Length and Time-Dependent Rates in Diffusion-Controlled Reactions with Conjugated Polymers

Abstract

Rate constants for diffusion-controlled reactions of solvated electrons with conjugated fluorene oligomers (oF) and polymers (pF) were measured in liquid tetrahydrofuran (THF). Preparative gel permeation chromatography (GPC) was used to separate the polyfluorenes into fractions having narrowed distributions of lengths. Both oF and pF's were used in determinations of the attachment rate constants k(inf) as a function of length, where k(inf) refers to the rate coefficients at long times where they are indeed constant. The results find that in going from oF(1) to pF(133), k(inf) increases by a factor of 16, which is much smaller than that of the 133-fold increase in length. The extent of this increase and its change with length are in excellent agreement with published theoretical models that describe diffusion to long thin objects as either prolate spheroids or one-dimensional arrays of spheres. As the concentration of polymer was increased, the effects of large transient terms in the rate constant were observed. As predicted by the Smoluchowski diffusion equation, with modifications by more contemporary theorists, these transient effects are larger and persist to longer times for the larger molecules. For the longest molecule, pF(133), k(t) increases by more than a decade at short times. In that case, the "transient term" becomes dominant and the rate coefficient is approximately proportional to the square of the effective reaction radius in contrast to the linear dependence usual for diffusional reactions. The size of these transient effects and their quantitative confirmation are unprecedented.

Determining the optimum morphology in high-performance polymer-fullerene organic photovoltaic cells

“…The polymer was assumed to be outstretched and an effective radius was calculated from the length of the chain (~140 nm for 92,000 Da MW, assuming equilibrium bond lengths) and a capture radius from the chain approximated as 1 nm (reasonable in comparison to the capture radius calculated from the DPP-NMe2 complex). These parameters were used to approximate the straight polymer as a highly prolate spheroid, which can be used to generate an effective spheroidal capture distance of 14 nm using the method described by Sreearunothai et al 54 The simulated decay for a 60-nm-diameter sphere of PC 71 BM with 0.2 wt% of PTB7 homogenously mixed in to it is faster than is observed experimentally (Fig. 2e), suggesting that even a very small amount of PTB7 in the sphere causes significant quenching.…”

Giant infrared absorption bands of electrons and holes in conjugated molecules

“…From the measured M n , the average number of units is estimated to be nB170. The syntheses and characterization of oligofluorenes (F) and polyfluorene (pF 30 ) were reported previously 42 . The obtained pF was fractionally separated with preparative scale gel permeation chromatography to provide samples with different average lengths.…”

Polarons, Bipolarons, and Side-By-Side Polarons in Reduction of Oligofluorenes

“…Synthesis of F 1 −F 10 oligofluorenes by the method of Klearner 64 has been described. 65 Tetrahydrofuran (THF) was purified by distillation from Na/benzophenone. 1,4-Dicyanobenzene (DCNB) and the 2.2.2 Cryptand (C222) were used as received from Aldrich.…”