Article pubs.acs.org/JPCB
Identification of Ion-Pair Structures in Solution by Vibrational Stark Effects John Hack,†,‡ David C. Grills,† John R. Miller,† and Tomoyasu Mani*,† †
Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973-5000, United States Chemical Engineering Department, University of Virginia, 102 Engineers’ Way, PO Box 400741, Charlottesville, Virginia 22904-4741, United States
‡
S Supporting Information *
ABSTRACT: Ion pairing is a fundamental consideration in many areas of chemistry and has implications in a wide range of sciences and technologies that include batteries and organic photovoltaics. Ions in solution are known to inhabit multiple possible states, including free ions (FI), contact ion pairs (CIP), and solvent-separated ion pairs (SSIP). However, in solutions of organic radicals and nonmetal electrolytes, it is often difficult to distinguish between these states. In the first part of this work, we report evidence for the formation of SSIPs in low-polarity solvents and distinct measurements of CIP, SSIP, and FI, by using the ν(CN) infrared (IR) band of a nitrile-substituted fluorene radical anion. Use of time-resolved IR detection following pulse radiolysis allowed us to unambiguously assign the peak of the FI. In the presence of nonmetal electrolytes, two distinct red-shifted peaks were observed and assigned to the CIP and SSIP. The assignments are interpreted in the framework of the vibrational Stark effect (VSE) and are supported by (1) the solvent dependence of ion-pair populations, (2) the observation of a cryptand-separated sodium ion pair that mimics the formation of SSIPs, and (3) electronic structure calculations. In the second part of this work, we show that a blue-shift of the ν(CN) IR band due to the VSE can be induced in a nitrile-substituted fluorene radical anion by covalently tethering it to a metal-chelating ligand that forms an intramolecular ion pair upon reduction and complexation with sodium ion. This adds support to the conclusion that the shift in IR absorptions by ion pairing originates from the VSE. These results combined show that we can identify ion-pair structures by using the VSE, including the existence of SSIPs in a low-polarity solvent.
1. INTRODUCTION Ion pairing between oppositely charged ions is fundamental to many areas of chemistry and applications including batteries and organic photovoltaics.1−3 It is widely accepted that ion pairs exist in solvents having dielectric constants De < 30.3 Ion pairing affects both the energetics and dynamics of ions. Ion pairings of electrolytes and those between organic anion radicals and metal cations are well studied, but studies on ion pairing between organic radicals and nonmetal electrolytes are scarce despite their significant implications in the control of the energetics of these molecules, including redox potentials measured by means of electrochemistry. Ion pairing is particularly important in solvents of low dielectric constant (De < 11, here we use the definition by Van Der Hoeven and Lyklema 4 based on Fuoss’s theory 5 ) where Coulomb interactions are less screened by the solvent. The exact form of ion pairs in solution is a topic of debate,3 and is often difficult to identify experimentally. In general, we classify ion pairs into three populations: contact ion pairs (CIPs) or tight ion pairs, solvent-separated ion pairs (SSIPs) or loose ion pairs, and solvent-shared ion pairs (SIPs) (Figure 1). We can consider SIP as one case of SSIP with one solvent molecule between the two ions (therefore shared). For © 2016 American Chemical Society
Figure 1. Pictorial representation of free ions (FI), a solvent-separated ion pair (SSIP) or solvent-shared ion pair (SIP), and a contact ion pair (CIP). Void circle = solvent molecule.
simplicity and due to the currently achievable experimental resolution, we do not attempt to make any distinction between SIPs and SSIPs, and call them SSIPs collectively, assuming that there is a single solvent molecule between ions. The formation of a SSIP can have significant implications for the kinetics of charge separation and thermodynamic properties, including electrical conductivity, of a solution6,7 and photoinduced charge transfer processes in condensed phases.8,9 The concept of a SSIP was first introduced to explain unusual Received: December 5, 2015 Revised: January 24, 2016 Published: January 25, 2016 1149
DOI: 10.1021/acs.jpcb.5b11893 J. Phys. Chem. B 2016, 120, 1149−1157
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The Journal of Physical Chemistry B conductivity and kinetic data by Fuoss, Grunwald, and Winstein in three independent studies.6,7,10 The proposed SSIP species rests in a relative potential energy minimum, separated from the CIP by a solvation energy barrier. Various studies have been performed to identify and characterize SSIPs, but many are limited to pairing with metal cations.3 Identifying and distinguishing SSIPs from CIPs and free ions (FIs) in solution, especially of organic radicals and nonmetal electrolytes, is not a trivial task. Until recently, spectroscopic techniques such as electron paramagnetic resonance, visible, and vibrational spectroscopy have been able to observe distinct peaks assigned to CIPs and SSIPs, but unambiguous measurements of FIs in neat solvents, especially in media of low polarity, were difficult.2,11−13 This technical limitation left some ambiguity as to the assignment of SSIPs as distinct thermodynamic states with unique properties and behaviors from FIs. In previous work, we reported a distinct IR absorption band of the free anion of F1CN, a nitrile-substituted fluorene (Chart 1), in moderately nonpolar neat tetrahydrofur-
Figure 2. IR spectra of the ν(CN) stretch of F1CN anion in THF. The FI spectrum (νmax = 2110 cm−1) was obtained 50 ns after pulse radiolysis. A further red-shift occurs when F1CN is reduced electrochemically in the presence of 0.1 M TBA+PF6− or TBA+BF4−. The ion pair spectrum fits to two Voigt functions, assigned to the CIP (νmax = 2094 cm−1) and SSIP (νmax = 2108 cm−1). The data shown in the figure were taken from ref 14.
Chart 1. Structures of the Nitrile-Substituted Fluorenes Studied
be used to investigate the properties of ionic liquids. In the case of ion pairing between F1CN•− and TBA+, the inert nonmetal ion TBA+ induces an external electric field on the CN dipole (the difference dipole moment points N → C),23 causing a change in the energy of its vibrational transition (Supporting Information Figure S1). The observed red-shift in the ion pairs of F1CN•− and TBA+ implies that a cation is oriented on the nitrile side of F1CN•− in the ion pairs. We assumed that the ion pair spectrum, shown in Figure 2, includes both CIP (F1CN•−, TBA+) and SSIP (F1CN•−∥TBA+) based on the goodness of fits, but more support is required for a clearer confirmation of the existence of a SSIP as one of the distinct ion-pair structures and as a thermodynamically stable species. Within the framework of the VSE, we also hypothesize that we can induce a blue-shift in ν(CN) IR frequency of the nitrile-substituted fluorenes when a cation is positioned on the other side of the nitrile of anions, away from the CN. Such a blue-shift was previously observed in the cases of simple salts such as Na+SCN−,24 Li+SCN−,25 Li+SeCN−,26 and inorganic cyanide compounds,27 but the relationships between the VSE and ionpair structures are often obscured because of the lack of a priori structural information in such intermolecular complexes in solution. In the first part of the current paper, we present evidence that supports the existence of the SSIP in the ion pairs of F1CN anion and TBA+ by (1) the solvent dependence of the SSIP/ CIP ratio in dimethylformamide (DMF)/THF mixtures, (2) the agreement of peak position in cryptand-separated sodium ion pair that mimics the formation of a SSIP, and (3) electronic structure calculations. In the second part of the paper, we report a blue-shifted ν(CN) IR vibration due to the VSE in the nitrile-functionalized fluorene radical anion by using a newly synthesized fluorene derivative (Chart 1) whose intramolecular ion-pair structure is known a priori. These works combined highlight the strength of the VSE in the studies of inter- and intramolecular ion pairs. We will discuss ion-pair structures in media of low polarity and their implications in the energetics of ions in such environments.
an (THF, De = 7.52),14 using nanosecond time-resolved infrared (TRIR) detection15 following pulse radiolysis at the Laser-Electron Accelerator Facility (LEAF) at Brookhaven National Laboratory.16 The ν(CN) IR peak for the free ion of F1CN•− (νmax = 2110 cm−1) was red-shifted in comparison to the peak in the neutral form (νmax = 2224 cm−1). Two further red-shifted peaks were observed upon ion pairing with tetrabutylammonium ion (TBA+), which we assigned to the CIP (νmax = 2094 cm−1) and the SSIP (νmax = 2108 cm−1) (Figure 2). We also determined the rate constants for the formation of ion pairs by monitoring the growth of the ion pair’s IR band.14 The observed red-shifts in ν(CN) IR frequency of the F1CN anion with ion pairing can be interpreted in the framework of the vibrational Stark effect (VSE).14 This interpretation for ion pairing between F1CN•− and a positive charge was supported by electronic structure calculations.14 The VSE relates shifts in the vibrational energy to the dot product of the difference dipole of the vibration (between ground and excited states) and an exerted external electric field. Vibrational shifts of nitrile and carbonyl probes in neutral molecules have been calibrated to a known external field in frozen glass and in solution.17,18 These neutral probes can be used to obtain a quantitative measure of the local electric field in proteins, other macromolecular complexes, or environments, pioneered by Boxer and colleagues.18,19 Neutral molecules (benzonitrile)20 and charged species (e.g., thiocyanate)21,22 can
2. EXPERIMENTAL METHODS 2.1. General. All reagents and solvents were used as received from standard sources. Silica gel (pore size 60 Å, 70− 230 mesh, Sigma-Aldrich) was used for column chromatog1150
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solutions were transferred into a demountable liquid flow cell DLC-S25 (Harrick Scientific) equipped with 2 mm thick CaF2 windows and a 950 μm thick spacer. 2.5. Pulse Radiolysis with Time-Resolved Infrared (TRIR) Detection. Pulse radiolysis experiments were conducted in LEAF at Brookhaven National Laboratory. A detailed description of the experimental setup is given elsewhere.15 An airtight IR solution flow cell was used (1.1 mm path length), equipped with 0.35 mm thick CaF2 windows. Continuous wave external-cavity quantum cascade lasers (models 21047-MHF and 21043-MHF, Daylight Solutions, Inc.) were used as the IR probe source. Samples (5−20 mM) were dissolved in THF or DMF and purged with argon. 2.6. Quantum Calculations. Computations were performed with either Gaussian0931 or Q-Chem 4.232 using density functional theory (DFT). All calculations on anions were spin-unrestricted. All hexyl groups at the 9-position of fluorenes were replaced by ethyl groups. The geometry optimizations were performed without symmetry constraints. Calculations used the 6-31G(d) basis set and the LC-ωPBE (ω = 0.1 bohr−1)28,30,33 or B3LYP34,35 functional. A PCM solvation model36,37 (Gaussian) or C-PCM solvation model38−40 (QChem) for THF was used.
raphy. FTIR spectra were obtained using a Thermo Nicolet Nexus 670 FTIR spectrometer. UV−vis−NIR spectra were obtained using a Cary 5 spectrophotometer (Varian) or Cary 5000 spectrophotometer (Agilent). 1H and 13C NMR spectra were obtained with a Bruker Avance III spectrometer operating at 400.16 and 100.62 MHz, respectively. Samples were prepared under an atmosphere of argon for measurements other than NMR spectroscopy. 2.2. Synthesis. Syntheses and characterizations of F1CN,14 BrF1CN,28 and 4-bromobenzo-15-crown-529,30 are reported elsewhere. 2.2.1. 9,9-Dihexyl-7-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)-9H-fluorene-2-carbonitrile (BpinF1CN). A dry flask with an argon atmosphere was charged with BrF1CN (0.61 g, 1.39 mmol), bis(pinacolato)diboron (0.45 g, 1.74 mmol), Pd(dppf)Cl2 (6.0 mol %), and KOAc (0.273 g, 2.78 mmol). After addition of 5 mL of DMF, the reaction mixture was stirred at 80 °C for 5 h, after which it was cooled down to room temperature and poured into 50 mL of H2O. The mixture was extracted with DCM (50 mL). The organic layer was collected and washed with brine three times and then dried over MgSO4. After filtration and removal of the solvents in vacuo, the crude mixture was purified by column chromatography on silica gel (hexane:DCM = 7:3) to afford the title compound as a pale yellow solid (0.40 g, 59%). 1H NMR (CD2Cl2, 400 MHz): δ 7.81 (m, 4H), 7.65 (m, 2H), 2.03 (m, 4H), 1.36 (s, 12H), 1.10−0.97 (m, 12H), 0.76 (t, J = 7.1 Hz, 6H), 0.51 (m, 4H). 13 C NMR (CD2Cl2, 100 MHz): δ 152.4, 151.0, 145.9, 142.4, 134.2, 131.6, 127.2, 121.0, 120.4, 120.1, 110.8, 84.4, 56.0, 40.4, 31.9, 29.9, 25.1, 24.1, 22.9, 14.1. 2.2.2. 9,9-Dihexyl-7-(2,3,5,6,8,9,11,12-octahydrobenzo[b][1,4,7,10,13]pentaoxacyclopentadecin-15-yl)-9H-fluorene-2carbonitrile (15-Crown-5-Ph-F 1 CN). The compound BpinF1CN (0.200 g, 412 μmol), 4-bromobenzo-15-crown-5 (0.158 g, 453 μmol), Pd(OAc)2 (11 mg, 49 μmol), SPhos (41 mg, 99 μmol), and K3PO4 (0.179 g, 824 μmol) were combined in a 10 mL round-bottom flask. Toluene (2 mL) and H2O (0.1 mL) were added, and the resulting mixture was deoxygenated by a couple of evacuation−refill (Ar) cycles. The mixture was stirred at 80 °C for 2 h and then cooled down, and the solvents were removed in vacuo. The crude mixture was purified by column chromatography on silica gel (5% THF in DCM) to afford the title compound as a yellow solid (0.183 g, 71%). 1H NMR (CD2Cl2, 400 MHz): δ 7.81−7.79 (m, 2H), 7.66−7.64 (m, 2H), 7.60 (dd, J = 7.9, 1.5 Hz, 1H), 7.57 (s, 1H), 7.23 (dd, J = 8.3, 2.1 Hz, 1H), 7.19 (d, J = 2.1 Hz, 1H), 6.98 (d, J = 8.2 Hz, 1H) 4.22−4.15 (m, 4H), 3.91−3.87 (m, 4H), 3.74−3.67 (m, 10 H), 2.06−2.01 (m, 4H), 1.83−1.80 (m, 2H), 1.13−1.01 (m, 12H), 0.76 (t, J = 7.1 Hz, 6H), 0.61 (m, 4H). 13C NMR (CD2Cl2, 100 MHz): δ 152.6, 152.0, 149.8, 149.6, 145.9, 142.1, 138.5, 134.7, 131.7, 127.0, 126.4, 121.6, 121.4, 120.53, 120.48, 120.3, 114.3, 113.6, 110.1, 71.19. 71.16, 70.7, 60.6, 69.9, 69.8, 69.6, 69.2, 40.5, 31.9, 29.9, 24.1, 22.9, 14.1. 2.3. Spectroelectrochemistry. FTIR spectroelectrochemical measurements were performed in a spectroelectrochemical transmission cell GS20900 (Specac Limited) coupled with a CHI 600E potentiostat (CH Instruments, Inc.). All samples contained 0.1 M TBA+PF6−. 2.4. FTIR of Reduced Species. Chemical titrations were performed with sodium biphenyl (Na+BP−) or sodium chunks, either in the absence or presence of cryptand-222 (C222), in a glovebox. The concentration of C222 was at least 1 equiv of neutral molecules before reduction unless otherwise noted. The
3. RESULTS AND DISCUSSION 3.1. SSIP vs CIP. 3.1.1. Ion-Pair Populations in DMF/THF Mixtures. In the first part of this work, we examine the existence of a SSIP in the ion pairs of F1CN•− and TBA+ in solvents of low polarity. In THF solution containing 0.1 M TBA+PF6−, which is a typical total concentration of electrolytes in electrochemical measurements, the results indicated that >95% of the ions exist as ion pairs based on fits such as those shown in Figure S2. We determined that the spectrum of the SSIP is distinct from that of the FI. To further support the assignment of the SSIP peak (Figure 2), IR spectra in the region of the ν(CN) stretch were measured spectroelectrochemically in mixtures of DMF (De = 38.25) and THF containing 0.1 M TBA+PF6− (Figure 3). The solvent properties of the mixtures are reported in Supporting Information Table S1. The spectra obtained in mixtures up to 20% DMF by volume fit to two Voigt functions centered at 2094 cm−1,
Figure 3. Spectroelectrochemical measurements of the ν(CN) stretch of F1CN•− in mixtures of DMF and THF containing 0.1 M TBA+PF6−. The spectra obtained in mixtures up to 20 vol % DMF fit well to two Voigt functions centered at 2094 cm−1, assigned to the CIP, and 2108 cm−1, assigned to the SSIP, with a SSIP/CIP ratio that increases with DMF composition. 1151
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The Journal of Physical Chemistry B Table 1. Observed ν(CN) (cm−1) of Anion Species in THFa ion pairs TBA+ molecules F1CN 15-crown-5-Ph-F1CN
FIb 2110 (12.1) 2124 (18.4)
CIPc
Na+ SSIPc
2094 (21.5) 2106 (23.6)
2108 (18.8) 2122 (26.3)
Na+ d 2094 (22.8) 2136 (23.1)
Na(C222)+ d e
2108 (15.9), 2106f (20.0) 2122 (24.0)
a The numbers in parentheses are the fwhm values determined by fitting with a Voigt function. Uncertanities are ±1 cm−1. bObtained by pulse radiolysis. cObtained by spectroelectrochemistry. dObtained by chemical reductions. eFitted to two Voigt functions. The reported value in the table is assigned to the species that “mimics” the SSIP. The other peak was observed at 2097 cm−1. fFitted to one Voigt function.
assigned to the CIP, and 2108 cm−1, assigned to the SSIP, with a SSIP/CIP ratio that increases with DMF composition. The characteristics of their spectra are listed in Table 1. The two Voigt functions were constrained to the same position, full width at half-maximum (fwhm), and shape as the functions used to fit the spectrum of ion pairs in pure THF solvent. Broader line widths observed for the CIP and the SSIP bands in the presence of TBA+ compared to that for the FI indicate that multiple conformations exist in both the CIP and the SSIP. However, as mentioned above, in this work we do not attempt to distinguish these conformers. The fittings of the spectra at each concentration are reported in Figure S2. Beyond 20% DMF, the peaks shift noticeably and no longer fit cleanly to the same two Voigt functions. As DMF becomes a larger fraction of the bulk solvent, several confounding effects may occur. As the dielectric constant of the bulk solvent increases the ν(CN) peak maximum can shift to the red probably due to solvent-induced VSE,17,18 as seen for F1CN•− free ions, νmax = 2101 cm−1 in DMF, vs νmax = 2110 cm−1 in THF (the 9 cm−1 red-shift can be seen in Figure S3). As the dielectric constant of the solvent increases, the Coulomb attractions between oppositely charged species are more screened. The free ion becomes more stabilized and may begin to contribute to the spectra. The observed change in FI from THF to DMF may be explained by a simple Onsager-like model of solvation as in the case of neutral aromatic nitriles, but more local solute−solvent interactions41 are likely to play an important role in anions. Interestingly, the spectrum reported in 100% DMF solvent containing 0.1 M electrolyte is centered, except for a slight electrolyte-induced red-shift, at almost the same position, 2101 cm−1, as the free ion peak in neat DMF, observed by TRIR detection following pulse radiolysis (Figure S4a). We can attribute this red-shift to the presence of ion pairs. We can fit the spectra to two functions by fixing one function to the spectrum of the free ion in DMF while adjusting the other, assumed to arise from ion pairs (Figure S4b). Here, we did not make any distinctions among ion pairs, and we find adequate, though not excellent fits. Assuming that the ratio of the areas under the curves reflects the population ratio, we can estimate the association constant for ion pairing between F1CN•− and TBA+ in DMF to be KA ∼ 3 M−1, which is about 4 orders of magnitude smaller than that in THF (KA = 9.2 × 104 M−1).14 The value KA ∼ 3 M−1 is 1 order of magnitude smaller than that for TBA+PF6− in acetonitrile reported by Geiger and coworkers (KA = 35.7 M−1),42,43 which seems reasonable given that KA(F1CN•−,TBA+) is about 4 times smaller than KA(TBA+,PF6−) in THF (see Table S2). An alternative is to interpret a slight broadening in the redder side in the spectroelectrochemical peak in terms of changes in the dielectric constants due to the presence of 0.1 M electrolyte. The first interpretation which identifies a reasonable KA(F1CN•−,TBA+) seems preferable. In both cases, the
observation supports the picture that a radical anion is mainly “free” in a polar solvent in the presence of electrolytes, while some may be stabilized by ion pairings. This is different from the picture we previously put forward that ions are mainly stabilized by a single ion pair in nonpolar environments.14 In order to calculate association constants for the CIP and SSIPs, the SSIP/CIP ratios obtained in mixtures up to 20% DMF were fit to the model represented in Scheme 1. This Scheme 1. Ion-Pairing Equilibria in DMF/THF Mixtures
model allows for the formation of a CIP, a SSIP separated by one THF molecule, and a SSIP separated by one DMF molecule. We abbreviate these as SSIPTHF and SSIPDMF. The SSIP peak in Figure 3 is taken to be a combination of contributions from both SSIP species. The model makes the following assumptions. First, we assume that there is only one solvent molecule separating ions in the SSIP species, though it is possible that there are multiple.3 Second, we assume that in mixtures up to 20% DMF we can neglect formation of free ions and assume that DMF does not preferentially solvate either type of ion pair. Third, we assume that the ratio of the extinction coefficients of ν(CN) absorption in CIP and SSIP is unity. The second assumption is supported by the absence of a clear peak corresponding to that of the FI in DMF. The last assumption is supported by DFT calculations, which show that the extinction coefficients of ν(CN) absorption of anions differ by only 1−1.5 times over a distance of 4−5 Å between F1CN•− and a positive charge.14 The maximum difference in the distance between SSIP and CIP was reported to likely be ∼4−5 Å. 8,9 This difference is partially confirmed by computations (Figure S5). Importantly, using a ratio of 1.5 does not yield significantly different results from those reported (Table S3). A similar approach estimating extinction coefficients of IR absorbance using the outputs from electronic structure calculations was recently adopted by Ludwig and coworkers for far-IR absorption bands.12,13 Calculated association constants for the formation of CIP and SSIPs are reported in Table 2. The association constants KA for TBA+PF6− were taken to be mole-fraction-weighted linear combinations of association constants determined by Geiger and co-workers42 in THF (3.73 × 105 M−1) and DMF (35.7 M−1)43 and not adjusted. The association constant for the 1152
DOI: 10.1021/acs.jpcb.5b11893 J. Phys. Chem. B 2016, 120, 1149−1157
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The Journal of Physical Chemistry B Table 2. Ion-Pairing Equilibria for F1CN•− with TBA+ equationa 2 3 3 4
ΔG0 b (meV)
KAb K2 K3 K3 K4
anions. This model is similar in nature to the concept of penetrated ion pairs.49−51 In the presence of cryptand-222 (C222), a main peak is observed at 2108 cm−1 together with a shoulder at 2097 cm−1, the former of which is within one wavenumber of the SSIP observed with TBA+. C222, a chelating agent, encapsulates the Na+ ion, creating a “separated” ion pair with F1CN•− as F 1 CN • − ∥Na(C222) + , which can mimic the SSIP (F1CN•−∥TBA+). This strategy prevents close contact between alkali metals and anions, as shown elegantly by Kochi and coworkers.52−54 The notable agreement between the observed peak and the peak at 2108 cm−1 in the presence of TBA+ further supports the assignment of the SSIPTHF (F1CN•−, THF, TBA+) observed in Figures 2 and 4. The shoulder observed at 2097 cm−1 (fwhm = 15.8 cm−1 from multipeak curve fitting) is relatively close to that of the CIP observed with TBA+ and Na+ (νmax = 2094 cm−1). This may indicate either an incomplete encapsulation of Na+ by C222 or the possibility that some Na(C222)+ can be positioned close enough to resemble the CIP. Changing the concentration of C222 (from 1 equiv of neutral F1CN to 3 equiv) appears not to change the ratio of the two peaks, which suggests the latter is the case. It is important to note that the observed spectrum of “separated” ion pair with Na(C222)+ is clearly different from that of the FI, showing that while the cryptands can reduce the effects of ion pairing they will not create FIs in media of low polarity. Combining the solvent dependence and chemical reduction data clearly shows that we can distinguish the SSIP from the FI and in turn supports our initial assumption that anions in THF containing 0.1 M TBA+PF6− primarily exist as ion pairs. While it is expected from the thermodynamic equilibria (KA = 9.2 × 104 M−1 for ion pairs as a whole14) that 2% of F1CN•− will be present as FIs in such a solution, our IR measurements cannot readily detect this small population. Analysis indicates that it would likely be possible to detect if at least 5% FIs are present. 3.1.3. Energetics of Ion Pairs. We now turn our attention to the effect of ion paring on the energetics of the ions, obtaining estimates of the standard reduction potential (E0) in the absence of electrolytes and in the presence of electrolytes (typically 0.1 M) determined by cyclic voltammetry. The standard energetics of the SSIPTHF and CIP in THF (vs Fc+/0) are shown in Figure 5, including the previously determined energies of the FI and ion pairs.14 We further compare the experimental values with estimates by electronic structure calculations. The typical calculated structures of the SSIPTHF and the CIP are displayed in Figure S5. The SSIPTHF was calculated as a F1CN•−, TBA+ pair surrounded by four explicit THF molecules. We found that the TBA+ ion is stabilized by approximately four THF molecules (Figure S7) in a similar manner to DMF and DMSO.55 The CIP was calculated by removing one THF molecule and allowing F1CN•− to move closer to the cation. The distances between the nitrogen atoms in F1CN•− and TBA+ (dNN) are ∼3.8 Å for the CIP and ∼7.8 Å for the SSIP. We did not fully optimize the structures, but selected the structures, obtained in the course of the optimization processes, which are consistent with our IR observations and interpretation by VSE; namely the configuration in which TBA+ is positioned on the same side as the nitrile of F1CN•− (see Supporting Information, pp 2 and 3, for the details). Our current result of intramolecular ion pairs further supports that the IR shift is induced by the VSE (vide inf ra). The CIP was calculated to be more stable than the SSIPTHF by a free energy
−1
= (9.8 ± 1.8) × 10 M = (2.9 ± 1.1) × 103 M−2 [THF] = (3.4 ± 1.3) × 104 M−1 = (2.6 ± 1.1) × 104 M−2 4
−300 −200 −270 −260
± ± ± ±
5 10 10c 10
a
Equations as defined in Scheme 1. bThe values are the averages from five different DMF/THF ratios. c100% THF ([THF] = 12.3 M).
formation of SSIPDMF, K4, is about an order of magnitude larger than for SSIPTHF, K3. This result matches the expectation that DMF, a more polar solvent than THF, has a higher association constant for SSIP formation, and explains the observed growth in the combined SSIP peak with increasing DMF composition. Standard free energy changes (ΔG0) are reported in Table 2 as well. K3 was multiplied by the concentration of THF so that the energy of the SSIPTHF could be compared to the energy of the CIP. It was found that the CIP (ΔG0 = −300 ± 5 meV) is stabilized by 30 meV compared to the SSIPTHF (ΔG0 = −270 ± 10 meV). This value is not much larger than the average thermal energy, kBT, at room temperature. 3.1.2. Macrocycle Polyether-Separated Intermolecular Ion Pair. The FTIR spectrum of F1CN•− in THF obtained by chemical reduction of F1CN by sodium biphenyl is shown in Figure 4. The ν(CN) absorption band of the CIP (F1CN•−,
Figure 4. FTIR spectra obtained for F1CN anions in THF. The red spectrum, peaking at 2094 cm−1, labeled F1CN•−, Na+, was produced by a chemical reduction with sodium biphenyl. The green spectrum, labeled F1CN•−∥Na(C222)+,was produced by reduction with excess sodium biphenyl in the presence of cryptand-222 (C222). A main peak is observed at 2108 cm−1 with an additional shoulder at 2097 cm−1. C222 encapsulates the Na+ ion, creating a “separated” ion pair, which mimics the SSIP.52−54 The FI spectrum, labeled F1CN•− (νmax = 2110 cm−1), was recorded with TRIR detection obtained 50 ns after pulse radiolysis in neat THF. The balls in the top of the figure represent Na+.
Na+) appears at 2094 cm−1, within one wavenumber of that of the CIP with TBA+ in THF (Figure 2 and Figure S6). Here we assign the peak to CIP based on the previous studies by Szwarc and co-workers showing that Na+ preferentially forms a CIP with anions in THF except for bulky anions (e.g., tetraphenyl boride).1,44 This agreement, despite the large difference in ionic radii of Na+ and TBA+ (crystal ionic radii for Na+ and TBA+ are 0.95 and 4.13 Å, respectively),1,45,46 may support the theoretical model presented by Fry47,48 that the alkyl chains in TBA+ contribute negligible steric hindrance to ion pairing with 1153
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where R is the gas constant, T is the temperature, F is the Faraday constant, and [M+] is the concentration of free counterions M+ from the electrolyte. The energy diagram in Figure 5 and our previous report14 used a standard condition for all solutes including the electrolytes, giving E0([M+] = [M+]0 = 1 M). We now consider the case where CIP and SSIP are present. Assuming that only free ions contribute to the electron transfer reactions at the electrode, we obtain the equation E 0([M+]) = E 0([M+] = 0) +
× ln(1 + K CIP[M+] + KSSIP[Solv][M+])
Figure 5. Standard energy diagram in THF (E0 vs Fc+/0 in eV) of the ion pairs, CIP, SSIP, and FI of F1CN•− in THF. CIP = (F1CN•−, TBA+). SSIP = (F1CN•−, THF, TBA+). FI = F1CN•−. The energy of the ion pairs is taken from ref 28, and the energy of the FI was determined using eq 5 with the value of KA from ref 14. Note in ref 14 the reduction potential was measured with 0.1 M TBA+BF4−, which is −2.74 V vs Fc+/0. Although the difference is only 20 meV, for clarity, we used the reduction potential determined under the same conditions as those used in the current study (0.1 M TBA+PF6−). The energy of the FI shifts by 20 meV accordingly while KA does not change. The energy spacing in the graph is arbitrary.
RT ln(1 + KA[M+]) F
(6)
where KCIP and KSSIP are defined in Supporting Information, pp 4 and 5. This shows that the standard energy of ion pairs E0([M+]), obtained by cyclic voltammetry, is affected by the additional contribution of stabilization by SSIPs. In the current case, the standard energies of the CIP and ion pairs obtained by cyclic voltammetry are within the experimental errors (±10 meV), and we are unfortunately not able to clearly observe the contributions from the SSIP in the standard redox potentials measured electrochemically. 3.1.4. Differences in Standard and Experimental Conditions. As mentioned above, in our previous report,14 we defined the reduction potential in the presence of electrolytes at the standard condition, meaning that we have E0([M+]0), where usually [M+]0 = 1 M and use E1/2 from the measurement of cyclic voltammetry as E0([M+]0) referenced to the ferrocene couple (vs Fc+/0).59 This convention allows us to use eq 5 in the simplest form, making it easy to estimate and compare the redox potentials in the absence of electrolytes within the assumption that the major stabilization of redox-active ions by electrolytes comes from single ion pairs. However, the experimental concentration of f ree counterions from 0.1 M of typical electrolytes is much lower in media of low polarity (e.g., [M+] = [TBA+] ∼ 500 μM for TBA+PF6− in THF). In this regard, it may be more appropriate to define the E1/2 measured by cyclic voltammetry as the reduction potential with 0.1 M TBA+PF6− instead of with 0.1 M of free TBA+ ions. Here the concentration of f ree counterions in eq 5 is no longer [M+]0 and becomes the value at the experimental condition in specific media with specific electrolytes. On the basis of this definition, we obtained the contribution of ion pairs as ∼100 meV for the condition of 0.1 M TBA+PF6− in THF. The reduction potential of F1CN in the absence of electrolytes is then calculated to be −2.82 V vs Fc+/0 where the oxidation potential of ferrocene is defined with 0.1 M TBA+PF6−. This value is ∼190 mV more positive than the energy estimated under the standard conditions (Figure 5). We would like to emphasize that this difference is solely from the differences in the definition, at either standard or specific experimental conditions for electrolytes, and it still holds that the measurements of association constants between redox-active species and counterions from electrolytes allow us to estimate the redox potentials in the absence of electrolytes, assuming that only ion pairing shifts the potentials. 3.2. Blue-Shift VSE. 3.2.1. Molecular Design. In the second part of the study, we examine the possibility of inducing a blue-shift by VSE. Recall that a positively charged TBA+ sits on the same side of the molecule as the nitrile group in F1CN•−, inducing a red-shift in ν(CN). In the framework of the VSE a positive charge positioned on the opposite side, away
difference of approximately 40 meV. This value is in good agreement with the experimentally determined value (∼30 meV). However, we would like to note that the structures used here are among the many stable conformations, and more samplings of conformations of ion pairs would be required to further validate these preliminary computational results. In a solution of single solvent where the concentration of solvent is constant, the SSIP/CIP ratio should not change eqs 2 and 3 in Scheme 1. We previously demonstrated that the reduction potentials in the absence of electrolytes can be determined by measuring the association constants for ion pairing.14 In the previous analysis,14 we did not distinguish SSIP/CIP contributions, instead treating ion pairing as a mixture of the two. Here, we could determine the respective standard energies of the CIP and SSIP within a couple of assumptions. The estimated energy difference of ∼kBT makes it difficult to measure the contribution of individual species by cyclic voltammetry measurements whose experimental uncertainties are typically about 10−20 mV.56 While it would be desirable to measure the difference by slowly scanning the potential, we do not expect to alter the ratio of CIP and SSIP peaks by adjusting potentials if the two forms are in equilibrium with each other for each ion pair. While the SSIP/CIP ratios are likely to depend on the molecules of interest and electrolytes of choice, based on our current study, we can safely say that both species are present in ion pairs between other molecules and electrolytes in a similar environment. Therefore, the standard reduction potentials measured in the presence of counterions M+ from electrolytes by electrochemical methods (E0([M+])) should be considered to reflect the contributions from both species. In general, E0([M+]) is related to the standard reduction potential in the absence of electrolytes (E([M+] = 0)) and to the association constants (KA) of ion pairing between redox-active species and counterions from electrolytes through the equation57,58 E 0([M+]) = E 0([M+] = 0) +
RT F
(5) 1154
DOI: 10.1021/acs.jpcb.5b11893 J. Phys. Chem. B 2016, 120, 1149−1157
Article
The Journal of Physical Chemistry B from the nitrile group, might produce a blue-shift in ν(CN). Such a blue-shift was previously observed in simple inorganic salts.25−27 The blue-shift was interpreted based on the framework of the VSE: The difference dipole moment of ν(CN) is aligned antiparallel to the external electric field induced by the metal cation and cyanide-containing anions. However, the relationships between the VSE and ion-pair structures are often obscured because of the lack of a priori structural information in these complexes in solution. Here, to obtain a clearer relationship between the VSE and ion-pair structures and to further clarify the origin of IR shifts, we synthesized and studied a new molecular system whose ionpair structure is better defined through covalent bonding. The new molecule is named 15-crown-5-Ph-F1CN where a benzo crown ether (15-crown-5-Ph) is tethered to the phenyl on the opposite side, away from the nitrile group (Chart 1). The molecule can take either syn or anti conformations (Figure S8). DFT calculations predict that the syn conformer is only slightly (
