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Sorption kinetics of cesium on natural mordenite
Pergamon
0969-8043(93)E0021-C
Appl. Radiat. Isot. Vol. 46, No. I, pp. 7-12, 1995 Copyright ~5 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0969-8043/95 $9.50 + 0.00
Sorption Kinetics of Cesium on Natural Mordenite TIEN-JUI LIANG and JOSEPH YUE-CHEUNG
TSAI
Radiation Laboratory, Taiwan Power Company, P.O. Box 7, Shihmen, Taipei, Taiwan, Republic of China (Received 19 July 1993; in revised form 4 November 1993) The characteristics of sorption kinetics of cesium on natural mordenite, including apparent rate constant, intraparticle diffusion coefficient and reaction mechanisms, were investigated in this study. The apparent rate constant of sorption, as derived from the semi-empirical Elovich equation, was indicated from the experimental results to be about 56.9/~equiv • g- t. s- ~. The rate-determining step of sorption reaction was identified as the intraparticle diffusion of cesium cation from the main channel to site B, which is located in the side void, through the side channel system of mordenite. The linear and nonlinear intraparticle diffusion coefficients of Cs ÷ were observed via calculation by the spherical diffusion model as being 4.7 x 10-~8 and 3.5 x 10-~Sm2-s -I, respectively.
Introduction Mordenite is regarded as a candidate of buffer material in the radwaste disposal program due to its excellent sorption ability on many radionuclides such as Cs, Sr and transuranic elements. The sorption characteristics of cersium on mordenite have been investigated in previous research (Liang, 1993). However, the reaction mechanisms and kinetics have not yet been identified. Both the semi-empirical Elovich equation and the spherical diffusion model are suggested in this present study for assessing the kinetics of sorption reaction.
The rate constant, k, can be derived from the slope of the relationship between q and ln(t ); in addition, the intercept, a, means k . l n ( X / k ) . The semi-empirical kinetic equations may generally be regarded as optimum results of data-fitting, and their theoretical implications are apparently insignificant. On the other hand, Aharoni and Ungarish (1976, 1977) have indicated that the validity of the Elovich equation is limited by the time interval of the experiment, and shorter time results are more feasible. 2. Spherical diffusion equation
1. Elovich equation The Elovich equation has been previously applied in the kinetic study of soil science in many investigations (Atkinson et al., 1970; Chien and Clayton, 1980; Sparks et al., 1980; Elkhatib et al., 1984; Havlin and Westfall, 1985). A traditional Elovich equation may possibly be expressed as follows: dq dt
X exp(- Y.q) k = I/Y
(1)
in which q is the concentration of Cs ÷ in the solid phase (#-equiv. g - l ) ; X is the experimental fitting constant; k is the reaction rate constant (/~equiv, g-J • s-l). After integration, equation (1) may be rewritten as equation (2), if q = 0 when t = to: q=k.ln
~-
+kln(t)=a+k-ln(t).
(2)
The rate of sorption may be determined by the spherical diffusion model under the conditions in which: (a) the shapes of geomedia are assumed as being ideal spheres with the same radius; and (b) the rate-determining step of sorption is controlled by intraparticle diffusion (Boyd et al., 1947; Helfferich, 1966, 1983; Rasmuson and Neretnicks, 1983). The concentration gradient between ambient solution and the center of the soil particle is the driving force of diffusion. A typical diffusion equation in the spherical coordination system may be as follows:
ac a-7 =
:ac) \ 7-ff +-;
(3)
in which C is the concentration of solute in the liquid phase (/a-equiv. dm 3), r is the radical distance from the center of the geomedium particle (/tin); D is the linear intrapartical diffusion coefficient (m 2 • s-l).
Tien-jui Liang and Joseph Yeu-cheung Tsai Introducing the dimensionless equation (3) can be rewritten as ~u (~2U --
t~t
factor u =Cr,
= D -
(4)
Or 2"
The initial and boundary conditions of equation (4) are u=0
r=0,
u=aCo
t>0
r=a,
t>0
while a is the radium of the geomedium particle (m- t); Co is the initial concentration of solute in the liquid phase (#-equiv. dm-3). The solution of equation (4) may be expressed as equation (5):
q(t)
C(t)-Ce
q-~-= ~Co_
1 ~
1-~. E,=
1
x ~-i'exp
(
O "n2"~z2"t) a-2
+K
(5)
in which: q (t) is the concentration of solute in the solid phase (#-equiv.g ~); qe is the equilibrium concentration of solute in the solid phase (#equiv, g- l); C (t) is the concentration of solute in the liquid phase (#-equiv. dm-3); Co is the equilibrium concentration of solute in the liquid phase (#equiv, dm-3); K is the integration constant. The relationship between q (t) and C(t ) is presented as
q ( t ) = C ( t ) . V/m. This solution is valid if the ratio of solution volume to geomedium mass (V/m) is quite large and no diffusion reflection has been observed during the test. Considered in the earlier time interval of experiment, the equation (5) may be simplified as equation (6):
q(t) qe
6 { D ' t ' ] l/z
~-~\--~-] q-K' .,/;+K'
(6)
Comparing the relationship between q/qe and ~/t, the diffusion coefficient, D, may be derived from the slope of this equation. The nonlinear sorption of mordenite should be taken into account if the concentration of Cs + is high enough. A modified Freundlich model was proposed (Liang, 1993) for describing this kind of sorption behavior and may be written as
q = K~ C I,,,H+ KL C I,',,L
(7)
in which: Kil is the data-fitting constant in the higher solute concentration region; K L is the data-fitting constant in the lower solute concentration region; n, is the intensity of sorption in the higher solute concentration region; nL is the intensity of sorption in the lower solute concentration region. Experimental data indicated that nL is close to 1 if
the solute concentration is lower than 10 3 N. This result implicated that the linear sorption model is feasible in that low concentration region. The nmvalues, on the other hand, are far from unit. This Freundlich-type modification is also introduced in the spherical diffusion model for evaluating the influences of the nuclide concentration gradient. Suzuki and Kawazoe (1974a,b) have applied a simplified analytical solution towards modifying the Freundlich-type diffusion coefficient as: -
q [(' '): =
qe
--
nH
+
(8)
nil
Experimental
I. Chemical composition analysis Natural mordenite was produced by Asahi Chemical Co., Japan, and was washed, crushed, and heated to about 750°C for removal of the organic compositions prior to experiments. Mordenite was digested by HCI and HF, heated by a microwave oven, and analyzed by inductively coupled plasma-mass spectroscopy (ICP-MASS). The chemical compositions of mordenite are listed in Table 1.
2. Particle size analysis The sizes of mordenite particles have a significant role, and the spherical diffusion model was employed in this study for evaluating the intraparticle diffusion coefficient. The assumption of identical particle radius is actually invalid, and the concept of "equivalent radius" has become more reasonable. Two methods employed in measuring the equivalent radius of mordenite particle, dynamic light scattering (DLS) method and BET method, were used in this study. Three different size analysis modes, i.e. r(F), r (weight) and r (amount), were supplied by Otsuka LPA 3000/3100 Laser Particle Size Analyzing System (1990). Hunter (1989) suggested that r (F) is apparently a more feasible analysis mode than the other two. Another method applied in estimating the equivalent radius of particle could possibly be derived from the relationship of r = 3 V/S. V and S in this formula represent the bulk volume (m 3. g-l) and specific surface area (m 2 • g-~) of mordenite, respectively. The value of S measured by BET method was approx. Table I. Chemicalcompositionsof natural mordenite Chemical composition Weight (%) SiO2 72.06 AI203 12.90 Fe203 2.17 MgO 0.81 CaO 2.58 Na20 1.81 K20 1.05 H20 6.73 Total 100.11
Sorption kinetics of cesium on natural mordenite 800 -
130.4 m 2. g - ' . Roughly 95% ofsorption reaction were indicated by Suzuki (1990) to have occurred in the internal surface of zeolite minerals; that is, the application of BET method towards assessing S was more reasonable than that which used the geometric surface area.
600
3. Batch method The ratio of solution volume of mordenite mass in this study was 100 ( m L . g - ' ) so as to satisfy the condition of semi-infinite source. A mixture of 3.00 g mordenite and 290.00 mL deionized water was prepared and adequately mixed overnight at a constant rate of 600 rpm by magnetic stirrer. When the experiment started, 10 mL of 0.3 M CsNO3 solution was rapidly injected into the sufficiently mixed mordenite/ deionized water suspension. Vacuum extraction/separation apparatus and 0 . 4 5 # m disc filters were employed for rapid and effective separation of the liquid and solid. This improvement could potentially increase the precision of study markedly, in comparison with the tradition centrifugal separation techniques. The variances of concentrations of cations, Cs + , Na + , K + , Ca 2+ , Mg 2+ and Fe 3+, in the liquid phase were analyzed by ICPMASS after dilution. Results
and
Discussion
1. Particle size of mordenite The average radius of mordenite particle, analyzed by LPA 3000/3100 Laser Particle Size Analyzing System in DLS mode, was approx. 1.06 + 0.88/~m in r (F) mode, 2 . 2 0 + 0 . 4 0 / ~ m in r(weight) mode and 0.52 + 0.72 p m in r (amount) mode. The average radius o f a mordenite particle was set at 1.06 # m according to the r(F) mode. The specific surface area of mordenitc tested by BET method was 130.4 m 2 . g - ~, and the specific bulk volume of mordenite was nearly 4.67 × 10 5m3.g i. The size of mordenite particle, which was calculated by the formula o f r = 3 V/S, was about 1.03 pm. The sizes of particle determined by two different methods were obviously almost the same.
2. Sorption rate constant determined by Elovich equation
:L
400
q(t) = 158.9 + 56.9 * In(t)
2
(9)
trated in Fig. 2. The fitted linear function may be described as
I
I
8
10
Fig. 1. Sorption kinetics of Cs + on mordenite analyzed by Elovich equation.
q (t_._))= 0.0068' x/t + 0.52. qe
(I 0)
The diffusion coefficient may be derived from the slope of this equation. The linear diffusion coefficient of Cs ÷ in the mordenite structure was indicated from equation (6) to be 4 . 7 x 10 ~8m2.s ~(thatis, i f t h e average equivalent radius of mordenite particle was 1.06/~m).
Distinguishing between intraparticle diffusion and so-called diffusion of nuclides in the geomedia is important, especially for a buffer material in radwaste disposal. The intraparticle diffusion describes the diffusion process of Cs + within the mordenite particle 1.0
/
0.8
../
o/
o,,Y"
°,s"
0.6
The apparent rate constant of sorption was 56.9 + 1.8/~-equiv • g-~ • s -j, and the square of correlation coefficient, r 2 was 0.995.
3. [ntraparticle diffusion coefficient determined by spherical diffusion model The relationships between q/qe and x/t are illus-
I 6
In(t) (s)
The variance of Cs ÷ concentration in solid phase that are dependent on the test time are shown in Fig. I. A linear regression function was fitted as
q(t) = 158.9 + 56.9. ln(t).
[ 4
q(t) / qe -- 0.0068 X/7+ 0.52 0.4
I
I
I
t
I
I
I
10
20
30
40
50
60
70
X/7(s 1/2) Fig. 2. Sorption kinetics of Cs + on mordenite analyzed by spherical diffusion model.
Tien-jui Liang and Joseph Yeu-eheung Tsai
10
Table 2. Distributionsof cationsin rnordenitestructure Distributionsof cations in exchangeablesites Cation Mg2+ Ca2+ K+ Na+ Cs÷
A 0.5 ~ 0.5 0.5 -0.43 --
B --0.42 -0.50
C 0.2~0.3 0.18 ----
D 0.1 0.15 0.38 0.36 0.25
E -0.18 0.18 0.21 0.24
that occurs as a result of the concentration gradient between ambient solution and the center of the particle. This diffusion takes place in the complex intraparticle channel systems of mordenite crystal structure, and will be discussed later. However, the general term "diffusion" applied in the assessment of nuclide migration process implies the phenomenon of interparticle diffusion/transportation, and this is especially valid in the compacted buffer material. The nonlinear sorption character of mordenite has been previously reported (Liang, 1993), and must be taken into account if the nuclide concentration is high enough. The Freundlich-type nonlinear diffusion coefficient is indicated from equation (8) (Suzuki and Kawazoe, 1974a,b) to be 3.5 x 10 -~8 m 2. s -~, if the intensity of sorption, na, is 4.95. 4. Reaction mechanisms and rate-determining step o f Cs + sorption on mordenite structure Mortier and Schlenker have examined the locations of various cations in the mordenite structure, which are summarized in Table 2 (Mortier, 1977;
Mortier et al., 1975, 1978; Schlenker et al., 1978, 1979). The structure of mordenite is complicated, i.e. it contains two different types of channel and void systems. The main channel is elliptical, while the major and minor axes are 7.0 and 6.7 ~. The side channel system of mordenite, nevertheless, is near a circle with dia of 2.8 ~. The main void of mordenite is the main channel; however, the side void is surrounded by eight tetrahedrons, and its major and minor axes are 2.9 and 5.7 ~. Eight possible sites are available where ion exchange reaction may take place in the mordenite structure. The locations of those eight sites are illustrated in Fig. 3. Site occupancies for Cs + are sites B (50%), D(25%) and E (25%). Sites B and D are located at the side channel with a coordination number of 4. Site E is located at the main channel. Only a smaller cation, e.g. Na +, Ca 2+ and Mg 2+, whose radius is < 1.3/~, can occupy site A. That is, the larger cation, e.g. K ÷ and Cs +, cannot stimulate an exchange reaction at this site. This phenomenon is called the "ionic sieve" effect. Table 3 lists the variances of concentrations of exchanged cations in liquid phase, e.g. K +, Na + , Ca 2+, Mg 2+ and Fe 3+. Approximately 66% of K ÷, 30% of Na ÷, 18% of Ca 2÷ and 6% of Mg 2+ were exchanged within a short time interval when the reaction was initiated. On the other hand, nearly all of K +, 54% of Na +, 36% of Ca 2+ and 10% of Mg 2+ are released into the solution when the reactions approach equilibrium. The distributions of K + in mordenite structure are
w
Fig. 3. Locations of exchangeable sites in mordenite structure.
b
Sorption kinetics of cesium on natural mordenite
11
Table 3. Variances of concentrations of exchanged cations in liquid phase from natural mordenite Percentage of dissolved exchangeable cations (%) Reaction time (rain) Fe"~+ Mg2+ Ca2+ Na + K÷ I 5 10 60 360 1410 2873 4295 5040
o. I o. 1 0.1 o. I 0.2 0.2 0.2 0.2 0.2
5,6 6.1 5.9 6,6 6.9 7.8 8.5 9.0 9.0
at sites B (42%), D (38%) a n d E (18%). In the early stage o f C s + / K ÷ reaction, the K + located sites D a n d E may be replaced by Cs + , additionally, K + in site B is exchanged slowly. The kinetic o f C s + / N a ÷ exchange shows that almost all N a n in site E (21%) a n d most o f that in site D are immediately exchanged. However, Cs ÷ c a n n o t react with N a n located in site A in light of the ionic sieve effect. This is why only roughly 54% o f N a n is exchanged at equilibrium. The analogous results were also observed in Cs+/ Ca z+ a n d C s + / M g 2+ reactions. The C s + / C a 2+ reaction only occurred in sites E (18%) a n d D (15%), a n d the former reaction is faster t h a n the latter. The Cs ÷ m a y only replace the M g 2÷ which is located at site D (10%). The rate-determining step o f Cs + ion exchange on m o r d e n i t e m a y be concluded to be the diffusion o f Cs + from main channel to site B t h r o u g h the side channel. The reaction occurred first in site E, later in site D, and finally in site B.
Conclusion T h e s o r p t i o n kinetics of cesium o n n a t u r a l m o r d e n ite were studied in present research effort, Several key factors, e.g. the a p p a r e n t rate c o n s t a n t of sorption, intraparticle diffusion coefficient a n d reaction mechanisms, were investigated in this study. The a p p a r e n t rate c o n s t a n t of sorption, which was derived from the semi-empirical Elovich equation, was indicated from experimental results to be 56.9 # - e q u i v ' g ~ - s - ~. The rate-determining step o f reaction was identified as the intraparticle diffusion o f cesium from the main channel t h r o u g h the side channel system, a n d then intruding into site B which was located in the side void of m o r d e n i t e structure. The intraparticle diffusion coefficient o f cesium was observed from the spherical diffusion model as being 4.7 x 10-~Sm 2. s -~. A nonlinear modification of 3.5 × 10- ~ m 2- s-~ was made if the Freundlich type of sorption was taken into account.
References Aharoni C. and Ungarish M. (1976) Kinetics of activated chemisorption. 1. The non-Elovichian part of the isotherm. J. Chem. Soc. Faraday Trans. 72, 400.
18.0 20.4 20.8 25.5 28.5 33.5 36.5 36.5 36.2
29.6 34.8 37.6 43.9 48.3 51.5 53.6 53.8 53.4
66.0 76.4 81.5 91. I 97.3 97.8 97.9 98. I 98.0
Aharoni C. and Ungarish M. (1977) Kinetics of activated chemisorption. II. Theoretical models. J. Chem. Sot'. Faraday Trans. 73, 456, Atkinson R. J., Hingston F. J., Posner A. M. and Quirk J. P. (19703 Elovich equation for the kinetics of isotope exchange reactions at solid-liquid interfaces. Nature (London) 226, 148. Boyd G. E., Adamson A. W. and Meyers L. S. (1947) The exchange adsorption of ions from aqueous solutions by organic zeolites. II. Kinetics. J. Am. Chem. Soc. 69, 2836. Chien S. H. and Clayton W. R. (1980) Application of Elovich equation to the linetics of phosphate release and sorption in soils. Soils Sci. Soc. Am. J. 44, 260. Elkhatib E. A., Bennett O. L. and Wright R. J. (19843 Linetics of arsenate sorption in soils. Soil Sci. Soc. Am. J. 48, 758. Havlin J. L. and Westfall D. G. (1985) Potassium release linetics and plant response in calcareous soils. Soil Sci. Sac. Am. J. 49, 366. Helfferich F. (1966) Ion exchange kinetics. In Ion Exchange (Ed. Marinsky J. A.), Vol. 1. Dekker Co., New York. Helfferich F. (19833 Ion exchange kinetics--Evaluation of a theory. In Mass Transfer and Kinetics of Ion Exchange (Eds Liberti L. and Helfferich F.). Martinus NijhoffPubl., Dordrecht. Hunter R. J. (1989) Foundations of Colloid Sciem'e. I. Oxford University Press, New York. Liang T. J. and Hsu C. N. (19933 Sorption of cesium and strontium on natural mordenite. Radiochim. Acta 61, 105. Mortier W, J. (1977) Temperature-dependent cation distribution on dehydrated calcium-exchanged mordenite. J. Phys. Chem. 81, 1334. Mortier W. J., Pluth J. J. and Smith J. V. (19753 Positions of cations and molecules in zeolites with mordenite-type framework. I. Dehydrated Ca-exchanged ptilolite. Mater. Res. Bull. 10, 1037. Mortier W. J., Pluth J. J. and Smith J. V. (19783 Positions of cations and molecules in zeolites with mordenite-type framework. Dehydrated K-exchanged ptilolite. In Natural Zeolites (Eds Sand L. B. and Mumpton F, A.). Pergamon Press, New York. Otsuka Electronic Co. (19903 LPA 3000/3100 La~cr Particle Size Analyzing System: Instruction Manual, Tokyo. Rasmuson A. and Neretnicks I. (1983) Surface migration in sorption processes. SKBF/KBS TR-83-37. Swedish Nuclear Fuel and Waste Management Co., Stockholm. Schlenker J. L., Pluth J. J. and Smith J. V. (19783 Positions of cations and molecules in zeolites with mordenite-type framework. VII. Dehydrated Cs-exchanged mordenite. Mater. Res. Bull. 13, 901. Schlenker J. L., Pluth J. J. and Smith J. V. (19793 Positions of cations and molecules in zeolites with mordenite-type framework. VIII. Dehydrated Na-exchanged mordenite. Mater. Res. Bull. 14, 751. Sharpley A. N. (19803 Effect of soil properties on the linetics of phosphorus desorption. Soil Sci. Soc. Am. J. 47, 462. Sparks D. L., Zelazny L. W. and Martens D. C. (1980).
12
Tien-jui Liang and Joseph Yeu-cheung Tsai
Linetics of potassium exchange in Paleudult from the Coastal plain of Virginia. Soil Sci. Soc. Am. J. 44, 37. Suzuki M. (1990) Adsorption Engineering. Elsevier, Amsterdam. Suzuki M. and Kawazoe K. (1974a) Concentration decay in a batch adsorption tank--Freundlich isotherm with surface diffusion kinetics. Seisan Kenkyu 26, 275.
Suzuki M. and Kawazoe K. (1974b) Concentration decay in a batch adsorption tank--Freundlich isotherm with pore diffusion kinetics. Sensan Kenkyu 26, 299. Tyburce B., Kappenstein C., Cartaud P. and Gavnier E. (199 I) Effects of exchangeable cations on the adsorption properties of Na ÷ mordenite. J. Chem. Soc. Faraday Trans. 87, 2849.
0969-8043(93)E0021-C
Appl. Radiat. Isot. Vol. 46, No. I, pp. 7-12, 1995 Copyright ~5 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0969-8043/95 $9.50 + 0.00
Sorption Kinetics of Cesium on Natural Mordenite TIEN-JUI LIANG and JOSEPH YUE-CHEUNG
TSAI
Radiation Laboratory, Taiwan Power Company, P.O. Box 7, Shihmen, Taipei, Taiwan, Republic of China (Received 19 July 1993; in revised form 4 November 1993) The characteristics of sorption kinetics of cesium on natural mordenite, including apparent rate constant, intraparticle diffusion coefficient and reaction mechanisms, were investigated in this study. The apparent rate constant of sorption, as derived from the semi-empirical Elovich equation, was indicated from the experimental results to be about 56.9/~equiv • g- t. s- ~. The rate-determining step of sorption reaction was identified as the intraparticle diffusion of cesium cation from the main channel to site B, which is located in the side void, through the side channel system of mordenite. The linear and nonlinear intraparticle diffusion coefficients of Cs ÷ were observed via calculation by the spherical diffusion model as being 4.7 x 10-~8 and 3.5 x 10-~Sm2-s -I, respectively.
Introduction Mordenite is regarded as a candidate of buffer material in the radwaste disposal program due to its excellent sorption ability on many radionuclides such as Cs, Sr and transuranic elements. The sorption characteristics of cersium on mordenite have been investigated in previous research (Liang, 1993). However, the reaction mechanisms and kinetics have not yet been identified. Both the semi-empirical Elovich equation and the spherical diffusion model are suggested in this present study for assessing the kinetics of sorption reaction.
The rate constant, k, can be derived from the slope of the relationship between q and ln(t ); in addition, the intercept, a, means k . l n ( X / k ) . The semi-empirical kinetic equations may generally be regarded as optimum results of data-fitting, and their theoretical implications are apparently insignificant. On the other hand, Aharoni and Ungarish (1976, 1977) have indicated that the validity of the Elovich equation is limited by the time interval of the experiment, and shorter time results are more feasible. 2. Spherical diffusion equation
1. Elovich equation The Elovich equation has been previously applied in the kinetic study of soil science in many investigations (Atkinson et al., 1970; Chien and Clayton, 1980; Sparks et al., 1980; Elkhatib et al., 1984; Havlin and Westfall, 1985). A traditional Elovich equation may possibly be expressed as follows: dq dt
X exp(- Y.q) k = I/Y
(1)
in which q is the concentration of Cs ÷ in the solid phase (#-equiv. g - l ) ; X is the experimental fitting constant; k is the reaction rate constant (/~equiv, g-J • s-l). After integration, equation (1) may be rewritten as equation (2), if q = 0 when t = to: q=k.ln
~-
+kln(t)=a+k-ln(t).
(2)
The rate of sorption may be determined by the spherical diffusion model under the conditions in which: (a) the shapes of geomedia are assumed as being ideal spheres with the same radius; and (b) the rate-determining step of sorption is controlled by intraparticle diffusion (Boyd et al., 1947; Helfferich, 1966, 1983; Rasmuson and Neretnicks, 1983). The concentration gradient between ambient solution and the center of the soil particle is the driving force of diffusion. A typical diffusion equation in the spherical coordination system may be as follows:
ac a-7 =
:ac) \ 7-ff +-;
(3)
in which C is the concentration of solute in the liquid phase (/a-equiv. dm 3), r is the radical distance from the center of the geomedium particle (/tin); D is the linear intrapartical diffusion coefficient (m 2 • s-l).
Tien-jui Liang and Joseph Yeu-cheung Tsai Introducing the dimensionless equation (3) can be rewritten as ~u (~2U --
t~t
factor u =Cr,
= D -
(4)
Or 2"
The initial and boundary conditions of equation (4) are u=0
r=0,
u=aCo
t>0
r=a,
t>0
while a is the radium of the geomedium particle (m- t); Co is the initial concentration of solute in the liquid phase (#-equiv. dm-3). The solution of equation (4) may be expressed as equation (5):
q(t)
C(t)-Ce
q-~-= ~Co_
1 ~
1-~. E,=
1
x ~-i'exp
(
O "n2"~z2"t) a-2
+K
(5)
in which: q (t) is the concentration of solute in the solid phase (#-equiv.g ~); qe is the equilibrium concentration of solute in the solid phase (#equiv, g- l); C (t) is the concentration of solute in the liquid phase (#-equiv. dm-3); Co is the equilibrium concentration of solute in the liquid phase (#equiv, dm-3); K is the integration constant. The relationship between q (t) and C(t ) is presented as
q ( t ) = C ( t ) . V/m. This solution is valid if the ratio of solution volume to geomedium mass (V/m) is quite large and no diffusion reflection has been observed during the test. Considered in the earlier time interval of experiment, the equation (5) may be simplified as equation (6):
q(t) qe
6 { D ' t ' ] l/z
~-~\--~-] q-K' .,/;+K'
(6)
Comparing the relationship between q/qe and ~/t, the diffusion coefficient, D, may be derived from the slope of this equation. The nonlinear sorption of mordenite should be taken into account if the concentration of Cs + is high enough. A modified Freundlich model was proposed (Liang, 1993) for describing this kind of sorption behavior and may be written as
q = K~ C I,,,H+ KL C I,',,L
(7)
in which: Kil is the data-fitting constant in the higher solute concentration region; K L is the data-fitting constant in the lower solute concentration region; n, is the intensity of sorption in the higher solute concentration region; nL is the intensity of sorption in the lower solute concentration region. Experimental data indicated that nL is close to 1 if
the solute concentration is lower than 10 3 N. This result implicated that the linear sorption model is feasible in that low concentration region. The nmvalues, on the other hand, are far from unit. This Freundlich-type modification is also introduced in the spherical diffusion model for evaluating the influences of the nuclide concentration gradient. Suzuki and Kawazoe (1974a,b) have applied a simplified analytical solution towards modifying the Freundlich-type diffusion coefficient as: -
q [(' '): =
qe
--
nH
+
(8)
nil
Experimental
I. Chemical composition analysis Natural mordenite was produced by Asahi Chemical Co., Japan, and was washed, crushed, and heated to about 750°C for removal of the organic compositions prior to experiments. Mordenite was digested by HCI and HF, heated by a microwave oven, and analyzed by inductively coupled plasma-mass spectroscopy (ICP-MASS). The chemical compositions of mordenite are listed in Table 1.
2. Particle size analysis The sizes of mordenite particles have a significant role, and the spherical diffusion model was employed in this study for evaluating the intraparticle diffusion coefficient. The assumption of identical particle radius is actually invalid, and the concept of "equivalent radius" has become more reasonable. Two methods employed in measuring the equivalent radius of mordenite particle, dynamic light scattering (DLS) method and BET method, were used in this study. Three different size analysis modes, i.e. r(F), r (weight) and r (amount), were supplied by Otsuka LPA 3000/3100 Laser Particle Size Analyzing System (1990). Hunter (1989) suggested that r (F) is apparently a more feasible analysis mode than the other two. Another method applied in estimating the equivalent radius of particle could possibly be derived from the relationship of r = 3 V/S. V and S in this formula represent the bulk volume (m 3. g-l) and specific surface area (m 2 • g-~) of mordenite, respectively. The value of S measured by BET method was approx. Table I. Chemicalcompositionsof natural mordenite Chemical composition Weight (%) SiO2 72.06 AI203 12.90 Fe203 2.17 MgO 0.81 CaO 2.58 Na20 1.81 K20 1.05 H20 6.73 Total 100.11
Sorption kinetics of cesium on natural mordenite 800 -
130.4 m 2. g - ' . Roughly 95% ofsorption reaction were indicated by Suzuki (1990) to have occurred in the internal surface of zeolite minerals; that is, the application of BET method towards assessing S was more reasonable than that which used the geometric surface area.
600
3. Batch method The ratio of solution volume of mordenite mass in this study was 100 ( m L . g - ' ) so as to satisfy the condition of semi-infinite source. A mixture of 3.00 g mordenite and 290.00 mL deionized water was prepared and adequately mixed overnight at a constant rate of 600 rpm by magnetic stirrer. When the experiment started, 10 mL of 0.3 M CsNO3 solution was rapidly injected into the sufficiently mixed mordenite/ deionized water suspension. Vacuum extraction/separation apparatus and 0 . 4 5 # m disc filters were employed for rapid and effective separation of the liquid and solid. This improvement could potentially increase the precision of study markedly, in comparison with the tradition centrifugal separation techniques. The variances of concentrations of cations, Cs + , Na + , K + , Ca 2+ , Mg 2+ and Fe 3+, in the liquid phase were analyzed by ICPMASS after dilution. Results
and
Discussion
1. Particle size of mordenite The average radius of mordenite particle, analyzed by LPA 3000/3100 Laser Particle Size Analyzing System in DLS mode, was approx. 1.06 + 0.88/~m in r (F) mode, 2 . 2 0 + 0 . 4 0 / ~ m in r(weight) mode and 0.52 + 0.72 p m in r (amount) mode. The average radius o f a mordenite particle was set at 1.06 # m according to the r(F) mode. The specific surface area of mordenitc tested by BET method was 130.4 m 2 . g - ~, and the specific bulk volume of mordenite was nearly 4.67 × 10 5m3.g i. The size of mordenite particle, which was calculated by the formula o f r = 3 V/S, was about 1.03 pm. The sizes of particle determined by two different methods were obviously almost the same.
2. Sorption rate constant determined by Elovich equation
:L
400
q(t) = 158.9 + 56.9 * In(t)
2
(9)
trated in Fig. 2. The fitted linear function may be described as
I
I
8
10
Fig. 1. Sorption kinetics of Cs + on mordenite analyzed by Elovich equation.
q (t_._))= 0.0068' x/t + 0.52. qe
(I 0)
The diffusion coefficient may be derived from the slope of this equation. The linear diffusion coefficient of Cs ÷ in the mordenite structure was indicated from equation (6) to be 4 . 7 x 10 ~8m2.s ~(thatis, i f t h e average equivalent radius of mordenite particle was 1.06/~m).
Distinguishing between intraparticle diffusion and so-called diffusion of nuclides in the geomedia is important, especially for a buffer material in radwaste disposal. The intraparticle diffusion describes the diffusion process of Cs + within the mordenite particle 1.0
/
0.8
../
o/
o,,Y"
°,s"
0.6
The apparent rate constant of sorption was 56.9 + 1.8/~-equiv • g-~ • s -j, and the square of correlation coefficient, r 2 was 0.995.
3. [ntraparticle diffusion coefficient determined by spherical diffusion model The relationships between q/qe and x/t are illus-
I 6
In(t) (s)
The variance of Cs ÷ concentration in solid phase that are dependent on the test time are shown in Fig. I. A linear regression function was fitted as
q(t) = 158.9 + 56.9. ln(t).
[ 4
q(t) / qe -- 0.0068 X/7+ 0.52 0.4
I
I
I
t
I
I
I
10
20
30
40
50
60
70
X/7(s 1/2) Fig. 2. Sorption kinetics of Cs + on mordenite analyzed by spherical diffusion model.
Tien-jui Liang and Joseph Yeu-eheung Tsai
10
Table 2. Distributionsof cationsin rnordenitestructure Distributionsof cations in exchangeablesites Cation Mg2+ Ca2+ K+ Na+ Cs÷
A 0.5 ~ 0.5 0.5 -0.43 --
B --0.42 -0.50
C 0.2~0.3 0.18 ----
D 0.1 0.15 0.38 0.36 0.25
E -0.18 0.18 0.21 0.24
that occurs as a result of the concentration gradient between ambient solution and the center of the particle. This diffusion takes place in the complex intraparticle channel systems of mordenite crystal structure, and will be discussed later. However, the general term "diffusion" applied in the assessment of nuclide migration process implies the phenomenon of interparticle diffusion/transportation, and this is especially valid in the compacted buffer material. The nonlinear sorption character of mordenite has been previously reported (Liang, 1993), and must be taken into account if the nuclide concentration is high enough. The Freundlich-type nonlinear diffusion coefficient is indicated from equation (8) (Suzuki and Kawazoe, 1974a,b) to be 3.5 x 10 -~8 m 2. s -~, if the intensity of sorption, na, is 4.95. 4. Reaction mechanisms and rate-determining step o f Cs + sorption on mordenite structure Mortier and Schlenker have examined the locations of various cations in the mordenite structure, which are summarized in Table 2 (Mortier, 1977;
Mortier et al., 1975, 1978; Schlenker et al., 1978, 1979). The structure of mordenite is complicated, i.e. it contains two different types of channel and void systems. The main channel is elliptical, while the major and minor axes are 7.0 and 6.7 ~. The side channel system of mordenite, nevertheless, is near a circle with dia of 2.8 ~. The main void of mordenite is the main channel; however, the side void is surrounded by eight tetrahedrons, and its major and minor axes are 2.9 and 5.7 ~. Eight possible sites are available where ion exchange reaction may take place in the mordenite structure. The locations of those eight sites are illustrated in Fig. 3. Site occupancies for Cs + are sites B (50%), D(25%) and E (25%). Sites B and D are located at the side channel with a coordination number of 4. Site E is located at the main channel. Only a smaller cation, e.g. Na +, Ca 2+ and Mg 2+, whose radius is < 1.3/~, can occupy site A. That is, the larger cation, e.g. K ÷ and Cs +, cannot stimulate an exchange reaction at this site. This phenomenon is called the "ionic sieve" effect. Table 3 lists the variances of concentrations of exchanged cations in liquid phase, e.g. K +, Na + , Ca 2+, Mg 2+ and Fe 3+. Approximately 66% of K ÷, 30% of Na ÷, 18% of Ca 2÷ and 6% of Mg 2+ were exchanged within a short time interval when the reaction was initiated. On the other hand, nearly all of K +, 54% of Na +, 36% of Ca 2+ and 10% of Mg 2+ are released into the solution when the reactions approach equilibrium. The distributions of K + in mordenite structure are
w
Fig. 3. Locations of exchangeable sites in mordenite structure.
b
Sorption kinetics of cesium on natural mordenite
11
Table 3. Variances of concentrations of exchanged cations in liquid phase from natural mordenite Percentage of dissolved exchangeable cations (%) Reaction time (rain) Fe"~+ Mg2+ Ca2+ Na + K÷ I 5 10 60 360 1410 2873 4295 5040
o. I o. 1 0.1 o. I 0.2 0.2 0.2 0.2 0.2
5,6 6.1 5.9 6,6 6.9 7.8 8.5 9.0 9.0
at sites B (42%), D (38%) a n d E (18%). In the early stage o f C s + / K ÷ reaction, the K + located sites D a n d E may be replaced by Cs + , additionally, K + in site B is exchanged slowly. The kinetic o f C s + / N a ÷ exchange shows that almost all N a n in site E (21%) a n d most o f that in site D are immediately exchanged. However, Cs ÷ c a n n o t react with N a n located in site A in light of the ionic sieve effect. This is why only roughly 54% o f N a n is exchanged at equilibrium. The analogous results were also observed in Cs+/ Ca z+ a n d C s + / M g 2+ reactions. The C s + / C a 2+ reaction only occurred in sites E (18%) a n d D (15%), a n d the former reaction is faster t h a n the latter. The Cs ÷ m a y only replace the M g 2÷ which is located at site D (10%). The rate-determining step o f Cs + ion exchange on m o r d e n i t e m a y be concluded to be the diffusion o f Cs + from main channel to site B t h r o u g h the side channel. The reaction occurred first in site E, later in site D, and finally in site B.
Conclusion T h e s o r p t i o n kinetics of cesium o n n a t u r a l m o r d e n ite were studied in present research effort, Several key factors, e.g. the a p p a r e n t rate c o n s t a n t of sorption, intraparticle diffusion coefficient a n d reaction mechanisms, were investigated in this study. The a p p a r e n t rate c o n s t a n t of sorption, which was derived from the semi-empirical Elovich equation, was indicated from experimental results to be 56.9 # - e q u i v ' g ~ - s - ~. The rate-determining step o f reaction was identified as the intraparticle diffusion o f cesium from the main channel t h r o u g h the side channel system, a n d then intruding into site B which was located in the side void of m o r d e n i t e structure. The intraparticle diffusion coefficient o f cesium was observed from the spherical diffusion model as being 4.7 x 10-~Sm 2. s -~. A nonlinear modification of 3.5 × 10- ~ m 2- s-~ was made if the Freundlich type of sorption was taken into account.
References Aharoni C. and Ungarish M. (1976) Kinetics of activated chemisorption. 1. The non-Elovichian part of the isotherm. J. Chem. Soc. Faraday Trans. 72, 400.
18.0 20.4 20.8 25.5 28.5 33.5 36.5 36.5 36.2
29.6 34.8 37.6 43.9 48.3 51.5 53.6 53.8 53.4
66.0 76.4 81.5 91. I 97.3 97.8 97.9 98. I 98.0
Aharoni C. and Ungarish M. (1977) Kinetics of activated chemisorption. II. Theoretical models. J. Chem. Sot'. Faraday Trans. 73, 456, Atkinson R. J., Hingston F. J., Posner A. M. and Quirk J. P. (19703 Elovich equation for the kinetics of isotope exchange reactions at solid-liquid interfaces. Nature (London) 226, 148. Boyd G. E., Adamson A. W. and Meyers L. S. (1947) The exchange adsorption of ions from aqueous solutions by organic zeolites. II. Kinetics. J. Am. Chem. Soc. 69, 2836. Chien S. H. and Clayton W. R. (1980) Application of Elovich equation to the linetics of phosphate release and sorption in soils. Soils Sci. Soc. Am. J. 44, 260. Elkhatib E. A., Bennett O. L. and Wright R. J. (19843 Linetics of arsenate sorption in soils. Soil Sci. Soc. Am. J. 48, 758. Havlin J. L. and Westfall D. G. (1985) Potassium release linetics and plant response in calcareous soils. Soil Sci. Sac. Am. J. 49, 366. Helfferich F. (1966) Ion exchange kinetics. In Ion Exchange (Ed. Marinsky J. A.), Vol. 1. Dekker Co., New York. Helfferich F. (19833 Ion exchange kinetics--Evaluation of a theory. In Mass Transfer and Kinetics of Ion Exchange (Eds Liberti L. and Helfferich F.). Martinus NijhoffPubl., Dordrecht. Hunter R. J. (1989) Foundations of Colloid Sciem'e. I. Oxford University Press, New York. Liang T. J. and Hsu C. N. (19933 Sorption of cesium and strontium on natural mordenite. Radiochim. Acta 61, 105. Mortier W, J. (1977) Temperature-dependent cation distribution on dehydrated calcium-exchanged mordenite. J. Phys. Chem. 81, 1334. Mortier W. J., Pluth J. J. and Smith J. V. (19753 Positions of cations and molecules in zeolites with mordenite-type framework. I. Dehydrated Ca-exchanged ptilolite. Mater. Res. Bull. 10, 1037. Mortier W. J., Pluth J. J. and Smith J. V. (19783 Positions of cations and molecules in zeolites with mordenite-type framework. Dehydrated K-exchanged ptilolite. In Natural Zeolites (Eds Sand L. B. and Mumpton F, A.). Pergamon Press, New York. Otsuka Electronic Co. (19903 LPA 3000/3100 La~cr Particle Size Analyzing System: Instruction Manual, Tokyo. Rasmuson A. and Neretnicks I. (1983) Surface migration in sorption processes. SKBF/KBS TR-83-37. Swedish Nuclear Fuel and Waste Management Co., Stockholm. Schlenker J. L., Pluth J. J. and Smith J. V. (19783 Positions of cations and molecules in zeolites with mordenite-type framework. VII. Dehydrated Cs-exchanged mordenite. Mater. Res. Bull. 13, 901. Schlenker J. L., Pluth J. J. and Smith J. V. (19793 Positions of cations and molecules in zeolites with mordenite-type framework. VIII. Dehydrated Na-exchanged mordenite. Mater. Res. Bull. 14, 751. Sharpley A. N. (19803 Effect of soil properties on the linetics of phosphorus desorption. Soil Sci. Soc. Am. J. 47, 462. Sparks D. L., Zelazny L. W. and Martens D. C. (1980).
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Tien-jui Liang and Joseph Yeu-cheung Tsai
Linetics of potassium exchange in Paleudult from the Coastal plain of Virginia. Soil Sci. Soc. Am. J. 44, 37. Suzuki M. (1990) Adsorption Engineering. Elsevier, Amsterdam. Suzuki M. and Kawazoe K. (1974a) Concentration decay in a batch adsorption tank--Freundlich isotherm with surface diffusion kinetics. Seisan Kenkyu 26, 275.
Suzuki M. and Kawazoe K. (1974b) Concentration decay in a batch adsorption tank--Freundlich isotherm with pore diffusion kinetics. Sensan Kenkyu 26, 299. Tyburce B., Kappenstein C., Cartaud P. and Gavnier E. (199 I) Effects of exchangeable cations on the adsorption properties of Na ÷ mordenite. J. Chem. Soc. Faraday Trans. 87, 2849.