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Cook, Andrew R.

Publications and source records attributed to Cook, Andrew R..

Generation and Study of Am(IV) by Temperature-Controlled Electron Pulse Radiolysis

Used nuclear fuel (UNF) separation techniques that strive to separate radiotoxic americium (Am) from trivalent lanthanide fission products through oxidation state control have increased research efforts surrounding Am(V) and Am(VI). However, equivalent knowledge of the tetravalent state, Am(IV), has remained elusive, particularly in conditions more representative of UNF reprocessing, i.e., in concentrated nitric acid (HNO3). With this in mind, we have used electron pulse radiolysis to study the radiation-induced redox reaction of Am(III) with the oxidizing nitrate radical (NO3?) in 6 M HNO3: Am(III) + NO3? ? Am(IV) + NO3? . These experiments enabled us to observe the growth and decay of Am(IV) in a concentrated acidic solution for the first time. The transient Am(IV) species was found to have a lifetime of ~16 µs?sufficiently long-lived to play a critical mechanistic role in UNF reprocessing systems. Additionally, we performed the first-ever temperature-dependent kinetics study of an actinide element, elucidating unprecedented Arrhenius and Eyring activation parameters for the reaction of Am(III) with NO3?. This new knowledge provides much-needed molecular-level insights into the radiation-induced behavior of Am.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Correction: Impact of lanthanide ion complexation and temperature on the chemical reactivity of N , N , N ′, N ′-tetraoctyl diglycolamide (TODGA) with the dodecane radical cation

Correction for ‘Impact of lanthanide ion complexation and temperature on the chemical reactivity of N , N , N ′, N ′-tetraoctyl diglycolamide (TODGA) with the dodecane radical cation’ by Gregory P. Horne et al. , Phys. Chem. Chem. Phys. , 2023, 25 , 16404–16413, https://doi.org/10.1039/D3CP01119D.

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Early-stage oxidation and subsequent damage of the used nuclear fuel extractant TODGA; electron pulse radiolysis and theoretical insights

Radiation induced damage of extractant molecules is a well-known phenomenon responsible for reducing efficiency and increasing the waste and cost of reprocessing used nuclear fuel (UNF). As such, understanding early-stage (pico- to nanoseconds) radiation-induced reaction mechanisms is essential for informing the design of next generation extractants with enhanced radiation robustness. Here, in this work, we utilized picosecond and nanosecond electron pulse radiolysis experiments to probe the early-stage radioactive environment experienced by the organic phase extractant N,N,N',N'-tetraoctyldiglycolamide (TODGA), proposed for separating highly radioactive trivalent minor actinides (specifically americium and curium) from the trivalent lanthanides. Using comparisons to the similar ionization potential (IP) solute p-xylene, this work determined the mechanism of reaction with the ionized diluent (i.e., n-dodecane radical cation, DD˙ + ) is hole transfer to produce TODGA˙ + . At high TODGA concentrations (>100 mM), the majority of this transfer occurs faster than 10 ps via the capture of DD˙ + holes prior to their solvation with a C 37 = 300 mM. The surviving solvated holes were captured with k = (2.38 ± 0.15) × 10 10 M -1 s -1 . Attempts at subsequent hole transfer to lower IP solutes found that only 10% of holes were transferred, indicating bond rupture of TODGA˙ + occurs within 2.6 ns at 200 mM TODGA. Possible reaction pathways for the rapid decomposition of TODGA˙ + were explored using a combination of experiments and density functional theory (DFT) calculations.

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Influence of metal ion complexation on the radiolytic longevity of butyramide extractants under direct dissolution conditions

The direct dissolution of volox-treated used nuclear fuel (UNF) into an organic solution—comprised of diluent and specialized extractants—poses a promising alternative to the traditional liquid-liquid solvent extraction approach to reprocessing UNF. However, moving to direct dissolution removes the presence of a concentrated nitric acid aqueous phase, which has been shown to significantly influence the radiolytic longevity of extractants in liquid-liquid solvent extraction flowsheets. With this in mind, and given the limited knowledge of radiation effects under direct dissolution conditions, we present a time-resolved and dose accumulation study on the impact of direct dissolution conditions on the radiolytic longevity of two candidate butyramide extractants—N,N-di-(2-ethylhexyl) butyramide (DEHBA) and N,N-di-(2-ethylhexyl)isobutyramide (DEHiBA)—in pre-equilibrated n-dodecane solvent in the presence and absence of process relevant metal ions, uranium and rhenium. Rhenium, and by extension technetium, extraction had little impact (=10%) on the overall radiolytic stability of these ligands, despite observed increases in chemical kinetic reactivity (>2×) of the corresponding complexes with the n-dodecane radical cation. Uranium-loading on the other hand, significantly improved the lifetime of both ligands (>30%) under gamma irradiation, with a greater stabilization observed for DEHBA over DEHiBA. This draft manuscript has been prepared in fulfillment of NTRD-MRWFD-2024 M3FT-24IN030101115.

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Effect of f -element complexation on the radiolysis of 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEH[EHP])

A systematic study of the impact on the chemical reactivity of the oxidising n-dodecane radical cation (RH˙ + ) with f-element complexed 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEH[EHP]) has been undertaken utilizing time-resolved electron pulse radiolysis/transient absorption spectroscopy and high-level quantum mechanical calculations. Lanthanide ion complexed species, [Ln((HEH[EHP]) 2 ) 3 ], exhibited vastly increased reactivity (over 10× faster) in comparison to the non-complexed ligand in n-dodecane solvent, whose rate coefficient was k = (4.66 ± 0.22) × 10 9 M -1 s -1 . Similar reactivity enhancement was also observed for the corresponding americium ion complex, k = (5.58 ± 0.30) × 10 10 M -1 s -1 . The vastly increased reactivity of these f-element complexes was not due to simple increased diffusion-control of these reactions; rather, enhanced hole transfer mechanisms for the complexes were calculated to become energetically more favourable. Interestingly, the observed reactivity trend with lanthanide ion size was not linear; instead, the rate coefficients showed an initial increase (Lu to Yb) followed by a decrease (Tm to Ho), followed by another increase (Dy to La). This behaviour was excellently predicted by the calculated reaction volumes of these complexes. In conclusion, complementary cobalt-60 gamma irradiations for select lanthanide complexes demonstrated that the measured kinetic differences translated to increased ligand degradation at steady-state timescales, affording ~38% increase in ligand loss of a 1:1 [La((HEH[EHP]) 2 ) 3 ]: HEH[EHP] ratio system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Chemical Kinetics for the Oxidation of Californium(III) Ions with Select Radiation-Induced Inorganic Radicals (Cl 2 •– and SO 4 •– )

Despite the availability of transuranic elements increasing in recent years, our understanding of their most basic and inherent radiation chemistry is limited and yet essential for accurate interpretation of their physical and chemical properties. Here, in this work, we explore the transient interactions between trivalent californium ions (Cf 3+ ) and select inorganic radicals arising from the radiolytic decomposition of common anions and functional group constituents, specifically the dichlorine (Cl 2 •- ) and sulfate (SO 4 •- ) radical anions. Chemical kinetics, as measured by integrated electron pulse radiolysis and transient absorption spectroscopy techniques, are presented for the reactions of these two oxidizing radicals with Cf 3+ ions. The derived and ionic strength corrected second-order rate coefficients (k) for these radiation-induced processes are k(Cf 3+ + Cl 2 •- ) = (8.28 ± 0.61) × 10 5 M -1 s -1 and k(Cf 3+ + SO 4 •- ) = (9.50 ± 0.43) × 10 8 M -1 s -1 under ambient temperature conditions (22 ± 1 °C).

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Dioctyl ether radiolysis under used nuclear fuel reprocessing conditions: Foundational knowledge for the development of sacrificial ligand grafts

Radiation-induced ligand destruction and concomitant degradation product formation is unavoidable under envisioned used nuclear fuel reprocessing conditions, and ultimately limits the recyclability of a given solvent system formulation. With this in mind, a novel approach to ligand innovation for advanced separations processes is in the design of tailored “protomolecules,” which when exposed to ionizing radiation undergo desired chemical transformations, thereby allowing for a reprocessing solvent system to advantageously evolve with absorbed radiation dose. Here we provide foundational knowledge for the time-resolved (electron pulse) and steady-state (cobalt-60 gamma) radiolytic behavior of dioctyl ether, a protomolecule grafting surrogate. Gamma irradiation of single-phase solutions of dioctyl ether (5–100 vol.%) in n-dodecane resulted in the loss of dioctyl ether (G = -0.72 µmol J –1 ) and the formation of octane (G = 0.11 µmol J –1 ) and octanol (G = 0.15 µmol J –1 ) degradation products, the latter of which is a known reprocessing phase modifier and radioprotectant. Further, these radiation-induced changes were attributed to direct radiation effects, for more concentrated dioctyl ether solutions, and indirect radiation effects, predominantly driven by the reaction of dioctyl ether with the dodecane radical cation, for which we report a second-order rate coefficient of k = (1.53 ± 0.05) × 10 10 L mol –1 s –1 . Under typical biphasic extraction (4.0 mol L –1 HNO 3 ) and strip (0.1 mol L –1 HNO 3 ) reprocessing conditions, gamma irradiation of 5 vol.% dioctyl ether solvent systems afforded negligible change in the rate of parent molecule destruction but promoted significant differences in the radiolytic behavior of its degradation products. These differences are attributed to their respective interactions with [dioctyl ether/HNO 3 /H 2 O] and [octanol/HNO 3 /H 2 O] adducts extracted into the organic phase. Overall, these results support the grafting of ether linkages to advanced separations ligands (e.g., modified diglycolamides).

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Impact of lanthanide ion complexation and temperature on the chemical reactivity of N , N , N ', N '-tetraoctyl diglycolamide (TODGA) with the dodecane radical cation

The impact of trivalent lanthanide ion complexation and temperature on the chemical reactivity of N,N,N',N'-tetraoctyl diglycolamide (TODGA) with the n-dodecane radical cation (RH˙+) has been measured by electron pulse radiolysis and evaluated by quantum mechanical calculations. Additionally, Arrhenius parameters were determined for the reaction of the non-complexed TODGA ligand with the RH˙ + from 10–40 °C, giving the activation energy (E a = 17.43 ± 1.64 kJ mol –1 ) and pre-exponential factor (A = (2.36 ± 0.05) × 10 13 M –1 s –1 ). The complexation of Nd(III), Gd(III), and Yb(III) ions by TODGA yielded [LnIII(TODGA)3(NO3)3] complexes that exhibited significantly increased reactivity (up to 9.3× faster) with the RH˙ + , relative to the non-complexed ligand: k([Ln III (TODGA) 3 (NO 3 ) 3 ] + RH˙ + ) = (8.99 ± 0.93) × 10 10 , (2.88 ± 0.40) × 10 10 , and (1.53 ± 0.34) × 10 10 M –1 s –1 , for Nd(III), Gd(III), and Yb(III) ions, respectively. The rate coefficient enhancement measured for these complexes exhibited a dependence on atomic number, decreasing as the lanthanide series was traversed. Preliminary reaction free energy calculations—based on a model [Ln III (TOGDA)] 3+ complex system—indicate that both electron/hole and proton transfer reactions are energetically unfavorable for complexed TODGA. Furthermore, complementary average local ionization energy calculations showed that the most reactive region of model N,N,N',N'-tetraethyl diglycolamide (TEDGA) complexes, [Ln III (TEGDA) 3 (NO 3 ) 3 ], toward electrophilic attack is for the coordinated nitrate (NO 3 – ) counter anions. Furthermore, it is possible that radical reactions with the complexed NO 3 – counter anions dominate the differences in rates seen for the [Ln III (TODGA) 3 (NO 3 ) 3 ] complexes, and are likely responsible for the reported radioprotection in the presence of TODGA complexes.

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Impact of iodide ions on the speciation of radiolytic transients in molten LiCl–KCl eutectic salt mixtures

The fate of fission-product iodine is critical for the deployment of next generation molten salt reactor technologies, owing to its volatility and biological impacts if it were to be released into the environment. To date, little is known on how ionizing radiation fields influence the redox chemistry, speciation, and transport of iodine in high temperature molten salts. Here we employ picosecond electron pulse irradiation techniques to elucidate for the first time the impact of iodide ions (I – ) on the speciation and chemical kinetics of the primary radiation-induced transient radicals generated in molten chloride salt mixtures (e S – and Cl 2 ˙– ) as a function of temperature (400–700 °C). In the presence of I – ions (≥ 1 wt% KI in LiCl–KCl eutectic), we find that the transient spectrum following the electron pulse is composed of at least three overlapping species: the e S – and the Cl 2 ˙– and ICl ˙– radical anions, for which a deconvoluted spectrum of the latter is reported here for the first time in molten salts. This new transient spectrum was consistent with gas phase density functional theory calculations. The lifetime of the e S – was unaffected by the addition of I – ions. The newly observed interhalogen radical anion, ICl˙ – , exhibited a lifetime on the order of microseconds over the investigated temperature range. The associated chemical kinetics indicate that the predominate mechanism of ICl˙ – decay is via reaction with the Cl 2 ˙– radical anion. The iodine containing product of this reaction is expected to be ICl 2 – , which will have implications for the transport of fission-product iodine in MSR technologies.

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Radiolytic Evaluation of 3,4,3-LI(1,2-HOPO) in Aqueous Solutions

We report the octadentate hydroxypyridinone ligand 3,4,3-LI(1,2-HOPO) (abbreviated as HOPO) has been identified as a promising candidate for both chelation and f-element separation technologies, two applications that require optimal performance in radiation environments. However, the radiation robustness of HOPO is currently unknown. Here, we employ a combination of time-resolved (electron pulse) and steady-state (alpha self-radiolysis) irradiation techniques to elucidate the basic chemistry of HOPO and its f-element complexes in aqueous radiation environments. Chemical kinetics were measured for the reaction of HOPO and its Nd(III) ion complex ([Nd III (HOPO)] - ) with key aqueous radiation-induced radical transients (eaq - , H · atom, and · OH and NO 3 · radicals). The reaction of HOPO with eaq - is believed to proceed via reduction of the hydroxypyridinone moiety, while transient adduct spectra indicate that reactions with the H · atom and · OH and NO 3 · radicals proceeded by addition to HOPO's hydroxypyridinone rings, potentially allowing for the generation of an extensive suite of addition products. Complementary steady-state 241 Am(III)-HOPO complex ([ 241 Am III (HOPO)] - ) irradiations showed the gradual release of 241 Am(III) ions with increasing alpha dose up to 100 kGy, although complete ligand destruction was not observed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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 was investigated in tetrahydrofuran (THF). Because of rapid fragmentation of initially produced THF +• , solute radical cations are not expected and have not previously been reported. Using 9,9-Dihexyl-2,7-dibromofluorene (Br 2 F) at 5 to 1000 mM, Br 2 F +• was observed with radiation chemical yields up to G = 2.23 / 100 eV absorbed. While more than half of this was the result of direct solute ionization, the results highlight the importance of capture of holes from THF +• prior to solvation and fragmentation. The observed data show a time-resolution limited (15 ps) rise in transient absorption of Br 2 F +• , identical in form to reports of pre-solvated or dry electron capture in water and a few organic liquids, including THF. The results were thus interpreted with a similar formalism, finding C 37 = 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. Finally, 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 2x larger at 1 M Br 2 F, possibly capturing nearly all available holes from the solvent.

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Influence of uranyl complexation on the reaction kinetics of the dodecane radical cation with used nuclear fuel extraction ligands (TBP, DEHBA, and DEHiBA)

Specialized extractant ligands – such as tri-butyl phosphate (TBP), N,N-di-(2-ethylhexyl)butyramide (DEHBA), and N,N-di-2-ethylhexylisobutryamide (DEHiBA) – have been developed for the recovery of uranium from used nuclear fuel by reprocessing solvent extraction technologies. These ligands must function in the presence of an intense multi-component radiation field, and thus it is critical that their radiolytic behaviour be thoroughly evaluated. This is especially true for their metal complexes, where there is negligible information on the influence of complexation on radiolytic reactivity, despite the prevalence of metal complexes in used nuclear fuel reprocessing solvent systems. Here we present a kinetic investigation into the effect of uranyl (UO 2 2+ ) complexation on the reaction kinetics of the dodecane radical cation (RH˙ + ) with TBP, DEHBA, and DEHiBA. Complexation had negligible effect on the reaction of RH˙ + with TBP, for which a second-order rate coefficient (k) of (1.3 ± 0.1) × 10 10 M -1 s -1 was measured. For DEHBA and DEHiBA, UO 2 2+ complexation afforded an increase in their respective rate coefficients: k(RH˙ + + [UO 2 (NO 3 ) 2 (DEHBA) 2 ]) = (2.5 ± 0.1) × 10 10 M -1 s -1 and k(RH˙ + + [UO 2 (NO 3 ) 2 (DEHiBA) 2 ]) = (1.6 ± 0.1) × 10 10 M -1 s -1 . This enhancement with complexation is indicative of an alternative RH˙ + reaction pathway, which is more readily accessible for [UO 2 (NO 3 ) 2 (DEHBA) 2 ] as it exhibited a much larger kinetic enhancement than [UO 2 (NO 3 ) 2 (DEHiBA) 2 ], 2.6× vs. 1.4×, respectively. Complementary quantum mechanical calculations suggests that the difference in reaction kinetic enhancement between TBP and DEHBA/DEHiBA is attributed to a combination of reaction pathway (electron/hole transfer vs. proton transfer) energetics and electron density distribution, wherein attendant nitrate counter anions effectively ‘shield’ TBP from RH˙ + electron transfer processes.

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Curium(iii) radiation-induced reaction kinetics in aqueous media

Insight into the effects of radiolytic processes on the actinides is critical for advancing our understanding of their solution chemistry because the behaviour of these elements cannot be easily separated from the influence of their inherent radiation field. However, minimal information exists on the radiation-induced redox behaviour of curium (Cm), a key trivalent transuranic element present in used nuclear fuel and frequently used as an alpha radiation source. Here we present a kinetic study on the aqueous redox reactions of Cm(III) with radicals generated through the radiolysis of aqueous media. In particular, we probe reaction kinetics in nitric acid solutions that are used as the aqueous phase component of used nuclear fuel reprocessing solvent systems. Second-order rate coefficients (k) were measured for the reaction of Cm(III) with the hydrated electron (e aq - , k = (1.25 ± 0.03) × 10 10 M -1 s -1 ), hydrogen atom (H˙, k = (5.16 ± 0.37) × 10 8 M -1 s -1 ), hydroxyl radical (˙OH, k = (1.69 ± 0.24) × 10 9 M -1 s -1 ), and nitrate radical (NO 3 ˙, k = (4.83 ± 0.09) × 10 7 M -1 s -1 ). Furthermore, the first-ever Cm(II) absorption spectrum (300–700 nm) is also reported. These kinetic data dispel the status quo notion of Cm(III) possessing little to no redox chemistry in aqueous solution, and suggest that the resulting Cm(II) and Cm(IV) transients could exist in irradiated aqueous solutions and be available to undergo subsequent redox chemistry with other solutes.

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Radiolytic transformation of AHA under single-cycle conditions

Historically, the radiation robustness of extractant ligands and the impact of their radiolysis products have been used to evaluate the radiolytic feasibility of solvent system formulations for used nuclear fuel (UNF) reprocessing. However, other key additives (e.g., reducing and hold-back reagents) are employed by these solvent systems. These chemical species have typically been overlooked from a radiolytic perspective, and consequently little is known on how they impact process performance. Therefore, to holistically support the development of advanced, simplified, single-cycle flowsheets for UNF reprocessing, the radiation robustness of two key proposed additives – (i) the complexing reductant acetohydroxamic acid (AHA) and (ii) the hold-back reagent 1,2-cyclohexylenedinitrilotetraacetic acid (CDTA) – have been evaluated under envisioned process conditions using a combination of steady-state gamma and time-resolved pulsed electron irradiation techniques.

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Radiation-Induced Effects on the Extraction Properties of Hexa-n-octylnitrilo-triacetamide (HONTA) Complexes of Americium and Europium

The candidate An(III)/Ln(III) separation ligand hexa-n-octylnitrilo-triacetamide (HONTA) was irradiated under envisioned SELECT (Solvent Extraction from Liquid waste using Extractants of CHON-type for Transmutation) process conditions (n-dodecane/0.1 M HNO 3 ) using a solvent test loop in conjunction with cobalt-60 gamma irradiation. The extent of HONTA radiolysis and complimentary degradation product formation was quantified by HPLC-ESI-MS/MS. Further, the impact of HONTA radiolysis on process performance was evaluated by measuring the change in 243 Am and 154 Eu distribution ratios as a function of absorbed gamma dose. HONTA was found to decay exponentially with increasing dose, affording a dose coefficient of d = (4.48 ± 0.19) × 10 –3 kGy –1 . Multiple degradation products were detected by HPLC-ESI-MS/MS with dioctylamine being the dominant quantifiable species. Both 243 Am and 154 Eu distribution ratios exhibited an induction period of ~70 kGy for extraction (0.1 M HNO 3 ) and back-extraction (4.0 M HNO 3 ) conditions, after which both values decreased with absorbed dose. The decrease in distribution ratios was attributed to a combination of the destruction of HONTA and ingrowth of dioctylamine, which is capable of interfering in metal ion complexation. Furthermore, the loss of HONTA with absorbed gamma dose was predominantly attributed to its reaction with the n-dodecane radical cation (R˙ + ). These R˙ + reaction kinetics were measured for HONTA and its 241 Am and 154 Eu complexes using picosecond pulsed electron radiolysis techniques. All three second-order rate coefficients (k) were essentially diffusion limited in n-dodecane indicating a significant reaction pathway: k(HONTA + R˙ + ) = (7.6 ± 0.8) × 10 9 M –1 s –1 , k(Am(HONTA) 2 + R˙ + ) = (7.1 ± 0.7) × 10 10 M –1 s –1 , and k(Eu(HONTA) 2 + R˙ + ) = (9.5 ± 0.5) × 10 10 M –1 s –1 . HONTA-metal ion complexation afforded an order-of-magnitude increase in rate coefficient. Additional nanosecond time-resolved measurements showed that both direct and indirect HONTA radiolysis yielded the short-lived (< 100 ns) HONTA radical cation and a second long-lived (µs) species identified as the HONTA triplet excited state. The latter was confirmed by a series of oxygen quenching picosecond pulsed electron measurements, affording a quenching rate coefficient of k( 3 [HONTA]* + O 2 ) = 2.2 × 10 8 M –1 s –1 . Overall, both the HONTA radical cation and triplet excited state are important precursors to the suite of measured HONTA degradation products.

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Pushing the limits of the electrochemical window with pulse radiolysis in chloroform

Pulse radiolysis (PR) enables the full redox window of a solvent to be accessed, as it does not require electrodes or electrolyte which limit the potentials accessible in voltammetry measurements. PR in chloroform has the additional possibility to enable reaching highly positive potentials because of its large ionization potential (IP). We report PR experiments demonstrated the formation of the (deuterated) chloroform radical cation CDCl 3 + ˙, identifying it as the source of the broad absorption in the visible part of the spectrum. Results indicated that solutes with a redox potential up to +3.7 V vs. Fc/Fc + can be oxidized by CDCl 3 + ˙, which is far beyond what is possible with electrochemical techniques. Oxidation is not efficient because of rapid geminate recombination with chloride counterions, but also due to rapid decomposition of CDCl 3 + ˙ which limits the yield of otherwise longer-lived free ions. The rapid, 6 ± 3 ns, decomposition, confirmed by two independent experiments, means that a solute must be present at a concentration >100 mM to capture >90% of the free holes formed. Addition of ethene removes the broad, overlapping absorptions from ubiquitous (chlorine atom, solute) complexes created by PR in halogenated solvents enabling clear observation of solute cations. The results also unravel the complex radiation chemistry of chloroform including the large reported value G (–CHCl 3 ) = 12 molecules/100 eV for the decomposition of chloroform molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗