J . Phys. Chem. 1989, 93, 2666-2668
2666
tion,26and c and n are the external potential and the ground-state density, respectively. The corresponding softness combination rule is especially simple: S = 7-l = s s ( r ) d r =
s[
s s ( r , r ' ) dr'] dr
(66)
where S and s(r) are the global and regional softnesses, respectively. The AIM hardness combination rules also assume a simpler form when formulated in terms of the corresponding softness
parameter^.^^ Within the A I M resolution considered in the present paper, the kernels become the corresponding matrices with the softness matrix given by the inverse of the hardness matrix, s = q-'. The softness combination rule now reads m
S =
Inverting
t) by
m
m
Csj = i=l CICdjJl i=l 1=1
gives m
and hence all the regional and global softness parameters, by the relevant summations over constituent atoms.
Rote Added in Proof The development of this paper has recently been and applied both q ~ a l i t a t i v e l y ~ ~ ~ ~ ~ ~ ~specific * ~ ~ ~ ~problems ~ in the chemical and s e m i q ~ a n t i t a t i v e l yto stability and reactivity trends. Acknowledgment. This work was partly supported by research grants from the Polish Academy of Sciences, Projects CPBR 3.20 and CPBP 01.12.
(67)
diagonalization
UTt)U = h. UTU = 1, (h,J = {hi6,}
(68a)
s = Uh-'UT, \hi;'\ = 6,/h,
(68b)
(26) Parr, R. G.; Yang, W . J . A m . Chem. SOC.1984, 106,4049. Yang, W.; Parr, R. G. Proc. Natl. Acad. Sci. U.S.A. 1985, 82, 6723.
(27) Nalewajski, R. F., submitted for publication in Theoret. Chim. Acta (Berlin). (28) Nalewajski, R. F.; Korchowiec, J . J . Mol. Catal., in press. (29) Nalewajski, R. F. In Proceeding; of the Symposium on the Dynamics of Systems with Chemical Reaction, Swidno, 1988; Popielawski, J., Ed.: World Scientific Publishing: Singapore, in press. (30) Nalewajski, R. F.: Korchowiec, J., submitted for publication in Croat. Chem. Acta. ( 3 1 ) Nalewajski, R. F.; Korchowiec, J., submitted for publication in J . Mol. Struct. (THEOCHEM).
Uranium Isotope Effects in Uranyl Carbonate Complex System Taku Aoyama, Masao Aida, Yasuhiko Fujii,* and Makoto Okamoto Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 0-okayama, Meguroku, Tokyo 152, Japan (Received: July 20, 1988)
Uranium isotope effects in the uranyl carbonate complex system were observed by means of cation-exchange chromatography. The isotope separation coefficient t of the system has been determined as 3.4 X lo4 at 25 O C . The magnitude of the isotope effect was found to be in accord with the value expected from the IR spectral information.
Introduction For many years, we have been investigated the uranium isotope effects based on uranyl complex formation reactions.'-' It has been known that there is an empirical relationship between the frequency of the O=U=O asymmetric stretching mode u3 and the separation coefficient e determined by ion-exchange chromatography; the smaller values of u3 can yield the larger uranium isotope effect^.^ It seems likely that the frequency shift of u3 accompanied by a complex formation is an excellent probe in predicting the isotope effects on the corresponding system. IR spectral measurements have been performed on the uranyl carbonate complex in the solid state, and the unusually small value q = 843 cm-I has been reported.8 There is no reason not to ( I ) Okamoto, M.; Goda, R.; Nakagawa, A,; Sakuma, Y . ;Kakihana, H. Isotopenpraxis 1980, 16, 293. (2) Tanaka, Y . ; Fukuda, J.; Okamoto, M.; Maeda, M. J . Inorg. Nucl. Chem. 1981, 43, 3291. (3) Tanaka, Y.; Fujii, Y.: Okamato, M. J . Phys. Chem. 1982, 86, 1015. (4) Okamoto, M.; Tanaka, Y.:Fujii, Y.; Maeda, M. Isotopenpraxis 1982, 18, 285. ( 5 ) Goda, R.; Tanaka, Y.: Fujii, Y.: Maeda, M. Isotopenpraxis 1982, 18, 293. ( 6 ) Nakagawa, A.; Sakuma, Y . ;Okamoto, M.; Maeda, M. J . Chromatogr. 1983, 256, 231. (7) Kim, H. Y.; Kakihana, M.; Aida, M.; Kogure, K.: Nomura, M.; Fujii, Y . ;Okamoto, M. J . Chem. Phys. 1984, 81, 6266.
0022-3654/89/2093-2666$01.50/0
TABLE I: Experimental Conditions for Uranium Isotope Separation
and the Observed Elemental Separation Coefficient e' bed ht, cm
flow rate,
temp, "C
cm3 h-'
band velocity, cm h-I
10%
25 f 0.5
25.0
20.0
25.0
3.4
Operation manner breakthrough.
believe that the IR data in the liquid phase are similar to those in the solid state. From the standpoint of the view mentioned above, the isotope effects in the uranyl carbonate complex system are expected to be fairly large among the uranyl complex formation systems. In this study, cation-exchange chromatography was carried out to determine the isotope effects in the uranyl carbonate complex system. IR spectral measurements were also performed on the uranyl carbonate complex in the aqueous solution phase. The results were compared with those studied previously. Experimental Section Ion-Exchange Chromatography for Uranium Isotope Separation. Uranyl carbonate stock solution was prepared in the (8) Koglin, E.; Schenk. H. J.; Schwochau, K. Spectrochim. Acta 1979, 3SA. 641
0 1989 American Chemical Society
rhe Journal of Physical Chemistry. Yo/.93, No. 6, 1989 2661
Uranium Isotope Effects
I
p r c s s ~ r cpump
,High
Wafer Q d h
'0
20 Lf'i"e"l
-Wafer jacket Thcrmortolcd WOICI
"OIUme I
60 cm3
Figure 2. Chromatogram and isotol)ic ratios far uranyl carbonate camplex system.
-Cotion exchange r s i n
Needle valve
IhCrmOLBl
~"""m
Figure 1. Column system used far uranium isotope separation
following procedure. The UO,'+ ions adsorbed in the cationexchange resin packed in a small column were eluted with 1.0 mol/dm3 (M) Na2C0, solution. The effluent, uranyl carbonate solution, from the bottom of the column was collected. Excess amount of the Na,CO, solution was added to keep the uranyl carbonate complex stable. The solution was diluted with redistilled water, resulting in a stock solution 010.05 M uranyl carbonate complex solution. The column system used for uranium isotope separation is shown schematically in Figure I . T h e column, with inner diameter of 8 mm and overall height of 300 mm, was made of pressure-resistant Pyrex glass, surrounded by a water jacket for temperature control. T h e cation exchange resin of the H+ form was packed in the column. Then the 0.05 M uranyl carbonate complex solution was loaded in a breakthrough manner from the top of the column by use of a high-pressure pump. The pressure inside the column was maintained at 10-20 kg/cm2 to avoid the evolution of C 0 2 gas at the frontal part of the uranium adsorption band. The effluent from the bottom of the column was collected in small fractions. For each sample fraction, the pH, uranium content, and uranium isotopic ratio were determined. Details of analytical method have been described elsewhere.6 IR Spectral Measurements. IR samples of uranyl carbonate complex solution were prepared by eluting UO," ions adsorbed in the cation-exchange resin with 1.0 M N a 2 C 0 , solution. I R spectral measurements were carried out at room temperature on an IR spectrometer DS-701G (JASCO) using KRS-5 (25 X 25 X 2 mm) window plates without a spacer. The solvent was replaced with D 2 0 when necessary to reduce strong absorption by water.
Results and Discussion The experimental wnditions for the chromatographic operation are listed in Table I. The chromatogram obtained is shown in Figure 2, along with pH changes and uranium isotopic ratios, 23rU/238U.The uranium concentration profile in Figure 2 indicates that almost ideal displacement reaction was realized at the frontal boundary of the uranium band in the present system. The feature of the changes in the isotopic ratios indicates that the lighter isotope 235Uis enriched a t the frontal part of the uranium band,
Figure 3. Characteristic absorption band due to asymmetric U02stretching mode Y, of uranyl carbonate in aqueous solution at 25 'C. 4 a k '
880
"
"
"
900
920
940
I
' ' 4
9M
y, / cm-1 Figure 4. Correlation between elemental separation caefficicnt e and asymmetric UO1' stretching mode Y, of uranyl complexes. The solid line . indicates the empirical relation obtained from previous results (wmplexes b i ) ? The uranyl complexes and (a) carbonate (this work), (b) malate, (c) citrate, (d) lactate, (e) glycolate, (0 acetate, ( 9 ) tricarballylate, (h) chloride, and (i) perchlorate. i.e., 23sUis fractionated to the complex species in the aqueous solution. The same tendency was observed in all cases of other uranyl complex formation systems.' The isotope effect is evaluated by the elemental separation factor S, defined a s
where the brackets without and with an overhead bar denote the
J . Phys. Chem. 1989, 93, 2668-2671
2668
concentration of given isotopes in the aqueous solution phase and that in the resin phase, respectively. The elemental separation coefficient E (=S - 1) is calculated with the chromatographic data! The t value of the present system has been determined as (3.4 f 0.5) X The error ( l o ) of the separation coefficient is estimated from the uncertainty in the amount of the 235Uenrichment in the band boundary region. Figure 3 shows IR spectra for the uranyl carbonate complex in an aqueous solution covering the spectral range 950-850 cm-l. The characteristic absorption band due to the asymmetric stretching mode u3 of O=U=O bonds clearly appears when the water solvent is replaced with D 2 0 . The peak position of the band has been read as 885 cm-I. (9) Spedding, F. H.: Powell, J. E.; Svec, H. J. J . Am. Chem. Soc. 1955, 77, 6125.
The experimentally determined separation coefficient e for the uranyl carbonate complex system is plotted against the wavenumber of v3 in Figure 4, together with the results for other systems reported p r e v i ~ u s l y .The ~ solid line drawn in Figure 4 indicates a relationship between E and v3 empirically obtained from previous data by using a least-squares method: t
= 4.62 X lO”(960 - ~
3 )
(2)
It was found that the present results falls on the line extrapolated to the lower wavenumber region.
Acknowledgment. We thank Masao Nomura and Michiko Yugami of Tokyo Institute of Technology for their valuable discussion and assistance given in this work. Registry No. UOzC03, 12274-95-2; 235U,I51 17-96-1; 238U,744061-1.
Polymer Swelling. 7. A Molecular Interpretation of Polymer Swelling L. A. Errede 3M Corporate Research Laboratories, 3M Center, Bldg. 201 -2N-22, S t . Paul, Minnesota 55144 (Received: July 14, 1988)
The adsorption number, a,Le., the number of adsorbed molecules per accessible phenyl group in poly(styrene-co-divinylbenzene) at thermodynamic equilibrium with excess test liquid, was calculated from the corresponding relative swelling power, C in mL/g, determined experimentally for 40 aromatic liquids and 34 aliphatic liquids. The results obtained thereby support the point of view expressed in ref 9 that the solubility of a polymer in a given liquid depends primarily on the force of mutual attraction between the functional group in the liquid and the functional group in the polymer and that this force is reduced by steric hindrance due to the substituents attached near these functional groups. It appears, therefore, that CY is a measure of the dynamic packing efficiency of the molecules immobilized by adsorption to a monomer unit in the relatively immobile cross-linked polymer network in the gel state.
Introduction
where 2: is the total number of sorbed molecules per phenyl group in the polymer, the average cross-link density of which is 1/X, and Dole’,2 and subsequently Fowkes) reported that the number, cy is the number of these sorbed molecules that are adsorbed per cy, of sorbed molecules per functional group in a polymer sample accessible phenyl group. exposed to a vapor at constant temperature increases exponentially That there are indeed two types of sorbed molecules as sugto a characteristic asymptotic limit, which depends on the partial gested above is supported by kinetic data obtained in time studies pressure of the vapor as well as the functional group in the of evaporation from liquid-saturated poly(Sty-co-DVB) at 23 0C.7,8 polymer. Recently, we reported4 that the volume (S) of liquid The mobile nonadsorbed molecules escape first, and this process sorbed per gram of poly(styrene-co-divinylbenzene) (poly(Styfollows zero-order kinetics, the rate constant of which reflects the co-DVB)) immersed in excess test liquid a t constant temperature relative force of association with molecules of its own kind just also increases exponentially to an asymptotic limit characteristic as it does for evaporation from the liquid itself. The sorbed of that liquid and that this limit varies with the number, A, of molecules immobilized by adsorption escape thereafter, and this carbon atoms in the backbone of the poly(styrene) segments process follows first-order kinetics, the rate constant of which between cross-link junctions, the average of which is given by (1 x)/x where x is the DVB mole fraction in the c o p ~ l y m e r . ~ ~ ~reflects the relative force of association with the molecular structure of the monomer unit of the polymer in the gel state. This relationship is given by the equation We reported9 that the relative swelling power, C , of a liquid s = C(X1/3 - X0”3) (1) for poly(Sty-co-DVB) is related to the corresponding solubility parameter, 61iq,of that liquid (see Figures 1 and 2 of ref 8) by where C is the relative swelling power of the liquid in milliliters the equation of adsorbed liquid per gram of polymer, and l / X o is the critical cross-link density above which S is zero, Le., immeasurably small. C = A - B(6sty - 61j,J2 (3) Since the adsorption number, a,can be calculated directly from the corresponding C , eq 1 can be recast in the form where GstY = VIlqwhen 6Sty - VIiq= 0. The constants A , B, and bSty, however, are not universal for all z = 4 X V 3 - X0”3) (2) liquids. They are instead characteristic of the class of liquids based on a common functionality. For the aromatic liquids dSty is 9.5 ( I ) Dole, M. Ann. N.Y. Acad. Sci. 1949, 51, 705. cm-3/2,but the respective Gstr for the aliphatic chlorocarbons, (2) Dole, M.: Faller, 1. L. J . Am. Chem. SOC.1950, 72, 414. (3) Fowkes, F. W.; Tishler, D.0.;Wolfe, J. A.; Lannigan, L. A,; Ade-
+
mu-John,C. A.; Hallibel, M. J. J . Polym. Sci., Polym. Chem. Ed. 1984, 22, 547. (4) Errede, L.A,: Stoesz, J. D.;Sirvio, L. M. J . Appl. Polym. Sci. 1986, 31, 2721. (5) Errede, L. A. J . Appl. Polym. Sci. 1986, 31, 1749 (6) Errede, L. A. Macromolecules 1986, 19, 654.
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(7) Errede, L. A,; Kueker, M. J.; Tiers, G. V. D.;Van Bogart, J. W. C. J . Polym. Sci., Polym. Chem. Ed. 1988, 26, 3375. (8) Errede, L. A,; Van Bogart, J. W. C. J . Polym. Sci., Polym. Chem. Ed.,
in press. (9) Errede, L. A. Macromolecules 1986, 19, 1522.
0 1989 American Chemical Society
