The effect of an electric field on the reaction kinetics of a charge carrier migrating within a one-dimensional chain.

The aim of this study is to suggest a novel approach for estimating the intramolecular mobility of a charge carrier that migrates within a polymer chain and is involved in a pair reaction with a particle located on the same chain. The approach is based on the effect of an external electric field on the migration rate and, consequently, the kinetics of the reaction. As a first step, this problem is considered a stochastic one-step process with absorbing and reflecting boundaries, and an analytical solution is obtained in the case that the second reactant is immobile. With the use of computer simulations of stochastic migration, the effect of the mobility of both reactants and the influence of the Coulomb interaction between them are considered. It is found that the ratio of the pair reaction rates with and without an external field is relatively little dependent on these factors and that the analytical expressions derived can be applied to estimate the relative mobility of recombining particles with accuracy better than a factor of two in many realistic situations.

Evolution of spin coherence of radical pairs due to spin-selective recombination: Comparison of three models.

This study looked for a way to evaluate the validity of previously suggested models for describing the spin-selective recombination of radical pairs. As an example, for analysis, we used the conventional model, the model by Jones and Hore [Chem. Phys. Lett. 488, 90 (2010)], and the model by Salikhov [Am. J. Phys. Chem. 11, 67 (2022)]. To do this, analytical solutions to the evolution of the radical pair density matrix due to a radical pair's spin-selective recombination and singlet-triplet transitions in a strong magnetic field were obtained for the conventional model and the Jones and Hore model. Spin interactions included in the Hamiltonian were time-independent exchange interactions as well as Zeeman and hyperfine interactions. The most striking difference between the models' predictions appeared when considering the fraction of singlet pairs among all currently existing ones. In the Jones and Hore model, this ratio has the form of damped oscillations for any values of the spin-hamiltonian parameters. The conventional model and the Salikhov model both predicted that this ratio had the form of undamped oscillations in the absence of exchange interaction and at a sufficiently low recombination rate. Besides, the conventional model predicts the possibility of a resonance-like behavior of this ratio when singlet-triplet transitions in a part of the radical pair ensemble are completely suppressed by tuning the magnetic field strength. Possible experimental conditions in which distinguishing between the models seems to be most straightforward were suggested.

A spin statistical factor in electron transfer to oxygen molecules.

The oxygen molecule in its ground triplet state (3O2) is a strong electron acceptor. Electron transfer to 3O2 to form a superoxide anion is an important elementary step in many chemical and biological processes. If this transfer occurs from a spin 1/2 paramagnetic particle where the total spin of the reactants is equal to 3/2, the reaction is spin-forbidden. In liquids, the significant dipole-dipole electron spin interaction in 3O2 is supposed to mix the non-reactive quartet and reactive doublet states at a time scale of ∼10 ps, thus avoiding the barrier. To elucidate the role of spin effects in the electron transfer to 3O2, we studied this reaction over a range of more than three orders of magnitude of the relative diffusion coefficient (D) of the reactants. It was found that spin effects during electron transfer to 3O2 become insignificant when D < 10-9 m2 s-1. In the range of intermediate D values (10-9 m2 s-1 < D < 10-8 m2 s-1) - which corresponds to some reactions of oxygen with small radicals in aqueous solutions - the effective spin factor decreases with increasing D value. If D > 10-8 m2 s-1, the electron transfer is spin-selective with the spin factor of 1/3 as determined by the spin statistics. At such D values, the reaction encounter time may exceed the expected quartet-doublet mixing time by almost an order of magnitude. The reduced rate of quartet-doublet transitions within the encounter complex in the reaction with 3O2 has been explained by the spin-exchange interaction and chemical Zeno effect.

The role of Heisenberg spin exchange and the quantum Zeno effect in the spin-selective reaction between spin-1/2 and spin-1 particles.

The kinetics of spin-selective reactions involving triplet molecules, such as triplet-triplet annihilation or electron transfer to dioxygen molecules in the ground triplet spin state, are strongly dependent on the dipole-dipole interaction (DDI) of electron spins in spin-1 particles. The effect of this interaction on the intersystem crossing in the reaction encounter complex of the paramagnetic particles was previously considered for some particular cases using oversimplified approaches. In this study, we consider a rigorous kinetic model of the irreversible reaction between the spin-1/2 and spin-1 particles in an encounter complex with the reactive doublet state. This model explicitly includes both isotropic exchange coupling of the reactants and spin dependence of the reaction rate in the form of the Haberkorn reaction term. For the time-independent DDI, an analytical expression for the reaction kinetics was derived. The effect of DDI fluctuations was analyzed using numerical simulations. It was found that increasing both the exchange coupling and the reaction rate constants can significantly slow down the quartet-doublet spin transitions and, as a consequence, the observed spin-selective reaction rate. Additionally, the presence of the irreversible reaction in the doublet states affects a coherent evolution in the non-reactive quartet subsystem.

An Updated View of Primary Ionization Processes in Polar Liquids.

According to picosecond radiolysis data, primary radical cations in irradiated carbonates are very rapidly deprotonated. At the same time, analysis of the radiation-induced fluorescence from carbonate solutions indicates the formation of solvent-related radical cationic species with a relatively long lifetime. We use quantum chemical methods to develop a model of carbonate ionization that reconciles these conflicting data. Using ethylene carbonate as an example and assuming that its molecules exist in solution as a collection of dimeric associates, we show that both processes are the result of the loss of an electron from such dimers. This demonstrates that the generally accepted conceptualization of a primary ionization event, based on the idea of the formation of a radical cation of an individual molecule of an irradiated substance, requires revision in the case of polar aprotic liquids that tend to form molecular associates.

Probing an Isolated Conjugated Polymer Molecule with Radiation-Generated Spin-Correlated Polaron Pairs.

An understanding of the interplay between the spin and electronic degrees of freedom of polarons migrating along conjugated polymer molecules is required to further the development of organic electronics and spintronics. In this study, a novel experimental approach is proposed for studying spin-correlated polaron pairs (PPs) on an isolated molecule of a conjugated polymer. The polymer molecule of interest is immobilized in a nonluminescent poly(vinyl chloride) matrix, which is irradiated with X-rays to rapidly form secondary PPs on the conjugated polymer. The migration, recombination, and evolution of the spin state of the PPs can be monitored at nanosecond resolution by observing the recombination fluorescence under different magnetic fields. Examples supporting this concept are presented.

Primary Radical Cations in Irradiated Poly(isobutylene).

Using the method of time-resolved magnetic field effect in radiation-induced fluorescence, primary radical cations (RCs) in irradiated poly(isobutylene) (PIB) have been detected for the first time. A comparison of experimental results with the data of quantum chemical calculations suggests that the initial geometry of the ionized fragment of the PIB molecule is close to the geometry of the neutral polymer in the trans-gauche-trans-gauche conformation. The spin density of the RC in this geometry is delocalized over more than 10 polymer units, and the width of the RC's EPR spectrum is about ΔHpp ≈ 1.3 mT. At a temperature of 273 K and lower, the lifetime of the primary RCs with the delocalized spin density exceeds 10 ns. The structural relaxation of the RCs results in the spin density localization on a single C-C bond, which is extended to nearly 0.2 nm, and in the increase in the EPR spectrum width to ΔHpp ≈ 2.4 mT. It looks likely that this intramolecular structural relaxation is coupled strongly with those types of molecular motions that determine the process of dielectric ß-relaxation in the polymer.

Interaction of spin-correlated radical pair with a third radical: Combined effect of spin-exchange interaction and spin-selective reaction.

The reaction of electron transfer between two paramagnetic particles may be strongly dependent on the total spin state of the pair. Such dependence can be used to control electron transfer in a molecular medium via the control of the spin degrees of freedom. In this work, the spin-selective electron transfer has been studied in a three-spin system composed of a spin-correlated radical ion pair (RIP) and the nitroxide radical, TEMPONE. The RIPs were created in an n-hexane solution of tetramethylpiperidine (TMP) and para-terphenyl (p-TP) using X-rays. To monitor the spin evolution of the RIPs with a nanosecond time resolution, the method of time-resolved magnetic field effect in the RIP recombination fluorescence was applied. It was found that increasing the TEMPONE concentration increased the rate of both the radiation-induced fluorescence intensity decay and the paramagnetic relaxation of the spin-correlated RIP. For the three-spin system studied, we developed a theoretical model to calculate the singlet state population of the spin-correlated RIP that described both the spin-selective reaction and the spin-exchange interaction during an encounter between RIP partners and a third radical. It was found that the effect of the spin exchange could be neglected if the rate of the spin-selective reaction is high enough. Based on quantum chemical calculations and experiments, we found that there was a spin-selective distant electron transfer from p-TP radical anions to the TEMPONE radical. Another partner of the RIP, the radical cation formed from TMP, was only involved in the spin exchange interaction with TEMPONE radicals.

Dimer Radical Anions of Polyfluoroarenes. Two More to a Small Family.

While there is a body of experimental data concerning dimers formed by an aromatic molecule and its radical cation, information on the corresponding dimer radical anions (DRAs) is scarce. In this work, evidence for the formation of the DRAs of decafluorobiphenyl and 4-aminononafluorobiphenyl has been obtained by the optically detected electron paramagnetic resonance and the time-resolved magnetic field effect techniques. Theoretical investigation (DFT B3LYP-D3/6-31+G*) of these DRAs and the DRAs of octafluoronaphtalene and 1,2,4,5-tetrafluorobenzene previously detected by Werst has been undertaken to gain greater insight into the structure of the polyfluoroarene DRAs. Without substituents different from a fluorine atom, an extra electron is evenly delocalized over two fragments; the bonding interaction is π stacking. On the potential energy surfaces (PES), there are two minima of nearly equal energy corresponding to the structures of perfect and parallel displaced sandwiches. Such a PES structure is due to a conical intersection between two electronic states of different symmetry. The DRA of 4-aminononafluorobiphenyl is an ion-molecular associate stabilized by electrostatic interactions involving NH2 groups. The complex cyclic structure of the PES of this DRA suits the successive electron transfers between the dimer fragments. The calculated hyperfine coupling constants averaged over the PES minima agree well with the experimental ones.

Radiation-Induced Fluorescence from Doped Polyolefins on a Nanosecond Time Scale: Kinetics of the Processes Involving Geminate Radical Ions.

The delayed radiation-induced fluorescence from polyethylene and its alkyl- and fluorine-substituted analogues doped with aromatic luminophores was studied in the time range of 1-1000 ns. Qualitative analysis of the effects of a magnetic field on the fluorescence decay indicated that, in all polyolefins studied, the main portion of the fluorescence observed arose from the recombination of geminate spin-correlated radical ion pairs (RIPs). In the case of polyethylene, this conclusion was supported by observing the effect of an external electric field on the fluorescence decay. It was shown by comparison with the computer simulation of intratrack recombination that the tunneling character of the RIP recombination, which had an asymptotic time dependence of the geminate recombination rate close to t-1, was typical of most studied polyolefins at temperatures below 273 K in the time range studied. The increase to room temperature and above caused a gradual transition to a regime where the geminate recombination rate was mainly determined by the migration of RIP partners with time dependence close to t-3/2. The low estimate of the electron transfer distance upon the ion recombination in this regime was about 2 nm. In polyethylenes, exposed to an irradiation of 0.3-0.4 MGy, the role of charge carrier diffusion became hardly noticeable because of the cross-linking of polyethylene chains and the increase in polymer matrix stiffness. Oxygen, dissolved in a polymer doped with aromatic molecules, caused quenching of the recombination luminescence due to electron transfer from the dopant radical anion to the oxygen molecules. At room temperature, typical distances for such electron transfer were estimated to be ∼1.5 nm.

Unexpectedly Large Spin Coherence Effects in the Recombination Fluorescence from Irradiated Highly Polar Solutions on a Nanosecond Time Scale.

Spin correlation effects in the geminate recombination of radical ion pairs in irradiated highly polar liquids are typically believed to be negligible due to a high escape probability for the ions. This report presents the results of an exploratory study of organic polar solvents aimed at the searching for, and estimating the magnitude of, the time-resolved magnetic field effects (TR MFEs) in the delayed radiation-induced fluorescence from diluted solutions of a luminophore. It has been found that upon the high-energy irradiation of the solutions in polar liquids, such as dichloroethane (ε ≈ 10), methanol (ε ≈ 33), acetonitrile (ε ≈ 37), dimethylformamide (ε ≈ 37), dimethyl sulfoxide (ε ≈ 47), ethylene carbonate (ε ≈ 89), substantial spin coherence effects in the delayed fluorescence can be observed within a time range up to ∼100 ns. In most of the cases studied, magnetic resonance characteristics of primary or very early solvent-related radical ions were evaluated from the TR MFE curves. This approach can, therefore, be widely used to complement results obtained by the pulse radiolysis technique with structural and kinetic data extracted from the magnetic resonance characteristics of the short-lived radical ions formed in irradiated media.

Estimation of the fluorescence lifetime for optically inaccessible exciplexes in nonpolar solutions under ionizing irradiation.

X-irradiation of nonpolar solutions likely provides a possibility to create exciplexes for any donor-acceptor pair that would energetically and sterically allow this. Thorough study and characterization of X-radiation generated exciplexes usually cannot be carried out with conventional methods because of the complex and non-exponential formation and decay dynamics of these species. In this paper, we present a simple and universal experimental approach for the estimation of fluorescence lifetimes (τF) of X-radiation generated exciplexes. The suggested procedure is based on the comparison of quenching of the exciplex emission band and the emission band from a standard luminophore with a known excited state lifetime by dissolved oxygen. Using this approach we report the τF values for two systems with optically inaccessible exciplexes, diphenylacetylene-N,N-dimethylaniline (DMA) and p-terphenyl-DMA, and for two typical exciplex forming systems, naphthalene-DMA and anthracene-DMA. All the found τF values for the X-radiation generated exciplexes lie in the range of 50-70 ns. The accuracy of this approach was checked by time-resolved measurements under X- or near-UV irradiation for those pairs, whose properties make this feasible. The proposed method gives a possibility to avoid a complex numerical evaluation of the non-exponential kinetics of recombination luminescence, and can be used to estimate the characteristic τF values for luminophores and excited complexes formed under X-radiation.

Radical Cationic Pathway for the Decay of Ionized Glyme Molecules in Liquid Solution.

Chemical stability of primary radical cations (RCs) generated in irradiated matter determines substantially the radiation resistance of organic materials. Transformations of the RCs of the glyme molecules, R(-O-CH2-CH2-)nO-R (R = CH3, n = 1-4) has been studied on the nanosecond time scale by measuring the magnetic field effects in the recombination fluorescence from irradiated liquid solutions of the glymes. In all cases, the RCs observed were different from that expected for the primary ones and revealed very similar hyperfine couplings independent of the poly(ethylene oxide) chain length and of the substitution of terminal methyl groups by C2H5 or CH2CH2Cl, as has been shown with diglyme as an example. Quantum chemical analysis of possible chemical transformations for the monoglyme RC as a model system allowed us to discover the reaction pathway yielding the methyl vinyl ether RC. The pathway involves intramolecular proton transfer followed by C-O bond cleavage. Only one (-O-CH2-CH2-O-) fragment is involved in this transformation, which is nearly barrierless due to the catalytic effect of adjacent glyme molecules. The rapid formation of the methyl vinyl ether RC in the irradiated monoglyme was confirmed by the numerical simulation of the experimental curves of the time-resolved magnetic field effect. These findings suggest that the R'-O-CH═CH2(•+) formation is a typical decay pathway for the primary RCs in irradiated liquid glymes.

Structure and Stability of Pentafluoroaniline and 4-Aminononafluorobiphenyl Radical Anions: Optically Detected Electron Paramagnetic Resonance, Time-Resolved Fluorescence, Time-Resolved Magnetic Field Effect, and Quantum Chemical Study.

Radical anions (RAs) are the key intermediates of the selective hydrodefluorination of polyfluoroarenes. We used the techniques of optically detected electron paramagnetic resonance (OD EPR), time-resolved fluorescence, time-resolved magnetic field effect (TR MFE), and the density functional theory to study the possibility of RAs formation from 4-aminononafluorobiphenyl (1) and pentafluoroaniline (2) and estimate their lifetimes and decay channels. To our knowledge, both RAs have not been detected earlier. We have registered the OD EPR spectrum for relatively stable in nonpolar solutions 1(-•) but failed to register the spectra for 2(-•). However, we have managed to fix the 2(-•) by the TR MFE method and obtained its hyperfine coupling constants. The lifetime of 2(-•) was found to be only a few nanoseconds. The activation energy of its decay was estimated to be 3.6 ± 0.3 kcal/mol. According to the calculation results, the short lifetime of 2(-•) is due to the RA fast fragmentation with the F(-) elimination from ortho-position to the amine group. The calculated energy barrier, 3.2 kcal/mol, is close to the experimental value. The fragmentation of 2(-•) in a nonpolar solvent is possible due to the stabilization of the incipient F(-) anion by the binding with the amine group proton.

Spin-selective reaction with a third radical destroys spin correlation in the surviving radical pairs.

The goal of this work is to reveal the effect that an irreversible spin-selective reaction of a partner of the spin-correlated radical pair (SCRP) with a third paramagnetic particle has on the spin state of the surviving SCRPs in the absence of spin exchange interaction. As studied SCRPs, we used the geminate (excess electron/radical cation) pairs generated by ionizing irradiation of tetramethyl-para-phenylenediamine solutions in n-dodecane. As a spin-selective reaction, the scavenging of electrons by nitroxide radicals from the bulk of the solution was used. Both the electron scavenging reaction and the spin correlation in the surviving SCRPs were monitored by measuring the recombination fluorescence decays of the irradiated solutions under the same experimental conditions. It was found that the spin-selective electron scavenging results in the acceleration of spin correlation decay in the remaining unreacted SCRPs. In accordance with the suggested theoretical model, the rate of this additional spin correlation decay is revealed to be equal to the scavenging rate.

Radical cations of branched alkanes in solutions: time-resolved magnetic field effect and quantum chemical studies.

Radical cations of heptane and octane isomers, as well as several longer branched alkanes, were detected in irradiated n-hexane solutions at room temperature by the method of time-resolved magnetic field effect (TR MFE). To identify radical cations, the hyperfine coupling constants as determined by simulation of the TR MFE curves were compared to the constants calculated using the density functional theory (DFT) approach. The g-values of the observed radical cations were close to that of the 2,2,3,3-tetramethylbutane radical cation studied earlier by optically detected electron spin resonance (ESR) and TR MFE techniques. No evidence of the decay of the radical cations of branched alkanes to produce olefin radical cations was found, which was further supported by the observation of positive charge transfer from the observed radical cations to cycloalkane molecules. The lifetimes of the radical cations of the branched alkanes were found to be longer than tens of nanoseconds.

Comparison of the mobilities of negative and positive ions in nonpolar solutions.

The mobilities of organic radical ions of different molecular volumes have been determined in squalane and hexane solutions to study the influence of the ion charge sign on the ionic mobility in a weakly polar liquid. The relative mobility of geminate radical ions was measured using the method of time-resolved electric field effect in the recombination fluorescence. To determine the mobility of cations and anions separately, a trend in the value of the relative mobility was analyzed by varying the mobility of one of the geminate partners. The ratios between the mobilities of the anion and the cation of the same molecules were found to be about 1.1. It was shown that in liquid alkanes, the solvent electrostriction was the main factor determining a decrease in the mobility of an ion as compared to the parent neutral molecule. The strong dependence of the electrostrictive effect on the radius of the ionic solvation shell allows the observed difference between negative and positive charge carriers by a small but systematic difference in the effective radii of the ions to be explained.

Pseudorotation in radical cations of low-symmetric decalin molecules.

Adiabatic potential energy surfaces (PES) of isomeric decalin cations have been found to be the pseudorotational surfaces due to avoided crossing that is typical for the highly symmetric Jahn-Teller active ions rather than for low-symmetric bicyclic systems. According to the UB3LYP/6-31G* data, the height of the barrier to pseudorotation is less than 2 kcal/mol for the trans isomer and about 9 kcal/mol for the cis isomer. Another peculiarity of the cis isomer PES is that the structure of minimum energy lies beyond the pseudorotation gutter. The calculation results are in fair agreement with the experimental electron spin resonance data.

Semiempirical formula for the estimation of organic radical ion mobility in liquid n-alkanes.

The mobilities of radical ions of a series of organic compounds in n-alkanes with viscosities within the range of 0.2-4 cP were determined by applying the method of time-resolved electric field effect. The obtained data were used to express the correlation between the mobilities and solvent viscosity in the form of the modified Stokes-Einstein relation. The relation was parametrized in such a way that the specific molecular properties of both solvent and solute appear in the expression only as the ratio of the volumes of their molecules. A significant difference between aromatic and aliphatic compounds was found with respect to the dependence of radical ion mobility on this volume ratio, and two different parametrizations were suggested for mobility estimation in these cases.

Degenerate electron exchange reaction of n-alkane radical cations in solution.

The degenerate electron exchange (DEE) reaction involving radical cations (RCs) of n-nonane, n-dodecane, and n-hexadecane in n-hexane solution was studied over the temperature range 253-313 K using the method of time-resolved magnetic field effect in recombination fluorescence of spin-correlated radical ion pairs. In the dilute solutions the rate constant of DEE was found to be 200 times slower than the diffusion limit. Using n-nonane as an example, we showed that two reasons are responsible for the low value of the RC self-exchange rate: (1) conformational variability of molecules and RCs and (2) the activation barrier of DEE reaction. The calculations of the reaction enthalpy performed by the B3LYP/6-31G(d) method indicated that electron transfer can be effective only upon collision of RC with a neutral molecule either in the all-trans conformation or in the conformation differing from the latter by rotation of the end ethyl fragment. The activation barrier of the DEE reaction was estimated using the reorganization energy of the internal degrees of freedom calculated at the B3LYP level and was found to be about 6 kcal/mol. A possible influence of the interaction between RC and a neutral molecule in an encounter complex on DEE rate constant is also discussed.