Article pubs.acs.org/JPCB
Measurement of the Relative Mobility of Geminate Ions in Ethereal Solutions of Aromatic Compounds Using the Fluorescence Response of the Solutions to Pulsed Irradiation V. I. Borovkov*,†,‡ and I. S. Ivanishko† †
Institute of Chemical Kinetics and Combustion, SB RAS, Novosibirsk, Institutskaya St., 3, 630090, Russia Novosibirsk State University, Novosibirsk, Pirogova St., 2, 630090, Russia
‡
ABSTRACT: This work examines the possibility of using the fluorescence response of irradiated solutions of luminophores and the effect of an external electric field on the fluorescence decay to determine the mobility of geminate radical ions when using aliphatic ethers as the solvents. As an example, p-terphenyl solutions were studied in a series of ethers (diethyl, dibutyl, methyl tert-butyl ether, tetrahydrofuran, 2-methyltetrahydrofuran, 1,4dioxane, eucalyptol, and 1,2-dimethoxyethane). Verification of the nature of the charge carriers in the irradiated solutions was made by means of the method of the time-resolved magnetic field effect in recombination fluorescence of spin-correlated radical ion pairs. It was found that at a p-terphenyl concentration of about 10 mM, the observed fluorescent response from the solutions, in most cases, was due to the recombination of radical ions formed from the aromatic solute. The relative mobility of p-terphenyl radical ions in ethers was estimated by using a stochastic computer simulation of the radiation spur composed of 4 primary ion pairs. The ions’ mobility was found to be dependent on solvent viscosity in accordance with Walden’s rule, with no noticeable effect of solvent polarity.
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INTRODUCTION The transport of charge carriers in solutions is a phenomenon whose theoretical description is still a challenging problem since it requires taking into account many-particle interactions in molecular media. That is why the main source of information on ion transport is an experiment. However, there is no universal approach that could be applied to measure charge carrier mobility in an arbitrary solvent. As a result, available data on ion transport in liquids are very far from being complete, and many of the widely used solvents have not been studied in this respect. In particular, the applicability of an experimental approach for such studies is strongly dependent on solvent polarity. Highly polar liquids, like water, are best studied regarding ion transport since the dissolved substance readily dissociates into ions. The mobilities of these ions can be evaluated by measuring solution conductivity at a known concentration of the carrier. In liquids consisting of nonpolar molecules, e.g. alkanes, an appreciable quantity of free charge carriers can only appear after exposure of the medium to external ionizing irradiation. In such a case, ions are generated as partners of geminate radical ion pairs. The low polarity results in a comparatively strong Coulomb interaction between the oppositely charged ions and, consequently, in a high probability of recombination of the ion pairs in a time range of nanoseconds. Due to the interaction with the environment, some fraction of the ion pairs escapes recombination. The appearance of the free ions allows determination of the mobilities of the charged species by time-of-flight techniques1−3 where the time of ion travel to an electrode is measured. This © 2013 American Chemical Society
time can reach milliseconds, and a major issue in this technique is identifying the charge carriers. At shorter times, when a considerable number of ion pairs have not yet recombined, the ionic transport in solution can be studied by using time-resolved techniques.4,5 In this case, any approach is capable of probing the relative motion of geminate ions only since both partners of an ion pair contribute equally to the signal. So, the experiment yields the relative mobility of the ions that is the sum of their individual mobilities. In 1995,6 a new approach was suggested to determine the relative mobility of geminate ions: the method of the TimeResolved Electric Field Effect (TR EFE) in recombination fluorescence. In this approach,6−8 the response of the decay curve of radiation-induced fluorescence from a solution to an external electric field is analyzed. The external field reduces the probability of recombination of the geminate ion pairs, and, if a recombining ion pair yields an electronically excited fluorescing molecule, the external field leads to a faster decay of the intensity of the recombination fluorescence from the irradiated solution. The higher the mobilities of recombining geminate ions, the faster the field effect rises. The TR EFE technique can be most readily used for luminophores with a high quantum yield and a short fluorescence time. In such cases, the observed fluorescence intensity is directly proportional to the recombination rate of the ion pairs. At a constant mobility of the geminate ions, the TR EFE curve, determined as the ratio of the fluorescence Received: September 20, 2013 Revised: November 10, 2013 Published: November 22, 2013 15122
dx.doi.org/10.1021/jp4093942 | J. Phys. Chem. B 2013, 117, 15122−15130
The Journal of Physical Chemistry B
Article
intensity decay kinetics in the field, IE(t), to that without the field, I0(t), can be asymptotically approximated by an exponential decay9 ⎛ eE2μ ⎞ IE(t ) S ⎟ ≈ exp⎜⎜ − t⎟ I0(t ) ⎝ 4kT ⎠
hinders use of the TR EFE technique. It is the deprotonation of primary radical cations in the ether, which is generally assumed to occur within picoseconds, forming independent particles, neutral radicals, and cations.13−15 In this case, the IP value in eq 2 corresponds to the ionization energy of an open shell species that is much lower compared to molecules of similar structure. This significantly reduces the energy yield upon ion recombination. Additionally, such deprotonation reactions must exclude both spin correlation within ion pairs formed as the result of the deprotonation and magnetic field effects16 upon recombination fluorescence. On the other hand, it is known17 that the magnetic resonance spectra of radical ions of some aromatic solutes in liquid ethers can be detected by using the recombination fluorescence. This indicates unequivocally that, one way or another, at least a portion of the delayed fluorescence from an irradiated ethereal solution of aromatic compounds originates from the recombination of spin-correlated radical ions of solute molecules. Therefore, using the TR EFE method to study radical ion transport in liquid ethers is certainly not a universal approach, but does not seem to be a fruitless task either.
(1)
where μS is the sum of the mobility values (μ = De/kT) of the recombining ions. Actually, eq 1 is an inexact one but it correctly gives the dependence on the parameters involved. In particular, the quadratic field intensity dependence is closely related to the diffusive nature of the motion of the charge carriers in the solution.6,8 Importantly, it can be demonstrated with both experimental10 and theoretical7,9 results that eq 1 is actually weakly dependent on the initial distribution function and the structure of the radiation spur, which are typically unknown. Thus, the TR EFE method appears to be a suitable approach to estimate the relative mobility of radical cations and anions whose recombination yields a fluorescent state. Coupled with computer simulation10 of the ion recombination within a radiation spur, the method potentially allows the study of the ionic transport process in more complicated situations where the mobility of charge carriers changes due to chemical transformations. The TR EFE technique has provided a considerable amount of information on the mobility of radical ions of organic compounds in alkanes, 10,11 which exhibit the highest probability of geminate ion recombination due to their low polarity. In more polar organic solvents, with dielectric constant in the range 3−10, to our knowledge, the transport of organic radical ions, which are charge carriers with an open electronic shell, has not been systematically studied yet. In this work, we discuss the applicability of the TR EFE method to measuring the mobility of aromatic radical ions in aliphatic ethers. This issue requires careful consideration since the higher solvent polarity in some cases causes one to anticipate a significant reduction in the recombination fluorescence yield. First, the high polarity decreases the probability of geminate ion recombination. Second, this serves to reduce the yield of the fluorescing state of the lumonophore upon recombination. Indeed, an electronically excited state can be formed if the following condition is fulfilled:12 (IP − EA + P+ + P− − e 2 /εR ) > Efl
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EXPERIMENTAL SECTION The radiation-induced fluorescence of irradiated ethereal solutions of p-terphenyl (pTP), which is a good luminophore with a short fluorescence lifetime, was registered by using a nanosecond X-ray fluorimeter working in single photon counting mode.18 A solution was placed between the electrodes of a nonmagnetic material in a cuvette similar to that described in ref 8. The cuvette was positioned between the poles of an electromagnet. The strength of the electric field created between the electrodes in the solution was up to 40 kV/cm. Through the thin wall of one of the electrodes, the solution was irradiated with X-ray pulses with a quantum energy of about 20 keV and duration about 2 ns. The cuvette temperature was stabilized to within ±1 K by an encircling gas flow in the range 233−333 K. As solvents, we used diethyl ether (DEE, 99%), dibutyl ether (DBE, 98%), methyl tert-butyl ether (MTBE, 99%), tetrahydrofuran (THF, 99%), 2-methyltetrahydrofuran (MTHF, 99%), 1,4-dioxane (DO, 99%), eucalyptol (1,3,3-trimethyl-2oxabicyclo[2.2.2]octane, EUC, 99%), and 1,2-dimethoxyethane (monoglyme, MG, 99%). All the solvents, except for EUC, were additionally purified by distillation and passage through a column with activated alumina. The solvents were then stored over sodium. In the case of monoglyme, thorough purification is particularly important to reduce the residual conductivity of the solvent. As charge acceptors, we used p-terphenyl (98%) and p-terphenyl-d14 (98% D atoms) as received from Aldrich. Since the ion mobility values obtained in this work for THF were clearly lower as compared to MTHF, which has a very similar viscosity, we checked the viscosities of the solvents available using a capillary viscometer (VPG-3). Within an accuracy of about ±3%, the measured viscosities gave nearly the same value, 0.48 cP at 298 K, in agreement with literature data (see Table 1). Before the delayed fluorescence was measured, oxygen was removed from the solution by several freeze−pump−thaw cycles in a special compartment of the cuvette. The concentration of pTP was typically about 10 mM but in some experiments it was varied from 0.3 to 30 mM as permitted by the solubility of the p-terphenyl.
(2)
where Efl is the excited state energy. The left-hand portion is the energy released as a result of the charge recombination: IP is the electron donor’s gas phase ionization potential, EA is the gas phase electron affinity of the electron acceptor, and P+, P− < 0 are the solvation energies of the recombining ions. The term (−e2/εR) estimates the Coulombic interaction of ions separated by a distance R in a medium with dielectric constant ε. The solvation energy can be estimated by using the wellknown Born equation, P = −e2/2r(1 − 1/ε), where r is the characteristic ionic radius. If instead of alkanes, solvents with ε ≈ 10 are used, the solvation energy grows considerably, by 1−2 eV for not-too-large organic ions. Since r < R, especially for a distance electron transfer, which looks to be a very probable pathway for the exothermic recombination reaction, the energy yield of the recombination should be reduced in more polar liquids. Besides limitations due to their higher polarity, in liquid ethers there could be an additional factor that potentially 15123
dx.doi.org/10.1021/jp4093942 | J. Phys. Chem. B 2013, 117, 15122−15130
The Journal of Physical Chemistry B
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Article
COMPUTER SIMULATION
As mentioned above, eq 1 is an approximation. Results obtained in both ref 9 and this work demonstrate that when eq 1 in used in a straightforward manner, the value of the relative ion mobility is underestimated by about 10%, if the mobility may be considered constant. In particular, the TR EFE curves are affected by the finite fluorescence time of the luminophore and, to a small extent, the initial structure of the radiation spur. In solutions with a solute concentration of ∼1 mM, the effect of the typically more mobile primary charge carriers should be taken into account.9 At higher concentrations, ∼10 mM, TR EFE curves can be distorted due to various factors such as the annihilation of triplet molecules arising, e.g., from the recombination of triplet ion pairs within the radiation spur.19 In concentrated solutions, the charge carrier mobility can also be slowed down due to the formation of complexes between a radical ion and a solute molecule.10 To consider these factors thoroughly, a detailed computer simulation of nonhomogeneous ion recombination at various electric field strengths and solute concentrations is necessary. The details of the computer simulation model used in this work are described in Appendix A. To determine the mobility of the geminate ions from the experiment, a set of TR EFE curves obtained from the computer simulations performed for a variety of mobility values at different temperatures, field intensities and dielectric constant of the media was used. These calculated curves were approximated by an exponential dependence to determine their decay rate (inverse time) within the time range where the secondary charge carriers were formed. Further, the rates were compared to the decay rates of the experimental TR EFE curves, which were also approximated by an exponential dependence (see below). It was assumed that the relative mobility of geminate ions in a studied ethereal solution was equal to the value of the relative mobility used in the corresponding simulation multiplied by the ratio of the decay rates and corrected, if necessary, for other field strengths or temperatures in accord with eq 1. The difference between the evaluated mobility values obtained by using different reference TR EFE curves was within 3−4% which was primarily determined by the accuracy of the stochastic modeling.
Figure 1. (a) Fluorescence intensity decay curves for a solution of 10 mM pTP in THF in zero electric field (the upper curve) and at a field strength of 24 and 36 kV/cm (top to bottom), T = 298 K. (b) Ratios IE(t)/I0(t) of (top to bottom) 12, 18, 24, 30, and 36 kV/cm (noisy lines), T = 298 K. Circles show the calculated TR EFE curve at a relative mobility of secondary charge carriers equal to 6.3 × 10−8 m2/ (Vs), E = 24 kV/cm. Straight lines show an exponential approximation of the experimental TR EFE curves within the range where the ratios exceed 0.6.
accord with eq 1, they look very similar to exponential decays. Deviations are observed when the fluorescence is quenched by the electric field to such an extent that other channels of fluorescent state formation become significant. One such channel in a concentrated solution can be the annihilation of electrically neutral triplet-excited molecules moving independently of the electric field. To visualize the electric field dependence of the TR EFE curves in Figure 2, the time constants of exponential decay, which approximate experimental curves like that shown in Figure 1b, were compared to the field strengths for a number of solvents. The inverse quadratic dependence of τ on E well describes the experimental data, thus indicating the observed
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RESULTS AND DISCUSSIONS Fluorescent Response of Irradiated Ether Solution. Figure 1a shows kinetic curves I(t) of the fluorescence response of a 10 mM pTP solution in THF at different electric fields after an irradiation pulse. In both THF and other studied ethers, the response curves were nonexponential ones similar to that observed from the concentrated luminophore solutions in alkanes (see, e.g. refs 8 and 19) but the fluorescence intensity of the ethereal solution was lower as compared to hydrocarbon solvents. The decrease in the intensity amounted to from about 1 order of magnitude for monoglyme and more viscous ethers to about 2 orders of magnitude for THF and diethyl ether. The possible reasons for such a decrease could be the absence of the electronic excitation energy transfer from the solvent excited state to luminofore, which takes place in normal alkanes,19 or the above-mentioned deprotonation process, which results in the instant decay of a portion of primary solvent radical cations. As in the case of alkanes,10 an increasing electric field strength, E, leads to a faster decay of fluorescence intensity. Figure 1b shows TR EFE curves at different values of E. In
Figure 2. Dependencies of the characteristic times of decay in TR EFE curves vs field strength E for DEE (squares), THF (circles), and DO (triangles). Lines show an approximation for a τ ∝ E−2 type of dependence. 15124
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Figure 3. (a) Experimental TR MFE curves for the pTP-d14 solution in THF at concentrations of 0.3 mM (curve 1, circles) and 10 mM (noisy curve 2), as well as for the pTP-h14 solution at a concentration of 10 mM (noisy curve 3). Calculated TR MFE curves, corresponding to the geminate ions formed from pTP-d14 and pTP-h14, assuming that radical cations of pTP undergo fast dimerization, are shown by smooth curves 2 and 3, respectively. Dashed curve 4 is obtained by assuming no dimerization of any of the pTP-h14 radical ions, while curve 5 show effects of dimerization of both the ions. Specific modeling parameters can be found in the text and Appendix B. (b, c) Experimental TR MFE curves for pTP-d14 solutions in EUC (b) and MG (c) at concentrations of 0.3 mM (circles) and 0.01 M (noisy lines).
fluorescence to be a result of the recombination of radical ion pairs that is controlled by the ions’ diffusion and drift in electric fields created by other ions and external sources. Identification of Charge Carriers. One of the important issues related to measuring the mobility of short-lived species is identification of the latter. To resolve the problem, in this work we have used the method of Time-Resolved Magnetic Field Effect (TR MFE) in recombination fluorescence of spincorrelated radical ion pairs.16 The method refers to the ratio of the fluorescence decay curves measured in a magnetic field and without the field, IB(t)/I0(t). The B and 0 indexes show that the irradiated solution was in an external nonzero (0.1 T in this work) and zero (
