Spin-Correlated Radical Ion Pairs Generated in Liquid Haloalkanes

Article Cite This: J. Phys. Chem. B 2018, 122, 8750−8762

pubs.acs.org/JPCB

Spin-Correlated Radical Ion Pairs Generated in Liquid Haloalkanes Using High-Energy Radiation V. I. Borovkov*,†,‡ †

Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Science, 3, Institutskaya Street, Novosibirsk 630090, Russia ‡ Novosibirsk State University, 2 Pirogova Street, Novosibirsk 630090, Russia

J. Phys. Chem. B 2018.122:8750-8762. Downloaded from pubs.acs.org by UNIV OF SUNDERLAND on 09/22/18. For personal use only.

S Supporting Information *

ABSTRACT: The probability of formation of spin-correlated secondary radical ion pairs (RIPs) in diluted solutions of charge acceptors in irradiated haloalkanes is believed to be extremely low due to the dissociative attachment of excess electrons to solvent molecules. Contrary to this, it has been found that spin-correlated RIPs can be formed upon irradiation in some liquid chloroalkanes with yield sufficient to observe the recombination fluorescence of the RIP’s partners. This allowed the study of primary radical cations (RCs) as well as radical ionic states of molecules dissolved in haloalkanes using the method of time-resolved magnetic field effect (TR MFE) in radiation-induced fluorescence. With this method, the magnetic resonance characteristics of the solvent RCs in a series of liquid haloalkanes were examined for the first time. For the 1,2-dichloroethane RC, the rate of scavenging by solute molecules and the dominant mechanisms of paramagnetic relaxation were determined. Polysulfone and poly(ethyl methacrylate) were used to demonstrate that due to their high dissolving ability, chloroalkanes can be exploited as solvents to study the magnetic resonance characteristics of radical ionic states of polymeric molecules in solutions with the TR MFE method.

1. INTRODUCTION This study reports on spin-correlated secondary radical ion pairs (RIPs) created in dilute solutions of liquid haloalkanes (R−Hal) under high-energy radiation. At first glance, it seems that the formation of such pairs under these conditions is improbable. Indeed, in a diluted solution, the ionization of the solvent is the dominating process1−3 R−Hal → R−Hal•+ + e−

radical anion are not unambiguous. In a study by Saeki and colleagues8 performed with the picosecond radiolysis technique, experimental data, within the framework of the model used, suggested a τA of 1.5 ns. This is in drastic contrast with other data reported,5 indicating values of τA in femtoseconds. In this context, data for CH2Cl211,12 and CHCl312,13 are also of interest, in which the decay time of the solvent radical anion was shown to exceed that for CCl4. Primary negative charge carriers with a not-so-short lifetime in irradiated haloalkanes have been recently evidenced in ref 14. In the cited study, radiation-induced delayed fluorescence was observed in the 1 mM para-terphenyl solution in 1,2dichloroethane (DCE). The fluorescence was sensitive to the external magnetic field, and its dependence indicated the formation of spin-correlated RIPs, composed of the solvent radical cation (RC) and the radical anion (RA) of the aromatic solute. The spin coherence in secondary RIPs in dichloroethane suggests either that the excess electrons attach to the solvent molecules slowly or that the solvent RAs have a lifetime that is long enough to transfer electrons to the solute with a non-

(1)

The excess electron is generally accepted to vanish in a few picoseconds via a dissociative attachment (reaction 2) with a haloalkane molecule4−9 e− + R−Hal → (R ··· Hal)•− → R• + Hal−

(2)

Thus, even if the solution contains electron acceptors in a low concentration, reaction 2 prevents the formation of secondary radical anions (RAs) as the electron affinity of the halogen atoms exceeds 3 eV,10 which is much higher than that of the hydrocarbon molecules. This property of haloalkanes is frequently exploited in pulse radiolysis experiments to distinguish between optical absorption bands related to the positive or negative charge carriers in irradiated liquids.1,3,4 At the same time, even for the well-studied haloalkane, CCl4, estimates of the lifetime (τA) of the intermediate state (R··· Hal)•− in reaction 2 that can be considered as the solvent © 2018 American Chemical Society

Received: July 18, 2018 Revised: August 21, 2018 Published: August 22, 2018 8750

DOI: 10.1021/acs.jpcb.8b06884 J. Phys. Chem. B 2018, 122, 8750−8762

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The Journal of Physical Chemistry B

were measured under both high (IB(t)) and very low (I0(t), B < 0.05 mT) external magnetic fields at room temperature. To decrease the effect of temperature drifts, the on−off magnetic field cycles were repeated over a period of about 10 min. The ratio IB(t)/I0(t) between the decay curves recorded was referred to as the TR MFE curve. 2.1.1. Chemicals. 1,2-Dichloroethane (DCE, 99.9%), 1chlorobutane (1-ClBu, 99.2%), para-terphenyl-d14 (98%, pTP), polysulfone (PSF, average Mw ∼ 35 kDa), and poly(ethyl methacrylate) (PEMA, average Mw ∼ 340 kDa) were used as provided by Aldrich. 2-Bromopropane (2-BrPr), 2-chlorobutane (2-ClBu), tert-butylchloride (t-BuCl), dichloromethane (DCM), chloroform (CHCl3), and tetrachlorocarbon were distilled before use. Haloalkanes were stored over molecular sieves of 4 Å. 4,4″-Bis[1-(decyloxy)ethyl]-1,1′:4,1″-terphenyl (bDOTP), synthesized as described previously,21 was provided by A. Taratayko. Prior to experiments, oxygen was removed from the solutions containing the studied substances using several “freeze−pump−thaw” cycles. Since haloalkanes have a comparatively high ionization potential, the solvent RCs and their reactions can only be studied if the amount of impurities is small enough. Otherwise, positive charge from primary solvent RCs will be rapidly transferred to impurities to form other, secondary radical cations. The concentration of impurities in the used solvents was controlled with gas chromatography mass spectrometry system (HP/Agilent 6890/5973). It was found that the purest solvent was DCE, in which the main admixtures were 1-Br,2Cl-ethane (≈2 mM) and dichloromethane (≈1 mM). In DCM, there was about 5 mM CH2BrCl with a negligible amount of other compounds. In 1-chlorobutane, other chlorobutane isomers (≈2 mM), 1-chlorooctane (≈1 mM), 1-Br-butane (≈1 mM), and dibutyl ether (≈1 mM) were detected as the main admixtures. 2-Chlorobutane, even after several cycles of distillation, contained several octene isomers (triethylethylene, etc.) with a total concentration of about 5 mM. It is worth noting that the interaction between admixture molecules and solvent RCs depends on the difference in their ionization potentials. For example, the admixture of DCM, which has the ionization potential (IP) ≈ 11.3 eV,22 should not result in any significant effect on processes involving primary solvent holes in DCE with IP ≈ 11 eV.23 And vice versa, molecules of CH2BrCl with IP ≈ 10.6−10.8 eV22,24 in dichloromethane can capture solvent RCs. The rate of the solvent RC scavenging by admixtures with a lower IP-value is also dependent on the IPs’ difference. According to pulse radiolysis studies of 1-ClBu25 and DCE26 efficiency of a solute for hole scavenging decreases significantly as the IPs’ difference becomes lower than 1−2 eV. From this point of view, unsaturated hydrocarbons in 2-ClBu are to be effective scavengers of solvent RCs due to their relatively low ionization potential. In addition, it is important to avoid an admixture of chloroalkanes with several chlorine atoms that exhibit a high electron affinity and react with aromatic radical anions via a dissociative electron transfer similar to that in reaction 2. For example, 1% CCl4 content in the para-terphenyl solution in mono- and disubstituted chloroalkanes suppresses the recombination fluorescence within a few nanoseconds. In this study, the solvents without CCl4 and CHCl3 admixtures were used.

negligible probability. Otherwise, the formation of independent carriers of unpaired electron spin (R•) and negative electric charge (Cl−) in reaction 2 excludes the manifestation of any spin coherence effects upon geminate recombination of charge carriers. This is because the chloride anion has a closed electronic shell and, consequently, zero spin. Thus, the probability of the formation of solute RAs in some irradiated chloroalkanes is non-negligible even at a millimolar solute concentration that may put into question the completeness of existing notions of the primary radiationinduced processes in haloalkanes. However, the purpose of this study was to determine to what extent liquid haloalkanes can be used as a solvent for producing spin-correlated RIPs and investigating the spin correlation effects in delayed fluorescence arising due to the RIPs’ recombination. A particular emphasis was made on a quantitative characterization of reaction kinetics of the secondary RC formation. Searching for the recombination fluorescence of spincorrelated RIPs in irradiated solutions is motivated by the possibility to indirectly determine the magnetic resonance characteristics of the recombining RIP’s partners in this case.15−18 One can do this by comparing the delayed fluorescence intensity decays recorded under different external magnetic fields. Such comparison forms the basis of the timeresolved magnetic field effect (TR MFE) method in radiationinduced fluorescence. A specific feature of this method is selectivity to those radical ions that have been created as partners of a spin-correlated RIP or that originate from such partners due to electron-transfer reactions. The TR MFE method allows, in principle, determination of the same magnetic resonance characteristics of radical ions as those of the conventional electron paramagnetic resonance (EPR) technique: the hyperfine coupling (HFC) constants, the g factor, and the paramagnetic relaxation times. The advantage of the TR MFE method is that the lifetime of the radical ions studied can be as short as a few nanoseconds,19 and this method has been used previously to study radical ions that could not be detected in solutions with other techniques. However, the TR MFE method has been mainly used to study radical ions in alkane solvents, in which the probability of spin-correlated RIP geminate recombination is high. Nonpolar alkanes are very poor solvents for many molecular and polymeric substances that greatly limits the field of application of the approach discussed. Using haloalkanes as a medium to generate radical ions seems beneficial because of their high dissolving power. Besides, a high, ∼11 eV, ionization potential (IP) of haloalkanes allows, potentially, the creation and investigation of secondary radical cations of almost any organic molecule.

2. MATERIALS AND METHODS 2.1. Experimental Section. Haloalkane solutions of luminophores and other compounds were subjected to ionizing irradiation produced by X-ray pulses (20 keV, ∼1 ns, ∼100 nGy per pulse) in an X-ray fluorimeter, as described previously.20 The irradiated cuvette was placed between the poles of an electromagnet producing a magnetic field of up to 1 T. The kinetics curve of the radiation-induced fluorescence intensity decay (I(t)) from the irradiated solutions was detected using a time-correlated single-photon counting technique in the spectral band of 300−430 nm that was suitable for all studied fluorescent compounds. These decay 8751


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radical ions of the protiated compound.28,29 In some cases, for the RIPs composed of radicals with resolved EPR spectra, analytical solutions, which can be found elsewhere,30,31 were used. The solid line in Figure 1 exemplifies the TR MFE curve calculated for an RIP composed of two radicals with σc = 0.6

2.2. TR MFE Background. To present the basis for the TR MFE method in radiation-induced fluorescence, the fluorescence intensity decay I(t) as a first approximation can be considered as the product17,18 I(t ) ∝ F(t ) ·[θρss (t ) + (1 − θ )/4]

(3)

where F(t) is the RIP recombination rate, ρss(t) is the time dependence of the singlet-state population of the initially singlet-correlated RIPs, and θ is a semiempirical parameter to take into account the fact that in the multiparticle radiation spur, only a fraction of the recombining RIPs is spin-correlated, since some of them are composed of the radical ions originating from different primary ionization events. The second term in the brackets corresponds to such spinuncorrelated RIPs. Equation 3 implies that with all other things equal, the recombination probability of an RIP is independent of the RIP’s spin state. In the above approximation, the complexities related to the experimental determination of the RIP recombination kinetics F(t) can be avoided by studying the ratio of recombination fluorescence decay IB(t)/I0(t) θ·ρssB (t ) + (1 − θ )/4 IB(t ) ≈ I0(t ) θ·ρss0 (t ) + (1 − θ )/4

Figure 1. Calculated TR MFE curves at σc = 0.6 mT and σa = 0.2 mT. Other parameters: θ = 0.2, T1 = T2 = T0 = inf, Δg·B = 0 (solid line), Δg·B = 6 mT (dashed line). Scatter plots showed the same at T1 = T2 = 5 ns, Δg·B = 0 (circles) and Δg·B = 6 mT (triangles).

(4)

where superscripts B and 0 indicate the high and zero external magnetic fields, respectively. The RIP’s singlet-state population ρss(t) can be evaluated in magnetic field B as previously described17,18 ρssB (t ) =

ρss0 (t ) =

ij t yz 1 ij t yz 1 1 + expjjj− zzz + expjjj− zzz j Tz 2 j Tz 4 4 k 1{ k 2{ ij ΔgβB yz B × cosjjj ·t zzz·Gc (t )GaB(t ) ℏ k {

ij t yz 1 3 + expjjj− zzzGc0(t )Ga0(t ) j T0 z 4 4 k {

mT and σa = 0.2 mT in the absence of paramagnetic relaxation. A characteristic feature of the curve is the existence of two local maxima. These maxima are located at approximately 15 and 50 ns. The time points at which these arise are approximately proportional to the inverse EPR spectrum width of the corresponding RIP partners.17,18 The dashed line shows the changes that occurred in the TR MFE curve when both the difference between the g factors of the partners and external magnetic field B were high enough. Importantly, for inhomogeneous EPR spectra, this Δg effect becomes negligible after the first local maximum on the TR MFE curve. This can be seen easily from eq 5 as the contribution of the oscillating term, cos(ΔgβB·t/ℏ), decays rapidly with time as a Gaussian function (see eq 8). A rapid paramagnetic phase relaxation lead to the smoothing of the above features and to the attainment of a constant level (1 + θ) that is determined by the fraction of spin-correlated pairs. The difference in the rates of phase relaxation under various magnetic fields may cause additional distortions to the MFE curves. The TR MFE method can also be applied if one of the partners of the spin-correlated RIP transforms into another radical ion, allowing estimation of the rate of transformation.32 The corresponding expressions used to calculate the MFE curves in such a reaction, taking into account the nonstationary effects in bimolecular reactions, are given in the Supporting Information (eqs S1, S2, and S4). In some cases, such as the experiments performed under a high magnetic field, the rate of singlet−triplet transitions was very high. These cases required a more accurate description of I(t) to account for both a finite fluorescence lifetime and a nonideal apparatus response function. The corresponding expressions used in this study are detailed in the Supporting Information (see eq S5). In this study, the luminophore lifetime of τfl = 0.9 ns was chosen for both pTP and bDOTP.

(5)

(6)

where 1/T1,2 = 1/T(a)1,2 + 1/T(c)1,2 are the sums of the characteristic longitudinal and phase relaxation rates of RIP’s partners, T0 is the parameter to describe irreversible singlet− triplet mixing in zero magnetic field, Δg denotes the difference between the isotropic g values of the RIP partners, and β is the Bohr magneton. Subscripts “a” and “c” indicate the parameters relating to RA and RC, respectively. To describe the experimental TR MFE curves in this study, a theoretical model of the radical pair composed of the radicals with unresolved EPR spectra has been applied in most cases. According to this model, the contribution of HFC to the spin dynamics was calculated using the semiclassical approximation27 of the function G(t) as follows with field units for σ. G 0 (t ) =

1 × [1 + 2 × (1 − (γσt )2 ) exp[−(γσt )2 /2]] 3 (7)

G B(t ) = exp[−(γσt )2 /2]

(8)

where σ2 is the second moment of the radical ion EPR spectrum (ΔHpp = 2σ) and γ = gβ/ℏ is the electron gyromagnetic ratio. For reference, the σ values of the RA and RC of perdeuterated pTP were approximately 0.07 and 0.08 mT, respectively, as evaluated from the HFC data for the 8752


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phase electron affinity of the chlorine atom. Negative solvation energies of the recombining ions, P+ and P−, can be estimated using the well-known Born equation, P = −e2/(8πε0r)·(1 − 1/ ε), where r is the characteristic ionic radius, for which upper estimates are 0.4 nm for pTP RC (from its molecular volume35) and 0.2 nm for Cl−,36 and dielectric constant ε ≈ 2 for CCl4. One can see, even ignoring the negative Coulombic interaction energy of ions, UC, the released energy does not exceed 1.5 eV; thus, inequality (eq 9) does not hold. In more polar solvents, the energy released upon the recombination is still less. 3.2. TR MFE: t-BuCl and 2-BrPr. The effect of the external magnetic field on the radiation-induced fluorescence decays was investigated for all solvents studied. The TR MFE was absent not only in CHCl3 and CCl4 but also in 2-BrPr, as demonstrated in Figure 3. The absence of the magnetic field

The same value was also assumed for polysulfone luminescence.

3. RESULTS AND DISCUSSION 3.1. Kinetics of the Radiation-Induced Fluorescence. Figure 2 shows the kinetics curves of the intensity decay I0(t)

Figure 2. Time dependence of the radiation-induced delayed fluorescence intensity I0(t) of 1 mM pTP solutions in (from the top down at 30 ns) DCE (red line), t-BuCl (triangles), 1-ClBu (circles), 2-BrPr (green), DCM (blue), CHCl3 (black line), and CCl4 (solid circles) at 293 K. The curves were normalized to their maxima.

of the radiation-induced fluorescence of the 1 mM pTP solutions in a series of haloalkanes. The curves were normalized to their maxima to visualize the relative intensity of the radiation-induced fluorescence at t > 10 ns. The weakest and most rapidly decaying luminescence of the solutions was observed in chloroform and tetrachlorocarbon. If the solute RAs were formed, these rapidly transferred the excess electron into the solvent due to the higher electron affinity of the solvent molecules. In CCl4, the observed I(t) with full width at half-maximum equal to 0.8 ns appeared to be close to the apparatus response function. In the other haloalkanes studied, the delayed fluorescence was stronger. The kinetics curves show hyperbolic behavior, which is typical for intratrack recombination of ion pairs. Absolute yields of secondary RIPs, whose recombinations led to fluorescence, have not been estimated in this study. Qualitatively, these yields were about 2 orders of magnitude lower compared with those for alkane solutions of the same luminophore concentration. Nevertheless, in the absence of other channels for the formation of excited luminophore states, the observed fluorescence directly reflected the RIP recombination rate. Note that even if in nonpolar CCl4 the radical cation of pTP were formed, the recombination of Cl− and this RC would not result in luminescence. Indeed, the electronically excited state of luminophore upon the recombination would be created if the following condition were fulfilled33 (IP − EA + P+ + P− + UC) > Efl

Figure 3. Ratios (IB(t)/I0(t)) of the radiation-induced fluorescence decays at B = 0.1 T (noisy lines) or 1 T (circles) and zero magnetic fields, respectively, at 293 K for 1 mM solutions of pTP-d14 in tertbutylchloride (upper curves) and 2-bromopropane (two lower curves). Smooth lines show results of the calculations for a radical cation with HFC constants a(6H) = 1.5 mT and a(2H) = −1.05 mT. Other modeling parameters: σa = 0.07 mT, Δg = 0.0014 (solid lines), T0 = T2 = 20 ns, and T1 > 400 ns. Dashed line shows the same results as the black line at Δg = 0.0006. The ratios for the t-BuCl solution at B = 0.1 T are shifted up by 0.03.

effect in the latter case is very likely due to the fast spin−lattice relaxation in the primary alkylbromide RC (see below). Figure 3 also shows the pronounced magnetic field effect, with the manifestations of the resolved HFC structure in radical ions generated by radiation in the t-BuCl solution. As mentioned above, the σ value for the para-terphenyl-d14 RA in the field units was approximately 0.07 mT. Thus, according to eqs 5−8, this RA did not contribute significantly to the spin evolution within the studied time range. Consequently, the observed features were determined by HFC in an RC resulting from t-BuCl ionization, namely, primary solvent RC or radical cation formed from that on a timescale much shorter than typical time of singlet−triplet transitions, that is, within a few nanoseconds. Such transformation can be suggested on the basis of literature EPR data,37 revealing that in low-temperature matrices, instead of the t-BuCl+• RC, the product of its decomposition, which exhibited HFC splitting of approximately 1.4 mT, could only be observed. In the cited work, this product was identified as the 1,1-dimethylethylene RC.

(9) 1

where Efl is the excited-state energy. For pTP*, which exhibits the most intensive fluorescence at the wavelength of about 360 nm, a lower estimate Efl ≈ 3 eV looks reasonable. The left-hand side of eq 9 is the energy released upon the charge recombination: IP ≈ 7.8 eV34 is the gas-phase ionization potential of the luminophore and EA ≈ 3.6 eV10 is the gas8753


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Figure 4. Ratios (IB(t)/I0(t)) of the radiation-induced fluorescence decay at B = 0.1 T (circles) or B = 0.5 or 1 T (noisy lines) and in zero magnetic field, respectively, at 293 K for 1 mM solutions of pTP-d14 in (a) dichloromethane, (b) 1,2-dichloroethane, (c) 1-chlorobutane, and (d) 2chlorobutane. Smooth red lines show the simulation results obtained under the single radical pair approximation (see text for explanations). Parameters are given in Table 1. Curves for B = 0.1 T are shifted up by 0.05−0.1 for clarity.

Table 1. Parameters of Solvent Radical Cationsa Used for the Simulation of TR MFE Curves Shown in Figure 4 solvent

Δgb

T1 (ns)c

T2 (0.1 T) (ns)d

T2 (0.5−1 T) (ns)d

T0 (ns)d

lifetime (ns)e

dichloromethane 1,2-dichloroethane 1-chlorobutane 2-chlorobutane

0.027 0.024 0.023 0.023

50 50 50 >300

10 8 10 10

10 6 6 6

10 10 6 3.5

∼10 ∼10 ∼5 ∼3

For the RC, σc = 0; for the counter-ion RA of pTP-d14, σa = 0.07 mT; the paramagnetic relaxation was ignored. bFor the g factor of the pTP-d14 RA, g = 2.0027; the accuracy is approximately ±0.002. cParameter to describe the spin−lattice relaxation. dPhase relaxation time in the corresponding magnetic field. eEstimation of the time of primary hole scavenging or transformation. a

(≈2.0027, typical value for polyphenyl radical ions28,39) by Δg ≈ 0.0014(±1). This Δg value was higher than expected from literature data on low-temperature EPR studies with the dimethylethylene RC. It was reported that the g factor for this RC stabilized in the CCl3F matrix was g = 2.0033(±3).40 The use of the corresponding Δg value, 0.0006, in the TR MFE simulation, as shown in Figure 3 with dashed line resulted in a worse fit to the experimental curve. It can be suggested that such a significant difference originates from the different average geometries of this RC in a rigid matrix and liquid solutions. Considering the purpose of this study, it can be concluded that both t-BuCl and 2-BrPr are unsuitable for the study of secondary radical ions with the TR MFE method. For 2-BrPr, a fast paramagnetic relaxation will make the spin states of the radical ions composing the secondary RIPs uncorrelated. For tBuCl, to minimize the contribution of the rapidly formed 1,1dimethylethylene RC to the spin evolution using the rapid

The calculated curves shown in Figure 3 were obtained using the rather cumbersome analytical expressions derived in ref 31 assuming that the RIP included not only the particle with a narrow EPR spectrum (pTP•−) but also an RC with HFC constants a(6H) = 1.5 mT and a(2H) = −1.05 mT. These HFC constant values could be varied within the range of ±0.1 mT, and these are in accordance with the quantum chemical calculations of the 1,1-dimethylethylene RC in its optimized twisted geometry.38 The observation of distinct oscillations in the TR MFE curve indicates that this RC forms quickly during a range shorter than 1 ns. For t-BuCl+•, the pattern of oscillations should be different as the parity of the number of magnetic equivalent nuclei is different.17,30 Thus, the fitting results are consistent with the hypothesis of almost instant formation of dimethylethylene RCs from the ionized tBuCl molecules. The transformation of the peculiarity at ca. 25 ns into a dip upon the increase of the field to B = 1 T can be described assuming the g value of the RC differs from that of pTP•− 8754


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data available do not provide exhaustive information on the fate of primary chloroalkane RCs on a timescale of several nanoseconds. Impurities could also be an important factor in determining the lifetime of primary solvent RCs. As an example, 2-ClBu contains approximately 5 mM of octene isomers (see Section 2.1.1), which has a comparatively low ionization potential. Typical g factors of olefinic RCs are g ≈ 2.003,39 and the scavenging of chlorobutane RCs by olefins should result in a drastic decrease of Δg quantum beat frequency. If similar to aromatic solutes in 1-ClBu,41 these olefins scavenge RCs of 2ClBu with the rate constant of 2 × 1010 M−1 s−1, then the solvent RCs’ lifetime in 2-ClBu is limited by about 10 ns, which is only slightly longer than the time range when oscillations in the TR MFE curve are observed. As for other solvents studied, admixtures found in these solvents are aliphatic compounds, for which the differences between their IP values and that of their solvents’ is less than 1−2 eV. Thus, it can be expected that in these solvents, the effect of admixtures is weaker but not negligible. Since in the calculations shown in Figure 4 any transformation of solvent RCs was ignored, the values of paramagnetic relaxation times used in the simulations may actually not characterize the real paramagnetic relaxation in the primary solvent RCs. It is probable that the phase relaxation parameters T0 and T2 give a lower estimate for lifetimes of the primary solvent RCs (see Table 1) in the solutions. Besides, parameter T1, which describes the decay of TR MFE curves on longer times, characterizes, very probably, the relaxation process in some secondary RCs. Nevertheless, the calculations carried out in the framework of the single radical pair approximation allow certain conclusions to be drawn. All TR MFE curves shown in Figure 4 can be simulated assuming that the g value for the RC in the RIPs is ca. 2.025. This value can be compared with the literature data for the RC of 1,3-dichloropropane, in which the spin density on chlorine atoms is almost the same as that for the RC of 1,2-dichloroethane.45 According to this data, the isotropic g value of the 1,3-dichloropropane RC was approximately 2.02, strongly suggesting that it is reaction 10 that results in the delayed fluorescence from the irradiated pTP solution in chloroalkanes at early times. It is worth noting that in a previous study11 it was concluded that the primary RCs in dichloromethane decay on a picosecond timescale. However, the results obtained in this study (see Figure 4a) have shown that the lifetime of these particles amounts to at least 10 ns. The simulation results in Figure 4 may have been closer to the experimental results if the capture of the primary RC using relationships presented in the Supporting Information was taken into account. However, since sufficient information on the particles that can capture the primary RCs is unavailable, the purest solvent, DCE, was used in the experiment with a controlled addition of aromatic charge acceptors with a concentration high enough to prevent possible transformations of the primary RCs via other channels. 3.3.2. Degenerate Electron Exchange. It is known46,47 that in solid halocarbon matrices, the characteristic reaction of primary RCs is the reaction of degenerate electron exchange

capture of the positive charge by corresponding acceptors, it is necessary to have a too high concentration of scavengers. 3.3. TR MFE: Mono- and Disubstituted Chloroalkanes. 3.3.1. Observation of Haloalkane RCs. In the case of other studied chlorosubstituted alkanes, the role of both HFC and paramagnetic relaxation in the RCs observed was not so important. Figure 4 summarizes the results from MFE measurements performed in the 1 mM pTP-d14 solutions in a series of mono- and disubstituted chloroalkanes under various strengths of the high magnetic field B. In all cases, the effect of the increased magnetic field was well pronounced. The observed oscillations, which originated from the difference in the g factors of the RIP partners, are socalled Δg quantum beats in TR MFE.17,18 Figure 4 also shows the results of MFE curve simulation using eqs 4−8. It was assumed that recombining radical ions appeared instantly and did not change their characteristics. The simulation parameters used for these RCs in this singlepair approximation are listed in Table 1. On the basis of the previous result,14 it would appear reasonable that at early times the delayed fluorescence in the irradiated pTP solution studied arises from the recombination of RIPs composed of primary chloroalkane RCs and RAs of pTP R−Hal•+ + pTP•− → R−Hal + pTP*

(10)

This is also supported by pulse radiolysis data41 indicating that primary RCs in liquid chlorobutane and DCE exhibit lifetimes exceeding 100 ns, which is longer than the time range studied. Nevertheless, it cannot be excluded that in these particular systems, there are other pathways of solvent RC transformation before the RIP recombination. Such possibilities are discussed below. One can see that there is no close agreement between experiments and calculations. In particular, the calculated curves display regular oscillations within a longer time range compared with the experimental data for strong magnetic fields. The disappearance of the Δg quantum beats may be qualitatively explained by the formation on a timescale of 10 ns of secondary RCs that have the g-factor values or HFC constants very different from those of the primary RCs. Indeed, primary RCs can interact with surrounding solvent molecules as well as with impurities. It was shown with EPR spectroscopy in low-temperature matrices37 that RC and neutral molecule of haloalkanes tended to form a complex that resulted in a substantial redistribution of the spin density. However, there are no data on stability as well as reactivity of these radical cationic complexes in liquid solutions. At this stage, it cannot be excluded that such complexation could be an initial stage for further transformation of the haloalkane RCs. It is worth noting in this context that pulse radiolysis data on primary radiation-induced processes in pure chloroalkanes were typically obtained using time resolution of about 10−15 ns or longer.41,42 Such resolution would be too low to observe a transformation of primary RCs on the timescale of 5−10 ns, especially if the optical absorption spectra of the RCs and their possible transformation or scavenging products were similar and superimposed. On the other hand, in experiments with better resolution in time,43,44 highly concentrated (0.1−1 M) solutions of charge acceptors were studied. In those cases, charge transfer to solutes prevented any other process involving the primary RCs. Therefore, optical absorption

R−Hal•+ + R−Hal′ → R−Hal + R−Hal′•+

(11)

This reaction of the matrix hole migration facilitates the formation of secondary radical cations of molecules embedded 8755


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The Journal of Physical Chemistry B in the low-temperature matrix that determines a high effectiveness of EPR spectroscopy in studies of the stabilized RCs. For purposes of the present study, reaction 11 is very important since this leads to averaging out HFCs in solvent RCs. Indeed, in the chloroalkane RCs isolated in lowtemperature matrices, the isotropic HFC constants are about 2 mT for some protons and up to several millitesla for Cl nuclei.45 Thus, for the isolated R−Hal•+, the typical σc value can be roughly estimated as 5 mT. The occurrence of Δg quantum beats on the timescale of 5−10 ns is incompatible with such high σc value, at which Δg quantum beats should disappear within a couple of nanoseconds (see Figure 1 for a comparison). The condition for fast exchange, (γσcτDEE) ≪ 1,48 can be satisfied if the time τDEE of the uncorrelated degenerate electron exchange is short enough (τDEE ≪ 1 ns). Evidently, any chemical transformation of the solvent hole to another RC would result in the stopping of the electron transfer. Consequently, the spin phase coherence in the transformed RIPs would disappear due to substantial nonaveraged HFCs in the newly formed RC. Therefore, observing the radical cations with averaged isotropic HFCs also confirms the above hypothesis that the radiation-induced delayed fluorescence from chloroalkane solutions of luminophore originates from the recombination of spin-correlated RIPs involving primary solvent radical cations. 3.4. TR MFE: Scavenging of Primary RCs in DCE. 3.4.1. Magnetic Resonance Parameters. As an acceptor to study the scavenging of primary DCE RCs by aromatic molecules, bDOTP was used since due to long alkyl substituents, this compound exhibited a better solubility. Due to higher concentrations, it can be expected that in the discussed experiments, the most probable reaction of solvent RCs is the electron transfer from the solute DCE•+ + bDOTP → DCE + bDOTP•+

Figure 5. Ratios (IB(t)/I0(t)) of the radiation-induced fluorescence decay values at B = 0.1 T (circles) or at B = 1 T (noisy lines) and zero magnetic fields, respectively, at 293 K for solutions of bDOTP in 1,2dichloroethane. Smooth lines represent simulation results obtained using eqs S1, S2, and S4−S6, with relative diffusion coefficient D = 1.5 × 10−9 m2/s and reaction radius R = 1.5 nm (evaluated stationary value of the reaction constant for reaction 10 k0 = 1.7 × 1010 M−1 s−1). The solute concentration is given in the plot.

parameters were in agreement with the optically detected EPR data on bDOTP radical ions formed in the irradiated polyethylene matrix.21 The range of the values at which the visually similar simulation results were obtained is shown in brackets. In the simulations, HFC was neglected for the primary RC of DCE and the optimal values for the RC’s relaxation parameters were T2 = 8(±1) ns, T0 = 6(±1) ns, and T1 = 22(±3) ns. Although these parameters refer to the short-lived primary RCs, they were determined with a rather high accuracy. Indeed, results of the simulation were sensitive to the time T1 of spin−lattice paramagnetic relaxation of primary RCs as this time determines the magnitude of the effect. As shown in Figure 5, the TR MFE magnitude decreased noticeably with decreasing bDOTP concentration. Thus, when the scavenging time was of the order of 10 ns, the spin−lattice relaxation process in the primary solvent RCs had sufficient time to decrease the spin correlation in the RIPs. Similarly, the decay of the high-frequency oscillations in a high magnetic field makes it possible to determine T2 for the solvent RCs. Although the T0 parameter had no direct effect on the oscillation frequency observed, the MFE curve shape depended significantly on this parameter within a time range of 1−5 ns. 3.4.2. Kinetics Parameters. In the experiments with bDOTP, we analyzed the domain of fairly short times, especially for the highest solute concentration. Therefore, time dependence of the rate constant for irreversible diffusioncontrolled bimolecular reactions between solvent RC and bDOTP molecule should be taken into account. This dependence is determined by the factor R / πDt as follows49,50

(12)

Therefore, in these solutions, the delayed fluorescence is initially determined by recombination of (DCE•+/bDOTP•−) pairs. After scavenging the solvent RCs in reaction 12, the fluorescence is produced upon recombination of RIPs composed of bDOTP•+ and bDOTP•−. It was assumed that probabilities of the fluorescent state formation upon recombination of any RIP involving bDOTP radical ions were equal. Figure 5 shows the experimental TR MFE curves obtained in the range of bDOTP concentrations from 3 to 30 mM along with the simulation results. In line with that described in Section 2.2, the simulation has been performed using eqs S1, S2, and S4−S6, taking the nonstationary effects in bimolecular reactions into account.32 All calculated curves for different concentrations were obtained using fixed simulation parameters except for the time of phase paramagnetic relaxation of the secondary bDOTP radical ions, which was changed within a small range of ±5 ns. The changes, probably, could be assigned to the involvement of bDOTP radical ions in the degenerate electron exchange, whose rate corresponds to the limit of slow spectral exchange and depends on the solute concentration. To attain the optimum agreement with experimental data, it was assumed that for the bDOTP radical ions of both signs, σ = 0.24(±0.02) mT and T1 ≫ T2 = T0 = 40(±5) ns. These

k(t ) = 4πRD·(1 + R / πDt )

(13)

According to eq 13, with a reaction radius of R = 1 nm, a relative coefficient of reagent diffusion of D = 10−9 m2/s, and t = 1 ns, the factor in the parentheses is approximately 1.5, which was significant compared with the simulation results. Data for the direct measurement of diffusion coefficients for both the primary RCs and aromatic molecules in DCE were unavailable. Thus, these were estimated using the well-known 8756


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The Journal of Physical Chemistry B Stokes−Einstein relationship D = kT/6πηa, where a is the effective molecular radius of a diffusant and η is solvent viscosity, 0.82 cP.51 The values a = 0.26 nm for DCE and a = 0.54 nm for bDOTP were calculated using the Bondi data35 from molecular volumes that resulted in the relative diffusion coefficient at room temperature of D ≈ 1.5 × 10−9 m2/s. The Stokes−Einstein relationship underestimates the diffusion coefficient for neutral molecules. Noteworthily, the selfdiffusion coefficient in DCE at 293 K is 1.6 × 10−9 m2/s51 instead of 1 × 10−9 m2/s predicted using the Stokes−Einstein relationship. However, for radical ions, this relationship gives diffusion coefficients that are closer to the experimental values, which is explained by a stronger interaction between charged particles and surrounding molecules.52 The best description of the experiment shown in Figure 5 at D = 1.5 × 10−9 m2/s was obtained for the radius of electron transfer R = 1.5 nm. The calculated stationary value of the rate constant of reaction 12 for primary DCE RC capture by bDOTP molecules was k0 = 4πRD = 1.7 × 1010 M−1 s−1. The trial simulations with various parameters indicated that the error in the determination of k0 was no more than 20% for all cases studied. The effect of the degenerate electron transfer on the solvent RC’s diffusion coefficient is discussed below, in Section 3.6. The resulting k0 value is in qualitative agreement with the literature data,43 where the rate constant for the disappearance of primary DCE RCs upon reaction with toluene molecules was approximately estimated as (1.5 ± 1.0) × 1010 M−1 s−1. In another previous study,42 using indirect measurements, the rate constant of the formation of secondary biphenyl RCs in irradiated DCE was estimated to be 3 × 1010 M−1 s−1, exceeding by several times the calculated constant of the diffusion-controlled reaction in this solvent. The authors interpreted this result as a consequence of the fast degenerate charge transfer via reaction 11. We also investigated how well the experimental MFE curves can be described using eq S3, i.e., neglecting the timedependent term in eq 13. For example, for the bDOTP concentration C = 30 mM, the optimal description was attained using the characteristic time for reaction 12 of 0.65 ns, which was visually slightly worse than that shown in Figure 5. This was much smaller than the value 1/k0C ≈ 2 ns, which could be obtained if the rate of reaction 12 was estimated using the rate constant determined in diluted solutions. 3.5. DCE RC Relaxation Mechanism. The MFE curve simulations showed that the rate of chloroalkane RC paramagnetic relaxation was high. We then considered DCE to determine the dominating mechanisms of the relaxation. It should be noted that, for the observed RC, the rate of phase relaxation was almost independent of the value of field B within the entire range studied that was expressed by the approximate equality T2 ≈ T0. Furthermore, the rate of spin− lattice relaxation was around 3 times lower and was also independent of the field, as confirmed by the observation of similar magnitudes of effects observed at B = 0.1 and 1 T (Figure 5). The relaxation is known to be induced by fluctuations in spin interactions. For small radical ions in solution, these fluctuations are caused by both random rotation and modulation of isotropic HFC due to degenerate electron exchange. For 1,2-dichloroethane, the Stokes−Einstein approximation gives the rotational correlation time τrot = Vη/kT ≈ 15 ps53 at a molecular volume V ≈ 10−22 cm3.35 This

estimated value is approximately 1 order of magnitude higher than the NMR measurements for similar molecules.54 Furthermore, it was assumed that the most feasible τrot value for DCE radical cations should fall into the range of 2−15 ps. It is notable that the different relaxation mechanisms predict different dependencies of relaxation rate on the external magnetic field. The above-mentioned absence of a noticeable dependence of the relaxation on a magnetic field within the range 0.1−1 T, allowed us apriori to consider the modulation of the g-tensor anisotropy by rotation as an ineffective mechanism. Assuming that the g tensors of DCE RC are similar to those of 1,3-dichloropropane RC (2.04, 2.02, and 1.998),45 this can be supported by estimation using the known relationship for this relaxation mechanism53 (g ′: g ′) ·(βB)2 τrot 1 = · 2 2 T1 20π ℏ 1 + (γBτrot)2

(14)

−3

where (g′:g′) ∼ 10 is the direct product of the anisotropic part of the g-tensor. Therefore, T1 ∼ 10 μs at B = 1 T and τrot = 15 ps, indicating that this mechanism fails to account for the observed paramagnetic relaxation. Note that, for a given mechanism, the phase relaxation rate should be approximately the same. Similarly, it can be easily shown that in low-viscosity solutions, the modulation of HFC-tensor anisotropy by rotation also led to very slow relaxation, whose rate should be different in zero and high magnetic fields.55 The mechanism of paramagnetic relaxation, which is independent of a magnetic field, involves the modulation of spin−rotational interaction. Theoretically,56 in radicals with axial g-tensor symmetry, the rate of paramagnetic relaxation via this mechanism can be estimated as follows 1 1 1 = = ·(Δg 2 + 2Δg⊥2) T1 T2 9τrot

(15)

Assuming roughly that Δg∥ ≈ Δg⊥ ∼ 0.02, for the 2−15 ps range of τrot values, we get T1 ∼ 10−102 ns. Thus, one can expect the contribution of the spin−rotational relaxation mechanism to the observed relaxation to dominate the spin− lattice relaxation process. A significantly larger g-tensor anisotropy with Δg > 0.2, as for the ethyl bromide radical cation,57 should result in a relaxation time in the subnanosecond time domain independent of other relaxation mechanisms. Therefore, the absence of a magnetic field effect for the 2-BrPr solution can be explained due to the extremely fast paramagnetic relaxation originating from the spin− rotational interactions. 3.6. DCE RC Electron Residence Time. The above experimental data indicate that the phase relaxation rate of DCE RCs is higher than the spin−lattice rate by a factor of 3, although the above-mentioned relaxation mechanisms predict almost equal rates. It was assumed then that the obtained simulation values (T2 ≈ 8 ns) were determined not only by the spin−rotational relaxation mechanism but also by reaction 11 through degenerate electron exchange involving RCs and molecules of the solvent, i.e., by isotropic HFC modulation. There are EPR data on the RC of DCE, as stabilized in Freon matrix.45 In those conditions, the RCs were in a more stable cis-conformation and HFC splitting in EPR spectrum was determined by HFC constants with chlorine atoms a(235Cl) ≈ 4−4.5 mT, with a negligible contribution from protons. However, in liquid phase, rotamers, which are ionized and involved in the electron exchange, are gauche-DCE and 8757


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The Journal of Physical Chemistry B trans-DCE. The latter is slightly more stable by about 1 kcal/ mol, and the barrier for the trans−gauche transitions in molecules is about 5 kcal/mol.58 Therefore, the internal rotation in molecules of DCE can be considered to be fast on the EPR timescale. It looks likely that the internal rotation in RCs is also rapid enough. Otherwise, the RC’s conformations suitable for the electron transfer to a neutral molecule would be too rare to provide the high rate of the electron exchange. Consequently, HFC constants with magnetic nuclei in the RCs of DCE are averaged out over the conformations. It looks reasonable to assume that spin density in any conformation of RC is localized on the chlorine atoms45 with nearly the same HFC constants and that averaged HFC constants with protons do not exceed 1 mT. Therefore, for DCE RC, the σ value can be estimated as 6−7 mT. The contribution of charge exchange, upon fast spectral exchange, to phase relaxation rate can be evaluated as 1/T2 − 1/T1 ≈ 0.1 ns−1 ∼ (γσ)2·τDEE.48,53 Using the above-estimated σ values we get τDEE ≈ 0.07−0.1 ns, which is in agreement with the above upper estimate of the electron spin residence time for primary RCs in liquid DCE. With this τDEE time, the contribution of the electron exchange to charge mobility can be estimated. If the charge in reaction 11 is transferred to a neighboring DCE molecule, then the corresponding addition (DDEE) to the diffusion coefficient can be estimated as DDEE ∼ (2a)2/(6τDEE) ≈ 5−7 × 10−10 m2/ s, which is comparable with the above-estimated diffusion coefficient of DCE RC. With this correction to the relative diffusion coefficient, the estimated effective radius of electron transfer from solute to DCE RC would decrease to R ≈ 1−1.2 nm, which is closer to the contact radius, ca. 0.8 nm, of the reagents in reaction 12. Therefore, by comparing the rates of phase and spin−lattice paramagnetic relaxation, the characteristic time, τDEE ∼ 0.1 ns, of the electron exchange between primary RCs and molecules of DCE was estimated for the first time. With this τDEE value, the exchange resulted in increasing mobility of the primary RC by, at least, 50%. 3.7. Comparison with Chlorobutanes. The results in Figure 4 allow a speculation of the mechanisms of paramagnetic relaxation in monosubstituted chloroalkane RCs. For these chlorobutanes, in contrast to the disubstituted compounds, the slopes of the observed TR MFE curves at B = 0.1 T are positive at comparatively short times t < 5 ns. This indicates that the rate of singlet−triplet mixing at B = 0.1 T would be lower than that in zero magnetic field. Typically, a local maximum at 5 ns would be observed if one of the recombining radical ions involved HFC, corresponding to the EPR spectrum width ΔHpp ∼ 4 mT. However, this hypothesis can be rejected, as with such a large HFC, it would be impossible to observe a noticeable Δg quantum beat at 5−10 ns (see Figure 1 for a comparison). In the framework of the model applied, the appearance of a local maximum on the TR MFE curve with negligible HFC can be observed at T2 > T0, as illustrated in Table 1. Thus, at B = 0.1 T, the rate of irreversible singlet−triplet transitions between quasidegenerate spin states decreased slightly compared to that at B = 0 and 1 T. This implies that the paramagnetic relaxation in the studied monosubstituted butanes differs in some aspects from that in RCs of DCM and DCE; however, further studies are required to clarify the issue. 3.8. Ionized States of Polymers. In this study, the relatively high dissolving power of chloroalkanes was exploited

to study the radical ionic states of the molecules of dielectric polymeric materials, such as polysulfone (PSF) and poly(ethyl methacrylate) (PEMA), differing by their luminescent properties. PSF molecules exhibit delayed fluorescence in the nearUV and visible spectral bands that is intense enough to be observed without adding other luminophores. For PEMA, the pTP-d14 luminophore was added. The structures of the polymers studied are shown in Figure 6a,b.

Figure 6. Ratios (IB(t)/I0(t)) of the radiation-induced fluorescence decay at B = 0.1 T (circles) or B = 1 T (triangles) and in zero magnetic field, respectively, at 293 K for DCE solutions of (a) PSF and (b) PEMA + 1 mM pTP-d14. PSF concentration (v/v) was 10% (open circles and triangles, shifted up by 0.05) or 1% (solid circles and triangles). PEMA concentration was 10% (open circles and triangles). Smooth lines represent results of the simulation obtained using eqs S1, S2, and S4−S6, with the effective reaction radius R = 26 nm (PSF) and R = 27 nm (PEMA). For 10% PSF, only the simulation at B = 0.1 T is shown. Magnetic resonance parameters for the radical ionic states of the polymers are given in the text.

In both cases, the experimental curves were simulated using the same parameters for the primary solvent RCs as those used for the fitting in Figure 5. In the simulation, in the same fashion as in ref 59, it was assumed that eq 13 was applicable to the charge transfer to polymer molecules with an effective radius of the reaction. The relative diffusion coefficient was assumed to be D = 1 × 10−9 m2/s, in other words, both the motion and interaction of polymeric molecules as well as any hydrodynamic interactions were neglected. Trial calculations were also performed at D = 1.5 × 10−9 m2/s to take the effect of degenerate electron exchange of solvent RCs into account. Note that for even a concentrated polymer solution, the solvent RCs migration is not slowed down just due to the electron exchange. 3.8.1. Polysulfone. Upon transition from B = 0.1 to 1 T, the changes in the MFE curve for a 10% PSF solution in DCE were not significant. This indicated that the primary solvent RCs were rapidly scavenged by the polymer molecules, so the 8758


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The Journal of Physical Chemistry B fluorescence intensity was determined by recombination of RA and RC located on PSF molecules. Consequently, the TR MFEs observed were determined by spin interactions in these radical ions. Although the modeling is not shown in Figure 6a, the g-factor values of the charge carriers with different signs that were scavenged by PSF differed by approximately 0.0002. This allows reducing the number of parameters, which were varied in the simulation of experiments with a lower PSF concentration. A decrease in PSF concentration to 1% v/v caused the appearance of a prominent Δg effect at B = 1 T. This effect was due to the increase in the lifetime of the primary solvent RC, which exhibited a considerable shift in the g factor compared to that of organic molecules consisting of lighter atoms. The simulation has been performed assuming that for a 1% v/v PSF (∼35 kDa) solution in DCE, the molar concentration of polymer is 0.35 mM. The best agreement between simulation and experiment was achieved when the effective radius of the reaction between the solvent RCs and polymer molecules was R = 26 nm. Increasing the D value by a factor of 1.5 resulted in the decrease in the R value by 10−15% only since at a very high scavenging rate, i.e., at early times, eq 13 predicted that the reaction rate depended on the product R4D in contrast to RD on a longer time. Note that this factor reduces the effect of uncertainty in the charge migration rate in concentrated polymer solutions. As a reference, molecules of PSF used were composed of N ∼ 80 periodic fragments with a characteristic length of about L ≈ 1.5 nm. Therefore, the obtained value for R is higher than but comparable with a characteristic scale LN1/2 ≈ 13 nm that is the root-mean-square end-to-end distance for a polymer modeled as freely jointed segments. If the polymer molecule was presented as N = 80 spheres of radius L/2 ≈ 0.7 nm arranged along a line, then according to data from ref 59 (see Figure 6 in the cited paper), the effective radius would also be about 12−13 nm. Note that the interpretation of effective radii of reactions involving polymeric molecules is nontrivial.59 Such interpretation is not addressed in the present study. This would, in particular, require data on the scavenging rate obtained using diluted solutions that are unavailable at this early stage. Here, the effective radius values obtained with the same procedure are used to make a comparison between different polymers. As seen from Figure 6a, the features typical of RIPs composed of radicals with the unresolved inhomogeneous EPR spectrum, were almost unobservable in the MFE curves. This indicates that the EPR spectra of the secondary radical ions scavenged by the PSF chains are uniformly broadened to a great extent. The TR MFE curves presented in Figure 6a were simulated assuming that the magnetic resonance parameters for the secondary radical ions were as follows: σc = 0.15 mT; σa = 0.08 mT; Δg = −0.0002; T2 = T0 = 25 ns; and T1 = 1200 ns. At this stage, RAs and RCs of PSF cannot be distinguished, so assignment to a particular ion is arbitrary. For reference, if each parameter σc and σa was changed to 0.12 mT, with a corresponding increase in T2 and T0 parameters to ca. 35 ns, the simulation results were visually similar. However, neglecting inhomogeneous contribution led to a worse fit. The negative Δg parameter relates to the fact that the simulation is sensitive to the relative sign of the g values of the successive radical ions. This can be seen from the cosine term in eq S1, in which the Δg values of successive radicals are additive. In this case, a slightly better fit was obtained assuming

that the positive charge carriers on the PSF molecule, which originated from the solvent RCs with the largest g ≈ 2.027, exhibited a g value less than that of the PSF radical anionic states. At the value of Δg = +0.0002, a more or less acceptable fit was achieved for the phase relaxation times of approximately 20 ns. The significant contribution of homogeneous broadening suggests that the charge and spin carriers migrate along a polymeric chain due to the degenerate electron transfer. The rate of the migration is likely to correspond to an intermediate spectral exchange, and this could be estimated using data on EPR spectrum width of radical ions in the absence of the migration. However, no EPR spectroscopy data related to the radical ion states either in polysulfone or in its analogues are available for the author. Note that suggested migration of the charge and spin carriers in PSF indicate that both these carriers do not undergo a chemical transformation on the studied time range. This, in turn, correlates with a very high resistance of polysulfone to high-energy radiation.60 3.8.2. Poly(ethyl methacrylate). For PEMA, its average molecular weight (∼340 kDa) corresponds to N ∼ 3000 periodic fragments with a length of L ≈ 0.25 nm and the 10% v/v solution corresponds to a molar polymer concentration of approximately 0.32 mM. The simulated TR MFE curves shown in Figure 6b were obtained at the effective radius of the solvent RCs scavenging of R = 27 nm. This R value is dependent on an assumption of the properties of PEMA radical ionic states (see below) but cannot be taken below 22−23 nm at D = 1 × 10−9 m2/s. Thus, the optimal R values for both polymers are similar. This may be due to the similar geometric characteristics of these polymers since, in both cases, the product LN1/2 is almost the same (13−14 nm). However, it is possible that geometrical characteristics are not the only important factors affecting the charge scavenging reaction rate. The difference in ionization potentials of the used polymers may also be a factor.25,26 As compared with PSF, PEMA molecules do not contain aromatic fragments that would significantly increase their ionization potential and lead to a lower rate of positive charge capture. In any case, further studies are required to better understand specific features of diffusion-assisted reactions involving polymer molecules. The selection of magnetic resonance parameters for the secondary radical ions used in the simulation will now be discussed. Noticeable fluorescence in a PEMA + pTP solution in the studied time range is likely to arise due to the recombination of (i) excess electrons scavenged by carbonyl groups of the polymer and pTP+• or (ii) the pTP-d14−• and primary PEMA RC or radical cationic product of its transformation. Radical ions of the luminophore are formed via the scavenging of the solvent RCs or electrons concurrently with PEMA molecules, which are scavengers of both the primary charge carriers. This is why the characteristic time of secondary RC formation is determined by the scavenging rate of solvent RC by PEMA molecules for any secondary RIP. The yield of RIP PEMA+/PEMA− is much higher compared to that of RIPs, which include a pTP radical ion; however, they do not contribute to the observed fluorescence. Radical ions in irradiated poly(alkyl methacrylate) have been studied using the EPR technique at low temperature. Interpretation of the data on radical ionic states is somewhat ambiguous. In a previous study,61 a singlet line with the width 8759


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The Journal of Physical Chemistry B ΔHpp ≈ 0.6 mT and a g factor of 2.0024 was attributed to the RC signal of irradiated poly(methyl methacrylate). This was later queried,62 and this EPR line was assigned to the RA of the polymer matrix. In irradiated PEMA,63 the EPR line of the RA is similar to that mentioned above. No EPR signal was observed that could be assigned to the primary RC, even at 4.2 K.63 This particle seems to decay rapidly via proton transfer.62,63 Thus, it seems likely that the observed fluorescence from the PEMA + pTP solution appeared due to the recombination of pTP+•/PEMA−• RIPs. For pTP+•, it was assumed that g = 2.0027 and σc = 0.08 mT. As mentioned above, the g factor of the PEMA RA is 2.0024 so the simulation was performed at Δg = +0.0003 for the secondary RIPs. Similar to the polysulfone solutions, there was no visual evidence of a significant contribution from inhomogeneous HFC in PEMA−• in the TR MFE curves in Figure 6b. Therefore, it was assumed that the HFC was averaged to zero by the degenerate electron exchange and the HFC contribution was neglected (σa = 0). Other parameters were T0 = 35 ns and T1 = 500 ns. Phase relaxation times were T2 = 55 ns at B = 0.1 T and T2 = 30 ns at B = 1 T. Since the recombination of DCE radical cation and PEMA−• should not produce any fluorescence, the first term on the right-hand side of eq S4 was taken as zero. The migration of charge and spin along the polymeric chain in PEMA RAs would cause not only the narrowing of the EPR spectrum due to HFC averaging but also the phase relaxation. Assuming the rate of spectral exchange is fast, the time τDEE can be estimated from the relationship T2−1 ∼ (γσ)2τDEE.48,53 In this case, σ2 is the second moment of the PEMA−• EPR spectrum in the absence of exchange, where σ ≈ 0.3 mT. When T2 ∼ 50 ns, τDEE ∼ 7 ns, implying that the approximation of the fast exchange was more or less accurate. The simulation at B = 1 T indicated a noticeable acceleration of phase relaxation. This may occur due to stochastic modulation of the g-tensor anisotropy during the spin density migration. The significant difference between T0 and T2 was not clear at this stage. It is important to note that the interpretation of TR MFE curves is not as straightforward as that for conventional ERP spectra. For reference, the simulation of the TR MFE curves in Figure 6b can also be achieved at equal phase relaxation times T0 ≈ T2 ≈ 30 ns at different magnetic fields assuming that Δg ≈ 0.0007 in the secondary RIPs, which does not agree with the reported EPR data. To get a more clear interpretation, further studies within wider ranges of magnetic field and temperature are required.

The observation of such recombination fluorescence with a 1 ns time resolution allowed exploring radiation-induced processes in haloalkanes from a novel point of view. For the first time, the primary RCs of a series of chloroalkanes were studied in the liquid phase using a method that was sensitive to the magnetic resonance characteristics of these particles. Analysis of the effects of the external magnetic field on the fluorescence intensity decays allowed determination of the isotropic g factors of the RCs and estimation of their paramagnetic relaxation rates at room temperature. Analysis of the data on the 1,2-dichloroethane RC suggested that the dominant mechanisms of relaxation related to the spin− rotational interaction and degenerate electron exchange between the RC and the solvent molecules. Detailed information on the magnetic resonance characteristics of primary radical cations allowed a quite accurate determination of the rates of primary RC capture by aromatic molecules and polymers using the TR MFE method. Studying the secondary radical ions with this method is facilitated in those chloroalkanes where primary RCs are involved in the electron exchange, which is rapid enough to average out HFC in these RCs to a small value. The high dissolving power of haloalkanes made it possible to study radical ionic states of dielectric polymer molecules. In particular cases of polysulfone and poly(ethyl methacrylate), it was revealed that the spin density in these states migrates along the polymer chain with the rate corresponding to a fast or intermediate spectral exchange. Therefore, chloroalkanes can, in principle, be used as solvents to create and to observe spin-correlated radical ion pairs under high-energy radiation. Because of the properties of these solvents, this significantly extends the scope of the application of the TR MFE method in radiation-induced fluorescence and opens up new opportunities for studying short-lived radical ions in liquid solutions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b06884. Expressions to calculate the evolution of the spin state of a spin-correlated radical pair if one of the partners of the pair transforms into another radical (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

4. CONCLUDING REMARKS There are substantial experimental data that indicate a high rate of dissociative attachment of excess electrons to haloalkane molecules in the liquid state. Owing to this reaction, the probability of the formation of spin-correlated geminate pairs involving solute RAs in liquid haloalkanes is believed to be negligibly small compared to that of other radiation-induced processes in the solution. However, this study has shown that radiation-induced delayed fluorescence, which arises via the recombination of spin-correlated secondary radical ion pairs, can be observed even in diluted solutions of luminophores in mono- and disubstituted chloroalkanes. This is possible due to the absence of other channels for the formation of excited luminophore states.

ORCID

V. I. Borovkov: 0000-0001-8546-168X Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Russian Science Foundation (project no. 16-13-10163). The author thanks Prof. Y.N. Molin for helpful discussions and Dr. L.V. Kuibida for his help in preparing experiments.

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REFERENCES

(1) Pikaev, A. K. Modern Radiation Chemistry: Radiolysis of Gases and Liquids; Nauka: Moscow, 1986.

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Spin-Correlated Radical Ion Pairs Generated in Liquid Haloalkanes

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