127
EPRSTUDIESOF ION-PAIR EQUILIBRIA
Electron Paramagnetic Resonance Studies of Ion-Pair Equilibria
by Noboru Hirota Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York (Received September P7, 1966)
The epr evidence for the presence of several structurally different ion pairs is given for hydrocarbon and ketyl radical ions in ether solution. Temperature dependence of the alkali metal splittings and the line widths of the hyperfine splittings were measured and interpreted in terms of rapid equilibria among different ion pairs. Equilibrium constants, rate constants, and AH', AS", and AH* for several equilibrium processes were determined. The relationship between rapid ion-pair equilibrium and the rate of electrontransfer reaction is discussed. The magnitudes of alkali metal splittings and their connection to the structure of ion pairs are discussed.
I. Introduction A number of epr investigations of ion-pair radical ions have appeared in the literature, following the pioneering work of Adam and Weissman' and Atherton and Weissman.* There are, however, several important aspects which have not been fully understood. In particular, the following points are not well understood. (A) Although the presence of alkali metal splittings in the epr spectra of radical ions confirms that radical ions form ion pairs, the exact structure of the ion pairs is not known. The question whether or not an ion pair is contact or solvent shared has not been answered definitely. (B) Temperature dependence of the alkali metal splittings has been observed in a number of systems,2-e but the mechanism to produce such a temperature dependence is not well established. (C) Several mechanisms to explain the spin density at the alkali metal nucleus have been proposed2,4*' and several theoretical estimates have been made. The solution to this problem, however, is far from being well established. (D) In certain systems negative apparent activation energies were observed for the rapid electrontransfer reaction between radical anion and neutral molecule.8 The cause of the production of such negative apparent activation energies, however, has not yet been given clearly. The present article describes our attempts to clarify these points. Most of our interpretations are based
on the proposition that there are rapid equilibria among different ion pairs. Some preliminary results concerning this proposition have been reported recently by Hirota and K r e i l i ~ k . ~During the course of the present investigation, Smid,'O Szwarc,ll and their co-workers reported detailed studies of the optical spectra of radical ions and the electrical conductivities of ether solutions of radical ions. Both their results and ours indicate the existence of structurally different ion pairs. Some of the results described here are still preliminary and the details will be reported in the later reports.
11. Experimental Section Preparation of the radical ions was made according to the standard procedures described previously.'* ~~~
~
(1) F. C. Adam and S. I. Weissman, J . Am. Chem. SOC.,80, 1518 (1958). (2) N. M. Atherton and S. I. Weissman, ibid., 83, 1330 (1961). (3) N. Hirota and S. I. Weissman, ibid., 86, 2537 (1964). (4)E. de Boer,Rec. Trav. Chim., 84, 609 (1965). (5) P.R.Ayscough and R. Wilson, J. Chem. SOC.,5412 (1963). (6) H. Nishiguchi, Y. Nakai, K. Nakamura, K. Izhisu, Y. Deguchi, and H. Takaki, Mol. Phys., 9, 153 (1965). (7) S. Aono and K. Oohashi, Progr. Theoret. Phys. (Kyoto), 30, 162 (1963). (8) P. J. Zandstra and 9. I. Weissman, J. Am. C h m . Soc., 84, 4408 (1962). (9) N. Hirota and R. Kreilick, ibid., 88, 614 (1966). (10) T. E.Hogan-Esch and J. Smid, ibid., 87, 669 (1965); 88, 307, 318 (1966). (11) C. Carvajal, J. K. Toelle, J. Smid, and M. Sswarc, ibid., 87, 5548 (1965); R. V. Slates and M. Szwarc, J . Phys. Chem., 69, 4124 (1965).
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January 1967
NOBORU HIROTA
128
gauss
3.0
2.0
I .o
*C Figure 1. Temperature dependence of alkali metal splittings in anthracenide: 0, sodium splitting; A, potassium splitting; 0, cesium splitting. Solvent used: (1) DBE, (2) DEE, (3) 60% DEE 40% MTHF, (4) MTHF, (5) 65% MTHF 35% THF, (6) 35% MTHF 65% THF, (7) 70% DEE 30% THF, (8) DEE, (9) MTHF, (10) MTHF 0,T H F 0, and (11) DME.
+
+
+
+
All of the epr spectra were taken with a Varian 4502 spectrometer with 100-kc field modulation equipped with a field dial and variable-temperature control unit. Temperature was found to be accurate within i=3" over the whole temperature ranges of our present interest. Preparation of the radical ions was made in several different solvents, such as 1,Zdimethoxyethane (DME) tetrahydrofuran (THF), 2 methyltetrahydrofuran (MTHF), diethyl ether (DEE), n-dibutyl ether (DBE), and N,N-dimethylformamide (DMF). Studies of the rapid electron-transfer reactions were carried out according to the similar procedures previously described.l 3 The concentrations of the negative ions are usually 10-6-10-4 M .
kali Metal Splittings. Alkali metal splittings (Na, I(, and Cs) of the various ion pairs derived from anthracene and naphthalene in different solvents at various temperatures are summarized in Figures 1 and 2. There is a close resemblance between the temperature dependence in the two systems indicating that the fundamental natures of the ion pairs in both systems are similar. In both cases sodium splittings decrease as the temperature goes down. Cesium splittings in MTHF and T H F and potassium splittings in DEE and DBE were found to be rather temperature insensitive and slightly increased at lower temperatures. This behavior is very similar to what was observed by Nishiguchi, et a1.,6 in biphenyl radical
111. Results A . Hydrocarbon Radical Ions: Anthracene and Naphthalene. 1. Temperature Dependence of the Al-
(12) For example, T. R. Tuttle, Thesis, Washington University, 1957. (13) M.T. Jones and S. I . Weissman, J. Am. Chem. SOC.,84, 4269 (1962); N. Hirota, Thesis, Washington University, 1963.
-
The Journal of Physical Chemistry
129
EPRSTUDIESOF ION-PAIR EQUILIBRIA
Figure 2. Temperature dependence of alkali metal splittings in naphthalenide: 0, sodium splitting, A, potassium splitting; 50% THF, (3) THF, (4) DEE, and (5) MTHF. 0,cesium splitting. Solvent used: (1) DEE, (2) 50% DEE
+
ions. The magnitudes of the sodium splittings in DEE or DBE were found to be much larger than those reported so far2v6(2.14 gauss in sodium naphthalenide in DEE and 2.94 gauss in sodium anthracenide in DBE at 52"). Sodium naphthalenide in DEE is worthy of special attention. As is shown in Figure 3, two spectra due to two different species are superimposed. Around -loo", two superimposed spectra show sodium splitting of two different magnitudes (1.05 and 0.058 gauss at - 100"). The larger sodium splitting is temperature dependent as shown in Figure 2. The smaller sodium splitting seems to be temperature insensitive at low temperatures, but broadenings of the lines prohibited the resolution at higher temperatures. This observation gives direct epr evidence of the presence of structurally different ion pairs which are interconverting slowly (the conversion rate is slower than lo6sec-l). 2. Temperature Dependence of the Line Width. I n several systems it was found that the line widths of
the components of metal splittings depend on the magnetic quantum number of the alkali metal nucleus ( M z ~ ) .In several sodium radical ions hyperfine lines with MzNs = f lines were found to be broader A clear example is than those with MzNa = *1/2. seen in Figure 4 in which temperature dependence of the line widths of four sodium splittings in sodium naphthalenide in the mixed solvent of T H F and DEE is shown at various temperatures. It is clearly seen that two outside lines of the sodium hyperfine lines are completely broadened out at - 100". In many other systems (sodium anthracenide in MTHF and in DEE, sodium naphthalenide in DEE) dependence of the line width on MzNawas observed at low temperatures. In sodium anthracenide in DBE a spectrum was completely broadened out at lower temperatures, but another spectrum with different magnitude of sodium splitting appeared at further lower temperatures. 3. Rates of the Electron-Transfer Reactions. Rates Volume 71,Number 1 January 1967
KOBORU HIROTA
130
-1
00
'c
Figure 3. Sodium naphthalene in DEE at three temperatures. Lines indicated by arrows belong to the weakly associated ion pair. This species shows 0.058-gauss sodium splitting at - 100'.
+
+
of the electron-transfer reactions R-M+ R eR R-M + or RR S R R- were measured in sodium anthracenide in DME, MTHF, and the mixed solvent of MTHF and THF. Some preliminary results of the observed rates at various temperatures are shown in Figure 5 . Although the low solubility of anthracene and the complication due to the existence of sodium splittings prohibited the accurate determination of the rates over wider temperature ranges, it is clear that the ion-pair formation of MTHF slows down the rates by a factor of lo2 compared to the rates in DME in which ions are probably dissociated. In a mixed solvent of MTHF and THF, the magnitudes of the rate constants were somewhere between the above two values and they also depend on the mixing ratio. The plot of log k vs. 1/T in the mixed-solvent systems changes the slope from negative to positive where the sodium splitting starts to decrease sha.rply. This behavior is very similar to what was observed in sodium naphthalene in THF by Zandstra and Weissmam8 B. Ketyls. Since the detailed results on ketyl ion pairs are going to be reported elsewhere, we only describe some relevant observations in the present paper.
+
+
The J O U Tof ~Physical Chemistry
1. Temperature and Metal Dependence of the C13 Splittings in Ketyls. Temperature dependence of the carbonyl C13 splittings of various fluorenone monomer ketyls is shown in Figure 6. Metal splittings in fluorenone ketyls generally decrease at lower temperatures as in the benzophenone and xanthone ketyls reported in ref 3. One interesting observation is that the lithium splitting seems to change sign as the temperature goes down. This is very similar to what de Boer observed in pyracene negative ions.4 Figure 6 clearly shows that CI3 splittings of these ketyls decrease at low temperature. 2. Rigid-Media Epr Spectra of Hexamethylacetone and I t s Temperature Dependence. Rigid-media epr spectra of hexamethylacetone ketyls of various alkali metals were obtained at 77°K. The spectrum of sodium hexamethylacetone ketyl is shown in Figure 7(1). This spectrum indicates the existence of two species: one species with large spin-spin dipole interaction and the other with very small or zero dipole interaction. Figure 7(2) shows the spectrum obtained at 153°K which shows a weak spectrum due to the species with large dipole interaction and the central peak with seven hyperfine splittings due to two sodium ions attached to the ketyl negative ion.
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EPRSTUDIES OF ION-PAIR EQUILIBRIA
-75°C
-
I
I
-85°C
--------'L---\--
I
I
I
I
- 9 5 "C
-b
1.5 G 4-
Figure 4. Temperature dependence of the line width of sodium naphthalenide spectra in the mixed solvent of T H F (25%) and DEE (75%). Stick diagram indicates the expected relative intensities of hyperfine lines in the absence of the broadening due to the exchange process.
IV. Analysis and Discussion This paper does not describe the equilibrium process involving cluster or triple-ion formation in hydrocarbon negative ions, although such equilibrium processes are discussed briefly in ketyls. Ion cluster or tripleion formation could possibly exist in hydrocarbon negative ion systems depending on the nature of solvent and temperature. In the present paper, however, we are concerned with the ion pairs which are characterized by the presence of four sodium splitthgs. The possibility of the existence of different types of ion pairs such as ion cluster is the subject of further investigations. A . Perturbation of the HyperJine Splittings and the Structure of the Ion Pair. 1. Perturbation of Proton Hyperfine Splittings. Reddoch recently reported that the proton hyperfine splittings in anthracene are very sensitive to the perturbation due to the positive ion."
Since the magnitude of sodium splitting varies from almost zero to about 3 gauss, we have attempted to correlate it with the magnitude of proton hyperfine splitting. Figure 8 shows the correlation between the sodium splitting and the proton hyperfine splitting due to the protons at the 1,4,5,and 8 positions. Although the measured points are slightly scattered, a clear correlation between the proton and the sodium hyperfine splittings is seen. Similar correlation was also found for hyperfine splittings due to other protons. This correlation diagram reveals several interesting features. (1) The magnitude of sodium splitting and the size of the perturbation of the proton hyperfine splitting are uniquely related. Whenever a large sodium splitting was observed, a large perturbation on the proton splittings was observed. This would imply that in the (14)A. H. Reddoch, J . Chem. Phya., 43, 225 (1965).
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separation between potassium ion and the negative ion in potassium anthracenide in DEE. This implies that the positive and the negative ions in these ion pairs are more separated than one would expect from the contact ion pair structure separated with the van der Waals and ionic radii of negative and positive ions. Counterions are probably more separated because of the interaction of solvent molecules with the positive ion. The real structure of the ion pair in solution is still a matter for speculation, but one may consider possible models of various different types of ion pair structures with different degrees of solvation as illustrated below.
k M1src'
I
os
I Oe
I' 0 1
3.0
3.5
3.9
I /T
4.1
+
ion pair with large sodium splittings the average separation between the positive and negative ions is closer so that the spin density distribution in the anion is more perturbed. (2) Decrease in the magnitude of sodium splitting actually means that the positive and the negative ions are more separated. (3) Since the cesium splitting in MTHF and the potassium splitting in DEE are insensitive to temperature and increase only slightly at lower temperatures, the cesium and potassium anthracenides may be considered to be a contact ion pair or nearly a contact ion pair.14& (4) For sodium anthracenide (and also naphthalenide), the structure of the ion pair may approach that of a contact ion pair in DEE and DBE at higher temperatures. However, for the ion pair in MTHF and in the mixed solvent of MTHF and THF, perturbation due to the positive ion is smaller than in potassium anthracenide in DEE. This indicates that the separation between the sodium ion and the negative ion in these ion pairs is considerably larger than the The Journal of P h y s d Chembtry
3
x I d3
Figure 5. Rate constants for the electron-transfer reaction in sodium anthracenide. Solvent used: 0, DME; H,65% MTHF 35% THF; A, 70% MTHF 30% THF; 0,MTHF.
+
2
4
5
It should also be noted that the observed perturbation of the proton hyperfine splittings in sodium ion pairs is much larger than those calculated by Reddoch14 based on the model in which the positive ion is located on the ring and the distance from the plane of the ring to the positive ion is 3.2 A. 2. Perturbation of C13 Splitting. The C13 splitting of the carbonyl carbon in fluorenone changes with temperature as shown in Figure 6. The metal splitt,ings decrease in these systems as the temperature goes down. A correlation between the C13 splitting and the metal splitting like that between the hydrogen and the metal splittings in sodium anthracenide was also observed. The large dependence of the CI3 splitting on the nature of the positive ion is accounted for by the perturbation of spin density by the electrostatic interaction between ions. Stronger electrostatic interaction in the ketyls (14a) NOTEADDED IN PROOF.Bolton and Fraenkel mezsured 2.66 gauss proton splitting in the anthracene anion electrolytically reduced in DME with tetra-n-butylammonium perchlorate as a supporting electrolyte ( J . Chem. Phys., 40, 3307 (1964)). This splitting is about the same as that found in cesium anthracenide in THF. The radius of tetra-n-butylammonium ion was estimated to be 3.1 f 0.2 A for a folded structure. (G. N. La Mar, ibid., 43, 235 (1965)). This may suggest that cesium anthracenide is s t i l l not a real contact ion pair.
133
EPRSTUDIES OF ION-PAIR EQUILIBRIA
(2)
80
40
-40
0
-80
KO
C'
Figure 6. Temperature dependence of carbonyl C1* splittings in fluorenone ketyls: 0, lithium fluorenone in DME; A, sodium fluorenone in DME; 0,sodium fluorenone in THF; 0, potassium fluorenone in DME; 0,cesium fluorenone in THF; cesium fluorenone in DME; e, 0, A, sodium fluorenone in DMF.
.,
with smaller positive ion places more spin density on the carbonyl carbon and less on the oxygen atom. Thus one can expect larger C13 splittings for the ketyls with larger electrostatic interaction on the basis of the Fraenkel and Karplus e q ~ a t i o n . ' ~In ketyls one would expect small metal splitting when the metal ion lies on the nodal plane of 2p orbitals and the decrease in the metal splitting may not mean that the positive and the negative ions are more separated at lower temperatures. The decrease in the CI3 splittings at lower temperatures, however, indicates that the positive and the negative ions are more separated at lower temperatures as in hydrocarbon radical ions, although this may not be the sole mechanism reducing the magnitude of the alkali metal splittings. B. 1 . Temperature Dependence of the Metal Splittings. We have attempted to interpret the temperature dependence of the sodium splitting in terms of rapid equilibria among structurally different ion pairs. In the simplest case we may consider only two ions pairs, A and B. This two-jump model ade-
Figure 7. (1)Sodium hexamethylacetone in MTHF a t 77°K. (2) Sodium hexamethylacetone in M T m at 153OK. (3) Integrated curve of (1). In (1)and (2) the central peak was obtained with the modulation amplitude and the gain specsed in the figure.
quately explains the temperature dependence in many systems. The rapid equilibrium is given by ki
A Z B k l
Two distinct ion pairs, A and B, have different sodium splittings CYAand CYB,and the probability of finding form A and form B is given by PA and PB, respectively. The equilibrium constant K is given by
K = - P=B ? ! = PA
?A
kl IC-1
(1)
and T B are the lifetimes of the A and the B forms. In the limits of rapid exchange the observed sodium splitting C Y Nis~given by
TA
The temperature dependence of the sodium splittings (15) M. Karplua and G . K. Fraenkel, J . Chem. Phye., 35,1312 (1961).
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134
Sodium Sodium naphSodium anthracenide in Sodium thalenide in anthracenide THF-MTHF naphthalenide THF-DEE in MTHF (50:50) in THF (50: 50)
sou66
AHo,kcal ASo,eu 2.70
-4.6f0.3 -23f3
--6.2*0.5
-4.8f0.5 -20&4
-25f3
--6.4*0.8 -33f4
Temperature dependence of the sodium splittings in other cases may be treated in a similar way. However, we do not know the splittings CYAand CYBaccurately in many cases, and the quantitative estimates of AH" and ASo cannot be made for many other systems. If more than two different ion pairs are in equilibrium, the simple analysis described here cannot be applied. AH" values for sodium anthracenide and sodium naphthalenide in DEE would possibly be smaller than those given above, because the temperature dependence of the sodium splittings in these systems is less sharp than in sodium anthracenide in MTHF. 2. Temperature Dependence of the Line Width and the Rate Constants for the Interconversion among Ion
2.60
H
2.50
24(
I .O
0.0
2 -0 N3
Figure 8. Correlation diagram between sodium splitting and proton hyperhe splitting in anthracene radical ions. Two horizontal lines indicate the value of proton splittings in potassium and cesium anthracenides: 0 MTHF; A, MTHF (65%) THF (35%); W, DEE; 0,DBE.
K
'
o
~
r
+
in anthracenide in MTHF shown in Figure 1 suggests the existence of such equilibrium between two ion pairs below 40'. Another equilibrium seems to be starting a t higher temperatures, because the sodium splittings increase slightly with the temperature above 80". It appears that the similar types of equilibria are also taking place in sodium naphthalenide in THF and in the mixed solvents of DEE and THF, but the separation of the two different equilibrium processes does not seem to be so clear as that in sodium anthracenide in MTHF. Through the use of eq 2, equilibrium constants were determined for several systems with the proper choices of CYAand CYB. Some examples of the plots of log K US. 1/T are given in Figure 9. It is seen that reasonably good straight lines were obtained for these plots. The ion pair A has a large sodium splitting and B has very small splitting. We call them tight ion pair and loose ion pair, respectively. The obtained thermodynamic quantities for the equilibrium A B are listed at the top of the next column. The Journal of Physical C h a G t r y
B ~
O0
'3.2
3.6
4.0
4.4
5.2
5.6
4
II T
Figure 9. Temperature dependence of the equilibrium constants for the changes from the tight ion pair (A) to the loose ion pair (B) (avalues in gauss): (1) sodium anthraceneinMTHF: CZA = 1.55, a B = 0; (2)sodium anthracene in 65% MTHF 35% THF: CYA = 1.55, ~ t g= 0; (3) sodium naphthalene in THF: ab = 1.15, OLB= 0; (4) sodium naphthalene in 75% DEE 25% THF: CYA = 1.00, a g = 0.
+
+
EPRSTUDIESOF ION-PAIR EQUILIBRIA
135
Pairs. Temperature dependence of the line width of the hyperfine splitting is analyzed using the wellknown formula of exchange narrowing. The contribution of the exchange process to the line width is given in the limit of rapid exchange16
+
(1/7'2)ex = PA~PB'(WA - W B ) ~ ~ AK()~
(3)
where WA and WB are the resonant frequencies of ion pairs A and B. If the proton hyperfine splittings and g values remain the same in two different ion pairs, one can substitute (208 - WB) = M Z ~ ' ( C U-A C Y B ) ~into eq 3, assuming high-field approximation. CYA and CXB are the sodium hyperfine splittings in A and B. In this case (l/Tz)ex is proportional to the square of M z N a and it is expected that +3//z and -3//z (1,12 and -1/2) lines have the same line widths, provided that the relaxation due to the ion-pair equilibria is the predominant one compared to the other types of relaxation included in the usual general theory of relaxation." Proton hyperfine splittings are actually perturbed by the counterion, and each hyperfine component of the four sodium splittings has different WA - WB and different broadenings. Nevertheless, the outside lines were found to be much broader than the inside lines in many systems. This situation is clearly seen in sodium naphthalenide in the mixed solvent of THF and DEE (Figure 3). The observed line width dependence on MaN" agrees well with the prediction of eq 3, when the small changes in proton hyperfine splittings in different ion pairs are taken into consideration. T A values were estimated for several systems. T B values were also estimated from TA and K . From the observed temperature dependence of kl and L1, AHl and AH-1 were also estimated. Some of the preliminary values are given below. More accurate and detailed analysis of the line width in these systems will be reported later.
*
Sodium anthracenide in MTHF
kl,sec-l
kl, sec-l
*,
AH1 kcal AH1*, kcal
5 X l o 7 (at -60') 4 X IO8 (at -60') 3.0 7.4
*
Sodium naphthalenide in THF-DEE (25 : 75)
1 X 10' (-80') 7 X 108 (-80') 6.0 11.5
Sodium splittings with unequal intensities were observed in other systems, and the following preliminary crude estimates of the lifetimes are given: sodium 5 x 10-9 sec at -90"; naphthalenide in DEE, T A sodium naphthalenide in THF, T A S 5 X sec at -50". In all cases A refers to the tighter ion pair.
C. Equilibrium among Different Ion Pairs. On the basis of the observation and analysis given so far, we can describe the equilibria among different ion pairs. 1 . Sodium Anthracenide in MTHF and in the Mixed Solvent of the THF and MTHF. The sodium anthracenide ion pair at +50" seems to be the tight ion pair with sodium splitting of 1.55 gauss. At temperatures from room temperature to -70" the spectrum is characterized by that of two ion pairs in rapid equilibrium. At temperatures between -75 and -100" we observe the spectrum of ion pairs in rapid equilibrium and the spectrum of another species which is either a free ion or a very weakly associated ion pair. The nature of the latter species is not unambiguously assigned at this moment and will be studied further, but the preliminary results on the concentration dependence seem to suggest the existence of the equilibrium between a loose ion pair and a free ion at these temperatures. Reddoch's observation of the slight change in hyperfine splitting by dilution in THF14 also suggests the presence of the equilibrium between a weakly associated ion pair and a free ion. We temporarily postulate that the new spectrum which appears at -75" is a free ion. Summarizing these results we can write the equilibria
ki
R-Na+ C Y N> ~ 1.55 gauss (4
R-Na+ C Y N'V ~ 1.55 gauss (b)
R~
-
Na+ N B 0 (4
A
R-
+ Na+
high temperature -+-+low temperature IC1
-
5 X lo7 sec-' at -60"
As we discussed earlier, the ion pair b is a tight ion pair, but the ions are more separated than we expect from the van der Waals and ionic radii. (Tight ion pair b has 1.55-gauss sodium splitting and 2.62-gauss proton splitting, but sodium anthracenide in DBE has 2.9gauss sodium splitting and 2.44-gauss proton splitting.) The equilibria shift to the right at lower temperatures. The addition of THF also shifts the equilibria to the right. From the studies of the thermodynamic quantities described earlier we can construct an energy diagram for the various ion pairs as shown in Figure 10. (16) J. A. Pople, W. G. Schneider, and H. J. Bernstein. "High Resolution Nuclear Magnetic Resonance," McGraw-Hill Book G o . , New York, N . Y., 1959, p 222. (17) (a) J. H. Freed and G. Fraenkel, J . Chem. Phys., 39,326 (1965); (b) A. D. McLachlan, Proc. Roy. SOC.(London), A280, 271 (1964).
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136
tZ?
----T-q
T A H ! = - 3
MTHF
Kcal
in sodium naphthalene in T H F which transfers electrons at the rate of lo9 mole I.-' sec-' with the activation energy of a few kilocalories. This seems to show the existence of the real free ion besides the species studied by Zandstra and Weissman.8 4. Sodium Naphthalenide in DEE. The data for this ion pair can be adequately explained by postulating the presence of three ion-pair species. fast process
R-Na+
slow process
eR-Na+ e. R-Na+ (a)
CYNa
Figure 10. Energy diagram for various ion pairs.
The details of sodium anthracenide in various solvents will be given later. 2. Sodium Anthracenide in DEE. The sodium anthracenide ion pair in DEE appears to be in a rapid equilibrium between two or more different tight ion pairs. The high-temperature form of the tight ion pair approaches more nearly the true contact ion pair.
CYNa
R-Na+
R-Na+
(a)
(b)
> 2.8 gauss
C Y N ~=
2.0 gauss
3. Sodium Naphthalenide in THF. As the temperature dependence of the sodium splitting indicates, the nature of sodium naphthalenide in THF is very similar to that of sodium anthracenide in MTHF, except that the equilibrium is shifted to higher temperatures. Again at higher temperatures this is the rapid equilibrium mixture of the tight ion pair, the loose ion pair, and the other species without sodium splitting.2 Zandstra and Weissmans measured the rate of the electron-transfer reaction of this system. The rate of electron transfer for the species without sodium splitting is faster than that for the species with sodium splitting, but it is slower than that expected for the free ion. The activation energy determined for the species without sodium splitting was also found to be abnormally high. Therefore, this author speculates that the species without sodium splitting is some kind of ion pair rather than a free ion.2 Recently, Johnson and ChangIs detected the existence of another species The Journal of Physical Chemistry
(1) > 2.2 gauss
CYNa
(b)
(2) E 0.8 gauss
=
(3) 0.06 gauss
Step (a) is obviously a fast step with rate constant k 2 lo8 sec-I at 20 to -80". Step (b) must be a very slow process since we observe two spectra with two different sodium splittings at low temperatures. 6. Sodium Naphthalenide in the Mixed Solvents of THF and DEE. Temperature dependence of the sodium splittings in the mixed solvents of T H F and DEE shows that the equilibrium processes in this solvent are basically similar to those in T H F except that the equilibrium is shifted toward the left at the same temperature. This also indicates that THF preferably solvates around the sodium ion, and the structure of the tight ion pair is similar unless the mixing ratio of DEE is very high. The equilibrium between tight and loose ion pairs in these mixed solvents is shifted toward lower temperatures than in pure THF, and the line width dependence on MzNa is very clearly seen (Figure 3). This shows that the ion pair equilibria are responsible for the temperature dependence of sodium splittings in THF and in the mixed solvents of THF and DEE. 6. Potassium and Cesium Naphthalenides and Anthracenides. Temperature dependencies of the cesium splittings in cesium naphthalenide and anthracenide in THF and MTHF are very similar. Cesium splittings in both systems slightly increase at lower temperatures. Cesium anthracenide in DAIE shows the equilibrium between two species, one species with cesium splitting of 0.45 gauss and another without cesium splittings. A t 25" the species with 0.45-gauss cesium splittings was found almost exclusively, but at -80" the species without cesium splitting was found almost exclusively. Therefore, the more solvation of DME toward cesium at lower temperature is clear and DME and T H F behave quite differently in this respect. Potassium splittings of potassium anthracenide and naphthalenide in DEE also behave in a similar manner. (18) R. Chang and C . S. Johnson, J . Am. Chem. SOC.,88, 2338 (1966).
EPRSTUDIES OF ION--PAIR EQUILIBRIA
From these observations it is quite clear that the ionpair structure in these cases does not change much with temperature except for cesium anthracenide in DME. Slight increases in the magnitudes of splittings at lower temperatures might mean slightly closer approaches of ions a t lower temperatures but definite statements cannot be made at this stage. These ion pairs are tight ion pairs. The magnitudes of cesium splittings in T H F and MTHF are almost identical and slightly smaller in DME. This seems to show that the structure is not very sensitive to the solvent and close to the contact ion pair. Further studies are being carried out in order to clarify the nature of ion pairs with large cations. '7. Ketyls. Detailed results on ketyls will be reported elsewhere. The observations on the temperature dependencc of the metal and C13 splittings seem to be interpreted by the rapid equilibrium among different ion pairs. Since ketyls have a negatively charged carbonyl group, they would form a contact ion pair more easily, and it is expected that the ketyl ion pair approaches the contact ion pair at higher temperatures. 8. The Nature of the Equilibrium and the Thermodynamic Quantzties. AH" = -4.6 kcal and AS" = -23 eu were obtained for the change from the tight ion pair A to the loose ion pair B, in sodium anthracenide in MTHF. Similar values are obtained for other systems. As discussed previously,* large negative changes in AH" and AS" indicate the stronger solvation in loose ion pairs. It also indicates the presence of strong interaction between solvent molecules and positive ions. Large magnitudes of AH" and AS" would probably imply that a large change in solvation sphere is taking place in going from the tight ion pair A to the loose ion pair B. Such changes in AHo and A S o could be interpreted by the change in ion pair structure from structure 2 and 3 in the previous model, although our discussion is highly speculative. Smaller negative AH" and A S o were estimated for the change between two forms of tight ion pairs in sodium anthracenide and naphthelenide in DEE. This change may be represented by the change from the structure 1 to 2 and may not require a large change in the solvation sphere. This change may take place with a faster rate constant than the change between structure 2 and 3. More detailed discussion of the changes in thermodynamic quantities in (Gonnection with the change of ion-pair structure will be given later. D. Rapid Ion-Pair Equilibrium and Electron-Transfer Reaction. Since the electron-transfer reaction between a loose ion pair and a neutral molecule could possibly be -IO2 times faster than that between a tight
137
ion pair and a neutral molecule, we may expect a drastic change in rate depending on the position of the equilibrium. Thus, if the change of the relative concentration of the tight ion pair to the loose ion pair with respect to temperature is sufficiently large, we can expect that the rates of electron transfer increase at lower temperatures and give apparent negative activation energies. Such phenomena were discovered by Zandstra and Weissman8 in sodium naphthalenide in T H F in the temperature range where the sodium splitting is changing rapidly. We have tried to see the similar phenomena in sodium anthracenide, since the nature of the ion-pair equilibrium is very similar. In the proper mixture of T H F and MTHF, sodium splitting starts to change sharply around 0". I n these solvents the rates were found to increase at lower temperatures as expected from our model. Therefore, the data on the rates of electron-transfer reaction are consistent with our model of the rapid ion-pair equilibria. E . Epr Evidence on the Presence of Contact and Solvent-Shared Ion Pair. I n the previous sections we have shown that epr studies indicate the existence of the equilibrium mixture of the structurally different ion pairs. We describe here direct epr evidence of the presence of two structurally different ion pairs, namely contact and solvent-shared ion pairs. The spectrum of sodium hexamethylacetone ketyl in MTHF rigid media can be interpreted with the superposition of two spectra due to two species. The spectra of the species with large dipole interaction can be well fitted to a spin Hamiltonian X
= g/3H.S
+ D S Z 2+ E ( S Z 2- Sy2)
with E E 0 and D = 0.0155 ern-'. The central peak with small dipolar interaction was assumed to be due to a dimer ion pair with small dipole interaction from the fact that this species interacts with two sodium ions.lg The value of D in the species with large dipole interaction can be well accounted for by assuming that it forms a contact ion pair shown below. We have calculated the expected value of D , assuming the structure shown by (A) below and assigning the spin density to the carbon and oxygen atoms by Hiickel MO calculation. The calculated value of D agrees well with the experimentally observed value of D. The D values for ketyls with different metals (19) Besides the fact that one ketyl negative ion interacts with two sodium ions, the observation that electron transfer between ketyl and parent ketone and sodium ion exchange between ketyl and sodium iodide are too slow to be measured by epr also supports the dimeric structure. The rate constants for these bimolecular reactions were found to be l O k l O Q M-1 sec-1 for monomer ketyls and -107 M-1 sec-* for dimer ketyls at 2 5 O . a
Volume 71 A'umber 1
January 1967
NOBORU HIROTA
138
vary and generally decrease as the size of the metal ion increases. The species with small dipole interaction is assigned to the solvent-shared dimer ion pair.l' Therefore, the equilibrium in this system is shown by R'i: -6 R'
@ 6-C IR - R&-5 @ @ O0-C /.R @)
R'
R '
@@@
R'
(B)
(A)
The relative concentration of (B) with respect to (A) was found to be 1.1 at 77°K for sodium hexamethylacetone and increases very rapidly with temperature. A t room temperature it is safe to state that the dominant component is the solvent-shared ion pairz0 (B). Details of the structure and equilibria involving ketyls will be reported elsewhere. F . Spin Density at the Alkali Metal. Several investigators previously reported the values of alkali metal splittings for many radical ion pairs. Several theoretical estimates2" were also made and estimated values were compared with the experimental values. However, the alkali metal splittings depend on the structures of the ion pairs and the exact structures were not known for most cases. It is desirable to obtain the splitting in the system in which the ion pair is a real contact ion pair. The largest alkali metal splittings and the corresponding spin densities obtained in this investigation are tabulated for Na, K, and Cs.
f a M , KaUSS
Naphthalene
1
'
(PM
-
x
10-8
LYM, gauss
Anthracene p~
x
10-3
Na
K
cs
2.14 (DEE, $23") 6.77
0.060 (DEE,
1.36 (MTHF, -80") 1.66
2.94 (DBE,
0.230 (DEE,
$50') 9.29
-80') 2.80
-80") 0.73
0.64 (MTHF, -80") 0.78
The alkali metal splittings given here are larger than those previously reported.2n6 The values for potassium and cesium may be close to the values for the contact ion pairs. The value for the sodium contact ion pair would possibly be larger than the value given here. Spin densities on the alkali metal ion depend largely on the nature of the positive and negative ion. Spin densities at the sodium nucleus are undoubtedly larger than at the potassium and cesium nuclei. In order to test the validity of the various mechanisms to produce alkali metal splitting, clear-cut experimental data for t,he splittings in the known ion pair structure must be obtained. We are presently carrying out a The Journal of Physical Chemistry
more systematic survey of the alkali metal splittings in order to clarify the mechanism producing - it.
Acknowledgments. The author thanks Professor R. Kreilick of the University of Rochester for stimulating discussions. He is also indebted to Messrs. R. Carra: way, W. Schook, and T. Takeshita for their assistance in obtaining and analyzing some of the epr spectra. Financial support from the National Science Foundation (GP-5040) is greatly appreciated.
Discussion J. R. BOLTON (University of Minnesota, Minneapolis). Would you care to comment on the negative value of AS" for the ionpair equilibrium?
N. HIROTA. The negative value of AS' in going from a tight ion pair to a loose ion pair is considered to be due to the difference in the solvation of solvent molecules to the positive ions in two different ion pairs. It is considered that the better solvation in a loose ion pair than in a tight ion pair brings more partial ordering of the solvent molecules around the positive ions. This situation is shown in the article by a model, though the model is speculative and mainly for illustrative purposes.
J. L. DYE (Michigan State University, East Lansing). Since solvents such as tetrahydrofuran can dissolve some alkali metals, perhaps the high-temperature form is partaking of "monomer" character such as one has in metal-amine solutions. N. HIROTA. Although the sodium splitting increases at higher temperatures, the spin density a t the alkali metal nucleus is still and this ion pair seems to be quite difvery small ( p 5~ ferent from the "monomer" in metal-amine solutions. The correlation between the sodium splitting and the proton splitting (Figure 7 ) indicates that the positive and negative ions come closer in the high-temperature form of the ion pair, and i t a p pears that the close approach of two ions is primarily responsible for the larger metal splitting. The alkali metal splitting would increase by the mechanism, such as charge transfer, when two come closer. The alkali metal splittings are usually larger in DEE than in DME or THE. I do not think that sodium and potassium dissolve in DEE, though they dissolve in DME a t lower temperatures. G. VINCOW (University of Washington, Seattle). Would you care to comment on possible differences in the structures of loose ion pairs 3 and 4 which might account for the kinetic differences observed? N. HIROTA. Since a loose ion pair 3 is interconverting rapidly with a tight ion pair 2, probable structure of ion pair 3 would be a solvent-shared (or separated) ion pair, such as shown by 3 or 4 of the model given in section IV.A.l. I do not have any definite answer as to the structure of the loose ion pair 4. The main reason to suggest that this is an ion pair rather than a free ion is the observation that the rates of electron transfer are rather slow and the activation energies are rather high. At this stage I would just like to mention some possibilities and wait for further investigations. One possibility is that the loose ion pair 4 is a solvent-separated ion pair in which ions are separated (20) This conclusion was also obtained from the recent investigation by G. R. Luckhurst, Mol. Phys., 9 , 179 (1965).
