Applied Clay Science 44 (2009) 15–20
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Applied Clay Science j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / c l a y
Cation exchange equilibria of cesium and strontium with K-depleted biotite and muscovite Yunchul Cho a, Sridhar Komarneni b,⁎ a b
Peter A Rock Thermochemistry Laboratory and NEAT ORU, University of California at Davis, Davis, CA 95616, USA Department of Crop and Soil Sciences and Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history: Received 2 October 2008 Received in revised form 14 December 2008 Accepted 16 December 2008 Available online 31 December 2008 Keywords: K-depleted biotite K-depleted muscovite Cation exchange Radioactive species
a b s t r a c t Cation exchange selectivity for Cs+ and Sr2+ with K-depleted biotite (Na-biotite) and K-depleted muscovite (Na-muscovite) was determined with equilibration for 4 weeks at room temperature. The cation exchange isotherms and Kielland plots indicated that both K-depleted micas show high selectivity for Cs+ at low equivalent fraction of Cs+ on solid. The K-depleted micas took up Cs up to approximately 50% of their theoretical cation exchange capacities. The XRD patterns after Na+ → Cs+ exchange reactions with K-depleted biotite showed that the d(001)-spacings collapsed from ~ 12.2 to ~ 11.2 Å with high Cs+ concentrations. This collapse suggests that K-depleted biotite is able to immobilize or fix Cs ions in the interlayers. In case of 2Na+ → Sr2+ exchange, K-depleted biotite showed high selectivity for Sr ions at low equivalent fraction of Sr2+ on solid. The XRD patterns showed that the main d(001)-spacing of the K-depleted biotite slightly increased from 12.16 Å to ~12.3 Å after the exchange reactions with the high Sr2+ concentrations. These results suggest that K-depleted biotite could be used as an ion exchanger to remove radioactive 137Cs as well as 90Sr from groundwater. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In order to remedy or treat soil and groundwater contaminated by radionuclides, several remedial technologies can be applied: ion exchange, precipitation, solidification/stabilization, and phytoremediation (Komarneni and Roy, 1988; Bagosi and Csetényi, 1998; Mollah et al., 1998; Soudek et al., 2006). Among these treatments, some researchers showed that ion exchange is a potential remediation technology to separate 137Cs and 90Sr from groundwater or aqueous nuclear waste (Dyer et al., 1993; Gualtieri et al., 1999). Important characteristics of the ion exchange material for separation of radionuclides are selectivity and radiation stability. Among various inorganic ion exchangers for separation of radionuclides (Adabbo et al., 1999; Kodama et al., 2001; Solbra et al., 2001; Shimizu et al., 2004), some micaceous minerals were found to show high selectivity for cesium and strontium radioisotopes (Komarneni and Roy, 1988; Stout and Komarneni, 2003), and these are expected to show radiation stability (Komarneni and Roy, 1988). Naturally occurring micas must be modified for use as commercial and cost-effective ion exchangers suitable to separate radionuclides from groundwater or aqueous nuclear wastes because micas have low cation exchange capacity (CEC). The low CEC of micas is due to interlayer potassium ions which are fixed. Some attempts have been made to improve CEC of the micas. Interlayer potassium ions can be ⁎ Corresponding author. 205 Materials Research Laboratory, The Pennsylvania State University, University Park, PA 16802, USA. Tel.: +1 814 865 1542; fax: +1 814 865 2326. E-mail address:
[email protected] (S. Komarneni). 0169-1317/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.clay.2008.12.015
removed using sodium tetraphenyloborate (NaTPB), resulting in Kdepleted micas (Scott and Smith, 1966). For example, K-depleted phlogopite (ideal formula NaMg3Si3AlO10(OH)2·H2O) produced from naturally occurring phlogopite by the K removal treatment has a CEC of 239 meq/100 g. However, phlogopite [KMg3Si3AlO10 (OH)2] without K-depletion is expected to have about 5–10 meq/ 100 g. The K-depleted phlogopite was found to show high selectivity for Cs and be able to immobilize Cs in the interlayers (Komarneni and Roy, 1988). Also, interlayer potassium ions can be removed with NaNO3 (Chaussidon, 1970). In addition to the chemical alteration or modification from naturally occurring micas, some researchers directly synthesized some swelling micas which have higher negative charge and greater cation exchange capacity than the Kdepleted micas. A novel Na-4-mica with theoretical CEC of 468 meq/ 100 g was synthesized (Gregorkiewitz and Rausell-Colom, 1987). This large CEC value is due to four exchangeable sodium ions in the interlayer per unit cell. Although the K-depleted mica has low CEC compared to Na-4-mica, exchange process with the K-depleted mica may be faster than that with Na-4-mica because of high charge density of the Na-4 mica (Shimizu et al., 2004). The purpose of this investigation was to study cation exchange properties of two K-depleted micas (K-depleted biotite, and K-depleted muscovite) using some alkali and alkaline earth metal ions (Cs+ and Sr2+). Thermodynamic approach was applied to investigate their cation exchange properties. For instance, cation exchange isotherms for Cs+ and Sr2+ were determined. Also, Kielland plots were constructed to estimate selectivity coefficients.
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2. Materials and methods 2.1. Preparation and characterization of K-depleted micas Biotite from Bancroft, Ontario, and muscovite from Effingham Township were procured from Wards Natural Science Establishment, Inc. (Rochester, NY, USA). These micas were wet ground in a blender with deionized water and b50 µm size fraction was obtained using a standard sieve. The K-depleted micas were produced according to the method by Scott and Smith (1966). A 15 g portion of b50 µm fraction of natural mica was stirred in a dark bottle containing 300 ml of 1.0 M NaCl–0.2 N sodium tetraphenyloborate (NaTPB)–0.01 M disodium ethylenediaminetetraacetic acid (EDTA) solution at room temperature for 1 day. After equilibration, the mica slurry was filtered through Whatman 50 filter paper under vacuum. The collected solid portion was washed with 40% 0.5 N NaCl–60% acetone (volume basis) solution several times. The product was then repeatedly washed with deionized water. This series of procedures was repeated several times to remove potassium completely from natural mica. K-depleted biotite and K-depleted muscovite used in this study were provided by the late Dr. A.D. Scott. The depletion of muscovite was carried out for several years as it is extremely difficult to remove K from muscovite compared to either phlogopite or biotite. All reagents were of analytical grade, and were used without further purification. Powder X-ray diffraction (XRD) analysis was carried out to confirm removal of potassium from natural biotite and muscovite using a Scintag diffractometer with CuKα radiation. The XRD patterns of the K-depleted phlogopite reported by Stout and Komarneni (2002) made it possible to confirm the removal of K from micas without the analysis of potassium in solution.
Where [Na+] and [Mn+] represent molalities of sodium and metal ions in solution, respectively. γnNa and γM are activity coefficients of n sodium and metal ions in the solution, respectively. fNa , and fM are activity coefficients of sodium and metal ions in the solid, respectively. —n — X Na and X M represent equivalent fractions of sodium and metal ion in — the solid, respectively. X i is defined by: h i h i + n+ Na n M h i ; XM = h i h i ð3Þ X Na = h n + i + n+ + + Na + Na n M n M The above Eq. (2) can be expressed in another way by substituting [Na+] and [Mn+] with XNa and XM, respectively . Thus, K can be given by: n K = XNa XM γnNa fM n−1 ½nðTNÞ = ð1 − XM Þn X M γMNa fM n n XM ð1 − X M Þ γ M fNa ½nðTNÞn − 1
n n XM X Na γ M fNa
ð4Þ
Where XNa and XM represent equivalent fraction of sodium and metal ions in solution. h i h i Na + n Mn + ; XM = n + ð5Þ XNa = n + n M n M + Na + + Na + n In case of dilute solution, the ratio of γnNa to γM (γNa /γM) is assumed as unity (Barrer and Klinowski, 1974). In terms of non ideal molar fraction effect in solid, K can be defined by:
M
K = KNa
fM n fNa
ð6Þ
Where KM Na is selectivity coefficient and is defined by: 2.2. Cation exchange isotherm determination
M
A 25 mg of the K-depleted mica (K-depleted biotite or K-depleted muscovite) of b50 µm size fraction was placed in a polypropylene centrifuge tube containing 25 mL of a solution containing different molar fractions of Mn+ / Na+ (Mn+ = Cs+ or Sr2+). The molar fraction of Mn+ / Na+ was 1, 0.75, 0.5, 0.3, 0.2, or 0.1. However, the total normality of the equilibrating solutions was kept at 0.00249 N. These batch experiments were carried out at room temperature for 4 weeks. The separation of solid and solution phases was done by centrifugation (HT centrifuge, IEC) at 5000 rpm. Triplicate runs were performed for all batch experiments to check for reproducibility. Powder X-ray diffraction (XRD) analysis was carried out to analyze the solid phases using a Scintag diffractometer with CuKα radiation. The solutions were analyzed by atomic absorption spectroscopy (AAS) using a Perkin-Elmer, PE 703 instrument. Based on the experimental data obtained in the batch tests, the equivalent fraction of ions in solution and the equivalent fraction of ions in solid were calculated to prepare ion exchange isotherms and Kielland plots.
n
n
KNa = XNa XM γNa ½nðTNÞn − 1 = ð1 − XM Þn XM γMNa XM ð1 − X MÞÞn γ M ½nðTNÞn − 1
ð7Þ
n XM X Na γ M
Where, TN represents total normality in the solution (TN = [Na+] + n[Mn+]). The corrected selectivity coefficient (KM Na) can be determined by M plotting the logarithm of KM Na (logKNa) versus equivalent fraction of — metal ion in solid (X M). The plot can be expressed as: M M logKNa = 2C1 X M + log KNa
XM ;X
MY0:
ð8Þ
Where, C1 is Kielland coefficient. If logKM Na N 0, the solid exchanger shows a preference for metal ions, while the exchanger shows a preference for sodium ions if logKM Na b 0. There is no preference between these ions if logKM Na = 0. 4. Results and discussion
3. Theory
4.1. Characterization of the K-depleted micas
The cation exchange between Na+ and metal cation (Mn+ = Cs+ or Sr2+) on the K-depleted mica can be represented by,
Both K-depleted micas gave the d(001)-spacing of about 12 Å (Fig.1). The slight variation in the d(001)-spacing values of two K-depleted micas is likely due to layer charge and structural features. The XRD results suggest that removal of interlayer potassium from the natural micas (biotite and muscovite) is complete. The increase in the d(001)spacing to ~12 Å results from a complete replacement of interlayer potassium ions with hydrated sodium ions because the d(001)-spacing of natural micas with potassium ions in their interlayers is ~10 Å (Fanning et al., 1989). In case of the K-depleted biotite, the d(001)spacing is about 12.2 Å with a shoulder at 11.18 Å under dry condition as revealed by the XRD pattern (Fig. 1a). The presence of the shoulder peak at 11.18 Å is likely due to dehydration leading to lower content of water
nNa
+
+M
n+
±nNa
+
+M
n+
ð1Þ
According to Gaines and Thomas's thermodynamic treatment (Townsend, 1984), thermodynamic equilibrium constant, K is expressed as; h in K = X M Na + fM γnNa n n X Na Mn + fNa γM
ð2Þ
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resulting in loss of selectivity for Cs+. On the other hand, the broadening of the (001) reflection was observed with the collapse of the interlayers. The broadening of the (001) reflection is due to a difference in amounts of Cs+ as well as water molecules in the interlayers (Stout et al., 2006). The Na+ →Cs+ exchange isotherm of the K-depleted muscovite shows a trend similar to that for the K-depleted biotite (Fig. 2a) and phlogopite (Komarneni and Roy, 1988; Stout et al., 2006). The K-depleted muscovite took up most Cs+ ions from solution at the lower Cs+ equilibrium — concentration. There is no more uptake of Cs+ ions at XCs N 0.5. A Kielland plot of the isotherm data did not give a good linear equation. However, the K-depleted muscovite is assumed to show a preference — for Cs+ at XCs b ~ 0.5 because majority of data points fall above the dotted line on the Kielland plot (Fig. 2b). Fig. 4 shows the XRD patterns after the
Fig. 1. XRD patterns of untreated K-depleted micas: (a) K-depleted biotite and (b) Kdepleted muscovite. d spacing values given in Å.
molecules in the interlayers. For the K-depleted muscovite, the d(001)spacing is 12.00 Å (Fig. 1b). 4.2. Na+ → Cs+ exchange with K-depleted micas The Na+ → Cs+ exchange isotherm with K-depleted biotite is shown in Fig. 2a. Each data point was obtained in triplicate runs and represents the average of a mean variation of less than ± 3%. In case of monovalent → monovalent ion exchange, the diagonal line on the isotherm represents equal preference between two monovalent ions. In this experiment, if the isotherm data points lie above the diagonal line, the K-depleted biotite shows a preference for Cs+ ion. At the low Cs+ equilibrium concentration, the K-depleted biotite took up most Cs+ ions from solution. In other words, the K-depleted biotite shows selectivity for Cs+ ions at low Cs+ concentrations. After Cs+ ions occupy ~ 50% of the total exchange sites of the K-depleted biotite — (XCs = ~ 0.5), there is apparently no more uptake of Cs+ ions. Fig. 2b shows a Kielland plot of the equilibrium data. The Kielland plots for ion exchanges in inorganic exchangers often yield linear relationships (Tsuji and Komarneni, 1989; Tanaka and Tsuji, 1997). The dotted line on the Kielland plot, where selectivity coefficient, KS, is equal to unity, indicates that there is no preference between Na+ and Cs+. When the points fall above the dotted line, the K-depleted biotite is selective for Cs + ion. The Kielland plot did not give a good linear equation because of the big scatter of the data points. The scattering may be due to the collapse of the interlayer which leads to steric limitation (Kodama and Komarneni, 2000). Thus the generalized Kielland coefficient (C1) was difficult to be determined because the C1 is related to the steric hindrance in the exchange site (Barrer and Sammon, 1955; Barrer and Meier, 1959). However, the K-depleted biotite seems to be selective — for Cs+ at XCs b ~ 0.5 because the majority of points are above the dotted line on the Kielland plot. It is clear that the interlayer collapse occurs in the K-depleted biotite when a certain amount of Cs+ ions occupy the interlayers (Fig. 3). When the K-depleted biotite was equilibrated with very low Cs+ concentration (0.249 mN CsCl + 2.241mN NaCl), the d(001)-spacing was 12.16 Å with a shoulder at 11.56 Å (Fig. 3f). This d(001)-spacing value is not quite different form that of original K-depleted biotite. There is no significant collapse of the interlayer at the low Cs+ concentration. However, for the high Cs+ concentrations, the basal spacings collapsed to ~11.1 Å without a shoulder peak (Fig. 3a, b, c, d, and e). The collapse of the interlayers is related to interlayer dehydration which Cs+ with low hydration energy produces (Sawhney, 1972). The collapse of the interlayers prevented further Na+ → Cs+ exchange in the K-depleted biotite,
Fig. 2. Na+ → Cs+ ion exchange with K-depleted micas (●: K-depleted biotite and ○: Cs K-depleted muscovite): (a) isotherms and (b) Kielland plots (KS = KNa ).
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reaction with the lowest Cs+ concentration (0.249 mN CsCl + 2.241 mN NaCl). These XRD patterns of the K-depleted muscovite are different from those of K-depleted biotite (Fig. 3) and phlogopite (Komarneni and Roy, 1988; Stout et al., 2006). The ~12 Å reflection in the K-depleted muscovite was still observed even after equilibrationwith the highest Cs+ concentration (2.49 mN CsCl) (Fig. 4a). Also, the broadening of the (001) reflection was not observed for all exchange reactions. Even though the K-depleted muscovite still retains ~12 Å, the uptake of Cs+ is less than that of the K-depleted phlogopite (Komarneni and Roy, 1988; Stout et al., 2006). The XRD results suggesttheNa+→Cs+ exchange reaction depends upon structural characteristics of mica such as mica type (dioctahedral vs. trioctahedral) as well as layer charge. The K-depleted muscovite is dioctahedral mica, while the K-depleted biotite is trioctahedral mica. In trioctahedral micas, there is maximum electrostatic repulsion between
Fig. 3. XRD patterns of K-depleted biotite after Na+ → Cs+ exchange reaction with (a) 2.49 mN CsCl, (b) 1.868 mN CsCl + 0.622 mN NaCl, (c) 1.245 mN CsCl + 1.245 mN NaCl, (d) 0.747 mN CsCl + 1.743 mN NaCl, (e) 0.498 mN CsCl + 1.992 mN NaCl, and (f) 0.249 mN CsCl + 2.241 mN NaCl. d spacing values given in Å.
Na+ → Cs+ exchange reaction with the K-depleted muscovite using the different equilibrating solutions. The K-depleted muscovite had the (001) reflection at ~12 and ~11 Å for all exchange reactions except for the
Fig. 4. XRD patterns of K-depleted muscovite after Na+ → Cs+ exchange reaction with (a) 2.49 mN CsCl, (b) 1.868 mN CsCl + 0.622 mN NaCl, (c) 1.245 mN CsCl + 1.245 mN NaCl, (d) 0.747 mN CsCl + 1.743 mN NaCl, (e) 0.498 mN CsCl + 1.992 mN NaCl, and (f) 0.249 mN CsCl + 2.241 mN NaCl. d spacing values given in Å.
Fig. 5. 2Na+ → Sr2+ ion exchange with K-depleted micas (●: K-depleted biotite and ○: Sr K-depleted muscovite): (a) isotherms and (b) Kielland plots (KS = KNa ).
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cation and H+ of the OH− groups in the octahedral sheet. Thus ion exchange with K-depleted biotite is easier than that with K-depleted muscovite. Also, the theoretical layer charge of K-depleted muscovite is higher than the other micas and the appearance of the peak at 9.86 Å (Fig. 4f) is likely due to dehydration of K-depleted muscovite because of its high layer charge. 4.3. 2Na+ → Sr2+ exchange with K-depleted biotite and K-depleted muscovite The 2Na+ → Sr2+ exchange isotherm with K-depleted biotite is shown in Fig. 5a. Each data point was obtained in triplicate runs and represents the average of a mean variation of less than ±5%. The plateau in the isotherm shows that the K-depleted biotite seems not to — take up Sr2+ at approximately XSr N 0.55. A Kielland plot of the data did not give a good linear relation because of the big scatter of the data points (Fig. 5b). Two data points fall slightly above the dotted line where the selectivity coefficient, KS, is equal to unity. From the Kielland plot, it is safe to assume that the K-depleted biotite shows a — preference for Sr2+ at XSr b 0.4. Fig. 6 shows the XRD patterns after the + 2+ 2Na → Sr exchange reaction with the K-depleted biotite using the different equilibrating solutions. The collapse of the interlayers was not observed for all exchange reactions. After the 2Na+ → Sr2+ exchange reaction, the d(001)-spacing of the K-depleted biotite slightly increased since the hydrated radius of Sr2+ (4.12 Å) is larger than that of Na+ (3.6 Å). In the case of the exchange reaction with the highest Sr2+ concentration (2.49 mN SrCl2), the d(001)-spacing increased to 12.34 from 12.1 Å. These XRD patterns suggest that the Kdepleted biotite preserves its hydrated interlayer structure after the 2Na+→ Sr2+ exchange reaction. Similarly, the preservation of this hydrated interlayer structure was observed in case of Na-4 mica after 2Na+ → Sr2+ exchange reaction (Kodama and Komarneni, 2000). The 2Na+ → Sr2+ exchange isotherm with K-depleted muscovite is shown in Fig. 5a. Each data point was obtained in triplicate runs and
Fig. 6. XRD patterns of K-depleted biotite after 2Na+ → Sr2+ exchange reaction with (a) 2.49 mN SrCl2, (b) 1.868 mN SrCl2 + 0.622 mN NaCl, (c) 1.245 mN SrCl2 + 1.245 mN NaCl, (d) 0.747 mN SrCl2 + 1.743 mN NaCl, (e) 0.498 mN SrCl2 + 1.992 mN NaCl, and (f) 0.249 mN SrCl2 + 2.241 mN NaCl. d spacing values given in Å.
Fig. 7. XRD patterns of K-depleted muscovite after 2Na+ → Sr2+ exchange reaction with (a) 2.49 mN SrCl2, (b) 1.868 mN SrCl2 + 0.622 mN NaCl, (No peak is visible because of compression in intensity), (c) 1.245 mN SrCl2 + 1.245 mN NaCl, (d) 0.747 mN SrCl2 + 1.743 mN NaCl, (e) 0.498 mN SrCl2 + 1.992 mN NaCl, and (f) 0.249 mN SrCl2 + 2.241 mN NaCl. d spacing values given in Å.
represents the average of a mean variation of less than ± 4%. The isotherm indicates that the K-depleted muscovite seems not to take up Sr2+ at all concentrations used in this study. Based on a Kielland plot of the data where all points fall below the dotted line, the K-depleted muscovite is not selective for Sr2+ (Fig. 5b). Unlike the 2Na+ → Sr2+ exchange with the K-depleted biotite, the K-depleted muscovite gave d(001)-spacing of ~9.6 and ~10 Å after the exchange reaction except with 2.49 mN SrCl2 solution and 1.868 mN SrCl2 + 0.622 mN NaCl solution (Fig. 7c, d, e and f). In these Sr2+ concentrations, the limited 2Na+ → Sr2+ exchange apparently caused the collapse of the interlayer to form dehydrated Na-muscovite, Sr-muscovite, or a mixed Na and Sr-muscovite. The (001) reflection of original K-depleted muscovite (hydrated Na-muscovite) is ~ 12 Å (Fig. 1). However, the K-depleted muscovite can give (001) reflection of ~ 9.6 Å after dry heat treatment at 60 °C ( Fig. not shown here). The 2Na+ → Sr2+ exchange may influence the degree of dehydration of the K-depleted muscovite. The collapse of the interlayers seems to prevent further 2Na+ → Sr2+ exchange. Another interesting thing is that a weak peak appeared at ~12 Å after the exchange reaction with high Sr2+ concentrations (2.49 mN SrCl2 and 1.868 mN SrCl2 + 0.622 mN NaCl) (Fig. 7a and b). No reflection is visible in Fig. 7b because of compression of intensity in the figure. These XRD results suggest that the basal spacing at the edges remained at ~12 Å with the increased concentration of Sr2+ ions and exchange at the edges of the interlayers (i.e., no expansion of interlayer of the K-depleted muscovite unlike K-depleted biotite is due to very limited exchange). Although it is not possible to give a definite explanation about these XRD results without further studies, it may be assumed that some exchange sites close to edge sites of the K-depleted muscovite are effective for the 2Na+ → Sr2+ exchange. The results presented here show that the K-depleted biotite is better than the Kdepleted muscovite for Cs and Sr exchange. In addition, K-depletion of muscovite is extremely difficult and hence other micas may be preferred for cation exchange after K-depletion.
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5. Conclusions Two K-depleted micas (K-depleted biotite and K-depleted — muscovite) were selective for Cs+ at low XCs values. However, the + K-depleted micas are not selective for Cs when the amounts of Cs+ exchanged on the micas are approximately 50% of the theoretical CEC. The above loss of selectivity can be explained by the collapse of the interlayers, which limited further entry of Cs+ ions into the interlayers. K-depleted biotite and muscovite could be used as inorganic ion exchangers for radioactive Cs+ remediation. In case of 2Na+ → Sr2+ exchange with two K-depleted micas, the — K-depleted biotite seemed to be selective for Sr2+ at XSr b 0.4, while the K-depleted muscovite did not show a preference for Sr2+. The XRD patterns showed that the d(001)-spacing of the K-depleted biotite slightly increased from 12.16 and 11.16 Å to 12.34 and 11.33 Å, respectively after the exchange reaction with the highest Sr2+ concentration. In case of the K-depleted muscovite, the 2Na+ → Sr2+ exchange did not cause the expansion of interlayers because of very limited exchange. Acknowledgements We acknowledge financial support by the Interfacial, Transport and Separation Program, Chemical and Transport Systems, Division of the National Science Foundation under Grant No. CTS-0242285 and by the College of Agricultural Sciences under Station Research Project No. PEN03963. References Adabbo, M., Caputo, D., de Gennaro, B., Pansini, M., Colella, C., 1999. Ion exchange selectivity of phillipsite for Cs and Sr as a function of framework composition, Micro. Meso. Mater. 28, 315–324. Bagosi, S., Csetényi, L.J., 1998. Caesium immobilisation in hydrated calcium-silicatealuminate systems. Cem. Concr. Res. 28, 1753–1759. Barrer, R.M., Klinowski, J., 1974. Ion-exchange selectivity and electrolyte concentration. J. Chem. Soc., Faraday Trans. I 70, 2080–2089. Barrer, R.M., Meier, W.M., 1959. Exchange equilibria in synthetic crystalline exchanger. J. Chem. Soc., Faraday Trans. I 55, 130–141. Barrer, R.M., Sammon, D.C., 1955. Exchange equilibria in crystals of chabazite. J. Chem. Soc. 2838–2849.
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