Hydration of Halide Anions in Ion-Exchange Resin and Their

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Anal. Chem. 2004, 76, 4564-4571

Hydration of Halide Anions in Ion-Exchange Resin and Their Dissociation from Cationic Groups Tetsuo Okada* and Makoto Harada

Department of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan The local structures of Cl- and Br- in an anion-exchange resin have been investigated by X-ray absorption fine structure (XAFS). The resins, which have been equilibrated under various partial water vapor pressures to allow the anions to have various hydration numbers, are provided for XAFS measurements. The XAFS spectra indicate that two scattering groups around the counteranion are present, that is, water molecules and an ionexchange group. Regression analyses allow the separation of the contributions from these two scattering groups; thus, the average hydration number (N) is determined. The hydration number linearly increases with increasing the number of water molecules (n) adsorbed by an ionexchange pair (an ion-exchange group and a counteranion) until the ion-exchange pair adsorbs ca. 3 water molecules, indicating that all of the adsorbed water molecules coordinate the counteranion. However, an increase in N with increasing n becomes small as n exceeds 3; N finally reaches 3.9 ((0.4) for Cl- and ca. 3.4 ((0.5) for Br-. Detailed studies of the water adsorption isotherms imply that the maximum hydration number of these anions is three when they are bound by the ionexchange groups, and as more water molecules are supplied, they are dissociated from the ion-exchange groups; ca. 40% of total counteranions are dissociated from the ion-exchange groups. Ion exchange is usually recognized as a matured technique because it has been successfully employed in various chemical research studies encompassing fundamental and practical fields. Separation of ions is, above all, its main application.1 Ion-exchange materials developed for this purpose can be divided into two classes in terms of the base matrixes, that is, organic ion exchangers and inorganic ion exchangers.1,2 Organic ion exchangers, which are much more widely used (various types are commercially available) than the latter, have a polymer skeleton and chemically bonded ion-exchange groups along the polymer chains. The flexible structure of organic chains results in relatively low separation selectivity and in difficulty in selectivity modifica* To whom correspondence should be addressed. Phone and Fax: +81-35734-2612. E-mail: [email protected]. (1) Abe, M.; Kataoka, T.; Suzuki, T. New Developments in Ion Exchange: Materials, Fundamentals, and Applications; Kodansha: Tokyo, 1991. (2) (a) Abe, M. In Ion-Exchange and Solvent Extraction; Marinsky, J. A., Marcus, Y., Eds; Marcel Dekker: New York, 1995; Vol. 12, Chapter 9. (b) Kney, A. D.; SenGupta, A. K. In Ion-exchange and Solvent Extraction; SenGupta, A. K., Marcus, Y., Eds; Marcel Dekker: New York, 2001; Vol. 14, Chapter 8.

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tion. In contrast, inorganic ion exchangers are crystals, and cavities having ion-exchange capability are periodically located in the crystal structure. Ions are captured by the confined space in the crystal, and thus the ion-recognition ability is higher in this type of ion exchanger than in the organic counterpart. However, the adsorption equilibrium is, in general, more rapidly established in organic ion exchangers; this is one of the reasons that this type has been utilized in water treatments and chromatography. Ion-exchange chromatography is a useful tool for separation, removal, and analyses of ions and has contributed to the compilation of fundamental data as well; chromatographic retention data can directly be related to ion-exchange selectivity coefficients.3 The basic separation selectivity obtained with organic ion exchangers is conservative in water. As is well-known, large and poorly hydrated ions are adsorbed by the ion exchangers better than small and well-hydrated ions. Some modification of separation selectivity has been shown to be possible by changing the structures of ion-exchange groups,3a-3g resin base materials,3g ionexchange capacity,3h and so forth. In some cases, the interaction of ions with resin base materials played an important role in the determination of separation selectivity of relatively large polarizable ions including organic ions.3i,3j However, an electrostatic interaction undoubtedly provides the major ion recognition mechanism at least for small inorganic ions. Even in inorganic ion exchangers in which ion-exchange spaces have very rigid structures according to the requirements of crystal configurations, important involvements of solvents have been indicated.4 Solvents should play a more important role in the determination of separation selectivity in organic ion exchangers, into which solvents can substantially penetrate.5-8 Although (3) (a) Okada, T. J. Chromatogr. A 1997, 758, 19. (b) Okada, T. J. Chromatogr. A 1997, 758, 29. (c) Okada, T. Bunseki Kagaku 1995, 44, 579. (d) Hu, W.; Tanaka, K.; Hasebe, K. Anal. Sci. 2002, 18, 1183. (e) Barron, R. E.; Fritz, J. S. J. Chromatogr. 1984, 284, 13. (f) Barron, R. E.; Fritz, J. S. J. Chromatogr. 1984, 316, 201. (g) DuVal, D. L.; Fritz, J. S. J. Chromatogr. 1984, 295, 89. (h) Gjerde, D. T.; Fritz, J. S.; Schmuckler, G. J. Chromatogr. 1979, 186, 509. (i) Rahman, A.; Hoffman, N. E. J. Chromatogr. Sci. 1990, 28, 157. (j) Hoffman, N. E.; Liao, J. C. J. Chromatogr. Sci. 1990, 28, 428. (4) Kanzaki, Y.; Suzuki, N.; Chitrakar, R.; Ohsaka, T.; Abe, M. J. Phys. Chem. B 2002, 106, 988. (5) (a) Hirata, Y.; Miura, Y.; Nakagawa, T. J. Membr. Sci. 1999, 163, 357. (b) Okada, T.; Xie, G.; Gorsth, O.; Kjelstrup, S.; Nakamura, N.; Arimura, T. Electrochim. Acta 1998, 43, 3741. (6) Tromp, R. H.; Neilson, G. W. J. Phys. Chem. 1996, 100, 7380. (7) Takahashi, Y.; Kimura, T.; Kato, Y.; Minai, Y.; Tominaga, T. Chem. Commun. 1997, 223. (8) (a) Toteja, R. S. D.; Jangida, B. L.; Sundaresan, M.; Venkataramani, B. Langmuir 1997, 13, 2980. (b) Nandan, D.; Venkataramani, B.; Gupta, A. R. Langmuir 1993, 9, 1786. (c) Nandan, D.; Gupta, A. R. J. Phys. Chem. 1975, 79, 180. (d) Nandan, D.; Gupta, A. R. J. Phys. Chem. 1977, 81, 1174. 10.1021/ac049602h CCC: $27.50

© 2004 American Chemical Society Published on Web 06/15/2004

some methods, including neutron diffraction,6 fluorescence measurements,7 NMR9 and so forth, have been utilized to elucidate the local structures of counterions in organic ion exchangers, clear molecular pictures have not been drawn, which allow the interpretation of separation selectivity. It has actually been known that changes in solvents result in drastic selectivity modification; as stated above, large and poorly solvated anions are better captured than small and well-solvated ones by an anion-exchange resin in water, while this selectivity is completely reversed in acetonitrile.3a The reversed anion-exchange selectivity found in acetonitrile has been structurally explained by X-ray absorption fine structure (XAFS) studies; in this solvent, Cl- and Br- are directly bound by the ion-exchange groups, and their local structures are the same as those in dried resins.10 The electrostatic energy for direct binding is governed by the interaction distance, in turn, the size of an counterion; the smaller the counterion size, the stronger the interaction. By analogy with this, ion-exchange selectivity in water may be discussed on the basis of the sizes of hydrated ions; the larger the radii of hydrated ions (usually the smaller their crystallographic radii), the weaker the interaction with the ion-exchange groups. This appears qualitatively correct in many cases.11 If this inference is correct on molecular bases as well, counterions should be completely hydrated in the resin and ion-exchange groups would not penetrate their solvation shell. In a previous work, we found that there exist two species of Brin ion-exchange resins soaked in water and methanol, that is, Brbound by the ion-exchange groups and that solvated similar to those in bulk solvents.10 This clearly indicates that Br- is not completely solvated in the resins soaked in these solvents and is (at least) partly bound by the ion-exchange groups. Ion-exchange selectivity has been discussed on the basis of the water uptake of resins as well. Venkataramani and co-workers studied the water sorption isotherms of cation-exchange resins using the D’Arcy and Watt equation, which assumed Langmuirtype adsorption as well as multilayer adsorption.8 They found some interesting aspects: (1) there are several types of water sorption sites exhibiting different water sorption ability, (2) there is a correlation between the water uptake amount and the hydration number of a countercation in bulk water, and (3) the degree of cross-linking is related to the multilayer adsorption of water as well as to swelling pressure. Although their analyses gave the average hydration numbers of counteractions, which were generally smaller than those in bulk solution, the hydration numbers depended on applied equations. Reichenberg, in an earlier monograph, inferred that a counterion should be bound by the ion-exchange group and thus the hydration occurred at half of its solvation shell opposite to the electrostatically interacting group.12 He also pointed out the possibility of the dissociation of counterions from the ion-exchange groups. However, these aspects have not been directly verified on molecular bases partly due to the lack of suitable approaches. (9) (a) Marton, A.; Miyazaki, Y. Prog.Colloid Polym. Sci. 2001, 117, 153. (b) Ohuchi, M.; Meadows, P.; Horiuchi, H.; Sakai, Y.; Furihata, K. Polym. J. 2000, 32, 760. (10) (a) Harada, M.; Okada, T. Anal. Sci. 2001, 17, 233. (b) Harada, M.; Okada, T.; Watanabe, I. J. Phys. Chem. B 2002, 106, 34. (c) Harada, M.; Okada, T. J. Ion Exch. 2003, 14, 25. (11) Haddad, P. R.; Jackson, P. E. Ion Chromatography: Principles and Applications; Elsevier: Amsterdam, 1990; Chapter 2.

We have already indicated that X-ray absorption fine structure (XAFS) is a powerful tool for studying the local structures of counterions in ion-exchange resins because coexisting light elements do not interfere with the X-ray absorption of targeted heavier atoms.10 Although, as mentioned above, XAFS spectra for Br- in anion-exchange resins have shown the coexistence of hydrated Br- and that bound by the anion-exchange group, the details on this aspect has not been interpreted by the spectra alone. On the other hand, previous studies have implied the usefulness of water adsorption isotherms of ion-exchange resins from thermodynamic viewpoints.8 Thus, we have considered that the cooperative interpretation of these two different approaches should give further insights into the hydration of counterions in an ion-exchange resin. In the present paper, we discuss water adsorption properties of anion-exchange resins as well as the local structures of Cl- and Br- in the anion-exchange resins on the basis of XAFS and water adsorption isotherm measurements and attempt to elucidate the origin in ion-exchange separation selectivity. EXPERIMENTAL SECTION The ion-exchange resin used throughout this work was Amberlyst A-26 (Rohm and Haas), which was a polystyrene-based macroreticular-type anion-exchange resin having a trimethylammonium group as an ion-exchange site; this resin is hereinafter referred to as R4. The chloride form of R4 (R4Cl), which was a commercially available form, was treated with aqueous NaBr solution, giving a Br- from resin (R4Br). These two forms of R4 were well-rinsed with methanol, acetone, and water and then powdered (typical particle diameter was 10 µm). After being powdered, the resins were thoroughly rinsed with the same solvents again and then dried over P2O5 in vacuo at 80 °C for 2 days and at 120 °C for a day. The resin was very hygroscopic, and therefore dried resins were treated under dried N2 or an Ar atmosphere. The ion-exchange capacity of the resins was determined by the titration with AgNO3: 4.26 (σ < 0.01) mmol g-1 and 3.62 (σ < 0.01) mmol g-1 for R4Cl and R4Br, respectively. The capacity determined for R4Br in our previous work was lower than that reported here because the resins came from different lots and special attention was paid to the dryness of the resin in the present work as described above. Aliquots of dried resins were equilibrated under different partial water vapor pressures at 25 °C; resin samples were stored in a sealed container together with an appropriate solution for longer than 1 week. Different humidity was obtained using saturated salt and aqueous sulfuric acid solutions.13 The attainment of a wateruptake equilibrium was gravimetrically confirmed by the constant weight of the resin. More than three resin samples were used for determining water uptake under a particular condition. The total number of water molecules (n) adsorbed by an ion-exchange pair (an ion-exchange group and a counteranion) for each sample are reported in terms of relative water activity aw ) Pw/P0, where Pw and P0 denote the water vapor pressure and saturated water vapor pressure at 25 °C as listed in Table 1. (12) Reichenberg, D. In Ion-exchange; Marinsky, J. A., Ed.; Marcel Dekker: New York, 1966; Vol. 1, Chapter 7. (13) (a) Kelloma¨ki, A. Acta Chem. Scand. A 1978, 32, 747. (b) Stokes, R. H.; Robinson, R. A. Ind. Eng. Chem. 1949, 41, 2013.

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Table 1. Number of Moles of Water Adsorbed by an Ion-Exchange Pair Pw/P0 a 0.113

0.33

0.582

0.842

R4Cl

n

1.14 (0.04)b

2.11 (0.01)

3.07 (0.10)

5.43 (0.10)

R4Br

n

0.79 (0.18)

1.61 (0.07)

2.33 (0.15)

3.93 (0.22)

a

0.9

1 14.7 (0.07)

6.49 (0.14)

12.7 (0.30)

Relative water vapor pressure. b Standard deviations in parentheses.

After being equilibrated with water vapors, the resins were provided for XAFS studies. The resin samples were sealed in a polyethylene pouch immediately before the XAFS measurements at Cl K and Br K edge, which were carried out at BL9A and BL10B of the Photon Factory, High Energy Accelerator Research Organization in Tsukuba, Japan, respectively. The spectra for Cland Br- dissolved in water were similarly obtained with their potassium salts. XAFS spectral data were analyzed using the same method as described in our previous papers10 except that FEFF ver. 8.20 was used instead of ver. 7.02. The scattering from hydrogen atoms has been debated in various applications of X-ray.14 Although we did not take the scattering from hydrogen atoms into account in previous analyses, this should be involved when relatively simple geometry is discussed. In this study, the scattering from coordinating H atoms in water molecules was taken into account. RESULTS AND DISCUSSION XAFS Spectra of Cl- and Br- in the Resins. Figure 1 shows the χ spectra of Cl- and Br- in the R4 resin as well as those of hydrated ions. XAFS spectra of halide ions, particularly Br-, in water have been well-studied from various viewpoints.15 The XAFS spectra of hydrated halide ions indicated similar structural properties to those previously reported (vide infra). The oscillation phases and amplitudes of the hydrated ions are entirely different from those for the same ion in the dried resins, and thus we can clearly distinguish these two states of ions. The oscillation amplitudes of the spectra for both the dry resins and anions dissolved in water decrease with increasing k (>2 Å-1), indicating that single coordination shells are established around the anions. The spectra for the resins soaked in water involve the features of these two states. In the previous work, we pointed out the possibility of the coexistence of two Br- species in the resin, that is, hydrated Br- and that strongly bound by the ion-exchange group.10b Since similar features were found for Br- interacting with surface monolayers,16 it appears that such local structures are common to Br- electrostatically attracted by the cationic sites. The spectra shown in Figure 1 also indicate the presence of two (14) (a) Benfatto, M.; Solera, J. A.; Chaboy, J.; Proietti, M. G.; Garcia, J. J. Phys. IV 1997, 7, C2165. (b) Fearnside, A.; Matthew, J. A. D. Am. J. Phys. 1997, 65, 795. (15) (a) Wallen, S. L.; Palmer, B. J.; Pfund, D. M.; Fulton, J. L.; Newville, M.; Ma, Y.; Stern, E. A. J. Phys. Chem. A 1997, 101, 9632. (b) Tanida, H.; Sakane, H.; Watanabe, I. J. Chem. Soc. Dalton Trans. 1994, 2321. (16) (a) Harada, M.; Okada, T.; Watanabe, I. J. Phys. Chem. B 2003, 107, 2275. (b) Harada, M.; Okada, T.; Watanabe, I. Anal. Sci. 2002, 18, 1167. (c) Harada, M.; Okada, T.; Tanida, H.; Watanabe, I. Bunseki Kagaku 2003, 52, 405. (d) Hadara, M.; Okada, T. Langmuir 2004, 20, 30.

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Figure 1. χ spectra for Cl- and Br- dissolved in water and those in the resin equilibrated at various water vapor pressures. Arrows show increasing water content in the resin. Relative water vapor pressures varied: 0.113, 0.33, 0.582, 0.842, 0.9, and 1.

different scattering groups not only around Br- but also around Cl- in the resins adsorbing water. Although we attempted to analyze the spectra with the usual curve fittings, it was difficult to derive significant parameters for two reasons: (1) the water oxygen and the methyl carbons of the ion-exchange groups have similar back-scattering abilities and (2) the interaction distances between the halogen ions and these scattering atoms are not very different (e.g., 3.2 Å for Br-O and 3.6 Å for Br-C). The spectra were therefore analyzed by the following procedure. If two different states coexist, the experimental χ spectrum can be represented by the linear combination of the independent spectra coming from the individual structures because the intensity of the normalized χ spectrum is proportional to the number of atoms comprising a particular scattering group,

χ ) Rχdry + βχhyd

(1)

where χ, χdry, and χhyd are the χ spectra obtained for a given resin sample, for the dry resin, and for the hydrated ions, and R and β are coefficients representing the contributions from χdry and χhyd, respectively. Figure 2 shows the results of curve fitting based on eq 1; the spectra for the resin samples are well-explained by this equation regardless of the water contents of the resins. Table 2

Figure 2. χ spectra (solid curves) and results of curve fitting based on eq 1 (broken curves) of Cl- and Br- in the resin.

Table 2. Curve-Fitting Parameter Determined Based on Eq 1 Pw/P0 a 1

in waterb

R

0.18 (0.15) 0.65 (0.07) 3.90

0.07 (0.15) 0.70 (0.07) 4.20

R4Brc R

0.58 0.47 0.36 0.31 0.30 (0.22) (0.22) (0.22) (0.22) (0.22) 0.34 0.41 0.49 0.54 0.56 (0.08) (0.08) (0.08) (0.08) (0.08) 2.04 2.47 2.92 3.22 3.37

0.25 (0.22) 0.59 (0.08) 3.55

0.113 R4Clc

0.33

0.582

0.842

0.61 0.55 0.37 0.23 (0.15)d (0.15) (0.15) (0.15) β 0.22 0.27 0.51 0.58 (0.07) (0.07) (0.07) (0.07) 6β 1.33 1.64 3.06 3.46

0.73 (0.22) β 0.25 (0.08) 6β 1.49

0.9

a Relative water vapor pressure. b Resin soaked in water. c Fitting range, k ) 1.5-5.5 Å-1 for R4Cl and k ) 1.5-6.5 Å-1 for R4Br. d Standard deviations in parentheses.

summarizes R and β coefficients determined by curve fitting. One of the important features of these values is that R decreases while β increases with increasing P/P0. If all of the counteranions were bound by the ion-exchange groups even when sufficient water molecules are available for hydration, R should be unity irrespective of P/P0. Although the standard deviation for R is rather large, its decrease with increasing P/P0 is significant. This must indicate the dissociation of the ion pair between the counteranion and ionexchange group by hydration. If the ion pair is not hydrated (the dried ion pair and hydrated Br- coexist), (R + β) should be equal

to unity, whereas this value should be larger than unity if Brbound by the ion-exchange site is hydrated. However, (R + β) listed in Table 2 is smaller than unity in all cases. This may come from the assumption that the structure of the ion pair (and in turn χdry) remains unchanged, even when the hydration of counteranions proceeds. When a few water molecules hydrate the counteranion bound by the ion-exchange group, the distance between the ions should become longer and thermal fluctuation must be enhanced. This possibly gave small R values in the calculation based on eq 1. In contrast, β values include much less ambiguity than R values because of the much larger oscillation amplitude of χhyd than that of χdry, which reflects the stronger interaction between the anions and water molecules. This consideration is supported by the interaction distances as well; the distance between Br- in the dried resin and the ion-exchange group was 3.6 Å,10 whereas that between water oxygen and an anion in aqueous solution was 3.27 Å for Br-. Thus, the following discussion is based on the β values listed in Table 2. Differences in β values for the resins soaked in water and those equilibrated with a saturated water vapor mostly come from the baseline noises and are not essential because spectral features for these are almost identical; actually, the difference is small for Br-. The resin samples equilibrated with a saturated water vapor are hereinafter regarded as being completely hydrated. The hydration of halide ions in bulk water has been investigated by various approaches, some of which have provided their hydration numbers.17 The most probable hydration number is six for both Cl- and Br-, as far as the first hydration shell is concerned; Analytical Chemistry, Vol. 76, No. 15, August 1, 2004

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Figure 3. Relations between N (the hydration number of anions in the resin) and n (the number of water molecules adsorbed by an ionexchange group). Dotted line with a unit slope as a guide for the eye.

hereinafter, the hydration number is regarded as six for the fully hydrated halide ions. Thus, 6β should be equal to the average hydration numbers of the halide ions in the resin at a given partial water pressure. The hydration numbers of the halide anions in the completely hydrated resins are 3.9 (σ ) 0.4) for Cl- and 3.4 (σ ) 0.5) for Br-, reflecting different hydration natures of these anions. Figure 3 shows the relation between the average hydration number (N) and the total number of water molecules (n) adsorbed by an ion-exchange pair. The hydration numbers in the resin first increase with n, but become almost constant after n exceeds ca. 3. It should be noted that N values for these two halide anions similarly depend on n. As mentioned above, the decreasing trend of R with increasing P/P0 predicts the dissociation of counteranions from the ion-exchange groups, which should allow the formation of a complete hydration shell and a substantial increase in N. This aspect will be discussed below in more detail. Water Uptake of the Resin. The earlier water adsorption research assumed water adsorption sites having different water adsorption abilities; for example, Venkataramani and co-workers8 indicated that there were two adsorption sites, that is, strong and weak adsorption ones. If this difference in adsorption ability originates from the circumstances, under which ion-exchange groups are situated, the water adsorption by ion-exchange resins should depend on the matrixes and degree of cross-linking. However, it was shown that the degree of cross-linking did not influence the water adsorption at low water-vapor pressures.8 We therefore assumed that all of the ion-exchange sites are present under identical circumstances, and the first water molecule more easily solvates a counterion than additional water molecules; this must be consistent with the assumption of two different adsorption sites in the earlier work. It has also been shown that water molecules primarily interact with counteranions, whereas the hydration of cationic ion-exchange groups is much weaker.18 Thus, (17) (a) Narten, A. J. Phys. Chem. 1970, 74, 765. (b) Licheri, G.; Piccaluga, G.; Pinna, G. Chem. Phys. Lett. 1975, 35, 119. (c) Wakita, H.; Ichihashi, M.; Mibuchi, T.; Masuda, I. Bull. Chem. Soc. Jpn. 1982, 55, 817. (d) Licheri, G.; Piccaluga, G.; Pinna, G. J. Appl. Crystallogr. 1973, 6, 392. (e) de Barros Marques, M. I.; Cabaco, M. I.; Sousa Oliveira, M. A.; Alves Marques, M. Chem. Phys. Lett. 1982, 91, 22. (f) Ohtomo, N.; Arakawa, K.; Takeuchi, M.; Yamaguchi, T.; Ohtaki, H. Bull. Chem. Soc. Jpn. 1981, 54, 1314.

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Figure 4. Water adsorption isotherms for R4Cl and R4Br. Solid curves; the abrupt hydration number change (from m ) 3 to m ) 6) was assumed.

water adsorption at low water-vapor pressures can be regarded as the hydration of an anion in the anion-exchange resin. Figure 4 shows water adsorption isotherms of the R4Cl and R4Br resins. The number of adsorbed water molecules on an ionexchange pair (n) increase with increasing water-vapor pressure in a specific fashion similar to that reported in the literature.8,13a The first plateau in the number of adsorbed water molecules appears at n ∼ 2-3 for Cl- and 1-2 for Br-, and then n steeply increases at Pw/P0 > 0.8. The number of adsorbed water molecules finally reaches to more than 10 in the saturated water vapor, suggesting the multilayer adsorption or water condensation in the resin pores. To avoid the effect of multiplayer adsorption, further discussion is focused on the part of adsorption isotherms for Pw/ P0 < 0.5. Molecular pictures can be drawn for the hydration of counterions in ion-exchange resins as schematically depicted in Figure 5: (a) the ion-exchange groups tightly bind counterions when no water molecules are available for hydration; (b) even though a few water molecules coordinate counterions, the structure of the ion pair between the ion-exchange sites and counterions is little changed (this may not be true in a rigorous sense as discussed above); (c) this type of hydration must occur until the average coordination number becomes 1-2 judging from the water adsorption isotherms. When the water vapor pressure becomes higher, several routes are possible for further hydration: (d1) the hydration stated above is sustained, meaning that counterions remain bound by the ion-exchange groups even when sufficient water molecules are available for hydration like the resin soaked in water; (d2) a part of counteranions are completely hydrated, but still present in the vicinity of the oppositely charged ionexchange groups (like solvent-shared ion pair); (d3) both counterions and ion-exchange groups are completely hydrated. In the cases of (d2) and (d3), the counteranion no longer forms the direct ion pair with the ion-exchange group. As noted above, the hydration principally occurs for counteranions, and thus water uptake should basically be attributed to their stepwise hydration. Km

-NMe3+ X-(w)m-1 + w {\} -NMe3+ X(w)m(1 e m e 6) (2) where w represents a water molecule and Km is a consecutive

Figure 5. Schematic representation of the molecular process of the hydration of an anion in an ion-exchange resin.

hydration constant. In the case of (d1), m is not more than 5 because the complete hydration shell is not formed around the counteranion, whereas the maximum m (mmax) is 6 for (d2) and (d3). Fittings of the water adsorption isotherms (Figure 4) for Pw/P0 < 0.5 with eq 2 were attempted assuming mmax ) 2, 3, and 4; the correlation coefficients were 0.972 (mmax ) 2), 0.995 (mmax ) 3), and 0.995 (mmax ) 4) for Cl- and 0.979 (mmax ) 2), 0.993 (mmax ) 3), and 0.997 (mmax ) 4) for Br-. The steep increase of the water adsorption isotherms at Pw/P0 < 0.1 cannot be explained with mmax ) 2. Assuming mmax ) 4 allowed the best fittings, it however resulted in negative (or almost zero) K3 or K4 with extremely large uncertainty for both Cl- and Br-. We thus concluded that mmax ) 3 with the following hydration constants: K1 ) 56.4 (σ ) 29.7), K2 ) 2.5 (σ ) 1.8), and K3 ) 3.4 (σ ) 2.9) for Cl- and K1 ) 18.8 (σ ) 3.1), K2 ) 0.73 (σ ) 1.2), and K3 ) 3.4 (σ ) 0.8) for Br-. These constants show that the first hydration much more easily occurs than the second and third hydration. As noted above, the hydration of the counteranions results in their weak interaction with the ion-exchange group. The free energy gain due to the hydration must be consumed for the relaxation of the electrostatic interaction, which causes much lower constants for the second and third hydration. The analyses of XAFS of the dried resin suggest the presence of five scattering atoms 3.6 Å apart from Br-.10 Although the number of scattering atoms should involve some ambiguity because of the inference from the hydration number of Br- in an aqueous solution, the real coordination number is not very different. If Br- is located at the center of the tripod of the -NMe3+ group, the number of scattering atoms should be four (three methyl carbon and one ammonium nitrogen atoms are located at almost the same distance from Br-); this should be one of the most probable configurations. The distance between (18) Irwin, K. J.; Barnett, S. M. J. Membr. Sci. 1989, 47, 79.

water oxygen and an anion in aqueous solution was determined to be 3.05 Å for Cl- and 3.27 Å for Br-; the latter distance agrees well with previously reported values.15 The distance between Brand the water hydrogen atom directly interacting with it is ca. 2.2 Å, and thus the surface area of the hydration sphere of Br- is ca. 60 Å2; the corresponding surface area for Cl- is ca. 53 Å2. The cross-sectional area of the ion-exchange group is ca. 15 Å2, which occupies a substantial part of the coordination shell, albeit the ion-exchange group is located slightly more apart. This steric effect must hinder the hydration of the counteranions with more than three water molecules when the ion pair between the anions and ion-exchange groups remains undissociated. XAFS analyses have indicated that the maximum hydration numbers of the counteranions are more than 3 when the resins are equilibrated at Pw/P0 ) 1 and also suggested the dissociation of the ion pair between the counteranion and -NMe3+ group. The hydration number should abruptly increase from mmax ) 3 to mmax ) 6 when the ion pair is dissociated, which allows the formation of the complete hydration around the anions.

-NMe3+ X-(w)3 + 3w a -NMe3+ X(w)6-

(3)

The equilibrium constants for eq 3 were set to 0.84 for Cl- and 0.72 for Br-; fitting curves are shown in Figure 4. These hydration constants have revealed that 37% Cl- and 29.7% Br- are present as completely hydrated anions. Although six was assumed to be the hydration number in the above equilibrium, this number itself is not essential. Since the complete hydration of counteranions facilitates the hydration of the ion-exchange group as well as water condensation in the pores, the final water molecule numbers adsorbed by an ion-exchange pair (-NM3X) may be larger. Hence, the hydration of the counteranions consecutively occurs until m reaches 3, and further hydration facilitates the dissociation of the Analytical Chemistry, Vol. 76, No. 15, August 1, 2004

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Figure 6. Gibbs free energy diagram representing the ion-exchange equilibrium between Cl- and Br-. The hydration energy of counteranions is shown with underlines. Energies are given in kJ mol-1.

direct ion pair between the -NMe3+ group and counteranion. However, there remains some ambiguity concerning the local structure of dissociated counteranions; that is, they are bound by the ion-exchange site like solvent-shared ion pairs (d2 in Figure 5) or are completely dissociated (d3 in Figure 5). Although precise conductivity measurements and/or calorimetric measurements may distinguish these two states, XAFS analyses cannot give a clear view on this aspect (no information is given on the hydration of the ammonium ion). Thermodynamic Consideration on Ion Exchange from the Viewpoint of Counterion Hydration. In water, all types of anionexchange resins show higher selectivity toward Br- over Cl-.

R-Cl- + Br- a R-Br- + Cl-

(4)

where R-Cl- and R-Br- represent the ions in the resin phase. Figure 6 shows an energy diagram for the ion-exchange equilibria represented by eq 4. The ion-exchange selectivity coefficient of eq 4 determined in 0.1 M aqueous electrolyte is equal to 3.53. Although this value is not a thermodynamic one, the difference between these is not very large.8c,8d If the selectivity coefficient is thus regarded as the thermodynamic value, ∆G° for eq 4 is equal to -3.1 kJ mol-1. The standard formation free energies (∆Gf°) of Cl- and Br- are reported as -131.2 and -104.0 kJ mol-1, respectively; thus, the contribution from the hydrated ions to the above equilibrium is -27.2 kJ mol-1.19 The difference in ∆Gf° between R-Cl-(aq) and R-Br-(aq) is thus 24.1 kJ mol-1. Nandan and Gupta8c,8d determined the swelling free energies (∆Gswell) of various cation-exchange resins from the water adsorption isotherms based on

∫

∆Gswell ) -RT

1

aw)0

n d ln aw

(5)

The numerical integration of the adsorption isotherms gave ∆Gswell ) -22.2 and -15.3 kJ mol-1 for R-Cl- and R-Br-, respectively. The difference in ∆Gf° between R-Cl-(dry) and R-Br-(dry) should thus be 17.2 kJ mol-1, which is due to the higher electrostatic interaction for Cl- than for Br-. From the above discussion (and hydration constants), the hydration energy of the counteranions can be calculated, -14.7 and -8.6 kJ mol-1 for Cl- and Br-, (19) Kagaku Binran (Chemical Index); Maruzen: Tokyo, 1993.

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respectively. Thus, the hydration of the counteranions comprises 66% and 56% of the total swelling free energies of R-Cl-(dry) and R-Br-(dry). A different interpretation is also possible. A simple consideration on the dehydration of an ion from bulk water to the ionexchange phase may lead to the conclusion that a highly hydrated ion is less preferably partitioned to the resin phase than a poorly hydrated one because the larger free energy loss is expected for the transfer of the former. However, the present study has shown that the dehydration of the anions in the resin is more pronounced for Br- than for Cl-; thus, the above simple inference based on complete dehydration is not necessarily applicable. As discussed above, the average hydration numbers in the resin are 3.9 and 3.4 for Cl- and Br-, respectively; 2.1 and 2.6 water molecules are stripped off from the first hydration shell when they are transferred from bulk water to the resin soaked in water. Although the free energy for the individual step in the hydration of the anions is not known, a difference in the extent of dehydration between Cland Br- should be large enough to make the transference of Brfrom bulk water energetically unfavorable; for example, assuming that the six individual steps of their hydration are energetically identical (though obviously oversimplified), the dehydration energies for Cl- and Br- can be estimated to be 121 kJ mol-1 ()347 × 2.1/6) and 139 kJ mol-1 ()321 × 2.6/6), respectively (-347 and -321 kJ mol-1 are the hydration free energies of these ions).20 In addition, Br- forms direct ion pairs with the ionexchange site to a larger extent; this should be accompanied by the dehydration from the ion-exchange site as well, albeit this contribution cannot be estimated from the present study. Thus, it is reasonably inferred that the transfer of Br- from bulk water to the resin is less preferable than Cl- as far as the dehydration energies are concerned. The unfavorable dehydration energy of Br- should be compensated by its larger electrostatic stabilization in the resin. Although details are not completely known at this stage, the direct interaction between the ion and ion-exchange site and the fraction of the counteranion forming this type of ion pair should be important factors because the electrostatic energy of the direct ion pair is much larger than that of a water-shared counterpart. CONCLUSION In the present work, the local structures of Cl- and Br- in the anion-exchange resin and thermodynamic origin in anionexchange selectivity between them have been discussed on the basis of XAFS as well as the water adsorption isotherms of the resins. The following aspects have been first elucidated in the present work: (1) The direct ion pairs between the counteranions and ionexchange groups are maintained until three water molecules are hydrated on the counteranions (structural perturbation is possibly involved), (2) Some counteranions are dissociated from the ion-exchange sites by hydration, but the degree of hydration differs for these anions. (3) The coexistence of the associated and dissociated counterions should be taken into account to discuss ion-exchange selectivity; the discussion based on either the crystalline or the hydrated ionic radii leads to a misunderstanding. (20) Marcus, Y. Ion Solvation; John Wiley: Chichester, 1985.

Hence, we believe that the present study has provided a novel approach to ion-exchange research and elucidated some essential aspects involved in this matured technique. Although the details have not been well-studied, the structural effect of the ionexchange groups on separation selectivity can also be discussed. The present results strongly imply that the interaction distance between the counteranions and ion-exchange groups appears to increase as the hydration of the counteranions proceeds; the large ion-exchange groups are expected to push the counteranions farther away and to allow further hydration of the counteranions. The hydration of the ion-exchange groups, which is not probed by XAFS, is another important factor, but has not been quantitatively discussed. Not only the extensive application of the present approach to various systems but also the combined use of other

useful methods that give the information on the solvation of ionexchange sites is important for further understanding of the molecular features involved in ion exchange. ACKNOWLEDGMENT The authors are grateful for the financial support from the Salt Science Foundation. This work was performed under the approval of the Photon Factory Advisory Committee (Proposal Nos. 98G311 and 2001G114).

Received for review March 15, 2004. Accepted May 10, 2004. AC049602H

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