pubs.acs.org/Langmuir © 2010 American Chemical Society
Selective Monovalent Cation Association and Exchange around Keplerate Polyoxometalate Macroanions in Dilute Aqueous Solutions Joseph M. Pigga,† Joseph A. Teprovich, Jr.,† Robert A. Flowers, II,† Mark R. Antonio,‡ and Tianbo Liu*,† †
Department of Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015, and ‡Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439 Received February 1, 2010. Revised Manuscript Received April 8, 2010
The interaction between water-soluble Keplerate polyoxometalate {Mo72Fe30} macroions and small countercations is explored by laser light scattering, anomalous small-angle X-ray scattering (ASAXS), and isothermal titration calorimetry (ITC) techniques. The macroions are found to be able to select the type of associated counterions based upon the counterions’ valence state and hydrated size, when multiple types of additional cations are present in solution (even among different monovalent cations). The preference goes to the cations with higher valences or smaller hydrated sizes if the valences are identical. This counterion exchange process changes the magnitude of the macroion-counterion interaction and, thus, is reflected in the dimension of the self-assembled {Mo72Fe30} blackberry supramolecular structures. The hydrophilic macroions exhibit a competitive recognition of various monovalent counterions in dilute solutions. A critical salt concentration (CSC) for each type of cation exists for the blackberry formation of {Mo72Fe30} macroions, above which the blackberry size increases significantly with the increasing total ionic strength in solution. The CSC values are much smaller for cations with higher valences and also decrease with the cations’ hydrated size for various monovalent cations. The change of blackberry size corresponding to the change of ionic strength in solution is reversible.
Introduction For various macroionic solution systems from functional catalytic materials to biological macromolecules, the interaction between macroions and their counterions is critical.1,2 Metal cations play key roles in biological processes, such as the folding of RNA and structure stabilization for various biological macromolecules. Polyoxometalates (POMs), nanometer-sized metaloxide molecular clusters with beautiful geometrical structures and fascinating physical and chemical properties, such as electronic, magnetic, and catalytic activities,3-8 represent some of the largest inorganic molecules known. Many types of POMs exist as anions in solution, making them ideal model systems as soluble macroions. The direct contact ion-pair formation between the high charge density hexaniobate Lindqvist polyanion and alkali metal cations in aqueous solution,9 the catalytic capability of the Keggin *Corresponding author. E-mail:
[email protected]. (1) Schiessel, H.; Pincus, P. Macromolecules 1998, 31, 7953. (2) Heilman-Miller, S. L.; Thirumalai, D.; Woodson, S. A. J. Mol. Biol. 2001, 306, 1157. (3) (a) Proust, A.; Thouvenot, R.; Gouzerh, P. Chem Commun. 2008, 1837. (b) Hill, C. L., Ed.; Chem. Rev. 1998, 98, 1. (c) Long, D.-L.; Cronin, L. Chem.;Eur. J. 2006, 12, 3698. (d) Cronin, L. Comprehensive Coordination Chemistry II; McCleverty, J. A., Meyerpp, T. J., Eds.; Elsevier: Amsterdam, 2004; Vol. 7, pp 1-56. (e) Long, D.-L.; Burkholder, E.; Cronin, L. Chem. Soc. Rev. 2007, 36, 105. (f) Cronin, L. Angew. Chem., Int. Ed. 2006, 45, 3576. (g) M€uller, A.; Roy, S. Eur. J. Inorg. Chem. 2005, 3561. (h) M€uller, A.; Roy, S. J. Mater. Chem. 2005, 15, 4673. (I) M€uller, A.; K€ogerler, P.; Dress, A. W. M. Coord. Chem. Rev. 2001, 222, 193. (4) Grigoriev, V. A.; Cheng, D.; Hill, C. L.; Weinstock, I. A. J. Am. Chem. Soc. 2001, 123, 5292. (5) Grigoriev, V. A.; Hill, C. L.; Weinstock, I. A. J. Am. Chem. Soc. 2000, 122, 3544. (6) Kobayashi, S.; Kawamura, M. J. Am. Chem. Soc. 1998, 120, 5840. (7) M€uller, A.; Todea, A. M.; van Slageren, J.; Dressel, M.; B€ogge, H.; Schmidtmann, M.; Luban, M.; Engelhardt, L.; Rusu, M. Angew. Chem., Int. Ed. 2005, 44, 3857. (8) Schr€oder, C.; Nojiri, H.; Schnack, J.; Hage, P.; Luban, M.; K€ogerler, P. Phys. Rev. Lett. 2005, 94, 017205. (9) Antonio, M. R.; Nyman, M.; Anderson, T. M. Angew. Chem., Int. Ed. 2009, 48, 6136.
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POM anions,4 and the self-assembly of Keplerate POMs in solution are just a few examples.10 Many of these processes depend on the size and the degree of hydration of countercations and additional electrolytes. Alkali metal cations with large ionic radii are less hydrated than those with small radii and are able to form more intimate ion pairs due to decreased solvent separation between the macroanion and the cation. In polar solvents, each type of POM cluster possesses an identical size, mass, and shape as well as an accurately adjustable charge.7,11-13 The highly soluble POM macroions are fundamentally important because their sizes are intermediate of two regimes: simple inorganic ions, on the one hand, and large colloidal suspensions, on the other. The POM macroions (diameter 2-6 nm) demonstrate intriguing behaviors in dilute solution. Although they are fully hydrophilic and highly soluble in polar solvents, they are found to self-assemble into large (tens to hundreds of nanometers in size), hollow (single layered), spherical “blackberry” structures (Scheme 1).10,14,15 Solutions of POMs cannot be adequately described by either Debye-H€uckel theory (10) Liu, T.; Diemann, E.; Li, H. L.; Dress, A. W. M.; M€uller, A. Nature 2003, 426, 59. (11) Todea, A. M.; B€ogge, H.; van Slageren, J.; Dressel, M.; Engelhardt, L.; Luban, M.; Glaser, T.; Henry, M.; M€uller, A. Angew. Chem., Int. Ed. 2007, 46, 6106. (12) M€uller, A.; Krickemeyer, E.; B€ogge, H.; Schmidtmann, M.; Peters, F. Angew. Chem., Int. Ed. 1998, 37, 3360. (13) M€uller, A.; Sarkar, S.; Shah, S. Q. N.; B€ogge, H.; Schmidtmann, M.; Sarkar, S.; K€ogerler, P.; Hauptfleisch, B.; Trautwein, A. X.; Sch€unemann, V. Angew. Chem., Int. Ed. 1999, 38, 3238. (14) (a) Kistler, M. L.; Bhatt, A.; Liu, G.; Casa, D.; Liu, T. J. Am. Chem. Soc. 2007, 129, 6453. (b) Liu, G.; Kistler, M. L.; Li, T.; Bhatt, A.; Liu, T. J. Cluster Sci. 2006, 17, 427. (c) Liu, G.; Liu, T. J. Am. Chem. Soc. 2005, 127, 6942. (d) Liu, G.; Liu, T. Langmuir 2005, 21, 2713. (e) Liu, T. J. Am. Chem. Soc. 2002, 124, 10942. (f) Liu, T. J. Am. Chem. Soc. 2003, 125, 312. (g) Liu, T.; Imber, B.; Diemann, E.; Liu, G.; Cokleski, K.; Li, H. L.; Chen, Z. Q.; M€uller, A. J. Am. Chem. Soc. 2006, 128, 15914. (15) M€uller, A.; Das, S. K.; Fedin, V. P.; Krickemeyer, E.; Beugholt, C.; B€ogge, H.; Schmidtmann, M.; Hauptfleisch, B. Z. Anorg. Allg. Chem. 1999, 625, 1187.
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Article Scheme 1. Self-Assembly of Keplerate {Mo72Fe30} Macroions into a Stable, Single-Layered, Hollow Spherical “Blackberry” Structure with the Blackberry Size Adjustable by Solvent Content, pH, or Additional Salts
(due to the large anionic size and the size disparity between cations and anions) or the DLVO theory for colloids (due to the facts that the POMs form true solutions and that van der Waals forces are not the dominant attractive forces that drive blackberry formation).14b POMs can be categorized in two distinct groups based on their solution behavior and self-assembly mechanisms: weak electrolytes and strong electrolytes. The highly soluble {Mo154},15 {Mo132},12 and {Mo72V30} (Na8K14(VO)2[{(MoVI)MoVI5O21(H2O)3}10{(MoVI)MoVI5O21(H2O)3(SO4)}2{VIVO(H2O)}20{VIV}10({KSO4}5)2] 3 ≈150H2O)7 are considered strong electrolytes, which carry many delocalized charges. For example, each {Mo72V30} cluster carries 31 negative charges and is balanced by 8 Naþ, 14 Kþ, 2 VO2þ, and 5 Hþ countercations in aqueous solution. Some other types of POMs, e.g., {Mo72Fe30} ([MoVI72FeIII30O252 (CH3COO)12{Mo2O7(H2O)}2{H2Mo2O8(H2O)}(H2O)91] 3 ≈150H2O)11 and {Mo72Cr30},11 exist as almost neutral clusters in crystals and carry a few localized charges in aqueous solution due to the partial deprotonation of their 30 surface water ligands coordinated to the 30 non-Mo metal centers. Therefore, they can be treated as weak acids in solution;their charge density increases with increasing solution pH. {Mo72V30}, {Mo72Fe30}, and {Mo72Cr30} are examples of Keplerate clusters (Scheme 1) which are hollow spheres built up of 12 pentagonal {(MoVI)MoVI5} units connected by 30 linkers (here non-Mo oxide units). The 30 potential deprotonation sites are the water ligands attached to the non-Mo metal centers. Blackberry formation occurs when the macroions carry a moderate amount of charge. The blackberry size can be accurately and reversibly tuned by simply changing the solvent content14,16 (e.g., the amount of acetone in a water/acetone mixed solvent) or the macroionic charge density (e.g., by adjusting the pH in {Mo72Fe30} solution).14g We recently provided direct evidence from small-angle X-ray scattering (SAXS) studies showing that some counterions like Kþ are closely associated (with a distance range of 2-9 A˚ from the macroionic surface) around discrete 2.5 nm diameter Keplerate {Mo72V30} macroanions in dilute aqueous solutions.17 Leroy et al. described simulations showing that monovalent counterions are distributed around the R-Keggin anion at ∼3-4 A˚ from its surface, indicating the formation of ion pairs in aqueous solution.18 (16) Kistler, M. L.; Liu, T.; Gouzerh, P.; Todea, A. M.; M€uller, A. Dalton Trans. 2009, 26, 5094. (17) Pigga, J. M.; Kistler, M. L.; Shew, C.-Y.; Antonio, M. R.; Liu, T. Angew. Chem., Int. Ed. 2009, 48, 6538. (18) Leroy, F.; Miro, P.; Poblet, J. M.; Bo, C.; Valos, J. B. A. J. Phys. Chem. B 2008, 112, 8591. (19) (a) Provencher, S. W. Biophys. J. 1976, 16, 27. (b) Morrison, I. D.; Grabowski, E. F.; Herb, C. A. Langmuir 1985, 1, 496.
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By realizing that counterion-mediated attraction is important for blackberry formation (hydrogen bonding is also important), we speculate that the type of counterion might play an important role in blackberry formation and blackberry size. A key question we want to explore here is whether the hydrophilic macroions can selectively bind one (or more) types of counterions when several types of counterions are present and whether the counterions with “higher attractiveness” can replace the original counterions already associated with the macroions. We choose the large Keplerate POMs as our model systems to study such interactions because they are very stable in aqueous solution and their uniform, spherical structure can generate characteristic X-ray scattering patterns. In particular, we plan to explore if the POM macroions are able to “distinguish” between similar monovalent cations, such as Liþ, Naþ, and Kþ. The question arises from our observation that the POMs are large enough so that they cannot be treated as point charges; i.e., the size ratio between the Keplerates and cations is approximately 10:1, which is noticeable but not as significant as in colloidal suspensions with a size ratio on the order of 1000:1;in this latter case, the counterions can be effectively treated as point charges. Therefore, in view of the former ∼10:1 ratio, the solution behavior of the POMs might be sensitive to the size of counterions. Furthermore, the addition of extra ions into the POM solution will change the electrostatic interactions between macroions and cations. Consequently, the self-assembly of POMs could also be affected. Herein we explore the interaction between POM macroions and various countercations by using various techniques including laser light scattering, anomalous small-angle X-ray scattering (ASAXS), and isothermal titration calorimetry (ITC). The selfassembled blackberry size can be used as a direct caliper to evaluate the change of the interactions between POM macroanions in solution, which consequently reflects the effects of cations. The very slow POM-to-blackberry self-assembly process makes it possible to introduce additional cations into the POM solution before blackberry formation occurs. For all the added salts, the same type of anion (Cl-) was used so that the effect of small anions can be reasonably eliminated.
Experimental Section 1. Sample Preparation. {Mo72V30} and {Mo72Fe30} single crystals were prepared according to the well-established procedures.7,13 All {Mo72Fe30} solutions for dynamic light scattering (DLS) were prepared by dissolving 0.5 mg/mL {Mo72Fe30} crystals into a 50 mL volumetric flask containing about 40 mL of deionized water. Once the POMs were completely dissolved, several microliters of a concentrated stock solution of salt was added to the POM solution and diluted to the 50 mL mark with water to achieve the proper salt concentration. The samples were then incubated at 40 °C until blackberry formation was complete. The whole process was monitored using DLS. The samples for DLS were first filtered through a 0.22 μm sterile filter to remove any dust or other particulates. 2. Laser Light Scattering. A commercial Brookhaven Instrument laser light-scattering (LLS) spectrometer equipped with a solid-state laser operating at 532 nm was used for DLS measurements. The DLS measurements were analyzed using the CONTIN19a and NNLS19b methods of analyses, from which the average hydrodynamic radius (Rh) was determined. We obtained the particle size distribution in solution from CONTIN by making a plot of ΓiG(Γi) vs Rh, where ΓiG(Γi) is proportional to the angular-dependent scattered intensity of a particle with an apparent hydrodynamic radius Rh. The polydispersity index was viewed from ( μ2/Γ)2, which comes from the CONTIN analysis. Larger values for ( μ2/Γ)2 indicate a larger polydispersity. More detailed descriptions of LLS can be found in our other publications.14d Langmuir 2010, 26(12), 9449–9456
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3. Isothermal Titration Calorimetry. A 2.0 mg/mL {Mo72Fe30} solution was placed in the 1.5 mL calorimetric cell. A KCl concentration of 344 mM was used for the KCl titration, and 40 mM RbCl was used for the RbCl titration. The pH of the distilled water was adjusted to 3.3 with dilute HCl to closely match the pH of the POM solution. The salt solutions were loaded into a 250 μL calorimetry syringe. The {Mo72Fe30} solution was placed in the 1.5 mL calorimetric cell, and the salt solution was loaded into a 250 μL calorimetry syringe. The temperature of the cell was kept constant at 25 °C. A 55 injection matrix was used for the 5 μL injections with each having a duration of 10 s. A 120 s delay was used in between injections. The cell was mixed at 300 rpm. The heat of dilution for each salt was performed with the same concentration of salt that was used for the POM solutions only with 1.5 mL of distilled water in the cell instead of POM. 4. Small-Angle X-ray Scattering. {Mo72V30} crystals were directly dissolved into deionized water to prepare a stock solution of 5 mg/mL (0.26 mM). All {Mo72V30} solutions used for ASAXS were prepared by dilution of the stock solution to a concentration of 1 mg/mL (0.052 mM) in order to avoid potentially vitiating effects from interparticle interactions.20 The samples containing 1 mM RbCl were prepared using the same procedure as for the 1 mg/mL (0.052 mM) {Mo72V30} solutions except RbCl was added before diluting the POM solution to the mark. The ASAXS experiments were performed at the 12-ID-C beamline, Advanced Photon Source at Argonne National Laboratory.21 Data frames were collected with 0.2 s exposure times using a MAR CCD detector and incident X-ray energies in the range between 15.05 and 15.25 keV, which encompasses the K-edge energy of Rbþ. An X-ray absorption near-edge structure (XANES) spectrum of RbCl was used to experimentally determine the K-edge energy of Rb under the experimental conditions used (Supporting Information). The spectrum shows that the edge peak is at 15.196-15.198 keV, and the edge rise starts just below 15.190 keV. Three frames were taken at all incident energies for each solution, which was placed in a 2 mm diameter, thin-wall quartz capillary tube. Only the data with less than 2% difference between each of the three frames were averaged and analyzed for this publication. The scattered intensity I(Q) from SAXS is given by IðQÞ ¼ I0 ðQÞSðQÞ
ð1Þ
where I0(Q) is the form factor and S(Q) is the structure factor;we assume it to be 1 in the absence of interparticle interactions in dilute aqueous solution.17 The scattered intensities, I(Q), were plotted vs momentum transfer, Q (A˚-1), where Q ¼ ð4π=λÞ sin q
ð2Þ
Here q is one-half the scattering angle, and λ is the wavelength of the incident X-ray beam. The background response and the isotropic Rb KR fluorescence arising for incident X-ray energies at and above the absorption edge were deliberately subtracted in identical fashion for all data to provide an accurate assessment of typically small anomalous effects on I(Q) arising from resonant atom-nonresonant atom correlations.22 The basis for ASAXS comes from the fact that the scattering length of the counterions (Rbþ in this case) depends strongly on the incident X-ray energy and is expressed as fRb ¼ f0Rb þ f 0 Rb ðEÞ þ if 00 Rb ðEÞ
ð3Þ
where E is the incident X-ray energy, f0Rb is the nonresonant term, and f 0 Rb þ if 00 Rb are real and imaginary energy-dependent (20) Ballauff, M.; Jusufi, A. Colloid Polym. Sci. 2006, 284, 1303. (21) Seifert, S.; Winans, R. E.; Tiede, D. M.; Thiyagarajan, P. J. Appl. Crystallogr. 2000, 33, 782. (22) Waseda, Y. Anomalous X-ray Scattering for Materials Characterization: Atomic-scale Structure Determination; Springer: Berlin, 2002.
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parts.23 The scattering cross section of a single macroion is as follows I0 ¼ FðQÞF ðQÞ
ð4Þ
where F(Q) is the scattering amplitude of a particle and F*(Q) is its complex conjugate. FðQÞ ¼ F0 ðQÞ þ Fres ðQÞ
ð5Þ
The resonant term is calculated using the following equation which contains v(Q), the scattering amplitude of the Rb counterions. Fres ðQÞ ¼ f 0 Rb ðEÞ þ f 00 Rb ðEÞvðQÞ
ð6Þ
The contrast variation in ASAXS, which is used to deconvolute the contribution to the scattering intensity from the counterions, comes from f 0 (E), which has strong variation in the vicinity of the Rbþ absorption edge determined using the XANES plot in the Supporting Information. The scattering intensity is the sum of energy-dependent (f 0 Rb and f 00 Rb) and energy-independent F0 terms is expressed as IðQÞ ¼ F0 2 ðQÞ þ 2f 0 Rb ðEÞF0 vðQÞ þ ½ f 0 Rb ðEÞ2 þ f 00 Rb ðEÞ2 v2 ðQÞ ð7Þ The first term is the scattering amplitude that comes from the traditional SAXS measurement far from the absorption edge; the second term is the scattering cross-term that includes the amplitudes of both the counterions and the macroion. By measuring the scattering intensity at different enegies, one below the edge (15.15 keV) and one at the edge peak (15.198 keV), it is expected that f 0 Rb (E) would decrease at the edge peak if Rbþ counterions distribute closely to the macroanions.
Results and Discussion 1. Self-Assembly of {Mo72Fe30} and {Mo72V30} in Solution. {Mo72Fe30} behaves like a weak acid in aqueous solution. At the {Mo72Fe30} concentration of 0.5 mg/mL, ∼7 protons are released from each cluster due to the partial deprotonation of the 30 FeIII(H2O) centers, resulting in a solution pH ∼ 3.8.14g Instead of remaining as discrete macroions in water, {Mo72Fe30} macroions attract to one another, forming blackberry structures with an average Rh ∼ 25 nm. Blackberry formation is believed to be driven by hydrogen bonding and counterion-mediated attraction.14b,d,g The blackberry size can be accurately tuned by adjusting pH, i.e., the effective charge density of the macroions. At pH < 2.9, the macroions carry a very low amount of (or almost zero) charge and stay as soluble discrete clusters in solution. At higher pH, the charge density on {Mo72Fe30} increases with increasing pH, leading to the blackberry formation with the blackberry size decreasing with pH (from Rh ∼ 50 nm at pH = 3.0 to ∼17 nm at pH = 6.6). Recently, by using SAXS, we showed that the close interaction between small counterions and large macroanions,17 often referred to as counterion association,1,14b,24 plays an important role in the blackberry formation process. {Mo72V30} has an overall molecular structure very similar to that of {Mo72Fe30}. It carries ∼31 charges upon dissolution in aqueous solution. The high charge density prevents the selfassembly of {Mo72V30} clusters. When acetone is introduced, the counterion association around discrete {Mo72V30} macroanions (23) Dingenouts, N.; Patel, M.; Rosenfeldt, S.; Pontoni, D.; Narayanan, T.; Ballauff, M. Macromolecules 2004, 37, 8152. (24) Rouzina, I.; Bloomfield, V. A. J. Phys. Chem. 1996, 100, 9977.
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Figure 2. CONTIN analysis of the DLS studies of 0.5 mg/mL {Mo72Fe30} solutions without additional salt and with 1.0 mM XCl salts (with X = Liþ, Naþ, Kþ, and Rbþ). The size distributions for solutions containing NaCl and LiCl are almost indistinguishable from that without added salt.
Figure 1. Change of blackberry size (in Rh) with added chloride salt concentration (A) and total ionic strength (B) for 0.5 mg/mL {Mo72Fe30} solutions. For each added cation salt there is a CSC (critical salt concentration), above which the blackberry size increases with increasing salt concentration.
decreases the effective charge density of the macroanions. In turn, the preferred curvature for the blackberries is increased, resulting in the formation of larger blackberries.16 2. Counterion Exchange Triggered by the Addition of a Small Amount of Salt As Monitored by the Size Change of the Assembled Blackberry Structures. An indirect but simple observation of the possible counterion exchange process occurring near the macroionic surface is obtained by monitoring the change of the blackberry size after introducing known amounts of additional electrolytes. As shown in Figure 1A, the {Mo72Fe30} blackberries without any extra salt have an average Rh ∼ 25.4 ( 1.0 nm, after mildly heating the solution for several weeks at 40 °C. This Rh value, achieved with H3Oþ counterions, can be used as a reference for our further experiments and discussions. Figure 1B will be discussed later in the text. Introducing a small amount of extra ions into the {Mo72Fe30} aqueous solutions was always executed immediately after dissolving {Mo72Fe30} crystals in water, i.e., before the blackberry formation started. We have carefully chosen the types of salts to make sure that, in most cases, the added salts will not significantly alter the solution pH. When small amounts of additional ions are introduced, the average Rh of the {Mo72Fe30} blackberries remains steady (the value might be different for different types of salt and away from the “baseline” for reasons that will be explained below). After passing a critical salt concentration (CSC), the Rh value starts to increase continuously with increasing salt concentration. The latter stage will be discussed in detail in the following sections. When 1-20 mM LiCl or NaCl is added, no obvious change in {Mo72Fe30} blackberry size (∼26.1 nm for LiCl and ∼26.4 nm for NaCl) from the salt-free solutions is observed. However, when 0.1-10 mM KCl is added, the average blackberry size becomes considerably larger (∼34.6 nm). The same result is observed when 9452 DOI: 10.1021/la100467p
introducing RbCl into the {Mo72Fe30} solution (Rh ∼ 35.7 nm). The major difference between KCl and RbCl is that the CSC value for RbCl is much lower. Corresponding CONTIN analysis of the DLS measurements on a series of {Mo72Fe30} solutions containing 1 mM different types of salts is shown in Figure 2. A reasonable explanation for the above results is that the small amounts of Liþ or Naþ added to the {Mo72Fe30} solution are not directly involved in the self-assembly process. That is, the affinity of the original cations (hydronium ions) to the {Mo72Fe30} macroions is stronger than that of Liþ and Naþ ions. However, the swelling of the blackberry size when Kþ ions are added indicates that the Kþ ions can change the interaction between {Mo72Fe30} macroions. The blackberry size is essentially constant for all Kþ concentrations between 1 and 10 mM, indicating that the concentration of Kþ ions in this range has no measurable effect on blackberry size. The blackberry size is controlled by several factors, including the solvent content, the charge density on macroions, and the attractive forces between macroanions.14a,g Here only the last factor is prone to variation when more Kþ ions are added into the solution. Therefore, we can speculate that Kþ ions have stronger affinity to the macroions and can replace the H3Oþ counterions to trigger the blackberry formation more readily than either Liþ or Naþ. Of course, this speculation needs further proof, which is provided by the ITC and ASAXS studies below. The addition of small amounts of RbCl has the same effect on the {Mo72Fe30} blackberry size (Figure 1 and illustrated in Figure 3). From Liþ, Naþ, Kþ to Rbþ, the ionic radii increase from 0.95, 1.33, 1.48 to 1.69 A˚, and the charge density of the cations decreases.25 Conversely, the hydrated radii and hydration numbers of the cations decrease from 3.40, 2.76, 2.32 to 2.28 A˚ and from 25, 17, 11 to 10, respectively.26 In other words, cations like Liþ and Naþ are much more hydrated than Kþ and Rbþ, which accounts for their preference to remain as aquated cations rather than binding to large POM macroions. Larger cations like Csþ and Rbþ are much less hydrated than the smaller alkali metals and are more polarizable, suggesting that smaller hydrated cations tend to have stronger affinities for the macroions than the larger ones and therefore can replace the original H3Oþ countercations.27 Among these cations, the H3Oþ ion is special because it is not a metal ion, and its hydration is very complicated (involving hydrogen bonding). Therefore, we place H3Oþ between Naþ and Kþ ions mainly based on our experimental results instead of ionic size. The O-H bond length (defined as the distance between the (25) Stern, K. H.; Amis, E. S. Chem. Rev. 1959, 59, 1. (26) Cotton, F. A.; Wilkinson, G.; Gaus, P. L. Basic Inorganic Chemistry; Wiley: New York, 1987; p 271. (27) Chourasia, M.; Sastry, G. M.; Sastry, G. N. Biochem. Biophys. Res. Commun. 1995, 336, 961.
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Figure 3. After the addition of XCl (X = Li, Na, K, Rb, and Cs) into {Mo72Fe30} blackberry aqueous solution (original counterions being protons), countercation replacement on the {Mo72Fe30} surface can be achieved by monovalent cations with small hydrated sizes only.
centers of oxygen and hydrogen atoms) of the hydronium ion is ∼0.99 A˚ and the radius of the hydrogen atom is about 0.52 A˚.20 However, the ionic radius of Hþ is
