Sub-picosecond Production of Solute Radical Cations in Tetrahydrofuran after Radiolysis

Ultrafast hole transfer from solvent radical cations produced by radiolysis with ∼10 ps, 9 MeV electron pulses to solutes in tetrahydrofuran (THF) was investigated. Because of rapid fragmentation of initially produced THF+•, solute radical cations are not expected and have not previously been reported. When 9,9-dihexyl-2,7-dibromofluorene (Br2F) at 5 to 1000 mM was used, Br2F+• with radiation chemical yields up to G = 2.23/100 eV absorbed was observed. While more than half of this was the result of direct solute ionization, the results highlight the importance of capturing holes from THF+• prior to solvation and fragmentation. The observed data show a time-resolution limited (15 ps) rise in transient absorption of Br2F+•, identical in form to reports of presolvated or dry electron capture in water and a few organic liquids, including THF. The results were thus interpreted with a similar formalism, finding C37 = 1.7 M, the concentration at which 37% of holes escape capture. The yield of solvent hole capture can be accounted for by the formation of solvent holes adjacent to solute molecules reacting faster than they can fragment; however, mechanisms such as delocalized holes or rapid hopping may play a role. Low temperature results find over two times more capture, supporting the speculation that if THF+• was longer lived, the yield of capture in under 15 ps would have been at least 2 times larger at 1 M Br2F, possibly capturing nearly all available holes from the solvent

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

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 kinf as a function of length, where kinf refers to the rate coefficients at long times where they are indeed constant. The results find that in going from oF1 to pF133, kinf 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, pF133, 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

Sudden, “Step” Electron Capture by Conjugated Polymers

Data showing significant time-resolution-limited “step” capture of electrons following radiolysis by 7 – 10 ps electron pulses in a series of different length and different concentration conjugated polyfluorene polymers in tetrahydrofuran (THF) are presented. At the highest concentration, ∼48 mM in repeat units for lengths from 20 to 133 fluorenes, ∼30% of the electrons formed during pulse radiolysis were captured in the step, with a constant efficiency per repeat unit. Step capture per repeat unit (<i>q</i> = 6.9 M^–1) is 60% of the presolvated electron capture efficiency previously reported for biphenyl in THF, giving capture per polymer molecule 12–80 times larger than that for biphenyl at the same concentration. This increase in capture efficiency is large compared to the rate constant per repeat unit for diffusion-limited electron attachment to the same molecules, which is 13% of that of a single unit of fluorene. Plausible mechanisms of this fast capture are explored. It is shown that both capture of quasi-free and localized presolvated electrons can adequately explain the observations. The large yield of radical anions at low concentration of polyfluorene enables observation of subsequent chemistry on the picosecond time scale in these systems, which would otherwise been limited by diffusional attachment to the nanosecond regime

Faster Dissociation: Measured Rates and Computed Effects on Barriers in Aryl Halide Radical Anions

Carbon−halogen bond dissociation rates for a series of aryl halide radical anions (ArX-•:  X = Cl, Br) in NMP were measured at room temperature by pulse radiolysis with 10-11 s time resolution. To obtain accurate dissociation rates, care was taken to measure and correct for competing decay channels. The observed rates correlated well with activation energies computed in the gas phase by density functional (DFT) calculations. The rates did not correlate well with electron affinities or dissociation energies obtained by the same computational methods, although such correlations are reported in the literature and are expected on the basis of simple models. The calculations also found that the transition state structures had bent carbon−halogen bonds. Bending enables large reductions of the activation energies by an electronic effect involving mixing of π* and σ* states. This bending-induced mixing is computed to increase the dissociation rates by a few orders of magnitude and is thus essential to understanding these reactions

Rapid “Step Capture” of Holes in Chloroform during Pulse Radiolysis

The fundamental process of hole capture in solution was investigated following pulse radiolysis with polyfluorene and 4-cyano-4″-pentyl-<i>p</i>-terphenyl scavengers. Contrary to expectation, a large fraction of holes were captured in experimental time-resolution limited ∼20 ps steps, by a process much faster than diffusion of the initially formed solvent molecular cation. At the highest concentrations, 1.92 mM for a 52 unit long polyfluorene and 800 mM for 4-cyano-4″-pentyl-<i>p</i>-terphenyl, 66% and 99%, respectively, of the initially formed holes were captured by 20 ps, with radiation chemical yield <i>G</i> = 1.2 × 10^–7 and 1.7 × 10^–7 mol J^–1. The data can be explained by capture of presolvated holes, analogous to presolvated electrons, possibly possessing extended wave functions, high mobilities, or excess kinetic energy for the first few picoseconds after their creation. Such a process is not generally known in solution; however, the observed step capture as a function of solute concentration is shown to be well explained by this model. In addition to understanding the capture process in solution, the very large step yields formed in 20 ps will provide the ability to resolve subsequent hole transfer on the polymers with >2 orders of magnitude better time resolution than expected

Electron and Hole Transport To Trap Groups at the Ends of Conjugated Polyfluorenes

Polyfluorenes (pF) were synthesized having anthraquinone (AQ) or naphtylimide (NI) end caps that trap electrons or di-p-tolylaminophenyl (APT2) caps that trap holes. The average lengths of the pF chains in these molecules varied from 7 to 30 nm. End capping was found not to be complete in these molecules so that some were without caps. Electrons or holes were injected into these polymers in solution by pulse radiolysis. Following attachment, the charges migrated to the end cap traps in times near 2 ns in pF12AQ or 5 ns in pF35NI. From these observations, electron mobilities for transport along single chains to the end caps in THF solution were determined to be smaller by a factor of 100 than those observed by microwave conductivity. Despite this, the mobilities were sufficiently large to provide encouragement to the use of such single chains in solar photovoltaics. Most charges were observed to transport over substantial distances in these polymers, but 23, 18, and 37% of the charges attached to pFNI, pFAQ, and pFAPT2, respectively, were trapped in the pF chains and decayed by slower bimolecular reactions. For pFAQ and pFAPT2, all of the trapped charges were accounted for by estimates of the fraction of molecules having no end cap traps. For pF35NI, 23% of the attached electrons were found to be trapped in the chains, but only 4% of chains were expected to have no end caps. This could indicate some trapping by kinks or other defects but may just reflect uncertainties in the capping of this long polymer. When the charges reach the trap groups, their spectra have no features of pF•− or pF•+, nor do the principal bands of the trapped ions resemble spectra of the radical ions of isolated trap molecules. The optical absorption spectra are rather dominated by new bands identified as charge-transfer transitions, which probably reinject electrons or holes into the pF chains. The energies of those bands correlate well with measured redox potentials

The Impact of Huge Structural Changes on Electron Transfer and Measurement of Redox Potentials: Reduction of <i>ortho</i>-12-Carborane

A massive structural change accompanies electron capture by the 1,2-dicarba-closo-dodecaborane cage molecule (1). Bimolecular electron transfer (ET) by pulse radiolysis found a reduction potential of E0 = −1.92 V vs Fc+/0 for 1 and rate constants that slowed greatly for ET to or from 1 when the redox partner had a potential near this E0. Similarly, two electrochemical techniques could detect no current at potentials near E0, finding instead peaks or polarographic waves near −3.1 V, which is 1.2 V more negative than E0. Voltammetry could determine rate constants, but only near −3.1 V. DigiSim simulations can describe the irreversible voltammograms but require electrochemical rate constants near 1 × 10–10 cm/s at E0, a factor of 10–10 relative to molecules undergoing facile ET. This factor of 10–10 compared to ∼10–5 for bimolecular ET presents a puzzle. This puzzle can be understood as a manifestation of one of the “Frumkin Effects” in which only part of the applied voltage is available to drive ET at the electrode

Chain Length Dependence of Energies of Electron and Triplet Polarons in Oligofluorenes

Bimolecular equilibria measured the one-electron reduction potentials and triplet free energies (Δ<i>G</i>°_T) of oligo­(9,9-dihexyl)­fluorenes and a polymer with lengths of <i>n</i> = 1–10 and 57 repeat units. Accurate one-electron potentials can be measured electrochemically only for the shorter oligomers. Starting at <i>n</i> = 1 the free energies change rapidly with increasing length and become constant for lengths longer than the delocalization length. Both the reduction potentials and triplet energies can be understood as the sum of a free energy for a fixed polaron and a positional entropy. The positional entropy increases gradually with length beyond the delocalization length due to the possible occupation sites of the charge or the triplet exciton. The results reinforce the view that charges and triplet excitons in conjugated chains exist as polarons and find that positional entropy can replace a popular empirical model of the energetics

Electron Transfer by Excited Benzoquinone Anions: Slow Rates for Two-Electron Transitions

Electron transfer (ET) rate constants from the lowest excited state of the radical anion of benzoquinone, BQ^–•*, were measured in THF solution. Rate constants for bimolecular electron transfer reactions typically reach the diffusion-controlled limit when the free-energy change, Δ<i>G</i>°, reaches −0.3 eV. The rate constants for ET from BQ^–•* are one-to-two decades smaller at this energy and do not reach the diffusion-controlled limit until −Δ<i>G</i>° is 1.5–2.0 eV. The rates are so slow probably because a second electron must also undergo a transition to make use of the energy of the excited state. Similarly, ET, from solvated electrons to neutral BQ to form the lowest excited state, is slow, while fast ET is observed at a higher excited state, which can be populated in a transition involving only one electron. A simple picture based on perturbation theory can roughly account for the control of electron transfer by the need for transition of a second electron. The picture also explains how extra driving force (−Δ<i>G</i>°) can restore fast rates of electron transfer