Enrichment of U-232 by U(IV)-U(VI) Redox Ion Exchange Chromatography.

Nakanishi, Takasi; Higuchi, Nobuhiko; Nomura, Masao; Aida, Masao; Fujii, Yasuhiko

doi:10.3327/jnst.33.341

Cited by 9 publications

(7 citation statements)

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“…Recent experiments have shown that chemical equilibrium isotope-exchange separation factors are not necessarily a linear function of the atomic mass differences of the isotopomers (1)(2)(3)(4)(5)(6)(7)(8). The most extensive experiments are those of Fujii et al U between an aqueous phase and an anion-exchange resin.…”

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Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Bigeleisen

1998

Proc. Natl. Acad. Sci. U.S.A.

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The nuclear field shift affects the electronic, rotational, and vibrational energies of polyatomic molecules. The theory of the shifts in molecular spectra has been studied by Schlembach U between an aqueous phase and an anion-exchange resin. The aqueous phase is principally U(IV); the resin phase is principally U(VI), hydrated or complexed uranyl ion. In each of these exchange reactions the heavy isotope concentrates in the aqueous phase, that is U(IV). The nonlinearity and the fact that the heavy isotope concentrates in the U(IV) species arise from the shift in the minimum of the electronic potential energy due to the different nuclear sizes and shapes of the isotopomers. This is known as the nuclear field shift. A quantitative calculation of this effect (9) is in excellent agreement with experiment.The calculation is based on the addition of a term due to the nuclear field shift to the Bigeleisen-Mayer equation for the logarithm of the isotopic separation factor and the reduced partition-function ratio. Analogous to the Bigeleisen-Mayer function, ᐉn(s͞sЈ)f 0 , we define ᐉn(s͞sЈ)f ns as the nuclear field shift correction and ᐉn(s͞sЈ)f T as the total reduced partitionfunction ratio corrected for the nuclear field shift.The nuclear field shift correction is simply,where (E H°Ϫ E L°) is the difference in the ground state electronic energy.The Bigeleisen-Mayer equation is based on the BornOppenheimer approximation and uses an isotope-independent potential energy; it also assumes simple harmonic vibrations. Because the vibrational force constants are the second derivatives of the electronic energy with respect to the mutual distances between atoms, a correction needs to be applied to ᐉn(sЈ͞sЈ)f 0 for the nuclear field shift. The formal theory of the nuclear field shift on the equilibrium force constant of a diatomic molecule has been given by Schlembach and Tiemann (10). From the theory and their data on the electronic and rotational spectra of diatomic Pb chalcogenides and Tl halides, Tiemann et al. (11) estimated the relative vibrational frequency shifts in these compounds resulting from the nuclear field shifts to be of the order of 10 Ϫ6. I now show that a relative frequency shift of this order of magnitude is a negligible, second-order correction to ᐉn(s͞sЈ)f 0 .In my study of the nonlinearity of the isotope separation factor, I found it convenient to use the first finite polynomial approximation to ᐉn(s͞sЈ)f 0 because this utilizes the isotopomer masses directly.For the present purpose it is more convenient to use the Bigeleisen-Mayer free energy function, G(u ), for the calculation of the correction to ᐉn(s͞sЈ)f 0 . We writewhere u boc ϭ h boc ͞kT and boc is the vibrational frequency corrected for the nuclear field shift and G(u) ϭ 1/2 Ϫ 1͞u ϩ (e u Ϫ 1) Ϫ1). To calculate (Ј boc Ϫ boc ) we set the nuclear field shift correction in the heavy isotope equal to zero. Then,where Ј BO is the Born-Oppenhemier frequency and ⌬Ј p is the perturbation due to the nuclear field shift. In Table 1 S). The correc...

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Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Bigeleisen

1998

Proc. Natl. Acad. Sci. U.S.A.

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“…Ion exchange separations are essentials parts of different techniques and technologies. Various applications of ion exchangers can be found in pharmaceauticals and medicine [1][2][3] , recuperation of metals 4 , biotechnology 5 catalysis 6 , food production [7][8][9][10][11][12] , recycling of industrial waste [13][14] , microelectronics, nuclear industry [15][16][17] , potable water preparation [18][19][20] and many other areas. Ion exchange is a powerful tool in chemical analysis and scientific research.…”

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Comparative Studies of Kinetics of Nanocomposite Poly-o-toluidine Zr(IV) Phosphate and Fibrous Nylon-6,6 Sn(IV) Phosphate Cation Exchange Materials

2013

Chem Sci Trans

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An organic-inorganic composite, poly-o-toluidine Zr(IV) phosphate and nylon-6,6 Sn(IV) phosphate was chemically synthesized by mixing ortho-toluidine and nylon-6,6 into the gel of Zr(IV) phosphate and Sn(IV) phosphate in different mixing volume ratios. The particle diffusion mechanism is confirmed by the linear τ (dimensionless time parameter) vs. t (time) plots. This study revealed the exchange process controlled by the diffusion within the exchanger particles. Some physical parameters like self-diffusion coefficient (D 0) , activation energy (E a) and entropy of activation (∆S°) have been evaluated under conditions favoring a particle diffusion-controlled mechanism.

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“…These differences lead to small shifts in the electronic energies of those atomic and molecular states with appreciable electron densities at the nucleus. The logarithm of the separation factor becomes Cn a = en (s/s')f (AY) -en (s/s')f (AX) + En Kf, [16] where en Kfs is [17] E°is the minimum in the ground electronic state potential energy. Eq.…”

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“…For the light elements, the values of en Kfs are negligible in comparison with en a and can be neglected. This is not the case for the heavy elements (11)(12)(13)(14)(15)(16). For the redox reaction between U(IV)aqueous and U(VI)resin, the relative magnitudes of En Kfs and En ao, en ao = En (s/s')U(IV) -En (s/s ')ftJ( VI), calculated from the analysis of the separation factors for this reaction as a function of temperature, are given in Table 1.…”

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Temperature dependence of the isotope chemistry of the heavy elements.

Bigeleisen

1996

Proc. Natl. Acad. Sci. U.S.A.

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The temperature coefficient of equilibrium isotope fractionation in the heavy elements is shown to be larger at high temperatures than that expected from the well-studied vibrational isotope effects. The difference in the isotopic behavior of the heavy elements as compared with the light elements is due to the large nuclear isotope field shifts in the heavy elements. The field shifts introduce new mechanisms for maxima, minima, crossovers, and large massindependent isotope effects in the isotope chemistry of the heavy elements. The generalizations are illustrated by the temperature dependence of the isotopic fractionation in the redox reaction between U(VI) and U(IV) ions.Stern and colleagues (1, 2) have studied the temperature dependence of equilibrium isotope fractionation for the elements hydrogen, carbon, nitrogen, and oxygen over the temperature range 20-2000 K; they used a computational approach to the problem. The vibrational frequencies of isotopomers of a large number of compounds of the above elements were calculated using the Wilson FG matrix method. Input parameters were valence force constants, F matrices, and the masses, bond distances, and bond angles of the molecules, G matrices. The calculated frequencies were then substituted into the Bigeleisen-Mayer equation (3) for the isotope fractionation factor. In accord with theoretical expectations, Stern and colleagues (1, 2) found, in all cases, that the logarithm of the fractionation factor obeys a 1/T law at low temperature and a 11T2 law at high temperature. The chemical basis for these two limiting temperature dependences can be readily understood through the Bigeleisen-Mayer free energy function.

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Enrichment of U-232 by U(IV)-U(VI) Redox Ion Exchange Chromatography.

Cited by 9 publications

References 3 publications

Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Comparative Studies of Kinetics of Nanocomposite Poly-o-toluidine Zr(IV) Phosphate and Fibrous Nylon-6,6 Sn(IV) Phosphate Cation Exchange Materials

Temperature dependence of the isotope chemistry of the heavy elements.

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