320
J. Phys. Chem. 1980, 84,320-323
Thermodynamics and Kinetics of Alkali Metal Ion Complexes with 5,6-Benzo-4,7,13,16,21,24-hexaoxa-l ,IO-diazabicyclo[8.8.8]hexacosane In Methanol 8. G. Cox,'' D. Knop,lband H. Schnelder*lb Max-Planck-Institut fur Biophyslkallsche Chemle, Karl-Frledrlch-Bonhoeffer-Instifuf.0-3400 Cofflngen, West Germany (Received July 17, 1979) Publication costs assisted by the Max-Planck-Institut fur Biophysikalische Chemie
Alkali metal ion complexes with the macrobicyclic ligand 5,6-benzo-4,7,13,16,21,24-hexaoxa-l,lO-diazabicy clo[8.8.8]hexacosane (2B,2,2) in methanol have been studied by potentiometric, calorimetric, and stopped-flow experiments. Stability constants and decomplexation rates show that K+(2B,2,2)is the most stable complex and has the lowest dissociation rate. Although K+ fits most effectivelyinto the cavity of the ligand, comparison with (2,2,2) cryptates suggests that the fit is not optimal. The stability constants of the Li+, Na+, Rb+, and Cs+ complexes are smaller, and the dissociation rates of the Na+ and Rb+ complexes larger, than those of K+. The entropies of complexation and activation, and the acceleration of the decomplexation rate through acid catalysis, shows that much of the conformational flexibility of ligand (2B,2,2) is retained in the Na+ cryptate. Acid catalysis was not found for K+ and Rb+ cryptates, there lack being attributed to the reduction in the cryptand's mobility by steric strain. The rates of complex formation increase with increasing ionic radius of the cation, similar to the rates of solvent exchange.
Introduction Cryptands are synthetic macrobicyclic diaza polyether ligands which contain a three-dimensional intramolecular cavity, and form stable inclusion complexes (cryptates) with alkali metal ions.1>2Like crown ethers3 and macrocyclic antibiotics,4g5they show a maximum in the stability constant when the preferred cation fits most closely into the cavity. However, in general, the stability constants of cryptates are several orders of magnitude larger and, the selectivity for different ions is more pronounced. Recently, in several studies on the kinetics of complex formation between cryptands and alkali metal ions in water6-0 and methanol,1° it was shown that the rate of complex formation is only slightly dependent upon the ionic radius, ri, while the variation of the dissociation rate with ionic radius is a mirror image of that for the corresponding stability constants. In the present paper, which is an extension of previous studies,1° we present results on the stability and kinetics of complexes formed between (2B,2,2) and alkali metal ions in methanol. Accompanying the large changes in cavity size on going from (2,1,1), with an estimated size of 1.6 A, to (2,2,1) with 2.2 A, and to (2,2,2) with 2.8 A, is a change in the ion forming the most stable complex, from Li+ to Na+ to K+, respectively. The benzene ring of (2B,2,2) increases the rigidity of the ligand and reduces the cavity size compared to that of (2,2,2), but the effect is smaller than that of removing one of the ethyleneoxy groups. Thus the stability constants are all smaller than those of (2,2,2), but K+ still forms the most stable complex. Since arguments concerning the geometric fit of the ions can give only qualitative explanations, the temperature dependence of the stability constants and dissociation rates was also studied. A better understanding may be obtained from an analysis of the Gibbs energy of complexation, AGc, into the enthalpy, AH,, and entropy, AS,, of complexation, and by a determination of the activation parameters for complex formation and dissociation. The structure of the activated complex, and its position between the reactants and the stable complexes, have been deduced from the activation energies. Experimental Section and Results Materials. The metal salts (Merck) were nitrates in all 0022-3654/80/2084-0320$01 .OO/O
cases except cesium, where fluoride was used. Silver nitrate was dried under vacuum at 90 OC to constant weight. Tetraethylammonium perchlorate (Pfaltz, Bauer) was recrystallized twice from water, washed with methanol and diethyl ether, and dried for 15 h under vacuum at 60 "C over P4010. The cryptand (2B,2,2) was used as purchased (Merck). Its purity was tested in connection with the determination of stability constants by potentiometric titrations. Methanesulfonic acid (Merck) and trifluoromethanesulfonic acid (Merck) were used without further purification. When both acids were used in alternate reactions with the same cation, no dependence was observed. Methanol was dried with molecular sieves (Merck, 4 A)and fractionally distilled under nitrogen. The water content from Karl-Fischer analysis was around 40 ppm. Stock solutions of cryptand, alkali metal salts, and acids were prepared in a glove box under nitrogen by dissolving weighed quantities of substances in methanol. In all cases, freshly dried and distilled methanol was used for the preparation of solutions. Stability Constant Measurements. The stability constants K, of all alkali metal ion complexes with (2B,2,2) were determined by the disproportionative reaction of alkali metal ions with the ~4g+(2~,2,2) complex, using the stability constant of the silver ion complex with (2B,2,2) in methanol (log K, = 11.9 at 25 "C). The metal ion concentration was varied between 8 X and 1 X M, the ionic strength was 2 X M, and N(C2H6)4C104 was the supporting electrolyte. The experimental procedure has been published previously.lOJ1 Heats of Complex Formation. The heats of complexation were measured at 25.00 f 0.05 "C by using a Tronac calorimeter, Model 450, equipped with a recorder (BBC, Servogor 310). In every experimental run a cryptand solution (7.5 x 10-2-0.104 M) was added with an automatic buret (2.3 mL, Tronac) to the solution of metal salt (3.6 M). The heat of dilution of the ligand X 10-3-5.3 X was found to be negligible. The heats of complexation, AHc, and also the stability constant for Cs+, were calculated by using the procedure of Christensen et Table I lists stability constants, Gibbs energies, and enthalpies and entropies of complexation for alkali metal ions with (2B,2,2) in methanol at 25 "C. Kinetic Measurements. Kinetic measurements were made with a home-built glass stopped-flow apparatus with 0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84, No.
Alkali Metal-Cryptand Complexes In MeOH
TABLE I: Stability Constant (log K s ) , Enthalpy (AHc), and Entropy ( riSc) of Alkali Metal Ion Complexation with ( 2 ~ , 2 , 2in) Methanol at 25 "C
-AHc, kJ/mol
-AGc,
M'
log KSa 2.19 7.50 9.21 7.19 2.99;2.9gb
Lit Na+
K+ Rb' Cs'
kJ/mol 12.5 42.8 52.6 41.0 17.0
39.7 t 0.4 65.3 f 0.4 57.7 t 0.8 31.8 t 0.8
-10 43 56 50
15
I _ 1 .
.
L 1 . -.-.--,-ZO~C 1
.
l - +
-+.-*+.-..---+-+22.-+-+ -+-+-+-19%
5j-2-
2 . 2 2 . - ,y. 10°C
~-c----7-~ 2I
I
3 3
I
I
5
4
0
10- C C F ~ S O ~~MHO I
I 6
1.~1
Flgure 1. Dissociation rate of Rb+(2,,2,2) for different acid concentrations as function of temperature.
conductivity detection. All kinetic runs were performed under pseudo-first-order conditions, mixing an excess of acid with an equilibrium cation-cryptand mixture. The concentration ratio of cation to cryptand was always larger than one in order to ensure that nearly all of the cryptand molecules were complexed as cryptates. From the change in conductance occurring during the reactions (eq l),in which the (2~,2,2)is quantitatively doubly protonated, an on-line computler calculated the rate constant k,. k
M+(2~,2,2)4- 2H+L,M+
(2~,2,2)H2'+
T,"C
(1)
I t was shown in previous studiesgJOthat cryptates can either dissociate directly, with rate constant kd, or by an acid-catalyzed pathway, with rate constant kH. The experimental rate constant, k,, is therefore a linear function of acid concentration: k, kd f k~["] (2) The rate constant k , was measured at at least seven different acid concentrations for every cryptate studied (e.g., Figure 1) and in all cases was independent of the
K'
Rbt
0.029 ?: 0.002 0.0522 i 0.0034
2.67 t 0.02 4.55 k 0.15 7.63 rt. 0.15 12.57 i 0.19 20.36 i 0.24
Na+ 0.52
0.08
t
1.26 f 0.12 2.74
0.17
t
0.158
5.56 f 0.31
rt.
0.007
-
0.447 i 0.018 0.732 i 0.032 1.18 f 0.04
-
0-
-.-.-
..__._
TABLE 11: Dissociation Rates, k d ( s - * ) ,of Alkali Metal Ion Complexes with (2B,2,2) in Methanol 5 10 15 20 25 30 35 40 45
From titrimetric
a T h e precision of log K, is i0.05. calorimetry.
i
-AS,,J/ (mol K)
3, 1980 321
LI'
Na
K
Rb'
Cs'
Figure 2. Stability constants (log K,) of alkali metal Ion cornpiexes with cryptands in methanol and water at 25 "C: (2,2,2) in methanol (0); (2,,2,2) in methanol (X); (2,,2,2) in water (0).
concentration of M+. Only in the case of Na+ was the observed rate constant acid dependent and k d values were obtained by linear extrapolation of the experimental rahe constants to zero acid concentration. The resulting kH values were corrected to zero ionic strength. The upper limit of the concentrations of the various species were 1 X 10-1 M for M+, 4.5 X M for (2B,2,2), and 4.5 X M for the acid. Reaction rates were determined at four to six different temperatures equidistantly spaced by 5 or loo intervals. At each temperature the mean lifetime was measured more than six times. The bath temperature was held constant to within f O . l "C. The rate constants, kd, calculated at selected temperatures from the linear dependence of In k d upon 1/T, are given in Table 11. The standard deviations listed are those of the experimental k, values at the neighboring temperatures. The dissociation rates of Li+(2B,2,2)and cS+(2B,2,:2) were too fast to be measured by the apparatus used, even at -20 "C. Discussion Stability Constants. The stability constants of alkali metal cryptates of (2B,2,2) are distinctly larger in methanol than in water.l In both solvents, K+forms the most stable complex (Figure 21, but the complex is more than four orders of magnitude more stable in methanol than in water. The corresponding difference in stability constants is slightly lower (by less than one log K , unit) in the case of Na+ and Rb+. The difference in the stability constants
322 The Journal of Physlcal Chemlstry, Vol. 84, No. 3, 1980
in the two solvents is related to the Gibbs energy of transfer, AGt, of the various species from water to methanol, as given by eq 3. If this difference depends only
Cox, Knop, and Schnelder
TABLE 111: Enthalpies and Entropies of Solvation and of Ligation in Methanol at 25 "C
M+ Na+ K' Rb+
cs+ upon the difference in the ionic Gibbs energy of solvation, AGt(M+),then the corresponding quantities for the cryptate and cryptand'l should be equal, and their difference (eq 3) zero. AGt(M+) values for transfer between water and methanol have been found to be 8.4 kJ mol-l for Na+ and 10.0 kJ mol-l for K+ and Rb+.13 These values lead to corresponding differences in AGt of cryptate and cryptand (eq 3) of -11.7 kJ mol-l (Na+), -14.6 kJ mol-l (K+), and -11.7 kJ mol-l (Rb+). The difference between K+ on the one hand and Na+ and Rb+ on the other, which is outside the experimental errors of h0.05 units in log K, and h0.3 kJ mol-l in the relative AG,(M+) values, is fundamental. It means that AGt(M+(2~,2,2)) depends upon the cation chosen. In the case of the K+ complex, the near-optimal fit of cation and cavity should mean that essentially only the hydrophobic groups of the ligand will come into contact with the solvent. For the other complexes, however, the donor groups of the ligand may interact with the solvent, because of the higher flexibility of the ligand in the Na+ complexes, and the difficulty of Rb+ fitting completely into the cavity. These factors might be expected to lead to differences in the behavior of Na+ and Rb+ cryptates compared to the K+ cryptate on transfer between the solvents. The stabilities of the (2B,2,2) complexes in methanol are all lower than the corresponding (2,2,2) comp1exes.l The differences in log K, (Figure 2) fall into two groups: one for Li+ and Nat which show only small A log K, values and one for K+, Rb+, and Cst which have larger A log K, values. This may be due to different effects resulting from the introduction of the benzene ring. Qualitatively, the benzene ring in (2B,2,2) (a) reduces the cavity size of the ligand, as the distance between the oxygen atoms bonded to the benzene ring is smaller, (b) changes the electronegativity of these oxygen atoms, and (c) increases the rigidity of the ligand, thereby reducing the possibility of optimal electrostatic interaction between the ligand's donor groups and the ions. Effects b and c are presumably mainly responsible for the relatively small decrease in log K, of Li+ and Na+ complexes, while the decrease in cavity size (a) and the reduction in conformational flexibility (c) lead to a much larger reduction in the stability constants of K+, Rb+, and Cs+ complexes, The similarity of A log K, values of K+ when compared to those of Rb+ and Cs+ suggests that the ionic radius of K+ is larger than that required for an optimal fit into the cavity. In contrast, no such distinction between ions of smaller and larger than optimal size is found for the two isomers A and B of dicyclohexyl-18-crown-6,3with the stability constants of isomer B being all roughly 0.5 units in log K, smaller than those of isomer A. The greater flexibility of the monocycles enables them to adjust more easily than the more rigid bicyclic ligands to the ions. The stability constants obtained in this work are in good agreement (f0.1in log K,) with those of Lehn and coworkers in methanol and 955 (wt %) mixtures of methanol and water,' with the exception of Na+ in methanol. Since a value of log K,(Na+) = 7.5 has been found in m e t h a n ~ P * ~ and in 9 5 5 (wt %) methanol-water mixtures,l the value reported earlier in methanol (log K, = 8.0) is probably in error.
-AHsolv,
kJ/mol 464.0 317.4 349.4 314.6
-ASsolv,
-AH1,
J/(mol K) kJ/mol 206 169 146 136
503.7 442.7 407.1 346.4
-AS1, J /
(mol K) 196 212 202 186
Enthalpy and Entropy of Complex Formation. Complexes of (2B7292) with alkali metal ions in methanol display favorable enthalpies, but either small (Na+)or unfavorable entropies of complexation (Table I), similar to their behavior in water and in methanol-water mixtures. The enthalpy term, AHc, shows qualitatively the same trend as the Gibbs energy of complex formation, AG,, with both being at a minimum for K'. The complexation entropy, AS,, is almost constant at approximately -50 J mol-l K-l for K+, Rb+, and Cs+, but is some 60 J mol-l K-l more positive for Na+. A complete discussion of the results is hampered by the fact that the solvation enthalpies, AHsolv, and entropies, AS,lv, are known only for the ions14J5and not the ligands. However, since, for a given ligand (in this case (2B,2,2)), this latter quantity is constant, the enthalpies and entropies of ligation? AH1 and A&, corresponding to equilibrium 4 may be calculated (eq 5 and 6). (M+)VBCUU~ + ( ~ B , ~ , ~ ) M ~ o (HM + ( ~ B , ~ , ~ ) ) M(4) ~oH iw, = MH, -k AHsolv (5) AS1 ASc ASsolv (6) The results are given in Table 111. They show that AHl follows the same trend as A",,, but that AS1changes more individually. These changes depend upon a variation in the loss of conformational freedom of the ligand on complexation, and in the entropy of the solvent molecules solvating the complex. If the complexes were rigid, this latter contribution could be expected to be constant and similar to that for a hydrophobic molecule of the same size and structure. However, the electronegative groups of the ligand may come in contact with the solvent molecules more frequently with a smaller ion, e.g., Na+, or a larger ion, e.g., Cs+, within the ligand cavity, than for Kt, because of higher ligand flexibility or less complete contact between the ions and binding sites. The loss in conformational freedom is, therefore, most pronounced for K+(2B,2,2). Reaction Rates. The rates of dissociation vary in a similar manner but in the opposite direction to the stability constants. Thus the most stable complex dissociates most slowly. The dissociation rates, kd, for Li+ and Cs+ complexes have been calculated from the corresponding stability constants, using estimated rates of formation, kf (eq 7). These were obtained from linear extrapolation of a k d = kf/Ks (7) plot of log kf against l / r i for the ions Na+, K+, and Rb', whose log kf values show only a small, but linear dependence upon l / r i . The results are given in Table IV. The rates of dissociation of (2B,2,2) complexes are compared with those of (2,2,2)1°in Figure 3. The dissociation rates of the Na+ complexes are identical within experimental error, as are those for the Li+ complexes, allowing for the larger uncertainty in estimating k d values for Lit. Thus the smaller cavity and greater rigidity of (2B,2,2) compared to (2,2,2) only increases the dissociation rates of K+, Rb+, and Cs+ complexes. The rates of formation of alkali metal (2B,2,2) complexes are 0.3-0.5 times as large as those for the corresponding (2,2,2) complexes.1° They are from 10-100 times lower +
+
The Journal of Physlcal Chemistry, Vol. 84, No. 3, 1980
Alkali Metal-Cryptand Complexes in MeOH
TABLE IV: ]Kinetics of Complexation between Alkali Metal Ions and ( 2 ~ , 2 , 2 ) ,Arrhenius Activation Energies, and Thermodynamic Functions of Activation in Methanol at 25 “C
M’
k d , S-’
Li’ Na+ K:+
2.1 x 105a
___-
Rb+
CS’ a
EA,d,
2.78 0.158 20.4 4.3 x 105a
kJ/rnol
57.6 i: 1.6 79.3 c 0.4 70.1 c 0.3
Calculated from R, and estimated k f values.
Lit
Na’
K+
Rb+
AGd*,
kJ/mol
*
70.5 0.2 77.6 I 0 . 1 65.6 i: 0.1
’, kJ/mol AHd
55.1 76.8 70.1
ASd*,
J/(mol
-522 5 -3* 1 7 + 1
K) k f , M-I 3.3 x
s-I
8.78 x 107 2.57 X 10’ 3.15 X 10’ 4.17 X
losb
AGf*,
323
-
kJ/mal-
28.0 25.0 24.5
Obtained by linear extrapolation of In k f vs. l / r i .
Cs’
Figure 3. Rates of dissociation of (Z8,2,2) and (2,2,2) cryptates in methanol at 25 OC: (2,,2,2) cryptate (X); (2,2,2) cryptate (0).
than the diffusion-controlled rates (3.5 X lo9 M-l s-l), and parallel the su:bstitution lability of M+. Thus, conformational changes occurring prior to complex formation are not rate-limiting steps in the overall complexation reactions. The introduction of the benzene ring into (2,2,2) then influences both kf and kd for the ions K+ and Rb+ (and Cs”), but only kf for Na+ (and Li+). The dissociation rate of the Na+ complex was the only one found to be subject to acid catalysis. For the complexes of K+, Rb+, and Cs+, conformational changes are serverely restricted, and protonation of the nitrogen lone pairs was negligible. The catalytic constant and activation energy for the l?la+(2B,2,2)complex at 25 “C are kH = 250 M-l s-l and EA,H = 36.3 f 2.6 kJ mol-’, respectively. The greater contribiition of proton catalysis to the dissociation of Na+(2,2,2),for which kH = 420 M-l s-l, is in keeping with the larger cavity size of the (2,2,2) ligand. Activation Parameters for Complex Formation and Dissociation. The Gibbs energies of activation for the dissociation reaction, AGd’, and the formation reaction, AGf‘ = AG, - AGd*, (Table IV) suggest that the structure of the activatedl complex is closer to that of the reactants than that of the complex. Thus AGd* is more than twice as large as AG?, indicating that the activated complex represents only a loose connection between cation and ligand, with both retaining most of the solvation they had as free particles. The activation energy for decomplexation, shows the same trend as -AHc, the overall enthalpy change for the decomplexation reaction, and has a maximum value for K+ (Table IV). The only other system for which com-
parable results are available is that of complex formation between Na+16J7and K+18and several crown etherri in methanol and dimethylformamide. From 23Naand 39K NMR studies, the activation energies for decomplexation were found to be almost constant (50-55 kJ mol-’) for the different reactions. Compared to the Na+-crown ether complexes, Nat(2B,2,2)has a considerably higher stability constant (103-3 X lo5 times larger), but a very similar activation energy for decomplexation (EAd = 57.6 kJ mol-l). This agreement is presumably a reflection of the flexibility of the ligands. Similarly, the much higher E*,d for Rb+(2B,2,2),despite a slightly smaller stability constant than Na+(2B,2,2),may result from the lower flexibility of the ligand in this case. Looking at the activation parameters for dissociation in terms of activation enthalpy, A&* = EA,d - RT, and activation entropy, A&*, one can see that for Kt and Rb+ the activation entropies are small, whereas for Na+ it is large and negative (Table IV). The formation of the activated complex is accompanied by solvation of the cation (AS < 0) and an increase in the conformational flexibility of the cryptand (AS > 0). For K+ and R+ the two contributions cancel one another, but, in the case of Na+, the solvation of Na+ may be the dominating factor.
References and Notes (1) J. M. Lehn, Struct. Bonding(Ber//n), 18, 1 (1973). (2) E. Kauffmann, J. M. Lehn, and J. P. Sauvage, Helv. Chim. Acta, 59, 1099 (1976). (3) R. M. Izatt, D. J. Eatough, and J. J. Christensen, Struct. Bonding (Berbn), 18, 161 (1973). (4) M. E w n and R. Winkler in “The Neurosciences, 2nd Stdy Program”, F. 0, Schmitt, Ed., Rockefeller University Press, New York, 1370, p 685. (5) E. Grell, Th. Funck, and F. Eggers in “Membranes, A Series of Advances”, Vd. 3-0. Emman, Ed., Marcel Dekker, New Yo&, 1975, P 1. (6) V. M. Loyoh, R. Wiklns, and R. Pber, J. Am. Chem. Soc., 97, 7382 (1975). (7) K. Henw, B. Tummler, and G. Maass, Angew, Chem., Int. Ed#. 18. 538 (1977). (8) R. Gressbr, A.‘M. Albrecht-Gary, P. Lagrange, and J. P. Schwlng, Now. J . Chim., 7 , 239 (1978). (9) B. G. Cox and H. Schneider, J. Am. Chem. Soc., 99. 2809 (1977). (10) B. 0. Cox, H. Schneider, and J. Stroka, J. Am. Chem. Soc‘.. 106, 4746 (1978). (11) J. Gutknecht, H. Schneider, and J. Stroka, Inorg. Chem., 17, 3326 (1978). (12) D. J. Eatough, J. J. Christensen, and R. M. Izatt, “Experiments in Thermometrlc Titrimetry and Tltration Calorimetry”, Brigham Young Universitv. 1977. (13) 8. 0. C&; G. R. Hedwig, A. J. Parker, and D.W. Watts, Aust. J. Chem., 27, 477 (1974). (14) 0. Kortum. “Lehrbuch der Elektrochemie”. 5th ed. Verho Chemie. West Berlin, 1972, p 119. ( 1 5 ) B. G. Cox In “The Chemical Society, Annual Reports”, Vol. A70, Tlle Chemical Society, London, 1973, p 249. (16) E. Shchorl, J. JaguJhdzinski, Z. Luz, and M. Shporer, J. Am. Chern. Soc., 93, 7133 (1971). (17) E. Shchori, J. Jagu-Qcdzinski, and M. Shporer, J. Am. Chem. Sot.., 95, 3842 (1973). (18) M. Shporer and Z. Luz, J . Am. Chem. SOC.,97, 665 (1975).
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