J . Phys. Chem. 1985,89, 3152-3151
3752
puddles when the solution is frozen.
Concluding Remarks The present study revealed that both solute and organic solvent molecules are excluded from growing ice crystals during freezing to form the "puddles" of organic solvent in which the solute molecules are concentrated, when the aqueous solution containing small amounts of organic solvent is quickly frozen. In previous studies, we found that the freeze-thaw cycles can effect the solubilization of hydrophobic solute molecules in ionic surfactant micelles and assumed that the accelerated solubilization observed on freezing and thawing is due to a concentration of both micelles and solute molecules in the liquid domain remaining between the ice crystals and dehydration of micelles leading to formation of more hydrophobic micel1es.'v2 The present system can be regarded as a model for investigating this concentration effect on freezing in the micellar system where micelles have been replaced by
acetone. The results obtained in this study strongly support the belief that the concentration effect of freezing contributes significantly to the acceleration of solubilization in micelles by freezing and thawing. Since the solute molecules can diffuse freely in these puddles, photochemical bimolecular processes, such as pyrene-excimer formation and the fluorescence quenching of pyrene by DMA, are drastically accelerated by freezing. Such a freezing effect is expected to be very useful in photochemical reactions in which two or more molecules participate.
Acknowledgment. We are grateful to Professor S. Hirayama for his help in analyzing the fluorescence decay curves. The support of the Asahi Glass Foundation for Industrial Technology is gratefully acknowledged. Registry No. P(3)P, 61549-24-4; ANS, 82-76-8; DMA, 121-69-7; pyrene, 129-00-0: acetone, 67-64-1; water, 7732-18-5.
Complexation of Alkali Metal and Barlum Cations by sym-Dibenzo-16-crown-5-oxyacetic Acld in 80 % Methanol-Water. Dependence by Calorimetric mratlon
Determination of pH
Raymond J. Adamic, Edward M. Eyring,* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
Sergio Petrucci, Department of Chemistry, Polytechnic Institute of New York, Farmingdale, New York I I735
and Richard A. Bartsch Department of Chemistry, Texas Tech University, Lubbock, Texas 79409 (Received: February 4, 1985; In Final Form: April 15, 1985)
The acid dissociation constant, K,, for sym-dibenzo-16-crown-5-oxyaceticacid, 1, in 80% methanol-water (w/w) has been determined potentiometrically. Dependence of K,,on NaI concentration was also determined. The thermodynamic parameters AH, AG, and TAS and stability constants have been measured by thermometric titration for complexation of alkali metal and BaZ+cations by 1 in 80% methanol-water (w/w) at 25 OC. Dependence on pH and Na+ concentration was investigated. A modest increase in complex stability (A log K = 0.92) was observed for the acid crown as the pH increases: this enhanced binding is attributed to the anionic participation of the ionizable side group in metal ion coordination. An equation relating the free energy changes of complexation in terms of contributions from the polyether ring and the carboxylate group is presented and discussed.
Introduction Recent advances in the synthesis of new ionophores capable of complexing alkali metal ions have included crown ethers specially designed to serve as the counterion to the metal ion they are One particular class of crown compounds, the so-called 'acid crowns", contains, in addition to the polyether ring, a pendant carboxylic acid group. These ionizable crown ethers have been shown to have higher extraction efficiencies and selectivities for alkali metal and alkaline earth metal cations over their nonacidic c o ~ n t e r p a r t s . ~Stability ,~ constant measurements of cation complexation by 15-crown-5 and 18-crown-6 macrocycles which bear pendant carboxylate groups have shown the complexes formed by the ionized acid crown in water and 90% (v/v)
methanol-water to have greater stability than those produced with the corresponding protonated f ~ r m . ~This ? ~increase in stability has been attributed to an electrostatic interaction of the charged side group(s) with the complexed metal ion. Proximity of the carboxylate moiety to the metal ion and the charge of the cation can both be expected to influence the strength of the interaction. Increasing the pH to favor the anionic form should, in principle, enhance the overall stability of the complex. Thus, just as cavity size is an important factor in determining cation selectivity of neutral crown ethers, pH, ionic charge, and degree of electrostatic interaction should also have important bearing on the stability of complexes formed from crown ethers with pendant ionizable side groups. To enhance understanding of the relative importance of these factors, we have conducted a pH dependence study of
(1) Bartsch, R. A.; Heo, G. S.;Kang, S. I.; Liu, Y.; Strzelbicki, J. J. Org. Chem. 1982, 47, 457. (2) Czech, B.; Kang, S.I.; Bartsch, R. A. Tetrahedron Lett. 1983,24,457. ( 3 ) Strzelbicki, J.; Bartsch, R. A. Anal. Chem. 1981, 53, 2247. (4) Strzelbicki, J.; Bartsch, R. A. Anal. Chem. 1981, 53, 2251.
( 5 ) Behr, J. P.; Lehn, J.-M.; Vierling, P. J.Chem. Soc., Chem. Commun. 1976, 621. ( 6 ) Frederick, L. A.; Fyles, T. M.; Gurprasad, N. P.; Whitfield, D. M. Can. J . Chem. 1981, 12, 1724.
0022-3654/85/2089-3752$01 SO10 0 1985 American Chemical Society
Crown Complexation by Alkali Metal and Ba2+ an acid crown complexing cations,in solution. The present investigation focuses on the acid crown sym-dibenzo- 16-crown-5-oxyacetic acid (1) which has earlier been 0 I
“rPc
H&oH
utilized for solvent extraction of alkali metal cations from water into chloroform.’ Potentiometric and calorimetric titrations are used to evaluate formation constants of 1 with alkali metal ions and Ba2+ in 80% methanol-water (w/w) at 25 OC. Log K and AH values are determined for the anionic ligand at pH 11 with Na+, K+, Rb+, and Cs+ cations and at pH 9 with Ba2+,along with the thermodynamic parameters AG and TAS. Furthermore, log K, AH, AG,and TAS values are reported for association of Na+, K+,and BaZ+with the un-ionized crown acid at pH 3 as well as for Na+ complexations at pH values in the range 2-11. An equation which relates the free energy changes associated with the contributions from both the polyether ring portion of the crown compound and the electrostatic interaction of the carboxylate group with the metal ion is developed. This relationship correlates well the results of the present study with those of previous investigations.
Experimental Section Chemicals and Solutionr. Two different samples of 1were used for the titrations. Although both samples gave satisfactory elemental analysis: the total acid content as determined by titration to the potentiometric endpoint was 95.5% for sample A and 97.4% for sample B. Within experimental error, log K values were identical when determined with the two different samples of 1. LiCl, Ba12-2H20,and NaI (all Fisher), NaCl (Baker Analyzed), KI and CsCl (MCB), and RbCl (Aldrich) salts were dried prior to weighing either under vacuum at 115 OC for 2 h or overnight in an oven at 90 OC. Acetone-free absolute methanol (Fisher) was used without further purification as was 20% (C2H5)4NOH in H 2 0 (Aldrich) and (CH3)4NCl(Aldrich). Dilute solutions of HCl (Fisher) and 20% (CzH5)4NOHin H20in 80% methanolwater (w/w) were prepared for pH adjustment. For potentiometric titrations 0.10 M solutions of titrant in isopropyl alcohol (Aldrich) were prepared from 1.O M n-Bu4NOH in methanol (Aldrich). Solutions of buffers for pH measurements were prepared from 0.01 m oxalic acid (B & A)-O.01 m ammonium hydrogen oxalate (made by adding an equivalent amount of N H 4 0 H to oxalic acid) and 0.01 m succinic acid (made by acidification of the dipotassium salt of succinic acid)-O.Ol m lithium hydrogen succinate (prepared by adding an equivalent amount of LiOH to succinic acid)? All solutions were prepared volumetrically and weight percentages were determined gravimetrically. Water used in all experiments was distilled three times and boiled prior to use. Apparatus, Procedure, and Calculations: Potentiometry. pH measurements and potentiometric titrations were camed out with a Sargent-Welch Model NX pH meter. A glass combination electrode (Fisher Cat. No. 13-639-271) was conditioned in an 80% C H 3 0 H - H 2 0 solvent mixture and calibrated with the oxalic acid-oxalate and succinic acid-succinate buffers.1° All titrations were conducted under a nitrogen atmosphere (boil off of liquid nitrogen). The acid dissociation constants were first calculated as mixed dissociation constants and are equal to the thermody(7) Strzelbicki, J.; Bartsch, R. A. Anal. Chem. 1981, 53, 1984. (8) Elemental analysis. Calcd for C21H2408:C, 62.38; H, 5.94. Found (sample A): C, 62.41; H, 6.02. Found (sample B): C, 62.47; H, 5.94. (9) DeLigny, C. L.; Luykx, P.F. M.;Rehbach, M.;Wiencke, A. A. R e d . Trau. Chim. Puys-Bas 1960, 79, 713. (10) Deligny, C. L.; Rehbach, R e d . Trau. Chim. Puys-Bus 1960,79,727.
The Journal of Physical Chemistry, Vol. 89, No. 17, 1985 3753 namic acid dissociation constant after activity corrections are applied. The ionic strength for the titrations varied from -0.006 M (no salt added) to -0.012 M (highest salt concentration). The activity coefficients were calculated from the Debye-Hiickel relationship: log y* = -
AZ~Z,’/~
1
+ BaZ,1/2
where A and B equal 1.265 and 0.446, respectively, for 80% methanol-water and a, the distance of closest approach, is taken to be 5 A, and I , is the ionic strength at the midpoint of the titration.“ Calorimetry. The thermometric titrations were done in a Tronac Model 450 isoperibol calorimeter. Stability constants, K, and the enthalpy changes, AH, were measured at a temperature of 25.00 f 0.02 OC. The procedure consisted of filling the buret with the appropriate salt solution in 80% methanol-water (-0.32 M) which had to be adjusted to the proper pH by addition of a 0.09 or a 0.01 M solution of (C2H5)4NOH or HC1 in 80% methanol-water, and titrating into the acid crown (-6 X M) in 80% methanol-water at the same pH. The reverse titration could not be carried out due to the limited solubility of 1 in 80% CH30H-H20. For Ba2+at pH 9 where log K is greater than 4, the titrate consisted of 1 plus RbC1. Heats of dilution were determined by titrating into the solvent adjusted to the approximate pH and to the ionic strength with (CH,),NCl in the absence of ligand. A titration in the absence of metal ions was also conducted. The heat changes were measured by a digital voltmeter interfaced to a Terak 8510 computer. The pH of the titrated solution was measured potentiometrically immediately after each experiment. The resulting titration curves were analyzed by a least-squares method to evaluate12log K and AH. For titrations in which the acid crown exists in solution as a single species (either the ionized or un-ionized form), the data were fitted well by the following equations: M+
+ CR- F! MCR
K1 =
[MCRI [M+l [CR-I
M+ + HCR
$
(2)
MHCRS
[ MHCR’]
K2 =
[M+l [HCRI
(3)
where HCR denotes the un-ionized crown ether, etc. At pH values where both protonated and anionic forms of 1 are present in solution, the data were fitted by the equation: M+ Me
+ CR- F! MCR
+ HCR
$
MHCRt (4)
where K’ is the overall stability constant, [MCR’] is the total concentration of metal ion complexed with ligand, and [L’] is the total concentration of uncomplexed ligand in both the neutral and anionic forms. Since the ionic strengths of the titrated solutions were less than 0.01 M, no activity corrections were applied.
Results Preliminary experiments conducted with 1 in water at pH 11 with K+ showed no heat of reaction other than the heat of dilution. Ligand 1 is completely ionized at this pH. When AH for cation ~~~~~
~
(1 1) Nancollas, G. H. “Interactions in Electrolyte Solutions”; Elsevier: New York, 1966; p 14. (12) Eatough, D. J.; Christensen, J. J.; Izatt, R. M. Thermochim. Acra 1972, 3, 219.
Adamic et al.
3754 The Journal of Physical Chemistry, Vol. 89, No. 17, I985 TABLE I: Acid Dissociation Constants, pK,, for 1, as a Function of NaI Concentration in 80%Methanol-Water NaI concn, M 0
1.8 X lo-' 3.07 X lo-' 5.61 X lo-'
PK* 5.90 f 0.09' 5.45 f 0.21b 5.24 f 0.18b 4.93 f O.1gb
"Averages of 6-16 values. The value reported is an average of three titrations with uncertainty expressed as mean deviation. *Averages of 10-13 values with uncertainty expressed as mean deviation.
complexation is assumed not to be zero, this finding suggests that the charge-localized13 nature of the carboxylate anion together with the strong solvation of K+ by water molecules precludes complexation of the cation by the crown ether oxygen atoms and the anionic side group. Thus, the electrostatic interaction between the metal and carboxylate ions is insufficient to stabilize a complex in a medium with such a high dielectric constant as water ( a = 78.54 at 25 OC). Subsequent measurements demonstrated that sufficient stabilization could be achieved by use of a solvent with a lower dielectric constant, 80% methanol-water (e = 42.60).14 Dissociation Behavior. The thermodynamic dissociation constant of 1 in 80% methanol-water was determined to be pKa = 5.90 f 0.09 at 25 O C . The pK, value reported' for 1 in water is 4.59 f 0.22. The result in aqueous methanol is quite reasonable since the leveling effect of alcohols on weak acids amounts to a ApK of about +1 pK unit for 60% methanol-water.15 This effect can be largely attributed to the energy of ionsolvent interaction with preferential solvation of the proton by water as the proportion of water in the solvent decreases. An opposite effect on pK, was observed in the presence of the salt, NaI. As shown in Table I, an increase in the dissociation constant (i.e., an increase in the acidity of the acid crown) was observed as the salt concentration increased. Similar behavior was also noted for the calorimetric titrations at different pH values and was verified potentiometrically by a titration of 1 at an initial pH of 5.14 at 25 OC with a N a I solution. A pH decrease with increasing metal ion concentration occurred with the dimunition in pH being the greatest during the initial period of the titration and reaching an asymptotic value as the titration proceeds toward completion. A final p H of 4.30 was measured. This type of behavior was observed in all calorimetric titrations except at pH 2 or 3. However, it should be emphasized that the pH decreases observed during the course of the titrations a t high pH (9 and 11) are small in magnitude compared to the ligand and salt concentrations used in the experiments; their change is insignificant. Anionic Crown Ether Complexation. If the difference (pKa - pH) of a solution of a weak acid is 4-4.0, then 99.99% of the acid is completely ionized. For 1 in 80% methanol-water, a pH greater or equal to 9.90 would, to this approximation, produce only the anionic form of the crown ether ligand. Table I1 gives the log K and AH values for the association of alkali metal cations with 1 and the thermodynamic parameters AG and T U . No heat other than the heat of dilution was measured for Li+. There is a decrease in log K as the metal ions become larger, and, in general, a less exothermic AH is observed. The data are interpreted in terms of a 1:l reaction of metal ion to ligand although a 1:2 ratio, as found16in other crown ether thermometric titration studies with neutral ligands, cannot be ruled out. However, in the absence of direct experimental evidence for 1:2 complex (13) The charge on the carboxylate anion is effectively distributed over both oxygen atoms but due to the closeness of the atoms a cation can interact with both. This results in a large ion, such as R C 0 2 - , having a small effective electrostatic radius and behaving as if the charge were localized. Gordon, J. E. "The Organic Chemistry of Electrolyte Solutions"; Wiley: New York, 1975; p 397. (14) Oiwa, T. I. J . Phys. Chem. 1956, 60, 754. (15) Albert,A,; Sarjeant, E. P. "Ionization Constants of Acids and Basts", Metheun: London, 1962; p 66. (16) Izatt, R. M.; Terry, R. E.; Nelson, D. P.; Chan, Y.; Eatough, D. J.; Bradshaw, J. S.; Hansen, J. S.;Christensen, J. J. J . Am. Chem. SOC.1976, 98, 1626.
SCHEME I
Kal +. M+ + CR-
___________ _ _ _K_!----MCR
formation with anionic crown ethers, a 1:l ratioI7?l8is assumed. pH Dependence of Cation Complexation. Na+ complexation by 1 was studied as a function of pH at initial pH values of 2, 3, 4, 5, 6, 7, 9, and 11. At pH 9 the ligand is 99.9% ionized and a value of 3.33 for log K was obtained as shown in Table 111. When the H+ concentration is enhanced, the concentration of neutral ligand increases which results in a competition for the metal ion at thp expense of the anionic form of 1. Finally at pH 3, the ligand is fully protonated and only the polyether ring portion of the crown ether complexes the metal ion. The cavity size of 1 is estimated' to be 2.0-2.4 A, whereas the cavity size of 15crown-5 is reportedlylg 1.7-2.2 A. Thermometric titrations of monobenzo-15-crown-5 in 80% methanol-water with Na' at an ionic strength of 0.1 M by Izatt et a1.16 produced a log K value of 2.26 f 0.02 and AH value of -8.32 f 0.03 kcal/mol. If monobenzo-15-crown-5 is assumed similar in cavity size to 15crown-5, these results are quite consistent with our calorimetric data that yield at pH 3 values of log K = 2.35 f 0.1 1 and AH = -8.6 f 0.8 kcal/mol. Moreover, no 1:2 complex formation for the monobenzo-15-crown-5 at this solvent composition was observed.16 log K and AH values were also measured for complexation of K+ by 1 at pH 3 and 11. Only a single titration at pH 3 and 9 was conducted for Ba2+ since limited quantities of 1 precluded additional titrations. The resultant values are presented in Table IV.
Discussion In basic solution at a high pH where 1 exists in the completely ionized form, the reaction between the alkali metal ion and macrocycle can be conveniently expressed by eq 2, where K1 represents the stability constant for unprotonated ligand complexation of metal ion. In acidic solution where deprotonation of the ligand is suppressed, the complexation reaction is described by eq 3 where K2 is the stability constant for association of the metal cation with the neutral ligand. At intermediate pH values, reactions represented by both eq 2 and 3 may take place. Both processes are coupled together by the H+ concentration and the overall system can be represented by Scheme I. Within the intermediate pH range of 3-9, the stability constant for the metal ion complexation by the neutral and anionic forms of the ligand is complicated by the presence of the following additional reactions: HCR s H+ K, =
MHCR'
K,' =
+ CR-
[H+ILCR-1 WCRI MCR
+ Ht
[MCRI [H+l [ MHCR+]
Equations 5 and 6 represent dissociation of H+ from the acid crown and the complexed crown ether, respectively, and are the primary sources for the decrease in pH observed during the titrations. In (17) 1:2 metal-ligand complexes could be detected by thermometric titrations if the reverse titration of crown ether into metal ion solution could be conducted. (18) Bartsch and co-workers have made extraction constant calculations for Li, Na, K, and Rb ions extracted from aqueous solution into chloroform with 1. The calculations suggest that the metal carboxylate in the chloroform phase is solvated by two neutral, carboxylic acid crown ether ligands in the pH region 3-7.5. (19) Frensdorff, H. K. J . Am. Chem. SOC.1971, 93, 600.
The Journal of Physical Chemistry, Vol. 89, No. 17, 1985 3755
Crown Complexation by Alkali Metal and Ba2+
TABLE II: log K and Thermodynamic Values for Interactions of 1 with Alkali Metal Cations in 80%Methanol-Water at 25 OC at pH 11
cation Li+ Na+ K+ Rb+
cs+
log Kasb
AH,b kcal/mol
AG,kcal/mol
TAS, kcal/mol
initialC
PH finalC
avd
-5.92 f 0.25 -6.5 f 0.5 -3.79 f 0.07 -1.12 f 0.07
-4.47 f 0.15 -4.2 f 0.22 -3.84 f 0.01 -3.69 f 0.02
-1.45 f 0.23 -2.3 f 0.55 +0.05 f 0.07 +2.58 f 0.07
11.03 f 0.01 11.02 f 0.02 11.02 f 0.03 11.00 f 0.02
10.79 f 0.15 10.80 f 0.07 10.69 f 0.08 10.70 f 0.05
10.91 f 0.12 10.90 f 0.12 10.82 f 0.17 10.82 f 0.15
e
3.27 3.11 2.81 2.70
f 0.11 f 0.16
f 0.01
f 0.02
a log K values are reported as mean values with uncertainty expressed as standard deviations. Values reported are averages of 3-7 titrations. pHlnillal and pH,,,, are average pH's for titrations with uncertainties expressed as standard deviations. dpH,, values are expressed with mean deviations. eNo evidence of complexation.
TABLE III: log K and Thermodynamic Parameters for Association of Na+ with 1 in 80% Methanol-Water at 25 OC as a Function of pH uH 2 3 4 5 6 7 9 11
log Ka,b 2.34 f 0.02 2.35 f 0.11 2.58 f 0.06 2.71 f 0.00 2.93 f 0.00 3.27 f 0.09 3.33 f 0.08 3.27 f 0.11
AH,"sb kcal/mol
-8.30 f 0.12 -8.6 f 0.8 -6.97 f 0.15 -6.45 f 0.08 -6.57 f 0.11 -5.83 f 0.15 -6.09 f 0.02 -5.92 f 0.25
AG. kcal/mol
TAX kcal/mol
-3.20 -3.21 -3.35 -3.70 -4.00 -4.41 -4.55 -4.47
-5.10 -5.39 -3.35 -2.75 -2.57 -1.36 -1.56 -1.45
f 0.02 f 0.15 f 0.17 f 0.00 f 0.00
f 0.12 f 0.10 f 0.15
0.12 0.8 0.17 0.08 0.11 f 0.19 f 0.10 f 0.3 f f f f f
initialC
PH finalC
avd
2.00 f 0.01 3.02 f 0.01 4.01 f 0.01 5.02 f 0.01 6.01 f 0.01 7.02 f 0.01 9.03 f 0.04 11.03 f 0.01
1.88 f 0.04 2.99 f 0.03 3.35 f 0.07 4.22 f 0.01 5.17 f 0.01 6.28 f 0.14 8.8 f 0.01 10.79 f 0.15
1.94 f 0.08 3.00 f 0.03 3.68 f 0.33 4.16 f 0.40 5.41 f 0.42 6.51 f 0.37 8.91 f 0.12 10.89 f 0.12
aUncertainties for log K and AH are expressed as standard deviations. bValues reported are averages of 2-7 titrations. 'Mean initial and final pH of titration solutions with uncertainties expressed as standard deviations. Average pH uncertainties expressed as mean deviations. TABLE IV: log K and Thermodynamic Parameters for Complexation of K+ and Baz+ with 1 in 80%Methanol-Water at 25 O C at Different pH Values cation pH log K AH AG TAS K+ 3 2.23 f 0.07 -7.28 f 0.79 -3.05 f 0.10 -4.22 f 0.80 K+ 11 3 . 1 1 f 0 . 1 6 - 6 . 5 f 0 . 5 -4.2f0.22 -2.3f0.55 Ba2+ 3 2.71 -4.24 -3.70 -0.54 BaZ+ 9 5.73 -4.83 -7.82 +2.99
addition, other reactions such as the ionization of water at or near neutral pH values may further complicate the system. Nevertheless, the reaction system represented by Scheme I contains sufficient information to relate K1, K2, K,, and K,' through K2K,' = K,Kl
(7)
Equation 7 can be used to check the internal consistency of the results, since K,' and K, may be determined independently from K2 and K,. For Na+ K, and K,' were determined by potentiometric titration to be 1.26 X lo6 and 1.17 X lo-', respectively. K, at pH 11 for Na+ was found by calorimetric titration to be 1.86 X lo3. Substitution of these values into eq 7 provides a calculated K2 value of 2.00 X lo2 (log K2 = 2.30). The log K2 value of 2.35 f 0.11 obtained from calorimetric measurement is quite consistent with this calculated result. Thus, Scheme I can be considered to adequately represent the present system. The selectivity of crown ether macrocycles for particular cations is determined in part by the cation size-cavity size relationship. Although there is some recent evidence'J1 that the hole size-cation size correlation may not be as dominant a factor in determining cation specificity as was once thought, the concept is quite useful for estimating crown ether selectivity. For the alkali metal ions complexed by 1, with a cavity size of 2.0-2.4 A, the best "fit" should be with N a + (ionic radius: 1.02 A). The log K value of 3.27 f 0.1 1 for Na+ noted at pH 11 surpasses the average log K value of 3.1 1 f 0.16 for association with K+ (1.38 A) with 1 at pH 11. Also, the log K value for Rb+ (1.49 A) is lower than that for K+ yet higher than that for Cs+ (1.70 A). A similar situation prevails for Na+ and K+ complexation at pH 3. However, the uncertainties in log K values preclude a definitive statement about the Na+/K+ selectivity. However, for Ba2+ (1.36 A) at pH 3 the log K value of 2.71 clearly exceeds that for either K+ or Na+. (20) Michaux, G.; Reisse, J. J . Am. Chem. SOC.1982, 104, 6895. (21) Gokel, G. W.; Goli, D. M.; Minganti, C.; Echegoyen, L. J. Am. Chem. SOC.1983, 105, 6786.
This result indicates that other factors besides the cation sizecavity size relationship play a role in determining selectivity. Analysis of the stability constants for interaction of 1 with Na+, K+, and Ba2+as a function of pH suggests that enhanced complex stability is acquired through the greater participation of the anionic crown ether over that of the neutral form. For Na+ at pH values of 2 and 3 a log K2 value of 2.35 f 0.1 1 is obtained. As the pH is increased the relative proportion of the anionic form of the ligand increases and a concomitant increase in stability is observed. Calorimetric titrations beginning at pH values of 4, 5 , 6, and 7 produced log K'values of 2.58, 2.71, 2.93, and 3.27, respectively. A maximum in stability is attained when the pH 3 9 and the ligand is completely ionized. Thus, an overall enhanced stability constant of approximately 0.92 log K units is ascribable to the participation of the carboxylate anion. Likewise, for K+ an increase in stability of approximately 0.85 log K units is achieved. Similar binding strength enhancements have been noted6 for the basic form of the monoamide carboxyl derivative of 15-crown-5 and 18-crown-6 with alkali metal ions in 90% methanol-water (v/v) at 25 OC. For association of Ba2+with 1 the log K value of 5.73 at pH 9 provides further evidence of a strong enhancement of complex stability by electrostatic interaction. Similar results were previously obtained22for an acylic analogue of benzo-18crown-6, the anionic form of o-hydroxyphenyl 3,6,9,12-tetraoxatridecyl ether, 2, in methanol at 25 OC. log K values of 2.99 and 3.40 for Na+ and K+ vs. 6.43 for Ba2+ were measured spectrophotometrically. Three general types of side-arm interactions in 1 can be envisioned: (i) neutral side-arm interaction with the ring oxygen atoms via intramolecular hydrogen bonding, (ii) neutral side-arm interaction of the carboxyl oxygen with the metal ion, and (iii) charged side-arm interaction with the metal ion. Hydrogen bonding between the acid proton and the ring oxygen atoms of 1 is certainly a plausible assumption providing the flexibility of the arm is sufficient to allow such interaction. However, evidence23 gathered from electric field effect relaxation studies of the acid dissociation constants of 1 in water and 80% methanol water as well as far-infrared spectra of 1 in deuterated chloroform show no intramolecular hydrogen bonding at room temperature. Interaction of the carboxyl oxygen of 1 with a complexed metal ion should produce an increase in complex stability since an additional (22) Ecolani, G.; Mandolini, L.; Masci, B. J . Am. Chem. SOC.1981, 103,
7487. (23) Adamic, R. J., unpublished data.
3756 The Journal of Physical Chemistry, Vol. 89, No. 17, 1985
I
t 4.5 -
= 4,Oc
co 0
a I
3.5-
Adamic et al. Equation 8 is an empirical relation that allows correlation of the free energy changes with pH of the solution for the interaction of an acid crown with metal ions. It should be emphasized that eq 8 views the AGh contribution as strictly electrostatic in nature. Equation 8 can provide a useful basis for comparison among different acid crown-metal ion systems by evaluating the relative contributions of each term. This allows comparison of the relative changes in free energy between different systems in terms of the free energy changes which make up the separate interactions within the complexes. Squaring both sides of eq 8 provides the relation
-f
t
340
1
2
3
4
5
6 7 8 9 1 0 1 1 PH Figure 1. -AGml vs. pH for association of Na' and 1. Dotted lines refer to limiting behavior observed when the ligand is fully ionized (A = 1 and AGIotal = AGcavity AGanion)and undissociated (A = 0 and AGIO,, =
+
AGcavity).
binding site would be available to the cation. A prerequisite, though, is the proper geometric arrangement of the side arm over the cation to effect complexation. Work by Echegoyen, Gokel, and co-workersz4involving I3C NMR studies of relaxation times of lariat ethers illustrates the requirement of correct geometry. Finally, interaction of the charged side arm with the metal ion again depends upon proper positioning of the carboxylate group as well as the amount of charge present. It is known from crystallographic studiesz5 that in the solid state the pendant carboxylate group of ionized sym-dibenzo- 14-crown-4-oxyacetic acid, 3, bridges to a Li+ cation by an apical water molecule. The length of the side arm apparently precludes direct interaction with the metal ion This may also be true for ionized 1 in solution. A direct ion-pair attraction between the metal ion and charged side group may not occur, but rather a solvent-separated interaction may be taking place. If this is the case, the solvent molecule situated between the metal ion and charged side group must effectively transmit the electrostatic interaction. Of course, higher ionic charge on the metal ion, e.g., changing from a monovalent to a divalent cation, should increase the electrostatic attraction. Additional studies26 will be needed to elucidate more precisely the interactions occurring by mechanisms ii and iii. Further insight into the enhanced stability of ionizable crown ether-alkali metal cation complexes may be gained by examination of the relative changes in free energy. Figure 1 shows a plot of the free energy change for complex formation vs. pH of the solution for interactions of 1 with Na+. Limiting behavior is observed at the pH extremes with a fairly linear dependence on pH in between. The free energy changes depicted in Figure 1 can be described as a function of two effects: (a) a polyether ring cavity size factor; and (b) the degree of electrostatic interaction between metal ion and carboxylate anion. Equation 8 summarizes these two effects in terms of the total free energy change as
(8) AGOtotaI = AGOcavity + XAGOanion where X = 0 for no interaction with the carboxylate anion and X = 1 for maximum interaction. When X = 0 the macrocyclic acid crown is in the neutral form and when X = 1 it is entirely in the ionized state. Intermediate values of p H will produce intermediate values of AGO, through the variation of X between 0 and 1. (24) Echegoyen, L.; Kaiter, A,; Durst, H.; Schultz, R. A.; Duhong, D. M.; Goli, D. M.; Gokel, G. W. J . Am. Chem. Soc. 1984,106, 5100. (25) Shoham, G.; Christianson, D. W.; Bartsch, R. A.; Ha,G. S.; Olsher, V.; Lipscomb, W. N. J. Am. Chem. SOC.1984,206, 1280. (26) Preparation of a compound similar to 1 with an additional methylene group in the side arm is in progress and further thermodynamic studies of complexation under similar conditions should help elucidate the actual role of the side arm.
(AGocavity)2 is again the contribution to metal ion complexation by the crown ether ring only and includes coordination by neutral oxygen atoms external to the ring, (XAGoad0,J2is the contribution of strictly Coulombic interactions between the metal ion and the charged side group, and 2XAGocavityAGoanion is the principal term reflecting increased stability attributable to the metal-crown ether anion complex. In actuality, AGOtotalis the free energy change involving ionsolvent, ligand-solvent, and ion-ligandsolvent interactions in the complexation process. The terms on the right side of eq 8 are the relative contributions of the ion-ligand interactions only. A complete analysis of AGo,o,alwould have to include the effects of solvation. Equation 9 can best be understood by illustrating the various ways a metal ion may associate with the ligand. Structures 4-6
9,
depict three fundamental types of ion-acid crown associations. Structure 4 is a representation of cation coordination by the ring oxygen atoms and neutral external oxygen atoms, if present, and its contribution to eq 9 is given by (AGofavity)Z.Structure 5 represents the complexation of the metal by both ring oxygen atoms and the carboxylate oxygen with its contribution given by the cross term of eq 9. Structure 6 is strictly the electrostatic interaction of uncomplexed metal ion and would be especially evident in solvents wherein either tight ion-pair formation could occur or solvent-separated ion pairs exist. Its contribution to (AGotoa)2 is determined by the (XAGoanion)2 term and would be minimal if singly charged ions of small size are present. However, if ions of higher charge, such as Ca2+,Sr2+,and Baz+, are present,
Crown Complexation by Alkali Metal and Ba2+
The Journal of Physical Chemistry, Vol. 89, No. 17, 1985 3757
TABLE V Stability Constants of both Acid and Basic Forms of Several Acid Crowns and an Acyclic Analogue with Free Energy Percentages As Determined by E4 9” entry 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
acid crown lb lb
cation Na+
solvent 80% CH,OH/H2O (w/w) 80% CHpOH/H2O (w/w) 80% C H 3 0 H / H 2 0 (w/w) 90% CH,OH/H20 (v/v) 90% CHpOH/HZO (v/v) 90% CHBOH/H’O (v/v) 90% CH,OH/H20 (v/v) 90% CHpOH/H20 (v/v) 90% CH30H/H20 (v/v) H20 H20 CHpOH CHpOH CHpOH CH30H CHpOH
K+
I* 7c 7c 7= 8C
Ba2+ Na+
8C
K+
8‘
Rb+
9 9
NH4+
K+ Rb+ Na+
K+ K+
2s 28
Na+ Rb+ Ca2+
28
2g 2s
Ba2+
log KI 3.27 3.1 1 5.73 3.4 2.9 2.7 4.4 5.8 5.0 5.48F 3.5lC 3.40 2.99 2.34 6.20 6.43
log K2 2.35 2.23 2.71 2.7 2.1 1.8 3.3 4.5 4.0 1.85’
