7452
J. Phys. Chem. B 1999, 103, 7452-7455
Activation Energy for Isotope Exchange Reaction between Gas
235UF
5
Nanoparticles and
238UF
6
Yoshikazu Kuga* and Koji Ando Department of Applied Chemistry, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, Hokkaido 050-8585, Japan
Jun Onoe and Kazuo Takeuchi The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan ReceiVed: May 5, 1999; In Final Form: July 7, 1999
The temperature dependence of the rates for two kinetic processes involved in the isotopic exchange reaction between 235U-enriched UF5 nanoparticles and natural UF6 gas was experimentally examined using our kinetic model that includes the fraction of high-reactivity molecules of UF5 on the outermost layer of the particles. The activation energies obtained from the Arrhenius plot for the fast process and the slow process were similar, 36.1 and 39.3 kJ/mol, respectively. This indicates that the two rate processes are mainly caused by the difference in the preexponential factor of the Arrhenius equation. It was suggested that such a difference in the reactivity of the UF5 molecules was caused by the difference in the adsorption configurations of UF6 molecules on the surface of UF5 molecules due to the steric hindrance of neighboring fluorine atoms.
1. Introduction The fluorine atom transfer reaction from nanoparticles to natural isotopic UF6 gas,
235U-enriched
UF5
UF5 (particles) + 238UF6 (gas) a
235
UF6 (gas) + 238UF5 (particles) (1)
235
was first found by Grigor’ev et al.2 and has been studied experimentally and theoretically.1,3-9 Since the transfer of the fluorine atom from 238UF6 to 235UF5 converts 235UF5 to 235UF6, this reaction behaves as if 235U and 238U are exchanged between UF5 and UF6. The investigation of the isotopic exchange reaction is very important for developing the molecular laser isotope separation (MLIS) of uranium10-12 because it deteriorates the enrichment of 235U in the product, UF5, in MLIS. It has been clarified in various experiments2-4,6 that there are two rate processes in the isotope exchange reaction. Grigor’ev et al.2 proposed a kinetic model with unverified assumptions in which the UF5 molecules on the outermost layer contributed to the fast reaction and the underlying UF5 molecules reacted slowly. Yato and co-workers3-5 tried to determine the kinetic rate constants from their experimental results using a similar assumption that not only UF5 molecules on the surface but also UF5 molecules under the surface were involved in the reaction. Although it is very important to determine the total number of UF5 molecules that participate in the reaction to investigate the reaction mechanism, no attempt has been made to experimentally examine the equilibrium of the isotope exchange reaction until our recent study.1 From the wellexamined mass balance study of the 235U involved in the reaction including the consumption of 235U by the dissociation of UF6 with a small amount of impurities, we demonstrated experi* To whom correspondence should be addressed: Telephone and fax: (+81)-143-46-5765. E-mail:
[email protected].
mentally that only UF5 molecules on the outermost layer of the particles participated in the reaction.1 On the basis of our experimental findings, we proposed a kinetic model that assumes two kinds of sites on the outermost layer with different reactivities while no UF5 molecules in the underlying molecules contribute to the reaction.1 The time dependencies of the isotopic fractions in the UF6 gas and in the UF5 particles during the isotope exchange reaction at room temperature were well described by our kinetic model. The activation energies for the fast process and slow process are expected to provide important information for understanding the nature of this isotope exchange reaction, such as the origin of the two rate processes. The aim of the present study is to determine the activation energies by examining the temperature dependence of the kinetic rate constants in the two rate processes, based on our kinetic model. 2. Experimental Procedures and Kinetic Model The experimental apparatus used in the present study was similar to those of the previous work1 except for a newly adopted temperature control system. In this section, the outline of the present experiment is briefly described. The reaction cell with a 383 cm3 volume was equipped with four CaF2 windows. One pair of opposing windows was used for the KrF excimer laser irradiation, while the other pair was for the UV spectroscopy to monitor the concentration of UF6 in the cell. We used an impeller made of a nickel-coated soft-iron disk rotor with four stainless steel blades in order to achieve homogeneous mixing of the 235UF6 and 238UF6 gases.8 Because UF6 and UF5 are moisture sensitive, the cell was kept leak-free using a helium leak detector (Shimadzu MSE-1000) and was passivated for an hour or longer with 20 Torr of ClF3 to remove any traces of water. Subsequently, it was evacuated for a day prior to introducing the UF6 gas. A mixture of UF6 (29.2 mg) containing 7.03% 235U and CH4 (1.33 mg) was introduced into the cell. The CH4 gas was used
10.1021/jp991484s CCC: $18.00 © 1999 American Chemical Society Published on Web 08/13/1999
Reaction between
235UF
5
and
238UF 6
J. Phys. Chem. B, Vol. 103, No. 35, 1999 7453
TABLE 1: Summary of the Experimental Conditionsa
case I case II
reaction time [h]
reaction temperature [°C]
0.5 24.0
23, 38, 52, 65 23, 38, 52
a The amount of UF particles, which contain 7.02% 235UF , was 5 5 27.6 mg, and the amount of UF6 gas, which contains 0.720% 235UF6, was 29.2 mg in both cases.
for scavenging fluorine radicals produced from the photoirradiated UF6.13,14 The gas mixture was then irradiated with 9600 shots (36.4 mJ, 2 Hz) from a KrF laser (LUMONICS EX-700) at 248 nm through the CaF2 window. Complete decomposition of the UF6 gas was confirmed by the UV spectrophotometer (Shimadzu UV-3100). The product of photodissociated UF6 was identified as β-UF5 by several studies with UV irradiation15,16 and IR irradiation17 and for the TEA-CO2 laser-induced plasma reaction.18 We waited 24 h after the irradiation so that the UF5 particles formed by the photodissociation of UF619 were allowed to settle on the inner wall of the cell. The residual gases were carefully evacuated so that the UF5 particles were not eliminated from the cell. The reaction cell was then placed in the thermostatic box. The temperature in the thermostatic box was kept at given values, such as 23, 38, 52, and 65 °C for at least 90 min before introducing the natural UF6 gas. The natural UF6 gas (29.2 mg) was then introduced into the cell to start the isotope exchange reaction. During the isotope exchange reaction, the UF6 gas was mixed by the impeller at 500 rpm to eliminate the effect of the 235UF -238UF incomplete mixing on the isotope exchange 6 6 reaction.8 Because we found that the fast process dominated the reaction within 3-4 h under our experimental conditions at 23 °C,1 the reaction time for investigation of the fast process was set at 30 min (case I), which was considered to be sufficiently short to neglect the contribution of the slow process to the reaction as discussed later in more detail. On the other hand, the slow process was found to dominate the reaction 6-8 h after starting the reaction under our experimental conditions at 23 °C;1 therefore, the reaction time for investigation of the slow process was set at 24 h (case II). The experimental conditions are listed in Table 1. After a given reaction time of either 30 min or 24 h, all the UF6 gas was recovered in the sample tube cooled with liquid nitrogen within a minute. The isotopic fraction, 235U/(235U + 238U), of the sampled UF gas was measured with a magnetic6 sector mass spectrophotometer (Finigan MAT-281). The measurement accuracy of the isotopic fraction was 5 × 10-4%. 3. Kinetic Model for Isotope Exchange Reaction In the previous studies,1 we proposed a kinetic model for the isotope exchange reaction based on the following two assumptions. (1) Only the UF5 molecules on the outermost layer of the particles participate in the isotope exchange reaction; no UF5 molecules in the underlying layer are involved in the reaction. (2) Two types of UF5 molecules different in reactivity exist on the outermost layer. Assumption 1 was experimentally verified in the previous work.1 Assumption 2 is a straightforward way to justify the presence of two rate processes. The derivation of the kinetic equations was described elsewhere;1 thus, it was not reproduced here. By use of the density of β-UF5 ()6.45 g/cm3)20 and the specific surface area diameter of the UF5 particles ()9.3 nm) obtained experimentally in the previous study,1 the fraction of UF5 molecules in the outermost layer of the particle was
Figure 1. Temperature dependence of isotopic fraction in UF6 gas after 30 min exchange reaction (case I).
TABLE 2: Kinetic Rate Constants kf for the Fast Process and ks for the Slow Process Experimentally Obtained Using Our Modela temp tempe kf × 1020 ks × 1022 [°C] [K] [cm3/(s molecule)] kf/kf0 [cm3/(s molecule)] ks/ks0 23 38 52 65
296.2 311.2 325.2 338.2
5.50 15.6 24.9 34.5
1.00 2.83 4.53 6.27
4.50 9.81 18.7
1.00 2.18 4.15
a The k f0 and ks0 represent the kinetic rate constants at room temperature (23 °C) for the fast process and the slow process, respectively.
estimated to be 0.31. According to our kinetic model, with the use of only three parameters, namely, the rate constant of the high-reactivity molecules, kf, the rate constant of the lowreactivity molecules, ks, and the fraction of the high-reactivity molecules, ξ, we can calculate the isotopic fraction of UF6 gas, that of the high-reactivity molecules of UF5 particles, and that of the low-reactivity molecules of UF5 particles. These values obtained from all the data from the isotope exchange reaction performed at room temperature with subscript 0 in a previous study1 were determined to be as follows: kf0 ) 5.5 × 10-20 cm3/(s molecule), ks0 ) 4.5 × 10-22 cm3/(s molecule), and ξ ) 0.078. 4. Results and Discussion Figure 1 shows the temperature dependence of the isotopic fraction, 235U/(235U + 238U), in UF6 gas 30 min after the start of the exchange reaction (case I). The isotopic fraction of UF6 was found to increase with an increase in the reaction temperature. The isotopic fraction of UF6 became highest (0.00852) at the highest temperature (T ) 338.2 K ) 65 °C) in this study. When we consider the experimental fact that the fast rate process dominated the reaction until the isotopic fraction reached 0.0085, it was reasonable to assume that only the fast process was dominant and that the effect of the slow rate process on the change in the isotopic fraction of UF6 gas was negligible in the early period ()30 min) of the reaction under our experimental conditions. Using our kinetic model with the value of the fraction of high-reactivity UF5 molecules on the outermost layer of the UF5 particles, ξ ) 0.078, we determined the rate constant for the fast process, kf, at a given reaction temperature to fit the isotopic fraction of UF6 gas calculated relative to that obtained experimentally. Table 2 summarizes the values of kf thus obtained from our kinetic model and the experimental results. The rate constant, kf, was found to increase with an increase in the
7454 J. Phys. Chem. B, Vol. 103, No. 35, 1999
Kuga et al.
Figure 2. Arrenius plot of the kinetic rate constant for the fast process (case I).
Figure 3. Temperature dependence of isotopic fraction in UF6 gas after 24 h exchange reaction (case II).
reaction temperature. In the table, the ratios kf/kf0 of the kinetic rate constant kf at a given temperature to that at 23 °C, kf0, are also listed. Figure 2 shows an Arrhenius plot of the kinetic rate constant ratio, kf/kf0, for the fast process. The figure shows that the temperature dependence of the kinetic rate constant was approximately expressed by the following Arrhenius-type equation
( )
kf ) A exp -
Ef RT
(2)
where Ef is the activation energy of the fast process of the isotope exchange reaction, A is a preexponential factor, and R is the gas constant. The activation energy, Ef, obtained from the slope of the Arrhenius plot was found to be 36.1 kJ/mol. We next investigated the temperature dependence of the slow process. Figure 3 shows the temperature dependence of the isotopic fraction, 235U/(235U + 238U), in UF6 gas 24 h after the start of exchange reaction (case II). The isotopic fraction was found to increase with an increase of the reaction temperature in a way similar to the case of the fast rate process (case I). According to the preceding experimental results,1 even at room temperature, which gives the slowest rate in our study, the fast process was known to be almost negligible in 6 h. Therefore, it was possible to treat the change in the isotopic fraction in UF6 in the 24 h reaction as being mainly caused by the slow process. Using our kinetic model with the value of ξ ()0.078)1 and the value of kf for the fast process listed in Table 2, we determined the rate constant for the slow process, ks. The values of ks thus determined are summarized in Table 2. The ks values were found to increase with an increase in the reaction temperature in a way similar to the case of the fast rate process. In the table, the
Figure 4. Arrenius plot of the kinetic rate constant for the slow process (case II).
ratio of the ks values at a given temperature to that at 23 °C, ks0, is also listed. The Arrhenius plot of the kinetic rate constant ratio for the slow process is shown in Figure 4. It is found from the figure that the temperature dependence of the kinetic rate constant, ks, is approximately expressed by the Arrhenius relationship. The activation energy for the slow process obtained from the slope of the Arrhenius plot, Es, is 39.3 kJ/mol, slightly higher than that of the fast process (Ef ) 36.1 kJ/mol). These are the activation energies of the isotope exchange reaction between 235UF particles and 238UF gas determined for the first time. 5 6 Thus, because the values of the activation energies for both the fast process and the slow process are similar, the 2 orders of magnitude of difference in the kinetic rate constants for the two processes were found to be caused mostly by a difference in the preexponential factor in the Arrhenius relationship. We then investigated the origin of such a difference. It is a straightforward way to assume the following mechanism for the isotope exchange reaction between 235UF5 particles and 238UF6.21 First, a 238UF6 molecule adsorbs on the surface of the outermost layer of the 235UF5 particle, and then a fluorine atom in the 238UF6 gas molecule transfers to a 235UF5 molecule on the surface of the UF5 particles via a transitional state as shown in eq 3. Subsequently, the 238U atom constitutes 238UF5 on the surface of the UF5 particles and the 235U atom constitutes 238UF and finally escapes from the surface of the UF particle 6 5 to the gas phase.
F5238UF + 235UF5 f [F5238U‚‚‚F‚‚‚235UF5] f UF5 + 235UF6 (3)
238
No activation energies were reported for the case of the heterogeneous isotope exchange reaction with the halogen atom transfer mechanism between particles and gas. On the other hand, several activation energies and kinetic rate constants were reported22 for the case of the homogeneous isotope exchange reaction in the liquid phase between alkyl halides and halogen ions, which are caused by the transfer of halogen ions such as iodide ion and bromine ion via a transitional state. Table 3 summarizes the activation energy22 and bond dissociation energy23,24 of the homogeneous isotope exchange reaction between typical alkyl halides and halogen ions compared with the results of the present study. Let us discuss the activation energies of the exchange reaction for isomers. It is found from the table that molecules such as n-C3H7I, n-C4H9I, n-C3H7Br, and n-C4H9Br have slightly lower activation energies than those of their isomers, although the normal isomers have slightly higher bond dissociation energies than those of the other isomers. Let us go back to the values of the activation energies
Reaction between
235UF
5
and
238UF 6
J. Phys. Chem. B, Vol. 103, No. 35, 1999 7455
TABLE 3: Summary of Activation Energies, Eact, and Bond Dissociation Energies, Edis, for Isotope Exchange Reaction between Typical Alkyl Halide and Halogen Ion and for the Isotope Exchange Reaction between 235UF5 and 238UF6 exchange reaction
Eact 22 [kJ/mol]
Edis 23 [kJ/mol]
n-C3H7I + I*- f n-C3H7I* + Ii-C3H7I + I*- f i-C3H7I* + I n-C4H9I + I*- f n-C4H9I* + Ii-C4H9I + I*- f i-C4H9I* + Is-C4H9I + I*- f s-C4H9I* + In-C3H7Br + Br*- f n-C3H7Br* + Bri-C3H7Br + Br*- f i-C3H7Br* + Brn-C4H9Br + Br*- f n-C4H9Br* + Bri-C4H9Br + Br*- f i-C4H9Br* + Brt-C4H9Br + Br*- f t-C4H9Br* + BrUF6 + U*F5 f UF5 + U*F6 (fast process) UF6 + U*F5 f UF5 + U*F6 (slow process)
77.0-85.4 88.7-103.8 77.0 78.7 91.2 77.8 98.3 79.1 93.7 96.2 36.1a 39.3a
224 222
289 285 264 287b 287b
a Obtained from the present study. b U-F bond dissociation energy in UF6 obtained from ref 24.
TABLE 4: Summary of the Ratio of Kinetic Rate Constants kiso/knor, ksec/knor, and kter/knor for the Isotope Exchange Reaction between Alkyl Halide and Halogen Ion, and ks/kf for the Isotope Exchange Reaction between UF5 and UF6a exchange reaction I*-
I-
C3H7I + f C3H7I* + C4H9I + I*- f C4H9I* + IC3H7Br + Br*- f C3H7Br* + BrC4H9Br + Br*- f C4H9Br* + BrUF6 + U*F5 f UF5 + U*F6
kiso/knor
ksec/knor kter/knor ks/kf
0.029-0.047 0.131 0.072 0.032 0.042
0.021 0.082
we take into account that the present isotope exchange reaction is caused by the fluorine atom transfer reaction that is similar to the reaction between alkyl halides and halogen ions, it is reasonable to conclude that the difference in the degree of steric hindrance of neighboring fluorine atoms causes a difference in the adsorption probability of UF6 molecules on the surface of UF5 molecules, which resulted in a difference in the reactivity of the fast process and that of the slow process. A more detailed discussion on the difference in the reactivity must utilize new results from theoretical kinetic investigations such as molecular orbital calculations and/or new experiments. 5. Conclusions The temperature dependencies of the isotope exchange reaction rates in two kinetic processes were experimentally investigated using our kinetic model, and the following results were obtained. (1) For both kinetic processes, Arrhenius-type temperature dependencies were found. (2) The obtained activation energy was 36.1 kJ/mol for the fast process and 39.3 kJ/ mol for the slow process. (3) The difference in the preexponential factor, which caused a difference in the reactivity, was considered to be caused by a difference in the degree of adsorption of UF6 molecules on the surface of UF5 molecules due to the steric hindrance of the fluorine atoms on the outermost layer of UF5 particles. Acknowledgment. Y.K. expresses his thanks to Messrs. K. Kuroki and H. Sasagawa at RIKEN for their technical support in this work.
a
knor, kiso, ksec, and kter represent the kinetic rate constants of the reaction involved for normal alkyl halide, isoalkyl halide, secondary alkyl halide, and tertiary alkyl halide, respectively. kf and ks represent the kinetic rate constants of the fast process and the slow process for the UF5-UF6 isotope exchange reaction, respectively.
obtained in the present study. They were found to be smaller than those of the homogeneous isotope exchange reaction listed in Table 3. Because the fluorine atom transfer occurs after the adsorption of UF6 molecules on the surface of UF5 particles, the smaller activation energy in the present study is reasonable. It must be noted that the values of the activation energy in our case are similar (Ef ) 36.1 kJ/mol and Es ) 39.3 kJ/mol). This will be discussed later in this section. Table 4 summarizes the ratio between the kinetic rate constant of the reaction involved for isomers such as iso-C3H7I and that for a normal isomer such as n-C3H7I. The rate constant of the isotope exchange reaction for the cases of the iso isomer, secondary isomer, and tertiary isomer of the alkyl halides was much smaller than that of the normal isomer. It is believed that steric hindrance reduces the reactivity for the nonnormal alkyl halide isomers and halogen ions.22 We found experimentally with use of our kinetic model that there are 2 orders of magnitude difference in the kinetic rate constant for the fast process, kf, and that for the slow process, ks. This finding is also similar to the difference in the kinetic rate constants in the exchange reaction between alkyl halide and the halogen ion involved for each isomer. For the case of the exchange reaction between alkyl halides and halogen ions, the different reactivity is caused by the steric hindrance of the isomers of alkyl halides.22 The similarity of our case to that may suggest the origin of the different rate process for the UF5UF6 exchange reaction. The β-UF5 has a large tetragonal unit containing eight UF5 molecules,25-27 and only two uranium atoms among the eight atoms on the surface are mainly exposed, while the other six uranium atoms are partly covered by adjacent fluorine atoms as shown in Figure 12 of ref 1. Therefore, when
References and Notes (1) Kuga, Y.; Takeuchi, K. J. Chem. Phys. 1998, 108, 4591. (2) Grigor’ev, G. Yu.; Dorofeev, S. B.; Zametalov, V. A.; Kolesnikov, O. N.; Terwnt’ev, A. A. SoV. J. Chem. Phys. 1986, 3, 2275. (3) Yato, Y.; Funasaka, H. J. Nucl. Sci. Technol. 1992, 29, 296. (4) Yato, Y.; Suto, O.; Funasaka, H. J. Nucl. Sci. Technol. 1995. 32, 430. (5) Yato, Y. J. Nucl. Sci. Technol. 1996. 33, 758. (6) Onoe, J.; Kuga, Y.; Isomura, S.; Takeuchi, K. J. Nucl. Sci. Technol. 1991, 28, 777. (7) Onoe, J.; Kuga, Y.; Takeuchi, K. Radioisotopes 1992, 41,135. (8) Kuga, Y.; Onoe, J.; Isomura, S.; Takeuchi, K. J. Nucl. Sci. Technol. 1996, 33, 889. (9) Takeuchi, K.; Kuga, Y.; Okada, Y.; Onoe, J. J. Nucl. Sci. Technol. 1997, 34, 1110. (10) Rabinowitz, P.; Kaldor, A.; Gnauck, A.; Woodin, R. L.; Gethner, J. S. Opt. Lett. 1982, 7, 212. (11) Jensen, R. J.; Judd, O. P.; Sullivan, J. A. Los Alamos Sci. 1982, 3, 2. (12) Takeuchi, K.; Tashiro, H.; Kato, S.; Midorikawa, K.; Oyama, T.; Satooka, S.; Namba, S. J. Nucl. Sci. Technol. 1989, 26, 301. (13) Kuga, Y.; Satooka, S.; Takeuchi, K. Appl. Phys. 1996, B63, 293. (14) Kato, S.; Satooka, S.; Oyama, T.; Takeuchi, K.; Midorikawa, K.; Tashiro, H.; Namba, S. J. Nucl. Sci. Technol. 1989, 26, 256. (15) Becker, F. S.; Jacob, E. Angew. Chem., Int. Ed. Engl. 1980, 19, 227. (16) Halstead, G. W.; Eller, P. G.; Asprey, L. B.; Salazar, K. V. Inorg. Chem. 1978, 17, 2967. (17) Obermayer, A. German Patent P3817173 C2, 1988. (18) Onoe, J.; Uehara, N.; Iimura, Y.; Oyama, T.; Suto, O.; Shimazaki, Y.; Takeuchi, K. J. Nucl. Mater. 1993, 207, 205. (19) Lyman, J. L.; Laguna, G.; Greiner, N. R. J. Chem. Phys. 1985, 82, 183. (20) Zachariasen, W. H. Acta Crystallogr. 1946, 2, 296. (21) Sanyal, D. K.; Winfield, J. M. J. Fluorine Chem. 1984, 24, 75. (22) Nippon Isotope Kyokai. Isotope Binran, 3rd. ed.; Maruzen: Tokyo, 1984; Vol. 2, p 101 (in Japanese). (23) Nippon Kagakukai. Kagaku Binran, 2nd. ed.; Maruzen: Tokyo, 1975; Vol. 2, p 976 (in Japanese). (24) Becker, F. S.; Kompa, K. L. Nucl. Technol. 1982, 58, 329. (25) Ryan, R. R.; Penneman, R. A.; Asprey, L. B. Acta Crystallogr. B 1976, 32, 3311. (26) Taylor, J. C.; Waugh, A. B. J. Solid State Chem. 1980, 35, 137. (27) Wyckoff, R. W. G. Crystal Structures, 2nd. ed.; John Wiley and Sons: New York, 1963; Vol. 2, p 177.
