Synergistic Solvent Extraction of Alkaline Earth Cations by Mixtures of

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Anal. Chem. 1999, 71, 2757-2765

Synergistic Solvent Extraction of Alkaline Earth Cations by Mixtures of Di-n-octylphosphoric Acid and Stereoisomers of Dicyclohexano-18-crown-6 Andrew H. Bond, Renato Chiarizia, Vincent J. Huber, and Mark L. Dietz*

Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 Albert W. Herlinger

Loyola University Chicago, Chicago, Illinois 60226 Benjamin P. Hay

Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352

The partitioning of Ca(II), Sr(II), and Ba(II) in solvent extraction systems comprising di-n-octylphosphoric acid (HDOP) and individual stereoisomers of dicyclohexano18-crown-6 (DCH18C6) in toluene has been investigated at 23(2) °C. Results of vapor pressure osmometric experiments, continuous variation studies, single- and doubleextractant dependencies, and acid dependencies have been used to determine the stoichiometries of the extracted complexes. Extraction of Ca(II) by HDOP alone affords Ca(H(DOP)2)2‚HDOP as the extracted species, and no synergism is observed in the presence of DCH18C6, presumably due to the strong complexation of Ca(II) with HDOP and the strained complexes this cation forms with DCH18C6. In the absence of DCH18C6, Sr(II) and Ba(II) are extracted as the M(H(DOP)2)2‚ 2HDOP (M ) Sr or Ba) complexes. Upon addition of DCH18C6, the extracted complexes are formulated as M(DCH18C6)(H(DOP)2)2 (M ) Sr or Ba), with Ba(II) showing greater synergistic effects than Sr(II). The effectiveness of the DCH18C6 stereoisomers as synergists decreases in the following order: cis-syn-cis > cisanti-cis > cis-trans > trans-syn-trans > trans-antitrans. This sequence has been explained by correlating the logarithm of the synergistic adduct formation constants with the ligand strain energies of the DCH18C6 stereoisomers calculated using molecular mechanics methods. Those stereoisomers having the largest strain energies afford the lowest extraction and synergistic adduct formation constants. Electroneutrality must be maintained during the partitioning of ions between phases in solvent extraction. For cations in particular, partitioning may be accomplished by the use of acidic * Corresponding author: (phone) 630-252-3647; (fax) 630-252-7501; (e-mail) [email protected]. 10.1021/ac9900681 CCC: $18.00 Published on Web 06/15/1999

© 1999 American Chemical Society

(e.g., organophosphorus acids, β-diketones), anionic (e.g., I-, cobalt dicarbollide), or neutral extractants (e.g., triorganophosphates, crown ethers). For the latter, electroneutrality is achieved by the coextraction of anions into the organic phase, which can limit the utility of certain separation systems as the diluent must have adequate anion solvating properties and/or water content.1-5 Liquid-liquid distribution using acidic extractants generally does not involve the coextraction of anions, as the extractant itself is anionic under the appropriate aqueous-phase loading conditions. Unfortunately, such systems typically do not exhibit high cation selectivity because the metal-extractant interactions are primarily electrostatic in nature. Conversely, solvent extraction by crown ethers can show exceptional cation selectivity2,6,7 but requires the coextraction of anions to maintain electroneutrality. Attempts to exploit the most favorable characteristics of acidic extractants (i.e., the simplicity of pH adjustment to facilitate loading or stripping) and crown ethers (i.e., the cation size selectivity) have led to their combined use in various extraction systems. When a combination of two extractants yields partitioning that is greater than the sum of their individual contributions, the system is synergistic and the enhanced extraction is most often attributed to the combined coordinating/solvating abilities of the two extractants.1,2,8 A variety of synergistic solvent extraction (1) Sekine, T.; Hasegawa, Y. Solvent Extraction Chemistry; Marcel Dekker: New York, 1977. (2) Principles and Practices of Solvent Extraction; Rydberg, J., Musikas, C., Choppin, G. R., Eds.; Marcel Dekker: New York, 1992. (3) Kinard, W. F.; McDowell, W. J.; Shoun, R. R. Sep. Sci. Technol. 1980, 15, 1013-1024. (4) McDowell, W. J.; Moyer, B. A.; Case, G. N.; Case, F. I. Solvent Extr. Ion Exch. 1986, 4, 217-236. (5) Horwitz, E. P.; Dietz, M. L.; Fisher, D. E. Solvent Extr. Ion Exch. 1990, 8, 199-208. (6) Hiraoka, M. Crown Compounds: Their Characteristics and Applications; Elsevier Scientific Publishing Co.: New York, 1982; Vol. 12. (7) Lindoy, L. F. The Chemistry of Macrocyclic Ligand Complexes; Cambridge University Press: New York, 1989. (8) Marcus, Y.; Kertes, A. S. Ion Exchange and Solvent Extraction of Metal Complexes; Wiley-Interscience: London, 1969.

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systems have been investigated, many involving combinations of trialkyl phosphates, trialkylphosphine oxides, dialkylphosphoric acids, or β-diketones.1,8 Unfortunately, such systems rely primarily on electrostatic interactions and do not offer the cation selectivity that is demanded by emerging environmental, waste management, and technological applications. Attempts to incorporate cation recognition capabilities into synergistic solvent extraction have resulted in the combination of crown ethers with alkylsulfonates,4,9-19 dialkylphosphoric acids,3,4,9,20-25 carboxylic acids,4,9,24,26-29 β-diketones,30-44 acylpyrazolones,45-51 cobalt dicarbollide,52-54 and heteropolytungstates.55 Despite the breadth of these studies, no (9) McDowell, W. J.; Case, G. N.; Aldrup, D. W. Sep. Sci. Technol. 1983, 18, 1483-1507. (10) Wakui, T.; Smid, J. J. Phys. Chem. 1986, 90, 4618-4621. (11) Ensor, D. D.; McDonald, G. R.; Pippin, C. G. Anal. Chem. 1986, 58, 18141816. (12) Bryan, S. A.; McDowell, W. J.; Moyer, B. A.; Baes, C. F., Jr.; Case, G. N. Solvent Extr. Ion Exch. 1987, 5, 717-738. (13) Chadwick, R. B.; McDowell, W. J.; Baes, C. F., Jr. Sep. Sci. Technol. 1988, 23, 1311-1324. (14) Moyer, B. A.; Westerfield, C. L.; McDowell, W. J.; Case, G. N. Sep. Sci. Technol. 1988, 23, 1325-1344. (15) Ensor, D. D.; Reynolds, P. S. J. Less Common Met. 1989, 149, 287-290. (16) Lumetta, G. J.; Moyer, B. A.; Johnson, P. A. Solvent Extr. Ion Exch. 1990, 8, 457-475. (17) McDowell, W. J.; Case, G. N.; McDonough, J. A.; Bartsch, R. A. Anal. Chem. 1992, 64, 3013-3017. (18) Moyer, B. A.; Delmau, L. H.; Lumetta, G. J.; Baes, C. F., Jr. Solvent Extr. Ion Exch. 1993, 11, 889-921. (19) Moyer, B. A.; Delmau, L. H.; Case, G. N.; Bajo, S.; Baes, C. F., Jr. Sep. Sci. Technol. 1995, 30, 1047-1069. (20) Kinard, W. F.; McDowell, W. J. J. Inorg. Nucl. Chem. 1981, 43, 2947-2953. (21) Clark, G. A.; Izatt, R. M.; Christensen, J. J. Sep. Sci. Technol. 1983, 18, 1473-1482. (22) Gloe, K.; Mu ¨ hl, P.; Beyer, L.; Mu ¨ hlstadt, M.; Hoyer, E. Solvent Extr. Ion Exch. 1986, 4, 907-925. (23) Izatt, R. M.; Clark, G. A.; Christensen, J. J. Sep. Sci. Technol. 1986, 21, 865-872. (24) Proyaev, V. V.; Romanovskii, V. V. Radiokhimiya 1992, 34, 156-161. (25) Takahashi, T.; Habata, Y.; Iri, Y. J. Inclusion Phenom. Mol. Recognit. Chem. 1991, 11, 379-388. (26) Moyer, B. A.; McDowell, W. J.; Ontko, R. J.; Bryan, S. A.; Case, G. N. Solvent Extr. Ion Exch. 1986, 4, 83-93. (27) McDowell, W. J.; Arndsten, B. A.; Case, G. N. Solvent Extr. Ion Exch. 1989, 7, 377-393. (28) Imura, H.; Mito, H. J. Radioanal. Nucl. Chem. 1995, 189, 229-235. (29) Masuda, Y.; Zhang, Y.; Yan, C.; Li, B. Talanta 1998, 46, 203-213. (30) Mihn, L. T.; Lengyel, T. J. Radioanal. Nucl. Chem., Lett. 1989, 136, 225230. (31) Shehata, F. A.; Khalifa, S. M.; Aly, H. F. J. Radioanal. Nucl. Chem. 1992, 159, 353-361. (32) Meguro, Y.; Cheng, W.; Imura, H.; Yoshida, Z. J. Radioanal. Nucl. Chem. 1992, 160, 435-442. (33) Billah, M.; Honjo, T.; Terada, K. Anal. Sci. 1993, 9, 251-254. (34) Mathur, J. N.; Choppin, G. R. Solvent Extr. Ion Exch. 1993, 11, 1-18. (35) Dukov, I. L. Monatsh. Chem. 1993, 124, 689-693. (36) Billah, M.; Honjo, T.; Terada, K. Fresenius J. Anal. Chem. 1993, 347, 107110. (37) Meguro, Y.; Yoshida, Z. Radiochim. Acta 1994, 65, 19-22. (38) Kitatsuji, Y.; Meguro, Y.; Yoshida, Z.; Yamamoto, T.; Nishizawa, K. Solvent Extr. Ion Exch. 1995, 13, 289-300. (39) Shehata, F. A.; Daoud, J. A.; Aly, H. F. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 753-758. (40) Shehata, F. A.; El-Dessouky, S. I.; Khalifa, S. M. J. Radioanal. Nucl. Chem. 1995, 196, 369-375. (41) Billah, M.; Honjo, T. Fresenius J. Anal. Chem. 1997, 357, 61-64. (42) Meguro, Y.; Kitatsuji, Y.; Kimura, T.; Yoshida, Z. J. Alloys Cmpds. 1998, 271-273, 790-793. (43) Reddy, M. L. P.; Varma, R. L.; Ramamohan, T. R. Radiochim. Acta 1998, 80, 151-154. (44) Thakur, P.; Chakravortty, V.; Dash, K. C.; Ramamohan, T. R.; Reddy, M. L. P. Radiochim. Acta 1998, 80, 155-161. (45) Lakkis, M.; Brunette, J. P.; Leroy, M. J. F.; Alstad, J. Solvent Extr. Ion Exch. 1986, 4, 287-299.

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systematic investigation of the principal factors governing synergism in the solvent extraction of cations has yet been reported. Before the rational design and application of synergistic extraction systems can be demonstrated, a fundamental understanding of the structure/function relationships that influence the equilibria in these systems is needed. In this study, the extraction of Ca(II), Sr(II), and Ba(II) by di-n-octylphosphoric acid (HDOP) and individual stereoisomers of dicyclohexano-18-crown-6 (DCH18C6) in toluene is reported. Vapor pressure osmometry, continuous variation studies, singleand double-extractant dependencies, and acid dependencies are used to characterize the synergistic extraction equilibria and to permit calculation of the extraction constants. The relationship between the synergistic adduct formation constants and the ligand strain energies of the DCH18C6 complexes of Sr(II) and Ba(II) is also discussed. EXPERIMENTAL SECTION Reagents. All chemicals were of ACS reagent grade quality or better. The cis-syn-cis and cis-anti-cis stereoisomers of DCH18C6 were purchased from Acros Organics at 98% purity and used as received. The syntheses of the trans-syn-trans and trans-anti-trans stereoisomers of DCH18C6 were completed using a new procedure, which is the subject of a forthcoming publication.56 The cis-trans-DCH18C6 was prepared according to the literature method.57 Di-n-octylphosphoric acid was purified by precipitation of the Cu(II) salt using the literature method.58 45Ca, 85Sr, and 133Ba were obtained from Isotope Products Laboratories and used as the nitrate salts in H2O. All H2O was purified using a commercial deionization system. Procedures. The aggregation properties of toluene solutions of HDOP and/or cis-syn-cis- or cis-anti-cis-DCH18C6 were studied using a Jupiter model 833 vapor pressure osmometer. Sucrose octaacetate in toluene was employed as the calibration standard and all microvolt values are the average of three successive additions against a toluene blank. Typical solute concentrations ranged from ∼0.0040 to 0.15 m. Measurements of pH were performed using Accumet or Orion combination glass electrodes connected to Accumet pH meters. Electrodes were calibrated with standard buffers at pH ) 4.00(1) and 7.00(1) immediately prior to use. No activity coefficient (46) Mundra, S. K.; Pai, S. A.; Subramanian, M. S. J. Radioanal. Nucl. Chem. 1987, 116, 203-211. (47) Yonezawa, C.; Choppin, G. R. J. Radioanal. Nucl. Chem. 1989, 134, 233-239. (48) Dukov, I. L. Solvent Extr. Ion Exch. 1992, 10, 637-653. (49) Rusdiarso, B.; Messaoudi, A.; Brunette, J. P. Talanta 1993, 40, 805-809. (50) Thakur, P.; Dash, K. C.; Reddy, M. L. P.; Varma, R. L.; Ramamohan, T. R.; Damodaran, A. D. Radiochim. Acta 1996, 75, 11-16. (51) Reddy, M. L. P.; Varma, R. L.; Ramamohan, T. R.; Damodaran, A. D.; Thakur, P.; Chakravortty, V.; Dash, K. C. Solvent Extr. Ion Exch. 1997, 15, 49-64. (52) Vanura, P.; Jedinakova, V.; Juklikova, I. J. Radioanal. Nucl. Chem. 1992, 163, 81-85. (53) Vanura, P. J. Radioanal. Nucl. Chem. 1998, 228, 43-46. (54) Novy, P.; Vanura, P.; Makrlik, E. J. Radioanal. Nucl. Chem. 1998, 231, 6568. (55) Lin, Z.; Zhongqun, L.; Wenjun, C.; Shaojin, C. J. Radioanal. Nucl. Chem. 1996, 205, 49-56. (56) Huber, V. J.; Dietz, M. L., Argonne National Laboratory, unpublished results. (57) Hayward, R. C.; Overton, C. H.; Whitham, G. H. J. Chem. Soc., Perkin Trans. 1 1976, 2413-2415. (58) McDowell, W. J.; Perdue, P. T.; Case, G. N. J. Inorg. Nucl. Chem. 1976, 38, 2127-2129.

corrections were made to the pH meter readings as the ionic strength seldom exceeded 0.02 M. The aqueous phases used for the continuous variation studies were 0.001 M solutions of M(NO3)2 (M ) Ca, Sr, Ba) in 0.010 M HNO3. The single- and double-extractant dependencies were determined from a 0.010 M phosphate buffer adjusted to pH ) 3.00(5) with concentrated solutions of LiOH or HNO3. (Representative extractant dependencies for Sr(II) were determined from 0.001 M Sr(NO3)2 in 0.010 M HNO3 and from the 0.010 M phosphate buffer system at pH ) 3.00(5). Comparable slopes were obtained for each aqueous phase and indicate similar extraction behavior.) The acid dependencies were determined by equilibrating 0.10 M HDOP and 0.025 M DCH18C6 in toluene with 0.001 M solutions of M(NO3)2 (M ) Ca, Sr, Ba) in 0.010 M HNO3 (O/A ) 0.5 or 0.33) and adjusting the pH with saturated M(OH)2 (M ) Ca, Sr, Ba) solutions. All pH values reported for the acid dependencies were equilibrium values and are represented as pHeq. This approach affords a constant ionic strength medium for the determination of the extraction constants. The distribution ratios were determined by vortex mixing 0.50.8 mL of the aqueous and organic phases (O/A ) 1) for ∼1030 min (preliminary kinetic experiments showed that the extraction reached equilibrium within 2 min). Each system was then centrifuged for ∼5 min, the phases were separated, and 200-µL aliquots of each phase were removed for assay by liquid scintillation (45Ca) or γ counting (85Sr and 133Ba). The distribution ratio is defined as

DM ) cpm in organic phase/cpm in aqueous phase

All count rates were corrected for background and all distribution ratios were collected at 23(2) °C. The extraction constants were determined from the acid dependencies by plotting log DM vs 2pH, which gives an intercept of log Kex plus a constant value (representing [DCH18C6] and [(HDOP)2]2). The data were fit using a Marquardt-Levenberg nonlinear least-squares algorithm embedded in a commercial software package. The estimated standard deviations of the equilibrium constants were calculated from the least-squares analyses. Computational Methods. Molecular mechanics calculations were performed using the MM3(96) program59 with an extended parameter set for the treatment of polydentate ether ligands and their complexes with alkali or alkaline earth cations.60 Conformer searches were performed on each DCH18C6 stereoisomer and on each cation complex with DCH18C6.61-63 All six oxygen donors were constrained to remain connected to the cation during these searches. Ligand strain energies, ∆Ureorg, were calculated as the difference in steric energy between the uncomplexed ligand and the ligand when bound to the cation. Steric energies of the ligand when bound to the cation were obtained by removing the cation (59) MM3(96); Tripos Associates: St. Louis, MO, 1996. (60) Hay, B. P.; Rustad, J. R. J. Am. Chem. Soc. 1994, 116, 6316-6326. (61) Hay, B. P.; Rustad, J. R.; Zipperer, J. P.; Wester, D. W. J. Mol. Struct. (THEOCHEM) 1995, 337, 39-47. (62) Paulsen, M. D.; Rustad, J. R.; Hay, B. P. J. Mol. Struct. (THEOCHEM) 1997, 397, 1-12. (63) Paulsen, M. D.; Hay, B. P. J. Mol. Struct. (THEOCHEM) 1998, 429, 4959.

from the optimized complex and performing an initial energy calculation on the remaining ligand coordinates.64,65 The lowest energy conformations for each pair (i.e., the uncomplexed ligand, ∆Uconf, and the metal complex, ∆Ucomp) were used in the calculation of the ligand strain energies. RESULTS AND DISCUSSION Both DCH18C6 and its di-tert-butyl derivatives have been studied extensively for the removal of 90Sr from nitric acid containing radioactive wastes2,66-70 and have provided the basis for a number of procedures for the separation of Sr(II) and Pb(II) for subsequent determination.71,72 Dicyclohexano-18-crown-6 may exist as any of the five stereoisomers depicted in Figure 1, where each diastereomer differs in the relative stereochemistry of the cyclohexano ring fusion. These structural differences have been shown to result in dramatically different binding constants73 and extraction properties.74 The current studies of synergistic solvent extraction target not only an understanding of the effect of crown ether stereoisomerization on complexation and partitioning but also the influence of the steric bulk of the acidic extractant. Din-octylphosphoric acid is the eight-carbon n-alkyl analogue of the widely used solvent extraction reagent bis(2-ethylhexyl)phosphoric acid (HDEHP), and our studies of synergistic extraction using DCH18C6 and branched alkylphosphoric acid extractants are reported elsewhere.75,76 Extractant Aggregation and Solvent Extraction Dependencies. Elucidation of the extraction equilibria in synergistic systems is vastly simplified in the absence of interactions between extractants, here HDOP and DCH18C6. Figure 2 shows the results of vapor pressure osmometric experiments confirming that HDOP is present as a dimer in toluene, in accord with the literature information.1,2,77 Measurements of the cis-syn-cis and cis-anti(64) Hay, B. P.; Zhang, D.; Rustad, J. R. Inorg. Chem. 1996, 35, 2650-2658. (65) Hay, B. P. In Metal Ion Separation and Preconcentration: Progress and Opportunities; Bond, A. H., Dietz, M. L., Rogers, R. D., Eds.; ACS Symposium Series 716; American Chemical Society: Washington, DC, 1999. (66) Horwitz, E. P.; Dietz, M. L.; Fisher, D. E. Solvent Extr. Ion Exch. 1990, 8, 557-572. (67) Horwitz, E. P.; Dietz, M. L.; Fisher, D. E. Solvent Extr. Ion Exch. 1991, 9, 1-25. (68) Law, J. D.; Wood, D. J.; Olson, L. G.; Todd, T. A. Demonstration of a SREX Flowsheet for the Partitioning of Strontium and Lead from Actual ICPP Sodium-Bearing Waste. INEEL/EXT-97-00832; Idaho National Engineering Laboratory, 1997. (69) Horwitz, E. P.; Schulz, W. W. In Metal-Ion Separation and Preconcentration: Progress and Opportunities; Bond, A. H., Dietz, M. L., Rogers, R. D., Eds.; ACS Symposium Series 716, American Chemical Society: Washington, DC, 1999. (70) Romanovsky, V. N. Chemical Separation Technologies and Related Methods of Nuclear Waste Management: Application, Problems, and Research Needs; Choppin, G. R., Khankhasayev, M., Eds. Proc. the NATO Adv. Stud. Inst. 1998. (71) Horwitz, E. P.; Chiarizia, R.; Dietz, M. L. Solvent Extr. Ion Exch. 1992, 10, 313-336. (72) Dietz, M. L.; Horwitz, E. P.; Bond, A. H. In Metal Ion Separation and Preconcentration: Progress and Opportunities; Bond, A. H., Dietz, M. L., Rogers, R. D., Eds.; ACS Symposium Series 716, American Chemical Society: Washington, DC, 1999. (73) Izatt, R. M.; Pawlak, K.; Bradshaw, J. S.; Bruening, R. L. Chem. Rev. 1991, 91, 1721-2085. (74) Dietz, M. L.; Bond, A. H.; Clapper, M.; Finch, J. W. Radiochim. Acta, in press. (75) Chiarizia, R.; Dietz, M. L.; Bond, A. H.; Huber, V. J.; Herlinger, A. W.; Hay, B. P. In Proceedings of ISEC′99; Society for Chemical Industry: London, 1999. (76) Bond, A. H.; Chiarizia, R.; Huber, V. J.; Dietz, M. L.; Herlinger, A. W.; Hay, B. P., Argonne National Laboratory, unpublished results.

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Figure 2. µV vs total solute molality for toluene solutions (25 °C) of HDOP, cis-syn-cis- or cis-anti-cis-DCH18C6, and mixtures of the acid and crown ethers.

Figure 1. The five stereoisomers of DCH18C6.

cis stereoisomers indicate that these crown ethers are monomeric in toluene. Addition of either cis-syn-cis- or cis-anti-cisDCH18C6 to HDOP in toluene at a constant ratio of 2:1 HDOP to DCH18C6 yielded an average aggregation number (nav) of 1.5, indicating no interaction of the crown ether with the HDOP dimers. Infrared experiments also indicate the existence of a simple mixture.78 While the vapor pressure osmometry studies were limited to the commercially available cis-syn-cis and cisanti-cis stereoisomers of DCH18C6, it is reasonable to assume that the remaining three stereoisomers do not interact with HDOP under similar conditions. Numerous experiments are typically required to fully characterize a synergistic solvent extraction system.79 Due to the limited quantities of certain stereoisomers of DCH18C6 available and the large number of systems to be studied, however, only the key experiments required to identify and confirm the extraction (77) Sastre, A.; Miralles, N.; Bosch, E. Anal. Chim. Acta 1997, 350, 197-202. (78) Herlinger, A. W., Loyola University Chicago, unpublished results. (79) Baes, C. F., Jr.; McDowell, W. J.; Bryan, S. A. Solvent Extr. Ion Exch. 1987, 5, 1-28.

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equilibria could be performed. These experiments include continuous variation studies, single- and double-extractant dependencies, and acid dependencies. Preliminary studies of metal loading in the synergistic systems showed nearly flat dependencies, indicating that only mononuclear complexes are formed up to 90% saturation of the crown ether. Figure 3 shows the results of continuous variation studies for Ca(II), Sr(II), and Ba(II) extraction by HDOP and all but the trans-anti-trans stereoisomer of DCH18C6. The distribution ratios for Ca(II) steadily decrease as the [HDOP] decreases (i.e., as χDCH18C6 increases), indicating that the dialkylphosphoric acid is solely responsible for the extraction of this cation. Because addition of DCH18C6 does not synergize the extraction of Ca(II), further experiments with this cation were limited. For Sr(II) and Ba(II) extraction, the cis-syn-cis and cisanti-cis isomers of DCH18C6 generally yield maximums near χDCH18C6 ) 0.2, which is consistent with a complex involving one molecule of DCH18C6 for every two dimers of HDOP. Only broad peaks are observed for trans-syn-trans- and cis-trans-DCH18C6, and this is likely a result of the weak extraction properties of these stereoisomers. From these continuous variation studies, it can be seen that the effectiveness of the stereoisomers of DCH18C6 in the synergistic extraction of Sr(II) and Ba(II) decreases in the following order: cis-syn-cis > cis-anti-cis > cis-trans > trans-syn-trans. Figure 4 shows some representative single- and doubleextractant dependencies for Sr(II) extraction by HDOP and all but trans-anti-trans-DCH18C6. Table 1 reports the values of the various extractant and acid dependencies for Ca(II), Sr(II), and Ba(II) extraction. The HDOP dependencies in the absence of DCH18C6 show slopes of 2.9 for Sr(II) and 2.8 for Ba(II), both of which are consistent with extraction by three dimers of HDOP.80 Addition of DCH18C6 results in HDOP dependencies decreasing to the range 2.1-2.3 for Sr(II) and 2.0-2.1 for Ba(II). Such values suggest that two HDOP dimers are present in the extracted complex. (80) Sistkova, N. V.; Kolarik, Z.; Barta, K.; Pankova, H. J. Inorg. Nucl. Chem. 1968, 30, 1595-1603.

Figure 3. DM vs mole fraction of DCH18C6 for Ca(II), Sr(II), and Ba(II) extraction by HDOP and four stereoisomers of DCH18C6 in toluene.

Figure 4. DSr vs extractant concentration in toluene for HDOP, DCH18C6, and DCH18C6 + HDOP.

In the absence of HDOP, extraction of Ca(II), Sr(II), and Ba(II) from a 0.010 M phosphate buffer at pH ) 3.00(5) into toluene solutions of the stereoisomers of DCH18C6 is negligible. Upon addition of 0.10 M HDOP, slopes of 0.80 for Sr(II) and 0.78 for Ba(II) are obtained below ∼0.01 M cis-syn-cis-DCH18C6 and are consistent with an extracted species containing a single DCH18C6 molecule. Above ∼0.01 M cis-syn-cis-DCH18C6, however, the extractant dependencies level off, a result consistent with previous observations of Sr(II) extraction from HNO3 by DCH18C6 in 1-octanol66 where the curvature was attributed to aqueous-phase solubility of the metal complexes of this extractant.74 The cis-anti-cis-DCH18C6 extractant dependencies are linear over the range 0.001-0.08 M but also have slopes significantly below 1. Partitioning of Sr(II) by the trans-syntrans and cis-trans stereoisomers at a constant HDOP concentra-

tion both show slopes of e0.48, which may simply be attributable to the poor extraction properties of these stereoisomers. The double-extractant dependencies were performed to monitor changes in the partitioning equilibria (e.g., arising from extractant aggregation) that could occur as the combined extractant concentration increases. Figure 4 and Table 1 show that above ∼0.02 M cis-syn-cis- or cis-anti-cis-DCH18C6, the plots of log DM vs log [DCH18C6 + HDOP] for Sr(II) and Ba(II) have slopes near the anticipated value of 3 (one DCH18C6 molecule and two HDOP dimers). That the slope for cis-syn-cis-DCH18C6 is not less than 3 due to aqueous-phase solubility of the strontium complex can be explained by its low ( cis-anti-cis > cis-trans > trans-syn-trans > trans-anti-trans, in agreement with the previous data. The acid dependence for Ba(II) extraction by 0.10 M HDOP affords a slope of 2.1, and the extraction is, as expected, lower than that of Ca(II) and Sr(II), respectively. The slopes of the acid dependencies for the extraction of Ba(II) by mixtures of HDOP

Table 2. Equilibrium Constants Determined for Extraction of Ca(II), Sr(II), and Ba(II) from 0.001 M M(NO3)2 (M ) Ca, Sr, Ba) into Toluene at 23(2) °C and Ligand Strain Energies for their Complexes with the Stereoisomers of DCH18C6 cation

isomer

Ca(II) Ca(II) Ca(II)

cis-syn-cis cis-anti-cis

Sr(II) Sr(II) Sr(II) Sr(II) Sr(II) Sr(II)

cis-syn-cis cis-anti-cis trans-syn-trans trans-anti-trans cis-trans

Ba(II) Ba(II) Ba(II) Ba(II) Ba(II) Ba(II)

cis-syn-cis cis-anti-cis trans-syn-trans trans-anti-trans cis-trans

Kexa

Kex,sb

4.5(1) × 10-2

Ksc

∆Ureorg (kcal/mol)d

3.7(2) × 10-2 3.9(3) × 10-2

2.30(6) × 10-3

1.06(9) × 10-4

12.87 13.76

2.5(2) × 10-1 7.3(7) × 10-2 7.7(4) × 10-3 6.0(5) × 10-3 2.17(9) × 10-2

1.1(1) × 102 3.2(3) × 101 3.3(2) × 100 2.6(2) × 100 9.43(4) × 100

11.23 12.18 14.92 17.86 13.51

5.6(5) × 10-1 1.4(1) × 10-1 3.8(9) × 10-3 1.7(3) × 10-3 4.3(4) × 10-2

5.3(6) × 103 1.3(2) × 103 3.6(9) × 101 1.6(3) × 101 4.1(5) × 102

10.67 11.09 14.25 17.28 12.94

a The extraction constant is given by eq 2 for Ca(II) and eq 4 for Sr(II) and Ba(II). b The synergistic extraction constant is defined by eq 6. c The synergistic adduct formation constant is defined by eq 8. d The ligand strain energy is defined by eq 9.

and stereoisomers of DCH18C6 range from 1.4 to 1.9. These values are taken to approximate 2 and indicate that two deprotonated dimers are present in the complex. The acid dependencies for Ba(II) (Figure 5) show that the synergistic effect is more pronounced for the cis-syn-cis, cis-anti-cis, and cis-trans isomers than for trans-syn-trans- or trans-anti-trans-DCH18C6. The latter two stereoisomers show acid dependencies that deviate significantly from the theoretical value of 2. Given the multicomponent nature of these synergistic solvent extraction systems and the inherent complexity of studying the effects of stereoisomerism, it is not unexpected that some of the slopes from the distribution ratio profiles deviate from the theoretically expected values. In most cases, however, the slopes closely approach the ideal values and permit realistic stoichiometries to be assigned to the extracted complexes. Extraction Equilibria. From the stoichiometry of the extracted complexes, deduced using the data in Table 1, the equilibria associated with their formation may be defined. For extraction of Ca(II) by HDOP alone, the extractant and acid dependencies yield slopes of 2.5 and 2.0, respectively, in agreement with the literature values.80 These values lead to the formulation Ca(H(DOP)2)2‚HDOP, where H(DOP)2- represents a singly deprotonated dimer of HDOP. The partitioning reaction and extraction constants in toluene, ignoring activity coefficients, can then be defined as

Ca2+ + 2.5(HDOP)2,org h Ca(H(DOP)2)2‚HDOPorg + 2H+ (1) Kex )

[Ca(H(DOP)2)2‚HDOP]org[H+]2 [Ca2+][(HDOP)2]2.5 org

(2)

where the subscript “org” refers to organic-phase species and the absence of a subscript implies an aqueous-phase species. Table 2 lists the extraction constants, Kex, obtained from the acid dependencies shown in Figure 5. The acid dependencies

collected for Ca(II) with or without DCH18C6 present as a synergist are nearly indistinguishable (Figure 5), and Table 2 shows that the extraction constants and synergistic extraction constants (Kex,s) are identical to within 3σ. The value of Kex ) 4.5(1) × 10-2 obtained for extraction by HDOP alone decreases slightly to the range 3.7(2) × 10-2-3.9(3) × 10-2 for the systems containing cis-syn-cis- or cis-anti-cis-DCH18C6, respectively. The larger ionic radii of Sr(II) and Ba(II) allow more solvating molecules of HDOP into the primary coordination sphere, and for partitioning by HDOP alone, the extractant dependencies approach 3. Combining this information with the acid dependencies of 2, the equilibria may be written as

M2+ + 3(HDOP)2,org h M(H(DOP)2)2‚2HDOPorg + 2H+ (3) where M ) Sr or Ba. A similar stoichiometry has been reported for Sr(II) extraction by HDEHP, the branched alkyl analogue of HDOP, in aromatic solvents.81,82 The extraction constant can thus be represented by

Kex )

[M(H(DOP)2)2‚2HDOP]org[H+]2 [M2+][(HDOP)2]3org

(4)

The Kex value for Sr(II) (2.30(6) × 10-3) is ∼22 times larger than that of Ba(II) (1.06(9) × 10-4) and is in agreement with the greater electrostatic bonding interaction of Sr(II) with HDOP. Because no synergism was observed for Ca(II), the following discussion is limited to Sr(II) and Ba(II). In general, the continuous variation studies yield plots exhibiting broad maximums centered around χDCH18C6 ) 0.2, a ratio consistent with the presence (81) McDowell, W. J.; Coleman, C. F. J. Inorg. Nucl. Chem. 1965, 27, 11171139. (82) Dubuquoy, C.; Guillaumont, R.; Bouissieres, G. Radiochim. Acta 1967, 8, 49-57.

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of one DCH18C6 stereoisomer to four HDOP molecules (present in toluene as two dimers) in the extracted complex. The various extractant dependencies were performed to identify the values of the HDOP and DCH18C6 stoichiometric coefficients. For synergistic extraction of Sr(II) and Ba(II), the HDOP dependencies afford slopes near the anticipated value of 2. The cis-syn-cis- and cis-anti-cis-DCH18C6 extractant dependencies in the synergistic mixtures yield slopes ranging from 0.71 to 0.83, and the slopes for all crown ether extractant dependencies are assumed to approach 1. (The deviation from unity observed for the DCH18C6 extractant dependencies has been discussed above.) Support for this assumption is drawn from analyses of the double-extractant dependencies (log DM (M ) Sr, Ba) vs log [DCH18C6 + HDOP]) where slopes approaching 3 are observed (one molecule of DCH18C6 and two dimers of HDOP). Finally, the acid dependencies generally have slopes near 2, as observed for extraction of divalent cations by structurally related monoprotic organophosphorus acid extractants.1,2,83-85 Taken together, these results suggest that the synergistic extraction reaction may be written as

M2+ + DCH18C6org + 2(HDOP)2,org h M(DCH18C6)(H(DOP)2)2,org + 2H+ (5)

for M ) Sr or Ba. The synergistic extraction constant is then represented by

Kex,s )

[M(DCH18C6)(H(DOP)2)2]org[H+]2 [M2+][DCH18C6]org[(HDOP)2]2org

(6)

The Kex,s values span a range of 2.5(2) × 10-1-6.0(5) × 10-3 for Sr(II) and 5.6(5) × 10-1-1.7(3) × 10-3 for Ba(II). For extraction of both Sr(II) and Ba(II) by the stereoisomers of DCH18C6, the Kex,s values decrease in the following order: cis-syn-cis > cisanti-cis > cis-trans > trans-syn-trans > trans-anti-trans. Arbitrarily assuming a stepwise mechanism in which complexation by DCH18C6 is preceded by formation of the M(H(DOP)2)2‚2HDOP (M ) Sr, Ba) species,1,2,8 the synergistic extraction reaction may be written as

M(H(DOP)2)2‚2HDOPorg + DCH18C6org h M(DCH18C6)(H(DOP)2)2,org + (HDOP)2,org (7)

where M ) Sr or Ba. This reaction is represented by the synergistic adduct formation constant, Ks, which is calculated as the ratio of eq 6 to eq 4:

Ks )

[M(DCH18C6)(H(DOP)2)2]org[(HDOP)2]org [M(H(DOP)2)2‚2HDOP]org[DCH18C6]org

)

Kex,s Kex (8)

(83) Kimura, K. Bull. Chem. Soc. Jpn. 1960, 33, 1038-1046. (84) Peppard, D. F.; Mason, G. W.; McCarty, S.; Johnson, F. D. J. Inorg. Nucl. Chem. 1962, 24, 321-332. (85) McDowell, W. J.; Coleman, C. F. J. Inorg. Nucl. Chem. 1966, 28, 10831089.

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The Ks values for Sr(II) and Ba(II) extraction by HDOP and the stereoisomers of DCH18C6 are summarized in Table 2. Synergistic constants are especially useful in that they represent a measure of the degree of interaction, or adduct formation, of the crown ether with the metal-dialkylphosphoric acid complex in the organic phase. Examination of the Ks values for Sr(II) and Ba(II) shows that the latter exhibits an order of magnitude greater synergistic effect than the former. Despite the good fit of Sr(II) in the cavity of 18-crown-6-based macrocycles,6,7,86 the larger Ba(II) cation exhibits greater metal complex stability constants with cis-syn-cis- and cis-anti-cis-DCH18C6,73 and when combined with the low Kex values for extraction by HDOP alone, Ba(II) displays the greatest synergistic effects observed in this study. That Ba(II) shows larger Ks values than Sr(II) for adduct formation with DCH18C6 is also in agreement with prior analyses of the steric effects in aliphatic crown ethers that have shown that a macrocyclic backbone composed of ethylene bridges provides an intrinsic steric preference for the larger alkali or alkaline earth cations.60,64,87 Molecular Mechanics Calculations. A significant body of literature explains the relative selectivity of macrocyclic ligands using the cation size/cavity size relationship.2,6,7 This approach does not, however, adequately describe the differences in complexation and extraction properties displayed by stereoisomeric macrocyclic ligands as the atomic connectivity is, by definition, identical. In an effort to develop an understanding of the importance of conformational changes in crown ether coordination chemistry, the effect of ligand strain energies on the complexation properties of a number of crown ether stereoisomers has been described in detail.60,65 Previous studies of nonsynergistic solvent extraction systems have described correlations of the ligand strain energy with extraction constants or distribution ratios, including systems involving various stereoisomers and tert-butyl-substituted derivatives of DCH18C6.65 The ligand strain energy is given by

∆Ureorg ) ∆Uconf + ∆Ucomp

(9)

where ∆Uconf is the energy required to convert the free ligand conformation into one predisposed for binding and ∆Ucomp is the energy difference between the binding conformer and the ligand conformation observed in the metal complex. The ligand strain energies provide a measure of the degree of binding site organization provided by each stereoisomer,64,65 where more highly organized cavities yield more stable complexes. The ligand strain energies for the Sr(II) and Ba(II) complexes of the five stereoisomers of DCH18C6 are listed in Table 2. Examination of these strain energies reveals a correlation with the synergistic constants for Sr(II) and Ba(II); that is, as the ligand strain increases, the degree of adduct formation decreases. For both Sr(II) and Ba(II), in fact, four of the stereoisomers yield a nearly linear relationship between log Ks and ∆Ureorg (r ) 99.2% for Sr(II) and 97.0% for Ba(II)). These correlations, depicted in Figure 6, provide strong evidence that the observed sequence of extraction by the stereoisomers of DCH18C6 is primarily due to the stability of the metal-DCH18C6 complex. Results for one of the (86) Shannon, R. D. Acta Crystallogr., Sect. A 1976, 32, 751-767. (87) Hay, B. P.; Rustad, J. R. Supramol. Chem. 1996, 6, 383-390.

CONCLUSIONS

Figure 6. Correlation of Ks with ∆Ureorg for the Sr(II) and Ba(II) complexes of the stereoisomers of DCH18C6. The synergistic adduct formation constant, Ks, is defined by eq 8. The points for trans-antitrans-DCH18C6 were not included in the least-squares analyses.

five stereoisomers, trans-anti-trans-DCH18C6, deviate markedly from linearity. This deviation cannot be attributed to errors in the measurement of the distribution ratios from which the Ks values are determined. (By example, substituting the distribution ratio into eq 8 and conservatively assuming a lower limit of accuracy of DM ) 10-4 permits Ks values as low as ∼2 × 10-4 to be accurately determined.) According to Hay,88 a linear relationship between equilibrium constants and ∆Ureorg is to be expected only for a series of reactions for which the entropy change is relatively constant or linearly related to the enthalpy change. This suggests that the deviation for the trans-anti-trans stereoisomer is entropic in origin. In the absence of detailed thermodynamic data for these systems, however, this explanation must be regarded as tentative. The absence of synergism for Ca(II) extraction cannot be explained using arguments based solely on ligand strain energy calculations, as ∆Ureorg for the cis-syn-cis and cis-anti-cis stereoisomers is within the range of values for Sr(II) and Ba(II), for which synergism is observed. Rather, the cause can be attributed to a combination of the strong electrostatic interaction in the Ca(II)-HDOP complex and the relatively poor organization of the stereoisomers of DCH18C6 for binding with this cation. In such a case, the interaction with DCH18C6 is not thermodynamically advantageous and synergism is not observed. (88) Hay, B. P.; Rustad, J. R.; Hostetler, C. J. J. Am. Chem. Soc. 1993, 115, 11158-11164.

Addition of DCH18C6 to toluene solutions of HDOP does not effect synergy in the extraction of Ca(II), most likely due to a combination of the very strong complexes formed with HDOP and the ligand strain resulting from the poor fit of Ca(II) in the DCH18C6 cavity. Synergistic extraction is observed for Sr(II) and Ba(II), with a host of experiments supporting formulation of the extracted complex as M(DCH18C6)(H(DOP)2)2 (M ) Sr, Ba). Both the Kex,s and Ks values are greater for Ba(II) than for Sr(II), which has been attributed to the combined effects of the low Kex values for Ba(II) extraction by HDOP alone and the greater complex stability constants and lower ligand strain energies of the Ba(II)-DCH18C6 complexes. The efficiency for extraction of Sr(II) and Ba(II) by DCH18C6 stereoisomers diminishes in the order, cis-syn-cis > cis-anti-cis > cis-trans > trans-syntrans > trans-anti-trans, which has been explained in terms of the ligand strain energies of the metal-DCH18C6 complexes. An inverse linear relationship has been established between log Ks and ∆Ureorg for both the Sr(II) and Ba(II) extraction systems. To our knowledge, this work represents the first demonstration of a correlation between equilibrium constants and ligand strain energies in synergistic solvent extraction. This work should serve as a platform for the rational design and application of these systems in both large-scale separations and chemical analysis. Future research will focus on synergistic systems combining stereoisomers of DCH18C6 with HDEHP or bis(diisobutylmethyl)phosphoric acid to determine how these more sterically demanding acidic extractants influence the partitioning equilibria.75,76 ACKNOWLEDGMENT The initial sample of cis-trans-DCH18C6 was generously donated by Dr. Richard A. Sachleben of Oak Ridge National Laboratory. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences (crown ether syntheses) and the Environmental Management Sciences Program of the Offices of Energy Research and Environmental Management (extraction studies), U.S. Department of Energy, under Contract W-31-109-ENG-38. Molecular mechanics calculations were performed at Pacific Northwest National Laboratory, a multiprogram national laboratory operated by Battelle Memorial Institute for the Department of Energy under Contract DE-AC06-76RLO1830.

Received for review January 27, 1999. Accepted April 20, 1999. AC9900681

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