1292
Y. M. Cahen, J.
L. Dye, and A. I. Popov
Lithium-7 Nuclear Magnetic Resonance Study of Lithium Ion-Lithium Cryptate Exchange Rates in Various Solvents Yves M. Cahen, James L. Dye, and Alexander 1. Popov* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (ReceivedJanuary 20, 1975) Publication costs assisted by Michigan State University
The kinetics of complexation reactions of the lithium ion with cryptand C211 in pyridine, water, dimethyl sulfoxide, dimethylformamide, and formamide and with cryptand C221 in pyridine were investigated by temperature-dependent 7Li NMR. The energies of activation for the release of Li+ from I,i+-C211 complexes increase with the increasing donicity of the solvent as expressed by the Gutmann donor number. The transition state of the complexation reaction must involve substantial ionic solvation. Using the formation constants of the Li+-C211 cryptate in water the rate constant for the forward reaction was found to be k f = 0.98 X IO3 sec-l.
Introduction During recent years a number of synthetic macrocyclic polyethers and polyamines have been synthesized which are capable of forming strong complexes with the alkali and alkaline earth ions. Among the most effective of these compounds are the polyoxadiamine macrobicyclic ligands (‘‘cryptands”,l I) synthesized and studied extensively by Lehn and coworkers.2
I C222, a = b = c = 1 C221, a = b = 1, c = 0
(2211, a = 1, b = c = 0
The stability of the cryptate complexes depends to a large extent on the size relationship between the threedimensional cavity of the cryptand and the diameter of the complexed ion. Thus cryptand C211, with a cavity diameter of 1.6 %I, forms a very stable complex with the lithium ion (d = 1.56 A). On the other hand, cryptands C221 and C222 with cavity diameters of 2.2 and 2.8 A, respectively, form only weak complexes with Li+ but strong complexes with the sodium (d = 2.24 A) and potassium ( d = 2.88 A) ions. In the case of the weaker complexes, the solvating ability of the solvent plays an important role in the complexation reaction. We have shown recently3s4that the Li+-C221 and Li+-C222 complexation reactions occur readily in a poorly solvating solvent, such as nitromethane, but cannot be detected in the strongly solvating solvent, dimethyl sulfoxide. The drastic effect of the solvent on the complexation reaction is also illustrated by the formation constants for the Li+-C222 complex which were found to be 9.8 in water and 960 in pyridine. Thus, the strong solvating ability of water drastically depresses the value of the Li+-C222 formation constant. The kinetics of complexation reactions of the Na+-C222 complex in ethylenediamine solutions were investigated by The Journal of Physical Chemistry, Vol. 79, No. 13, 1975
Ceraso and Dye5 by using 23Na NMR techniques. Similar studies on this system in a variety of solvents have recently been completed in our laboratory.6 Complexation reaction rates were also studied by Lehn and coworkers in aqueous and methanol solutions by NMR The lithium ion forms stable complexes with the cryptand C211, and the exchange between the free and the bound lithium ions is slow on the NMR time scale. Thus solutions containing lithium in excess can be examined by measuring the 7Li resonances. The exchange kinetics can be deduced from changes in line shapes as a function of temperature. We wish to report a study of the Li+-cryptate exchange kinetics in water and in several nonaqueous solvents.
Experimental Section Cryptands 211 and 221 were obtained from E. M. Laboratories Inc., Elmsford, N.Y., and were used as received. From 7Li NMR measurements it was estimated that their purity was 198%. Pyridine, dimethyl sulfoxide, dimethylformamide, formamide, lithium perchlorate, and lithium iodide were purified and dried by previously described technique^.^ Lithium perchlorate was used in nonaqueous solvents. Since this compound is only sparingly soluble in water it was replaced by lithium iodide for studies in aque- . ous solutions. Nuclear magnetic resonance measurements were carried out on a Varian DA-60 spectrometer by using the side band technique, with a V 4333 probe at 23.3 MHz and 1.4092 T. Spinning 5-mm sample tubes were used with a 1-mm 0.d. melting point capillary inserted coaxially in the spinning tube and filled with an external reference solution (usually 4 M LiC104 in water). Temperatures were measured with a calibrated thermocouple. Pressurized NMR tubes (30 to 50 psi of N2) were used when it was necessary to record a spectrum above the boiling point of the sample solution. Results and Discussion The complexation process between a ligand L and a cation M +in a solvent S can be represented by the following general equation L
+
kf
M*solvzz LM+ ‘b
+ solvent
( 1)
1293
Lithium-7 NMR Study of Lithium Ion-Lithium Cryptate Exchange Rates
I
which assumes a first-order process for the backward reaction, e.g., in our case, the dissociation reaction or the release of the lithium ion from the cryptate cavity. Such a mechanism was found to be predominant for the complexation of sodium ions by several 18-crown-6 complexing agents.1° The general case of exchange between two sites A and B with different relaxation times is described by the following modified Bloch equation^^,^^ ( 2)
G=u+iv = -yHiMo
2:
25.8'C
[$' 1
62.3OC
(3) 80.3'C
(4)
where G is the complex moment of magnetization, u and u are the pure absorption and pure dispersion line shapes, respectively, and
119. 2'C
, = A+ A + -7 T2A
T2B
(PAwA
+
7 ( w A - ~ ( w B- W )
(5)
T2AT2B
u= T =
109.2OC
1+
PBaB
T(PB/TPA
- w)
[
+
+
(OA
-
O)
+ (wB -
T2B
V =
~ P B w A+ P A u B
( 6)
PA/T~B)
"1
(7)
T2A
-
4
128.5'C
Figure 1. Spectra at various temperatures for an aqueous solution containing 0.50 MLil, 0.25 MC211.
( 8)
where p a and p~ are the relative population at sites A and B, respectively, and 7 is the lifetime of interaction defined by ( 9) T = TATB/(TA + 7B)
I
I
I 1
I
xoo
0
o
c x 0
.
I I
; P and WB are the resonance frequencies at the two sites a t P I a given temperature in the absence of exchange and T ~ A and T ~ are B the respective relaxation times a t each site at a given temperature in the absence of exchange. If a t a given , temperature the lifetime r is greater than f i / ( ~ A u )where H A w = I W A - UBI, two separate resonances are observed for the two respective sites; if 7 is less than d / ( n A w ) , only one Figure 2. Computer fit of spectra obtained with 0.50 M LiC104, 0.25 population-averaged resonance is observed. M C211 in formamide at 143.3'. X represents an experimental point, 0, a calculated point, =, an experimental and calculated point Since it was experimentally difficult and inconvenient in are the same within the resolution of the plot. the case of coalescing lines to obtain a pure absorption mode signal, a phase correction was made and the observed For the Li+-C211 systems, no exchange is observable at line shape was fitted by the following equation: room temperature. Measurable exchange, detected by the 21' = u sin 0 + 2: cos 0 c (10) onset of broadening of both resonance lines, begins a t highwhere 8 is the phase correction parameter and c the base er temperatures, t E , which were found to be about 1 5 , 80, line adjustment parameter. An example of the spectra ob105, 145, and 85' in dimethyl sulfoxide, water, formamide, tained a t various temperatures for aqueous solutions is pyridine, and dimethylformamide, respectively. It was shown in Figure 1. Spectra were analyzed on a CDC 6500 noted that WA' and WB varied linearly with temperature relacomputer by using the Fortran IV KINFIT program12 based tive to the lock frequency. The difference between the on a generalized weighted nonlinear least-squares analysis. chemical shift (ppm) of the solvated ion A and that of the Each spectrum was fitted with four parameters; the lifecomplexed ion B is a linear function of temperature as extime 7, the phase correction 8, the base line adjustment c, pressed by and a normalization factor. A typical computer output A(6) = A(60) - S(t - 25) (11) 6, - 6, (Figure 2) shows the fit of a spectrum (LiC104, C211) in formamide a t 143.3'. in which A(60) is 6~ - 6~ a t 25'. The values of A(&) and S Respective populations P A and p~ were obtained from are given in Table I. At temperatures higher than t ~OA, the stoichiometry (lithium to ligand) used, assuming a large and WB were obtained by extrapolation. The validity of this complex formation constant, and were checked by the inteextrapolation was verified by separate experiments on solugration of each resonance line below the coalescence temtions which contained only A or B. The T2.4 and T ~ values B perature. The areas were found to be temperature indepengiven in Table I were determined by measurement of the dent within experimental error. full width a t half-height of each resonance line and were
i
WA
X0
K
+
The Journal of Physical Chemistry. Vol. 79, No. 13, 1975
Y. M. Cahen, J. L. Dye, and A. I. Popov
1294
TABLE I: Descriution of P ( b ) a s a Function of Temperaturea Solvent
Salt
Pyridine Water Dimethyl sulfoxide Dimethyl formamide Formamide Pyridine a A(6) = A&) + %t - 25); A(6)
Cryptand
A(60), ppm
LiCIOd 211 LiI 211 LiC104 211 LiCIOd 211 LiC104 21 1 LiCIOd 221 6~ - 6~ at a given temperature t
S, ppm/"C
T2.4, sec
-
T2B,
3.425 0.520 -4.525 0,999
4.00696 0.796 0.637 -0.00222 0.796 0.3 54 0.00181 0,909 0.374 -0.00364 1.061 0.455 1.010 4.00370 0.909 0.374 -3.986 4.00746 0.707 0.637 ("C); A(&) = 6~ - 6~ at 25" (A = solvated ion, B = complexed ion).
TABLE 11: Exchange Rates and Thermodynamic Parameters of Lithium Cryptate Exchange in Various Solvents Solvent
DNe
cb
E,, kcal mol-'
kb x lo3, sec-' (298°K)
*HO*, kcal mol-'
Cryptand 211 Pyridine 33.1 12.3 19.6 (3.5)' 0.12 (0.24) Water 33.0 78.6 21.3 (1.2) 4.9 (2.0) 29.8 45.0 Dimethyl sulfoxide 16.1 (0.6) 23.2 (5.4) Dimethylfosmamide 26.6 36.1 16.0 (0.6) 13.0 (3.3) Formamide 24.0 111.0 14.1 (0.7) 7.4 (2.9) Cryptand 221 Pyridine 33.1 12.3 13.5 (0.4) 1230 (196) 0 Gutmann donor number.l* * Dielectric constant. Standard deviation. found to be temperature independent. I t should be noted that the cryptate resonance line is 2 to 3 times broader than the resonance line for the solvated ion. Therefore, the width of the cryptate resonance line cannot be entirely caused by field inhomogenities. In the case of the Li+-C221 system in pyridine, WA, WB, T ~ Aand , T ~ were B measured by separate experiments since some exchange occurs a t room temperature. Activation energy plots, log k b vs. 1/T are shown in Figrate constants ( h b ) , and ure 3. Activation energies (Ea), values of P H o f , ASof, and AGof for the release of Li+ from the cryptate are given in Table 11. A complete error analysis13 including cross correlation terms which account for the coupling of parameters (particularly evident between AH01 and A s o f ) was performed in all cases. Not surprisingly, AGO$, which is directly determined from k b , has the smallest standard deviation. The accuracy of the determination of the activation energy depends upon the range of temperatures over which exchange can be measured. For example, with the Li+C211 system in pyridine, the difference between the chemical shift of the solvated and the complexed lithium ion is 2.7 ppm, which is considerably larger than the shifts found in other solvents (0.5-1 ppm). Thus, for this system the exchange is observable over only a limited temperature range and coalescence could not be observed. Therefore, the activation energy could only be determined from the line broadening below the coalescence temperature, which accounts for the relatively large standard deviation. On the other hand for the Li+-C221 system in the same solvent, the exchange is observable over a large temperature range, 62.6-159.4', and the activation energy can be determined with a higher accuracy. The energies of activation for the release of Li+ from the Li+-C211 complexes in pyridine, water, dimethyl sulfoxide, dimethylformamide, and formamide seem to be determined by the donicity of the solvent as expressed by the Gutmann donor number,l* rather than the dielectric conThe Journal of Physical Chemistry, Vol. 79, No. 13, 1975
3.5
ASO*, AGO*, kcal cal OK-' mol-' mol-' (298°K)
19.0 (3.4) 20.7 (1.1) 15.5 (0.6) 15.4 (0.6) 13.5 (0.7)
-12.5 (9.2) +0.4 (3.0) -13.8 (1.4) -15.5 (1.4) -22.8 (1.8)
22.7 (1.1) 20.6 (0.25) 19.7 (0.14) 20.0 (0.1b) 20.8(0.23)
12.9 (0.4)
-14.9(0.9)
17.9 (0.1)
1
115
103
(OK-')
Figure 3. Log kbvs. I / J plot for 0.50 M LiCI04, 0.25 M C211 in (A) pyridine, (B) formamide, (C) dimethylformamide, (D) dimethyl sulfoxide, (E) 0.50 M Lil, 0.25 M C211 in water, and (F) 0.50 M LiC104, 0.25 M C 2 2 1 in pyridine.
stant. The activation energies vary from 14.1 kcal mol-l in formamide (DN = 24) to 21.3 kcal mol-' in water (DN = 33.0). By contrast, Shchori et al.1° found that the (smaller) activation energies for release of Na+ from dibenzo-18crown-6 were independent of the solvent used. However, two of the three solvents used, methanol and dimethylformamide, have the same donicity while that of the third solvent, dimethoxyethane, is not known. We expect that the net energy required to transfer Li+ from the cryptate to the solvent should decrease with increasing donicity of the solvent since this scale is a good
Lithium-7 NMR Study of Lithium Ion-Lithium Cryptate Exchange Rates
1295
Although E , and hence AHof are very sensitive to the solvent used, the values of AGO$ (298'K) are nearly independent of solvent. Changes in AHoJ are compensated for by corresponding changes in A S o f , a not uncommon occurrence.15 Using the formation constant of Li+-C211 cryptate in water determined by Lehn and coworkers2 (log K = 5.3) we can calculate the rate constant for the forward reaction, kf = Kkb = 0.98 x IO3 sec-1 for Li+-C211 in water.
YI -
react ion coordinate
Flgure 4. Schematic representation of the complexation of lithium ion by cryptands 211 and 221. SIrepresents a good donor solvent, S pa poor one.
measure of the primary solvation energy. The solvation energy of the cryptate and the secondary solvation energy of the lithium ion both depend primarily upon the dielectric constant of the solvent and change in the same direction from solvent to solvent. Since the activation energy increases with increasing donicity, opposite to the overall energy change, the transition state must involve substantial ionic solvation. The energy profile is illustrated schematically in Figure 4. The solid line represents the complexation path of Li+-C211 in a poor donor solvent (S2) and the dashed line in a good donor solvent&) with reverse activation energies of E,, and Ea,, respectively (Eal > EaJ. In the same solvent, for example S2, the energy level of the 221 cryptate will be higher than for the 211 cryptate because of the better fit of the lithium ion in the C211 cavity. On the other hand, if the transition state is similar to
