Solvation spectra. XVI. Ion-pair formation studied by electron spin

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M. C. R. SYMONS

172

Solvation Spectra. XVI. Ion-Pair Formation Studied by Electron Spin Resonance

by M. C. R. Spons Department of Chemistry, University of Leicester, Leicester, England

(Received September 97, 1966)

Structural and kinetic information about ion pairs that can be derived by application of electron spin resonance spectroscopy is reviewed, and recent results for certain semiquinones and aromatic nitro anions are used to illustrate the phenomena.

Classically, the study of ion-pair formation in solutions of electrolytes is the prerogative of the electrochemist, but recently various branches of spectroscopy have been applied with some success, particularly with respect to the problem of structure. This is especially true of electron spin resonance, which has reveaIed a surprising weaIth of structural information. Also, since the time scale for transition is in the region of sec, kinetic information is often forthcoming in a particularly direct way. In this paper the different ways in which information is obtained are summarized and are illustrated in particular by reference to recent results for various semiquinone and nitrobenzene anions. Hyperfine coupling from diamagnetic gegenions is discussed first (section A) since, if this is detected there can be no doubt of the presence of ion pairs. Then in section B the ways in which the magnetic properties of paramagnetic: ions are modified by ionic association are discussed, particularly with respect to changes in symmetry [section B (ii)]. Information from linewidth modifications is discussed in section C from a qualitative viewpoint, and finally in section D, evidence for the formation of ion clusters is reviewed. One aim of this study was to see if a combination of different pieces of evidence for similar systems would lead to a clearer understanding of the various types of ion pairing that can 0ccur.l Because of the differences in bonding, the behavior of transition metal and lanthanide ions has not been included.

especially in ethereal solvents. This phenomenon was discovered by Adam and Weissman12who studied the sodium ketyl of benzophenone. Each component of the normal spectrum of the solvated anion was split into four as a result of coupling to 23Nawhich has a nuclear spin of 3/2. Since then, such interaction has often been detected. It is always very small, in terms of spin density on the cation and there is some doubt about the way in which spin is acquired. For most purposes, however, the really important point is that, if it is detected, then an ion pair is involved. The converse, of course, is not true. Spin density giving rise to an isotropic hyperfine coupling can arise at the cation by a variety of mechanisms. These include indirect spin polarization of the inner s electrons and direct occupancy of the outer s orbital of the cation by the unpaired electron of the anion. It seems most probable that the outer s orbital is directly or indirectly involved and the following discussion is based upon this assumption. However, the detection of a small negative splitting from Csf does suggest that polarization plays a real part in some syst e m ~ . I~n view of the weak binding between cation and anion, we prefer not to invoke any specific set of molecular orbitals which would require a precise geometry but rather to imagine an over-all charge transfer which will depend both upon the degree of solvation of the cation and on its point of contact with the anion. Results for a selected range of ion pairs are summarized in Table I. The actual splittings in gauss

A. Hyperfine Coupling to Gegenions

(1) T. R. Griffiths and AI. C. R. Symons, Mol. Phgs.. 3, 90 (1960). (2) F. C. Adam and S. I. Weissman, J . Am. Chem. Soc., 80, 1518

Hyperfine coupling from alkali metal ions is often detected in the solution spectra of aromatic radical anions, The Journal of Physical Chemistry

(1958). (3) E. de Boer. Rec. Trav. Chim.,

84, 609

(1965).

ION-PAIR FORMATION STUDIED BY ELECTRON SPINRESONANCE

173

(Abf) are given together with the spin densities, calbut these are very often sites of low spin density and so the coupling may be very small. culated on the simplified assumption that there is Atherton and Weissman found a marked increase in negligible p character and that the outer (n) s orbital , , ~ , the hyperfine coupling to 23Nain sodium naphthalenide is involved. Then is set equal to A M / A ~ ~ and dissolved in various ethers as the temperature was the gas-phase atomic values that have been used are raised.’ I n tetrahydrofuran at very low temperatures also listed. This is probably a rather poor expression for the real spin density since charge transfer is so small the interaction tended to zero, so they postulated that that we are dealing essentially with a cation rather than the preferred site for the cation was over the node of an atom, although the positive charge is effectively rethe unpaired electron passing through the 9 and 10 posiduced by coordinated solvent molecules. The resultant tions such that the overlap with the 3s orbital was fiero. If this trap is shallow, then the cation should librate charge causes a reduction in the radial distribution and from side to side across the ring, thus bringing it into hence an increase in the hyperfine coupling for a given positions more favorable for weak interactions. This spin density. Hence the values are likely to be movement will increase with temperature and hence somewhat too large. the hyperfine coupling should also increase. Because The largest metal hyperfine coupling that has ever been reported is 36 gauss from potassium in isopropylof the small distance involved and the absence of any barrier, migration will be very fast and will not conamine at 1350e4 This corresponds to about 46% atomic tribute to the line widths as is found when the cation character, and clearly the description “ion pair,” whatmoves between two preferred sites [section C(ii) 1. ever that may mean in the context of solvated electrons, is inappropriatt:. The next largest is for potassium Although this attractive explanation seems to be in coupled to (20,- in 7-irradiated potassium f ~ r m a t e , ~ accord with the facts in many cases, at least one other is worthy of consideration. On cooling, the extent of where the atomic character was about 8.5%. These dissociation into solvated ions increases: this imresults are of particular interest in that they show that the anisotropic coupling is indeed small and can be plies that solvation becomes more effective and this must apply also to the ion pairs. Thus we envisage a understood in terms of an indirect dipolar coupling. “pulling-off ’’ mechanism in which the solvent tightens All the other results lie between zero and about 2.5y0. its grip on the ions prior to actual dissociation. This The magnitude of the hyperfine coupling to alkali metal ions is strongly dependent upon the properties of should result in a decrease of the hyperfine coupling to the solvent, the anion, and the cation. These will be the cation, since better solvation will make the outer s orbital less available to the unpaired electron. This considered in turn. The nature of the solvent dominates. Apart from explanation has been invoked to explain the results for controlling the extent of ionic association, it will, by durosemiquinone ions in mixed solvents.6 In general, solvating the ions to a greater or lesser extent, control both of these factors must be taken into account. their ability to gain or lose charge. This can be thought Recently, Hirota and Kreilick*have suggested a more of as complete insulation if there are sufficient solvent specific explanation for the decrease in hyperfine coumolecules between the ions within the ion pair to reduce pling to ? W a AN^) with decrease in temperature which they observe for the anions of anthracene and 2,6-di-tsignificantly the probability of charge transfer. Such ion pairs will be described as “solvent separated.”’ butylnaphthalene in 2-methyltetrahydrofuran. The Where there is effective contact, the role of the solvent particular aspects of their results are that the change is is to oppose tht: movement of charge, partly in a classinot linear but can be understood in terms of an equilibrium A S B in which A is an ion pair having Axa = cal sense, and partly by feeding lone-pair electrons into the outer s orbital of the cation. A good example is the 1.5 gauss and B is also an ion pair, but with AN^ = 0. effect of adding isopropyl alcohol to a solution of the They envisage a rapid equilibrium between these difsodium salt of duroquinone in t-pentyl alcohoL6 ferent ion pairs so that only one averaged spectrum is The structure of the anion is also important. I n obtained. As the temperature is lowered, a marked addition to its over-all ionization potential, there is the question of the location of the cation. This may consist (4) R. Catterall, M.C. R . Symons, and J. Tipping, J . Chem. Soc., of an ill-defined average of many sites of comparable prob4342 (1966). ability or of one or more strongly preferred sites. The (5) P. W. Atkins, N. Keen, and M . C . R . Symons, {bid., 2873 (1962). (6) T. E. Gough and M. C. R. Symons, Trans. Faraday Soc., 62, extent of magnetic interaction depends in part on the 271 (1966). overlap between the outer s orbital of the cation and (7) N. % Atherton I. and S.I. Weissman, J . Am. Chem. SOC.,83,1330 the orbital of the unpaired electron on the anion. Pre(1961). ferred sites will be those of high negative charge density, (8) N. Hirota and R. Kreilick, ibid., 88, 614 (1966). Volume 71,Number 1 January 1967

111. C.R. SYMONS

174

Table I: Hyperfine Coupling to Cations (Am)in Ion Pairs of Paramagnetic Anions (M+A-) Cation

Anion of

Naphthalene

Ph-Ph

Li Na S5Rb cs Na Li Na

T H P (RT) T H P (RT) T H P (RT) T H P (RT) T H F (RT) THP (RT) T H P (RT) T H P (RT) THP (RT)

K S5Rb ("Rb) cs @Li Na

Anthracene

K Na Na Na cs Li Na

Azulene

K Pyracene Duroquinone p-Benzoquinone o-Benzoquinone Benzil (Me&)zCO PhzCO

Na cs cs 6Li Na Na Li Na Na (Na)z 7Li

(?L~)z Na

K R\

Li Na

a::

K

O

K

O

R'

cs Na

z

N

P

s5Rb (8'Rb)

cs

Pyrazine

coz

Solvent" ("C)

Na Na

K Na

K

T H P (RT) Et20 (25) TMED (RT) TMED (RT) MeTHF (RT) MeTHF (-100) T H P (RT) T H P (RT) T H F (RT) T H F (RT) T H F (RT) MeTHF ( -80) T H F (-100) T H F (-20) t-AmOH (RT) t-AmOH (RT) t-BuOH (RT) t-BuOH (RT) 1-BuOH (RT) T H F (RT) T H F ( -70) DME (26) DME (26) T H F (RT) T H F (RT) T H F (RT) T H F (RT) T H F (RT) T H F (RT) T H F (RT) T H F (RT) T H F (RT) T H F (RT) T H F (RT) Formate crystals (RT) Formate crystals (RT) COz (77'K) Matrix

Am.

a h

gaum

%b

0.37 1.26 0.09 1.81 1.05 0.136 0.079 0.083 0.33 (1.1) 1.16 1.7 2.083 0.157 1.5 0.5 0.08 0.54 0.174 0.538 0.2 0.176 -0.2 -0.7 0.22 0.85 0.2 0.3 0.2 0.61 1.7 0.67 1,125 1.2 0.2 3.75 6.95 1.33 10.2

0.26 0.40 0.026 0.14 0.32 0.095 0.025 0.101 0,091 0.142 0.0 0.66 0.19 0.47 0.16 0.025 0.066 0.12 0.17 0.24 0.056 -0.024 $0.085 0.15 0.27 0.06 0.21 0.06 0.18 0.54 0.47 0.79 0.36 0.24 2.6 2.2 1.6 1.2

Ref C

e c c

d c c c c C

e

f f 9 9 C

c

f f f

h h h i i j j j

k 1 m m

n n P P P P

0.26 0.2 0 . 9 (3.1) 2.45 0.55 8.1

0.082 0.24 0.25 0.30 0.18 2.6

4 P 4 4

7.0

8.5

S

7.2 (5.8) 6.7

1 t

22.7 (18.3) 5.8

r S

TMED = tetramethylethylenediamine, T H F = tetrahydrofuran, MeTHF = 2-methyltetrahydrofuran, T H P = tetrahydroDerived from the atomic hyperfine coupling constants (gauss): 7Li, 143.3; e3Na, 316.2; pyran, and DME = dimethoxyethane. 89K, 82.4; URb, 362; 87Rb,1219; lZ3Cs,820.1. H. Nishiguchi, Y. Nakai, K. Nakamura, K. Ishizu, Y. Deguchi, and H. Takaki, N. M. Atherton and S. I. Weissman, J . Am. Chem. SOL, 83, 1330 (1961). * H. Winkler and R. BolMol. Phys., 9, 153 (1965). A. H. Reddoch, J . Chem. Phys., 43, 225 (1965). N. Hirota and R. Kreilick, J . Am. Chem. linger, Chem. Commun., 3,70 (1966).

'

The Journal

of Physical Chemistry

175

ION-PAIR FORMATION STUDIED BY ELECTRON SPINRESONANCE

Table I ( C o ~ ~ t i n u e d ) Soc., 88, 614 (1966). See ref 3. ‘ T. E. Gough and M. C. R. Symons, Trans. Faraday Soc., 62, 271 (1966). E. A. C. Lucken, J . Chem. Soc., 4234 (1964). G. It. Luckhurst and L. E. Orgel, Mol. Phys., 7, 297 (1963). G. R. Luckhurst, ibid., 9, 179 (1965). N. Hirota and S. I. Weissman, J . Am. Chem. Soc., 86,2537 (1964). ’ R = 2,4,6A. H. Reddoch, J . Chem. Phys., 43,3411 (1965). T. A. Claxton, trimethylcyclohexyl. p B. J. Herold, A. F. N. Correia, and J. dos Santos Veiga, J. Am. Chem. Soc., 87,2661 (1965). W. AI. Fox, and bl. C. R. Symons, unpublished results. N. Atherton and A. E. Coggins, Trans. Faraday Soc., 61,7 (1965). P. W. J. E. Bennett, B. Mile, and A. Thomas, Trans. Faraday Soc., Atkins, N. Keen, and M. C. R. Symons, J. Chem. Soc., 2873 (1962).

’

‘

61, 2357 (1965).

broadening is found which can be linked to a variable interaction with W a because the outer lines of each quartet are broadened far more than the inner pair (section C). Their interpretation is that A is a “tight ion pair” and B is a “loose ion pair.” That B is still an ion pair is established by the lack of rapid cation exchange and the fact that a separate spectrum due to the free ions can be detected. As it stands, this postulate raises some interesting questions since it is usually thought that in the sequence

a

tight ion pair

A

loose ion pair

b

A

solvated ions

equilibrium b is established at rates close to those of diffusion of the ions, whereas a is a relatively slow process. This intwesting problem is discussed further in section C(ii). As can be seen from Table I, there are in general no obvious trends in the cation hyperfine coupling constants. However, the results for the alkali metal chelates of the anion of o-dimesitoylbenaene’O do show a steady trend to weaker interaction on going from Li+ to Csf. The results for (a2,,) are roughly linear with r-l or r-‘I2 when r is the cation radius. This trend, which follows the electron affinities of the cation ions can perhaps be treated as normal and may arise because effective chelation largely eliminates complications from the solvent and from extensive movements of the cation. Also, perhaps for these reasons, the hyperfine interaction is much larger than usual and hence almost certainly is a good measure of spin density, in contrast with the very small values which are more likely to be made up from several indirect interactions. If this is correct, then attempts to discover significant trends in the small couplings usually found will be fraught with difficulties. The nature of the anion is clearly a major factor, but again it is hard to see any particular pattern. For example, no contribution from alkali metal cations has been seen in the spectra of the anions of tetracyanoethylene or 2,2,5,5-tetramethylhexan-3,4-dione[Me3CCO-CO-CNeaI- l1 in ethereal solvents in which ion

pairing is expected. The chelating anion of o-dimesitoylbenzene gives remarkably large hyperfine coupling constants to all of the alkali metals,10but the chelating anion of benzil gives a 23Nacoupling which is less by a factor of 10.” Results for the C02- ion paired with sodium and potassium are of some interest since these have been studied in two solid phases, quite different results being obtained (Table I).5s12 I n yirradiated sodium formate the spin density on the sodium ion5 is far less than that found for Na+C02- in a carbon dioxide matrix12 while interaction with K + is comparable with the two media. The “odd man out” is Na+ in sodium formate, the difference being almost certainly due to the coordination of neighboring formate ions in the host lattice, which will be stronger for sodium than for potassium. This seems to be a particularly direct example of the effect of coordination upon the extent of hyperfine interaction. The only other new feature revealed by these results is the small anisotropic coupling which is averaged to zero in solution spectra. This is symmetric about the symmetry axis of the parent formate ions for C02- in sodium formate as would be expected for the planar ion pair

\ 0/ since the unpaired electron is in the u (al) orbital rather than in the T level. However, the anisotropic coupling for one of the two types of Na+C02- pairs studied by Bennett, et al., deviates markedly from axial symmetry, suggesting that in this case the cation lies (9) M.Eigen and L. de Maeyer in “Technique of Organic ChemisVol. VIII, Interscience Publishers, Inc., New York, N. Y., 1963,Part 11. (10) B. J. Herold, A. F. N. Correia, and J. dos Santos Veiga, J . A m . Chem. Soc., 87, 2661 (1965). (11) G.R. Luckhurst and L. E. Orgel, Mol. Phys., 7, 297 (1963). (12)J. E. Bennett, B. Mile, and A. Thomas, Trans. Faraday Soc., 61, 2357 (1965).

try,”

Volume 71, Number 1 January 1967

114. C . R. SYMONS

176

Table 11: Examples of Some Minor Changes in Hyperfine Splitting Constants and g Values of Paramagnetic Anions on Varying the Counterions Anion of

Anthracene

Cation

Solventa

Noneb Li Na

THF THF THF THF TMED TMED DMSO DMSO DMSO DMSO DMSO

K Na

K Trini trobenzene

Noneb Li Na

K

cs

Mg Ca Ba

Noneb Ll Na

K

Nucleus

5.301 5.314 5.294 5.371 5.370 5.484 2.10 2.23 2.56 2.30 2.12 2.14 9.2 8.8

DMSO DMSO DMSO DMF DMF DMF DMF

Hf coupling

N N N N

9.1 10.5 10.3 9.7

Q

value

Ref

... ... ...

C C C

...

C

.

.

I

... 2.0044 2.0044 2,0044 2.0045 2.0045 2.0044 2.0044 2.0041

... ... ... . I .

C C

a d d

a a a d d

f f f f

a T H F = tetrahydrofuran, TMED = tetramethylethylenediamine, DMSO = dimethylsulfoxide, and DMF = dimethylformamide. Extrapolated or from tetraalkylammonium salts. See footnotef, Table I. S. H. Glarum and J. H. Marshall, J. Chem. Line-width alternation causes apparent loss of coupling to two nitrogen atoms. Phys., 41,2182 (1964). See ref 13.

’

out of the radical plane, probably directly over the two oxygen atoms. This is of some significance to the mechanism of the interaction which gives rise to the isotropic hyperfine splitting, which is comparable for the two trapping sites. This indicates, perhaps surprisingly, that charge transfer is not significantly altered by the changed geometry in this particular instance. No such interaction has ever been observed for anions with paramagnetic cations. This is almost certainly due to the fact that simple anions such as the halides have no low-lying acceptor orbitals and so will acquire electron spin by donation from the outer p level. Thus, any isotropic hyperfine coupling to their nuclei will be the result of spin polarization which is likely to be very small. I n this respect, for ion pairs in which covalent bonding is negligible, the alkali metal cations with their low-lying outer s orbitals are ideal for seeing this interaction, and yet even then the observed coupling is generally very small. It is therefore not surprising that hyperfine coupling to anions has never been detected. Perhaps a better manifestation of interactions between paramagnetic cations and simple anions would be trends in line widths and especially in g values with the nature of the anion. For example, iodide, with its large spin-orbit coupling constant and low ionization potential might well cause a detectable shift in the g value relative to the solvated cation. Such an effect has been sought at Leicester, but so far without success. The JouTnal of Physical Chemistry

B. Changes in Hyperfine Constants and g Values of Paramagnetic Ions (i) Minor Trends. I n general, the magnetic parameters of a radical ion are governed by its electronic structure and are only slightly modified by interaction with the environment. It is therefore often difficult to distinguish at all clearly between a shift caused by a change in solvation and one caused by ion pairing. Some ions, such as the naphthalenide ion discussed in section A, show practically no change on going from the ion pair to the solvated ion.’ Others show slight but finite changes, some of which are given in Table 11. Kitagawa, et al.,13found that the nitrogen hyperfine coupling (AN) in p-chloronitrobenzene anions was particularly sensitive to ion pairing in dimethylformamide. This work is important since it shows that ion pairing occurs significantly in this solvent, when there is an excess of added salt. Addition of tetraethylammonium perchlorate even up to 0.5 M had a negligible effect, but the cations of other salts induced large increases in AN in the order Kf < Na+ < Li+ < h/Ig2+. Here the governing factor is initially the degree of association, but the curves of A N against salt concentration level out showing that the final values for A N follow the same order. Since the change is a gradual increase (13) T. Kitagawa, T. Layloff, and R. N. Adams, Anal. Chem., 36, 925 (1964).

177

ION-PAIR FORMATION STUDIED BY ELECTRON SPINRESONANCE

rather than a jump involving two different spectra, equilibration of the solvated ions and the ion pairs must be rapid (see section C). In that case, no hyperfine coupling to the cations should be found, and this is indeed so. There is, however, a marked line broadening which is presumably a direct result of this rapid equilibration (section C). I t is unfortunately not possible to distinguish between contact and solvent-separated ion pairs from these results. Nore subtle changes have been revealed by careful monitoring of the proton hyperfine coupling in the anthracene and azulene anions.14 Changes, usually of the order of 1%, were detected when the solvent, temperature, and cations were changed, all the changes being attributed to ion pairing, even when no hyperfine splitting from the cations was d e t e ~ t e d . ' ~All proton couplings in a given anion were found to change in a systematic manner, some increasing and others decreasing, but always in such a way that constant trends were maintained. On dilution or cooling, the coupling constants shift toward the values for the solvated anions whereas addition of alkali metal salts shifted the coupling constants to those assigned to ion pairs. In general, the smaller cations caused the greater perturbations, as was found for the anion of p-chloronitrobenzene. ReddochI4 suggests that absence of metal splitting from spectra which show a cation-dependent proton splitting is caused by rapid dissociation and exchange of cations. I t is not clear what factors govern this exchange, which is usually found to be relatively slow especially in the ethereal solvents used. Another possibility is simply that interaction was too small to be detected under his conditions. When such very small coupling constants are involved and when they display extreme sensitivity to the nature of the environment, there are prob:tbly many factors which could cause this effect,one likely candidate being the presence of enough water to solvate the cation without actually removing it from the anion. Subtle changes in gaV values are also found on ion pairing. These shifts may stem from a modification of the levels of the anion as has been suggestedI5 for the anion of benzophenone. The effect of a cation close to oxygen is to shift spin density into the ring, reducing the orbital coni ribution which is due to spin on oxygen, but increasing the hyperfine coupling to the ring protons. I n other instances, especially for rubidium or cesium salts, spin-orbit interaction from spin on the cation may be iinportant. Examples of some of the small shifts that have been seen are given in Table 11. (ii) Modijication Involving Reduction in Symmetry. Reference has already been made to the likelihood that the cation will tend to wander around the surface of

large planar anions. If there is more than one site of high negative charge density, then the cation may tend to dwell in the vicinity of one for some time and to hop from one site to the other. The essential difference between the interaction of a cation with such anions and those of molecules like naphthalene is that, although, prior to ion pairing, the potential well in both cases may have a minimum at the center of the anion, in the former this can be induced to shift to give a negative charge centered on one or the other polar sites under the influence of an asymmetric environment, and with an over-all gain in energy. If the residence time is long compared with the resulting induced changes in hyperfine coupling constants, a new spectrum will be obtained which will reflect the reduction in symmetry. Thus in the case of the lithium salt of durosemiquinone discussed in section C (iii) the two methyl groups close to the lithium become different from the more distant pair, and two sets of hyperfine lines are detected. Although, in principle, an asymmetric solvation could give rise to the same effect, no such case has yet been reported, and so the effect can be taken as strongly diagnostic of ion pairing, even if no cation hyperfine coupling can be detected. The effect will be large or small depending upon the electronic structure of the paramagnetic ion and the magnitude of the perturbation. It is often of interest to compare the asymmetry induced by ion pairing with that resulting from protonation, which can, in a sense, be treated as a limiting effect. Examples are discussed in section C(ii).

C. Information from Line Widths I n this section a brief resume of the types of broadening that are found is presented, more with a view to seeing how far this can be used in the study of ion pairs rather than seeking a detailed understanding of the kinetics of relaxation. We consider separately broadening associated with changes in alkali metal hyperfine coupling and changes in hyperfine coupling to the anion nuclei. Superimposed upon these effects will be broadening stemming from spin-spin and spin-lattice interactions, but for dilute solutions in nonviscous solvents these do not interfere unduly. There are two general causes of line broadening, one based upon the lifetime of a given spin state and the other upon fluctuations in the actual energies of the two states. The former is dependent upon the uncertainty principle and causes a broadening when the lifetime of the spin state approaches the inverse of the ~

~~

(14) A. H. Reddoch, J. Chem. Phys., 43, 225 (1965). (15) A. H. Reddoch, ibid., 43, 3411 (1965).

Volume 7 1 , Number 1 January 1967

M. C. R. SYMONS

178

normal line width. As the lifetime is reduced, so the line broadens, but, depending on the system, this may ultimately result in the appearance of narrow "averaged" lines. I n general, both factors contribute together, and for the purpose of understanding the chemistry we do not need to differentiate between them. (i) Broadening of Hyper$ne Lines from Cation Nuclei. We consider the reactions

(ll+A-) (M+A-)

=

+ M+

(M+A-)l

+ A+ (A-M+)

M+ NI+

(M+A-)2

(1)

(2)

(3)

and the way the spectrum of A- is expected to change as the lifetimes of the different species decrease. Equilibrium 1 will be characterized by the separate spectra of R/I+A- and A-, weighted according to their relative concentrations. If RI+ has a nuclear spin of 3//2, as is often the case, then each hyperfine line of Awill be flanked by four lines of equal intensity from M+A-. As the rates increase and the lifetimes of each species decrease, one would expect both sets of lines to broaden. This is indeed found initially, but ultimately a spectrum characteristic of the anion (but with slightly modified magnetic parameters) with narrow lines is found. This happens because dissociation and recombination will not, in general, involve the same pair of ions, so that the nuclear spin states of the cation, as seen by the unpaired electron, are being very rapidly changed. This means that a single central line devoid of metal hyperfine coupling is found for M+A-, and this will combine with that characteristic of A- to give a single, slightly shifted line. Reaction 2 is the bimolecular equivalent of (1) and has the same effect provided the lifetime of the intermediate complex ;\I+A-;L3+ is short. Thus, for slow exchange, the spectrum of M+A- will be found, while for rapid exchange a spectrum very similar to A- but centered on the g and A values of M+A- will result. For example, Hirota and Weissman'e have shown that when sodium iodide is added to the sodium ketyl of xanthone, the spectrum of the ion pair broadens and ultimately changes to one characteristic of the solvated ketyl. This exchange is far more likely to occur when the radicals are prepared electrochemically since a supporting electrolyte is then used. It may often occur unwittingly, however, when alkali metals are used, since these may react slowly with the solvent or with impurities to give an unknown concentration of cations. If the M*A-hl+ complex has a long life, then one would expect to detect both M+A- and hl+A-R/I+, the latter being characterized by a septet from two equivalent cations of spin "2. Such spectra have often The Journal of Physical Chemistry

+3

- 21

-

- 1 2

+ 1

P

+h

Figure 1. Hypothetical spectra for two ion pairs in equilibrium, showing hyperfine coupling to a cation having IM = a / 2 and hyperfine coupling constants A1 and A*: (i) slow exchange, (ii) intermediate, and (iii) fast exchange.

been detected but are generally ascribed to ion tetramers rather than trimers; these are discussed in section D. Reaction 3 is meant to represent a change between two structurally different ion pairs having different metal hyperfine coupling constants. I n the limit, one of these could be zero. The essential factor is that the same cation is involved so that there is no smearing of the metal hyperfine coupling. Slow exchange will then give two sets of lines as shown in Figure 1 (i) for a nucleus of spin 3//2. On increasing the rates, each pair of lines will broaden and merge into a single broad line characteristic of each spin state. Since the h 3 / 2 lines cover a far larger range of field than the f1/2 lines, these will be very much broader [Figure 1 ($1, but ultimately, for fast exchange, a quartet of narrow lines will be observed [Figure 1 (iii)]. This sequence of line width is often found and has been ascribed to equilibrium 3 by Hirota and Kreilick.* The same effect would be produced if solvation and/or relative cation-anion orientations varied slightly from one ion pair to another. Since cation-anion interaction is largely electrostatic, this sort of uncertainty would be expected, especially for the polycyclic aromatic anions which have no small regions of very high (16) N. Hirota and S. I. Weissman, J. Am. Chem. Sac., 86, 2537 (1964).

ION-PAIR FORiKkTION STUDIED BY

charge density. Kormally, time averaging will be rapid, but at low temperatures and with viscous solvents, one might expect broadening to occur, and it mould be of the port envisaged. One major difference between these alternative explanations is that, in the former (reaction 3) in the limit of slow change, two distinct narrow-line spectra would be found, whereas in the latter, the lines would remain broad, their width being then a measure of the range of hyperfine coupling constants involved. The results reported here by Hirota show that the former situation can, indeed, occur. (ii) S p e c i j c Broadening of the Anion HyperJine Lines. In addition to the factors considered in section C(i), two important chemical processes will cause broadening of lines characteristic of the paramagnetic ions. One is the well-known electron-transfer process

+

179

ELECTRON S P I N RESONANCE

-1 0 +1 -1 -1 -1

(i)

0

0

-1 0 +1 +1+1 +1

0

Ill

bll

Ill I

I

+

A M+AA-;\I+ A (4) studied extensively by Weissman and co-workers, l7 which, in the limit of fast exchange, gives a single quartet from the cation at the center of the original spectrum. The anion lines are lost for the reasons given in section C(i) with respect to reaction 2. Again, if the transition complex, AM+A- has a long life, a new spectrum would result in which the cation interaction would be about the same, but the electron could be spread across both anions giving interactions with double the number of nuclei but with half the normal hyperfine coupling constants. No such spectrum has yet been observed. Even if such complexes never build up to high concentrations, their formation may contribute to line-width changes under favorable conditions. [The collapse in hyperfine interaction which results from the reactions given in ( 2 ) and (4)can be very useful as an aid to analyzing complex spectra. Thus, addition of excess A will give the hyperfine coupling to the cation unambiguously, while addition of a diamagnetic salt of this cation will remove this splitting, thereby reducing the number of lines by a factor of 41. One of the most interesting diseoveries in this field is that of alternating line widths. This is caused by the migration of the cation between specific equivalent sites in the anion at a rate comparable with the induced changes in the hyperfine coupling constants. The “static” situation was considered in section B(ii) and is illustrated in Figure 2(i) for the case of two equivalent nitrogen nuclei. Since 14Nhas a nuclear spin of unity, each nitrogen gives rise to a triplet. The free ion is then characterized by a 1:2:3:2:1 quintet, asalsoisthe ion pair when the cation migrates rapidly [Figure 2 (iv)]. For slow migration a nine-line spectrum will

-1 0 +1

I

-2

-1

0

+2

+1

Figure 2. Hypothetical spectra for a radical ion having two equivalent nuclei with IM= 1 but associated with a cation which induces a fluctuation such that NI has a hyperfine coupling of OL when N2 gives p and vice versa: (i) slow exchange, (ii) and (iii) intermediate, and (iv) fast exchange.

result, but when the time of residence of the cation at each site is similar to the inverse of the difference in the hyperfine constants, marked broadening occurs which only affects the second and fourth lines. The reason for this can be seen by reference to Figure 2(iii) where it is depicted as uncertainty in the position of these lines. I n the limit of extreme broadening, the spectrum will appear as a 1:1: 1triplet, apparently stemming from only one nitrogen nucleus but having twice the normal hyperfine coupling. This extreme, and confusing, limiting case will be encountered very rarely if the induced difference between the hyperfine coupling constants is small but will be of frequent occurrence if this difference is large relative to the total splitting. Just this situation arises with m-dinitrobenzene anions when, in the alkali metal ion pairs, the perturbation results in one nitrogen having a coupling of about 10 gauss and the other about 0.2 gauss. Hence, ions such as this quite often give rise to a spectrum characterized, apparently, by a single, strongly interacting nitrogen atom. This has resulted in considerable confusion in the past. (17) R.L. Ward and S . I . Weissman,J . Am. Chem.Soc., 79,2086(1957).

Volume 71,Number 1

Januarg 1967

M.C. R. SYMONS

180

Once again, observation of an alternation in line widths in the spectrum of an anion which is normally symmetrical does not prove the presence of ion pairs. If hyperfine splitting from the cation nuclei is detected, then the alternation almost certainly is a consequence of intramolecular cation migration (it must involve a single cation if the cation lines are narrow). If no cation interaction is found, then the effect may be the result of a fluctuation in solvation or in structure. This has been considered in depth by Fraenkel and co-workers** and again is strongly manifested by the m-dinitrobenzene anion and its derivatives. It is possible, however, that in a lot of this work ion pairs are still involved, since a fairly large concentration of carrier fllectrolyte is generally used. However, the discovery that addition of ethanol to m-dinitrobenzene anions in dimethylformamide causes marked alternation in widths with ultimate loss of the second and fourth linesIg and that this extreme broadening is still found in pure alcoholic solutions almost certainly rules out ion pairing as the cause. The contrast between the behavior of the anions of m-dinitrobenzene and duroquinone is interesting. As has been stressed, ion-pair formation induces an extremely large difference in the nitrogen coupling constants in the former, which seems to be a limiting situation since it is almost independent of the cation,’O and about the same as that caused by protonation of one of the nitro groups (AAN 10 gauss). I n contrast, the asymmetry induced in durosemiquinone is relatively ~ 2 gauss) compared small in the lithium salt ( A A M= with the monoprotonated radical ( A A M ~= 6 gauss).21 Results for p-benzosemiquinone are similar, with the distortion c-aused by lithium (AAH !x 0.75 gauss)22far smaller than that caused by protonation (AAH = 5.3 gauss),23 Many of the points made in the previous sections are well illustrated by durosemiquinone ion paired with a variety of cations in t-pentyl alcohol at room temperature.6 Thf> lithium salt shows hyperfine interaction with two different pairs of methyl groups and with the lithium nucleus. Thus, the lithium ion is tied down to one oxygen for a relatively long time. Replacement of lithium by sodium results in a spectrum [Figure 3(ii)] with every other line “missing.” The sodium quitrtet splitting is well defined and we conclude that the cation is migrating from one oxygen of the semiquinone to the other with a frequency in the region of 107-108sec-I. Addition of isopropyl alcohol causes the sodium ion pairs to dissociate, and, simultaneously, .4~,decreases [Figure 3(iii) 1. The spectrum of the potassium salt shows no metal hyperfine splitting, but there is still a well-defined line-

-

The Journal OF Physical Chemistry

Electron sDin resonance sDectra of sodium durosemiquinone in various solvents: (i) isopropyl alcohol, (ii) t-pentyl alcohol, and (iii) mixture of isopropyl and t-pentyl alcohols.

width alternation. The spectrum of the tetra-nhexylammonium salt shows no alternation and is almost identical with that of the freely solvated anion. Similarly at room temperature, the sodium salt of mdinitrobenzene shows sodium hyperfine structure together with two different nitrogen splittings and two different proton splittings (the protons concerned being equivalent in the free ion). The potassium salt shows agKhyperfine lines and anion hyperfine structure similar to that of the sodium salt except that many of the lines are greatly broadened. This broadening is the reverse of that usually found and can be understood in terms of a slow cation migration. The nitrogen lines broaden according t o the scheme shown in Figure 2(ii), and the proton triplets follow a comparable pattern. At room temperature the rubidium and cesium salts show just one large nitrogen splitting, but the protons have already become equivalent. On cooling, these change to give limiting spectra characterized by ~~

~

~~

(18) J. H. Freed and G. K. Fraenkel, J . Chem. Phys., 41, 699 (1964). (19) C. J. D. Gutch and W.A. Waters, Chem. Commun., 39 (1966). (20) T. A. Claxton, 1%’.M. Fox, and M. C. R. Symons, unpublished

results.

(21) T. A. Claxton, T. E. Gough, and M. C . R. Symons, Trans. Faraday SOC.,62,279 (1966). (22) E. A. C. Lucken, J . Chem. SOC.,4234 (1964). (23) T. E. Gough, Trans. Faraday Soc., 62, 2321 (1966).

I O N - P A I R FORMATION S T U D I E D BY

181

ELECTRON S P I N RESONANCE

weakly interacting triplet which gives rise to only a broad single line in the solid The former give very broad single-line spectra in fluid solution because the large magnetic anisotropy causes relaxation and broadening of the levels, while the latter give well-resolved fluid spectra with hyperfine lines from anion and cation nuclei. Perhaps the best examples of the former are the divalent metal chelates of the anions of 2,2'-bipyridine and related ligands.25 The solid-state spectra, for a wide range of cations (Be2+-Ba2+and Zn2+) and ligands, are fairly constant with a splitting between the outer shoulders generally between 150 and 200 gauss (Table 111). On a point-dipole model, this gives a mean separation between the electrons of about 7 A, which seems a fairly reasonable result for a neutral A-W+A- complex. The absence of an E term is taken to mean that the four nitrogen atoms are approximately tetrahedrally coordinated. Figure 4. Electron spin resonance spectra of the rubidium salt of m-dinitrobenzene in dimethoxyethane: (i) at 15", (ii) at - 6 5 O , and (iii) at -90".

parameters very similar to those for the sodium salt. These changes are illustrated in Figure 4 for the rubidium salt.

D. Ion Clusters I n addition to the triple ions, M+A-M+ and A-N + A - mentioned above, the quadruple ions (M+A-)2 are important and indeed seem to be the dominant species when clustering is detected by esr methods. Weissman and his c o - ~ o r k e r shave ~ ~ ~pioneered ~~ these studies, as indeed is the case with much of the work discussed in this paper. The results are clear-cut when solid-state spectra prove conclusively the presence of ground-state triplet species. For organic biradicals of this sort the line shapes for solids are dominated by electron spin dipolar interactions, which usually have near-axial symmetry (that is, with a large D term and a zero or small E term). A pair of lines consisting of a peak and shoulder is then found, the separation between the shoulders ( f 2 B ) or the peaks ( - B ) being directly linked to the effective separation (Y-~)-''' between the two electrons. I n view of the magnetic complexities revealed by studies of ion pairs, it is not surprising that, in general, results for ion clusters are even more diverse and complicated. Thus there appear to be at least two types of magnetic triplet species, one with clear-cut and relatively strong dipolar coupling (together with a characteristic AlIf = 2 line at half-field) and another

Table I11 : Doublet Separation (2B) and Calculated Mean Electron-Electron Separations Derived from Rigid Solutions of Some Triplet-State Ion Clusters Doublet sepn,

'/a,

(7-8)-

Anion of

Cation

gauss

4,7-Diphenyl-l,10phenanthroline

Be Mg Zn Ca Be Mg Zn Ca Sr Ba Be Mg K Na

190 196 225 121 168 172 198 145 154 156 238 240 161 326

6 6 6 7 7 6 6 7 7 7 6 6 6 5

Li Na

236 196 164 180 158

6.2 6.6 7.0 6.8 7.1

2,2'-Biquinoline

2,2'-Bip yridine

Hexamethylacet'one Fluorenone

K

Xanthone a

See ref 25.

Li Na

* See ref

A

Ref

75 67 3 52 0 95 7 25 15 11 24 2 95 6

a a a

a a a

a a a a

a

a a b

24.

The potassium complex gives a similar spectrum except that two extra shoulders are resolved. These arise (24) N. Hirota and S. I. Weissman, J . A m . Chem. SOC.,86, 2538 (1964). (25) I. M. Brown, S. I. Weissman, and L. C. Snyder, J . Chem. Phys., 42, 1105 (1965).

Volume 7 1 , h'umber 1

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AI. C. R. SYMONS

182

because the E term is no longer zero, which implies a loss of symmetry. This is explained in terms of a model in which one cation is coordinated tetrahedrally while the other, remaining close to the complex, destroys the symmetry.25 Various ketyl complexes seem to exist in both weakly and strongly interacting forms.24 The evidence for strongly coupled triplet species is again clear-cut and the results are closely similar to those described above. I n most cases estimated spin-spin separations (r-3)-”’ come to between 6 and 7 A. These complexes are favored in ethereal solvents by xanthone and fluorenone ketyls of lithium and sodium. On the other hand, most divalent cations and all salts of benzophenone seem to favor the weakly interacting species characterized by single lines with half-widths in the region of 10-15 gauss. The sodium salt of hexamethylacetone gives rise to a solid-state spectrum corresponding to (r-3)-”3 of 5.6 A. If one considers a model with a trans configuration R2CO“Na+OCeR2, with respect to the two ketyls, this distance is very reasonable since the major spin densities are on the carbonyl carbon atoms. One can then allow some of the spin density to spread out onto the aromatic rings for a similar complex involving the aromatic ketyls and approximate to the coupling by considering only the residual spin on the carbonyl groups. For a doublet splitting of 15 gauss this gives a spin density of about 0.3 on each carbonyl group, in fair accord with expectation.26 Thus, it seems that the intuitively most satisfactory structure is responsible for the weak interaction. The strong coupling must then be due to more closely held ketyls : various possible conformations are but none can be selected with any certainty. I n solution, the weakly interacting triplets give rise to quite well-resolved spectra because the relaxation induced by the tumbling motion is now no larger than that from fluctuation in electron-nuclear dipolar coupling. The most important result is that, for the alkali metal salts, two equivalent cations are found.24 The cation hyperfine coupling is quite similar to those found in ion pairs although there are interesting differences (Table I). I n contrast, spin exchange between the anions is slow so that each electron only interacts with the nuclei of one ring. This lack of exchange is reasonable for the weakly interacting complexes, especially if the two T systems are mutually perpendicular. The net result for these weakly coupled tripletstate clusters is that there is practically nothing to distinguish them from the doublet-state cluster M+A-M+. This would give virtually the same fluid and The Journal of Physical Chemistry

solid-state esr spectrum as the (M+A-)2 species envisaged. The main points in favor of the latter, apart from those already listed, are chemical expectation and the slow rate of loss of one cation, which is not expected for the species M+A-&I+. The observation that the species containing two cations exchanges electrons with the parent ketone at a rate too slow for measurement by esr line-broadening methods does not distinguish between these alternatives since the process A+ M+A-M+ M+A-?(’I+ A would be expected to be slow. The ion clusters containing the cations detected by Reddoch16 are probably weakly coupled triplet radicals, and absence of any characteristic solid-state spectrum is in accord with expectation since the solution spectrum consist of narrow lines. However, there seems to be no compelling reason for making this choice, and the species M +A-Jl+ cannot be ruled out. We conclude that in the general field of ion-ion interactions in solution, esr methods are revealing many intimate details, especially with respect to the structure of the resulting pairs and clusters, but also with respect to the kinetics of the reactions involved in their formation and interchange.

+

Acknowledgment. Thanks are offered to Drs. &J. I. Blandamer and T. A. Claxton for helpful discussions.

Discussion T. R. TUTTLE, JR. (Brandeis University, Waltham). With regard to the difference between the explanations of the temperature dependence of alkali metal splittings due to Weissman and Hirota, if degrees of freedom involving the solvent are included in Weissman’s sum over vibrational states, the two treatments become indistinguishable. Differences become a matter of semantics. G. K. FRAENHEL (Columbia University, New York, N. Y . ) . Although in principle Tuttle is right, concrete physical models of the type suggested by Symons are frequently more useful descriptions than infinite unevaluable sums.

T. R. TUTTLE, JR. My concern is not with the utility, but with the connection between the two different approaches. I agree that there is a difference between the two approaches if the two species are of different compositions. Whether compositions differ is a question to be decided by experiment.

T. E. GOUGH(University of Waterloo, Ontario). I should like to comment on the results obtained for the ion pair sodium+, durosemiquinone-. Under suitable conditions it is possible to observe simultaneously both the free-ion and the ion-pair species. The spectrum of the ion pair shows extreme line-width alternation, which we interpret in terms of cation exchange between the oxygens of the anion. We are, therefore, led to conclude that the rate constant for the intramolecular process is higher than that for the dissociation of the ion pair. This would suggest that the ion pair is a contact ion pair. (26) G . K. Fraenkel and R. H. Rieger, J.Chem.Phys.,37,2811 (1962).