Anal. Chem. 1994,66, 1654-1657
Efficient Chromatographic Evaluation of Crown-Ether Complexation with Alkali-Metal Ions Tetsuo Okada' and Toshlnorl Usul Faculty of Liberal Arts, Shizuoka University, Shizuoka 422, Japan
A chromatographic method based on the ion-exchange resin phase complexation of crown ethers with a countercation is proposed to determine the solution phase complexation constants, which can be extracted from dependences of the retention of crown ethers on the metal ion concentration in a mobile phase. A single experiment also allows the rough estimation of complexation constants as long as 1:l stoichiometry is maintained for the resin phase complexation. The column design for the precise evaluation of the complexation is also discussed using nonlinear regression. Growing attention is paid to crown-ether chemistry in a variety of scientific and technological areas though a quarter century has passed since Pedersen first synthesized this series of compounds.' The unique complexation selectivity of crown ethers to hard metal ions is an aspect of fundamental and practical importance and has attracted a number of researchers having diverse interests.2-10 The elucidation of crown-ether chemistry has been followed by studies on syntheses of compounds bearing superior complexation abilities and/or novel selectivity; such effort is still continuing. It is important to develop methods capable of the precise determination of complexation constants that could be the most powerful and simplest criterion to show the efficiency of a compound. Calorimetry,11J2conductometry,'3J4 potentiometry,I5and nuclear magnetic resonanceI6 have been used to determine the complexation constants of crown ethers or related ligands in various media. It is essential to keep the ligand purity as high as possible for the reliable evaluation of complexation in these methods. However, purification processes are often much more laborious than syntheses or measurements and comprise a large part of an experiment. One of the authors previously reported that chromatography ( I ) Pedersen, C. J. J . Am. Chem. SOC.1967, 89, 7017-7036. (2) Izatt, R. M.; Bradshaw, J. S.;Nielsen, S. A,; Lamb, J. D.; Christensen, J. J. Chem. Rev. 1985,85, 271-339. (3) Inoue, Y., Gokel, G . W., Eds. Cation Binding by Macrocycles; Marcel Dekker: New York, 1990. (4) Mazor, M. G . ; McCammon, J. A.; Lybrand, T. P. J . Am. Chem. SOC.1990,
is an effective tool to probe poly(oxyethy1ene) complexation,l7-I9and we can minimize the effort for the purification of ligands because the chromatographic measurement itself involves the purification process. In the present paper, the authors present an efficient chromatographic method, based on the resin phase complexation with a countercation bound by a cation-exchange resin. Although complexation constants are basically derived from the retention changes of crown ethers with the concentration of a metal ion existing in a mobile phase, a simple method based on a single experiment is also proposed, which is closely related with the retention mechanism of crown ethers on the stationary phase.
EXPERIMENTAL SECTION The chromatographic system was composed of a Tosoh computer-controlled pump CCPD, a Rheodyne injection valve equipped with 100-pL sample loop, a Jasco UV-visible detector, Model 875-UV, and a strip chart recorder or a SIC integrator Chromatocorder 12. A separation column was TSKgel IC-Cation-SW (4.6mm i.d. X 50 mm PTFE column packed with a silica-based cation-exchange resin with 0.3 mequiv g-I), which was immersed in thermostated water to keep the appropriate temperature. Benzo- or dibenzo-crown ethers were synthesized from catechol and an appropriate oligoethylene glycol dichloride according to Pedersen's method.' Methanol of analytical grade was distilled twice. Other reagents were of analytical grade. RESULTS AND DISCUSSION Principle. As previously described,17J8 polyethers coordinate metal ions bound by a cation-exchange resin under appropriate conditions and, thus, are retained with the stationary phase. When a mobile phase contains the same metal ion as a counterion of the stationary phase, the capacity factor of a polyether can be described by
112,4411-4419.
( 5 ) Dang, L. X.; Kollman, P. A. J . Am. Chem. SOC.1990, 112, 5716-5720. (6) Graves, H. P.; Detellier, C. J. Am. Chem. Soc. 1988, 110, 60196024. (7) Kakuchi, T.; Haba, 0.;Yokota, K. Macromolecules 1992, 25, 4854-4858. (8) Bartsch, R. A. Solvent Extr. Ion Exch. 1989, 7, 829-854. (9) Attiyat, A. S.;Christian, G. D.; Xie, R. Y.; Wen, X.; Bartsch, R. A. Anal. Chem. 1988,60, 2561-2564. (10) Shono, T. Eunseki Kagaku 1984, 33, E449-E458. (1 1) Lamb, J. D.; Izatt, R. M.; Swain, C. S.; Christensen, J. J. J . Am. Chem. SOC. 1980, 102,475-479. (12) Ozutsumi, K.; Ishighuro, S.Bull. Chem. SOC.Jpn. 1992, 65, 1173-1175. (13) Takeda, Y. In ref 3. (14) Zollinger, D. Ph.; Bulten, E.; Christenhusz, A.; Bos, M.; Van Der Linden Anal. Chim. Acta 1987, 198, 207-222. (15) Frensdorff, H. K. J . Am. Chem. SOC.1971, 93, 600-606. (16) Lin, J. D.; Popov, A. I. J . Am. Chem. SOC.1981, 103, 3773-3777.
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Analytlcal Chemistty, Vol. 66,No. IO, May 15, 1994
where s and m in parentheses denote the stationary and mobile phases. I$ is the phase ratio, and PE and PE-M are uncomplexed polyethers and polyether-metal complexes, respectively. It is known that crown ethers form a variety of solution phase complexes, which involve usual 1:1 complexes, multiple (17) Okada, T. Macromolecules 1990, 23, 4216-4219. (18) Okada, T. J. Chem. SOC.,Faraday Trans. 1991,87, 3027-3032. (19) Okada, T. J. Chem. Soc., Chem. Commun. 3991, 1209-1210.
0003-2700/94/0366-1654$04.50/0
0 1994 American Chemical Society
complexes containing more than two metal ions, sandwichlike complexes where two crown ethers coordinate a metal ion, and others having morecomplicated stoichiometry. Since all concentration terms in eq 1 can be replaced by complexation constants and by the concentration of the metal ion in either the mobile phase or the stationary phase, the dependence of a capacity factor on the metal ion concentration reflects the complexation behaviors of a crown ether. However, we cannot necessarily analyze all cases by this approach. In order to apply eq 1 to the present case, it was assumed that the contribution of the complexation in which two or more ligands participate is negligible. This assumption is valid if the concentration of a crown ether in the mobile phase is much lower than that of a metal ion: in all present experiments, 4 X M of a crown ether was injected as a sample; if thecapacity factor of a crown ether is 10, one-tenth of the total mass of this crown ether exists in the mobile phase; taking the dilution due to the longitudinal diffusion of a solute into account, we can conclude that the concentration of the crown ether in the mobile phase is lower than 10-6 M; when mM or sub-mM metal ion solution is used as a mobile phase, the ligand concentration is negligibly small in comparison with that of a metal ion. A sandwich-like complexation between benzo-15-crown-5 (Bl5C5) and K+ is well-known; the logarithms of complexation constants are reported to be 2.96 for 1:l and 3.20 for 1:2, respe~tive1y.l~If the concentration of K+ is 0.1 mM and that of the ligand 1 X 10-6 M, the concentrations of 1:l and 1:2 complexes are calculated as 8.3 X and 1.2 X 1O-Io M, respectively, indicating that the above discussion is valid for the present case because of the marginal contribution of the 1:2 complex to overall chromatographic retention. Equation 1 can be thus simplified as k’ = k’d(1+ C K , K ,
0.07
f
0.06 0.05
5
0.04
0.03 0.02 0.01
0
0.2
0.4
0.6
0.8
1
C /mM Figure 1. Plots based on eq 3‘ for complexation of crown ethers with K+ at 25 OC: 0,B15C A, B18C6; 0,DB18C6; X, DB21C7; 0 , DB24C8; 0 , DB3OC10.
summarized in Table 1 and agree well with literature values listed in parentheses.2 Relation between Capacity Factor and Complexation Constant. When the mobile phase is composed of a pure solvent (no complexation takes place in the mobile phase), a capacity factor reflects only the resin-phase complexation. We previously investigated the complexation of poly(oxyethy1ene) in the s 0 1 u t i o n ~ ~and J ~ the resin phase18 and found that this flexible molecule changes its conformation when forming a resin-phase complex. However, since crown ethers are much more rigid than the acyclic counterparts, the conformation change of the former will be marginal. Therefore, 1:l stoichiometry is thought to hold in the resin phase
... K,C’)
where k b denotes the capacity factor obtained with a pure solvent not containing a metal ion, Ki is an i:l (metal ion/ ligand) complex formation constant, and Cis theconcentration of a metal ion in the mobile phase. In most cases, multiple complexation is too weak to be detected as changes in the chromatographic retention. In such cases, equation 2 is further simplified as k’ = k’d(l+K,C)
(3)
llk’ = (1+ K,C)/k’,
(3’)
Equation 3’ shows that llk’is proportional to C and that an interceptisequalto l/kb,andaratioofaslopetotheintercept gives K1. Figure 1 shows example plots based on eq 3’, where the retention behaviors of B15C5, benzo-18-crown-6 (B18C6), dibenzo-18-crown-6 (DB18C6), dibenzo-21-crown-7 (DB21 C7), dibenzo-24-crown-8 (DB24C8), and dibenzo-30crown-10 (DB30C10) were investigated using K+ as a countercation. Linear relations suggest that only 1:1 complex formation is detected. Obtained complexation constants are
where [M+(r)] is the concentration of a metal ion in the resin phase and K, is the resin phase complexation constant. If there is no marked difference in the complexation between in solution and in the resin phase, we can expect a correlation between the resin phase complexation constant (K,) and the solution phase complexation constant (Kt). Figure 2 shows a log Kl-log ko’ plot. This relation can be represented by log K,= 1.186 + 1.157 log k’,
(r = 0.9654)
(5)
There has also been found a similar linear relation between enthalpic changes in the complexation in solution and those in the resin phase. Equation 5 allows the estimation of K1 from k b, which is obtained from a single experiment. Although these results seem to indicate the similarity of the complexation of crown ethers in solution and in the resin phase, there may exist the difference between these, which will be elucidated in the near future. Table 2 lists such values estimated with eq 5 . In some cases, k b cannot be measured due to too large complexation ability of a ligand. Stationary phases of lower total ionexchange capacity should be used for such ligands. In general, Analytical Chemistry, Vol. 66,No. 10, May 15, 1994
1855
Table 1. Llst of Complexatlon Constants Obtalned Based on Equatlon 3’ log K,
Na+
K+ Rb+
cs+
B15C5
B18C6
2.87 (2.87-3.37) 2.87 (2.80-3.15) 2.66
4.16 (4.03-4.50) 4.76 (5.05-5.70) 4.38 (4.62-5.10) 3.97 (3.66-4.10) 3.22
2.30 (1.91-2.03) -
NH4+
DB18C6 4.35 (4.36-4.50) 4.68 (4.80-5.10) 4.13 (4.23) 3.57 (2.92-3.55) 2.60
DB21C7
DB24C8
DB30C10 (2.0-2.1) 4.33 (4.60) 4.62 (4.60) 4.11 (4.20) 2.65
-
-a
(2.40) 4.09
(2.25) 3.49 (3.57-3.60) 3.80 (3.85-3.86) 3.76 (3.78-3.84)
4.45 4.27 (4.20) 2.84
-
Not determined due to very weak retention ability. Values in parentheses are taken from ref 2. 5
n=s ~
r . 4
4.5
b
2
4
Y-
t
3 c
/
I
-$ 3 5 1
*
2
b
M
=
I
S
2 2 ‘
0 5
1
I
I
I
I
1 5
2
25
3
3 5
log ko
Flgure2. log k’&g K, plot obtained at 25 OC: (1) B15C5, (2) B18C6, (3) DB18C6, (4) DB21C7, (5) DB24C8, (6) DB30C10; 0 Na+; 0,K+; 0 ,Rb’; X, CS;’ A,NH4’. Table 2. Complexatlon Constants Obtalned on the Beds of a Slngle Experlment
log Ki B15C5 B18C6 DB18C6 DB21C7 DB24C8 DB30C10 Na+ 3.06 1.92 2.40 2.14 K+ 2.80 3.29 Rb+ 2.55 3.56 4.01 3.68 4.32 3.68 3.95 Cs+ 2.24 2.72 3.10 2.17 NH4+ 1.74 3.53 3.07 a
Flgure 3. Variation of uKwlth K1 and the ion-exchange capaclty of stationary phase. Five measurementsusing mobile phases containing a metal Ion of 0.2-1 mM were assumed.
to derive the deviation of a K I value on the basis of eq 3. Both
K1 and k$ obtained from linear plots based on eq 3‘ were used as initial values to find optimum values. Starting with a Jacobian matrix (J), we can obtain a standard deviation for K1 as eq 6
k’o was not measured because of a too strong retention ability.
xi = 1/(1 + KICi) this approach is effective for the determination of relatively small complexation constants that cannot be evaluated using eq 3 or 3’. Results summarized in Tables 1 and 2 permit some consideration on the selectivity of crown ethers. It is generally believed that the match of the crystalline size of a metal ion with the cavity size of a crown ether predominantly determines the complexation selectivity. However, when the cavity size of a crown ether increases, the crown ring becomes flexible and capable of forming stable complexes even with the smaller ions. The size fitting theory is not valid in such cases, as seen for DB24C8 or DB30C10. The insufficient flexibility of these crown ethers leads to the drastic decreases in the complexation constants with Na+. Precision of Complexation Constants. According to the theory of statistics, to apply the method of least squares to the present case, eq 3 rather than eq 3’ should be used, because k’that is an experimental value will show normal distribution while 1lk’will not. Nonlinear regression was therefore used 1656
AnalyticalChemistry, Vol. 66,No. IO, May 15, 1994
where n is the number of experiments, r is a residual sum of squares, and Ci is the concentration used in the ith experiment. In order to facilitate the derivation of eq 6 and the simulation shown below, variances of all measurements (by) were assumed to be constant. We can predict k b for a crown ether having a particular K1 value on the basis of eq 5 , if the retention mechanism is not changed by varying the total ion-exchange capacity. A dependence of UK on the total ion-exchange capacity (or metal ion concentration in the resin phase) was simulated using eq 6 as shown in Figure 3, where five measurements (the concentration of a metal ion ranges 0.2-1 mM) were assumed for the determination of K1. Regardless of the magnitude of K1, smaller QK is obtained with a higher capacity resin, and a minimum can be seen at log K1 = ca. 3. UK is also varied with the mobile phase concentration as shown in Figure 4, where a constant ion-exchange capacity was assumed. Suitable concentration ranges are varied with
4r
~
A
Table 3. Optlmum Condltlonr To Mlnimlze the Deviation of Complexatton Constant8 Obtained.
log KI
ion-exchange capacity of the stationary hase/ m eqwv g P
maximum concn of a metal ion/M
k’oc
2 2.7 3 4 5
>lb 0.62 0.34 0.045 0.006
3.03 X 10-9 1.84 x 10-9 9.20 X lo-‘ 9.89 X 1od 9.50 X 10-8
15.04 37.4 37.5 40.0 38.5
r
\3
3 -
I
2
I
I
3
4
5
log K, Figure 4. Varlation of uKwilh K1,the ion-exchange capactty of stationary phase, and the Concentration range of the mobile phase.
I
0 Five ex erimenta were assumedtobe done to determine K1 values using mobje phases containing a metal ion at the concentrations ranging from zero to the maximum concentrationslistedabove.These values were calculated under the restriction of k’ = 4-150. Because of the low reality in preparing an ion-exchange resin having such high capacity, optimum ion-exchange capacity was saught over the range of 104-10s. A column, total ion-exchange capacity of which is smaller than above by a factor of 0.12, was prepared and used for the determination of Kl ranging 104-10s. Relative standard deviations obtained by using this column were 8.4%(log K I = 4.97) for B18C6, 12.0% (4.85) for DB18C6,8.7% (4.07) for DB21C7, and 9.5% (4.56) for DB30C10 with K+; these are much improved in comparison with values listed in Table 4. Hence, the present method has proved to be effective for the determination of complexation constants of crown ethers. In addition, the simple retention mechanism allowed the optimization of the experimental conditions by altering the ion-exchange capacity and the mobile phase concentration. However, the low metal ion concentration may cause the other problem; e.g. the formation of sandwich-like complexes is not negligible, when taking place, under such a condition.
ACKNOWLEDGMENT This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture, Japan. We thank Tosoh Co. for generous gifts of separation columns. Received for review July 7, 1993. Accepted February 23, 1994,@ a
Abstract published in Advunce ACS Absrructs, April 1, 1994.
AnalvticalChemistrx Vol. 68, No. 10, May 15, 1994
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