <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086370#pone.0086370-Botelho1" target="_blank">[24]</a>.</p>b<p>Original parameters from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086370#pone.0086370-Su1" target="_blank">[19]</a>.</p

Subgroups of calculated bandgaps compared to experimental: a) simple rings, b) parallel fused rings, c) perpendicular fused rings, d) copolymers, e) PAHs, and f) - stacking systems.

<p>Dashed and solid lines are and deviations from experimental values, respectively.</p

The PM2.5 and PM10 dry deposition flux during the daytime and the night-time.

<p>The PM2.5 and PM10 dry deposition flux during the daytime and the night-time.</p

Dry deposition velocity of PM2.5 and PM10 during different periods.

<p>Dry deposition velocity of PM2.5 and PM10 during different periods.</p