C. HEITNER-WIRGUIN AND V. URBACH
3400
interesting, we have used this phenomenon only as a tool and have tried to indicate in someway the factors influencing the gel melting point. No attempt was made to elucidate the nature of the forces governing the gelation. Very recently, Liquori, et U Z . , ~ ~ have proposed a structural model for the syndiotacticisotactic interaction which provides an explanation for the gelation phenomenon. Their proposal provides also an explanation for the dependence of the gel melting point upon the molecular weight of the syndiotactic component contained in the gel.
D. L. Glusker and C. L. Levesque for their encouragement and enthusiasm during this work, and to Mr. J. Gormley and all of our other colleagues at Rohm & Haas who supplied us with polymer samples. We acknowledge the support of Dr. H. S. Yanai who provided X-ray information, Dr. A. Spell for J-value measurements, and Dr. K. S. McCallum for n.m.r; results. I n particular we wish to thank Dr. Glusker for encouraging the writing of this paper. Without his assistance this paper would not have been submitted for publication.
Acknowledgments. The authors are indebted to Dr. W. H. Watanabe for directing this work, to Drs.
(32) A. M. Liquori, G. Anzuino, V. M. Coiro, M. D’Alagni, P. DeSantis, and M. Savino, Nature, 206, 358 (1965).
Kinetics of Ion Exchange in the Phosphonic Resin Bio-Rex 63
by C. Heitner-Wirguin and V. Urbach Department of Inorganic and Analytical Chemistry, Hebrew University, Jerusalem, Israel (Received April 6, 1966)
The exchange of the cations Ca, Cu, UOZ, and T h on the phosphonate resin Bio-Rex 63 was studied. The slow step which determines the rate of exchange of copper and calcium ions is diffusion through the resin particles, while for uranyl and thorium the chemical reaction seems to be the rate-determining step, probably because of the formation of inert complexes with the phosphonic resin. Diffusion coefficients, rate constants, and activation energies for the various cations were calculated.
Introduction Interest in chelating resins has grown in the last few years because of their possible specific analytical uses. The rate of exchange on this type of resin is generally slower than on normal cation exchangers, and the kinetics of some of these exchangers has therefore already been studied in further detail. Generally, in ion-exchange reactions the rate of exchange is controlled either by diffusion t h o u g h the resin bead (in concentrated solutions), or by diffusion through the film surrounding the particle (in dilute solutions). Boyd, et al.,l also developed equntiolns for exchange kinetics where the slow step was the chemical reaction, The Journal of Physical Chemistry
but this case is practically not encountered. Helfferich2 observes that the chemical reaction could be the slow step in ion exchange on chelating resins. Up to now only the exchange kinetics of the chelating resin BioChelex 100 (containing the iminodiacetic group) were studied under various experimental conditions. Turse and Rieman3 studied the rate of exchange of a series of cations under the limited bath conditions using the (1)G.E.Boyd, L. L. Myers, Jr., and A. W. Adamson, J. Am. Chem. SOC.,69, 2836 (1947). (2) F. Helfferich, “Ion Exchange,” McGraw-Hill Book Go., Inc., New York, N. Y., 1962. (3) R.Turse and W. Rieman, 111, J . Phys. Chem., 65, 1821 (1961).
KINETICS OF I O N ~ ~ C H AIN NG THE E PHOSPHONIC RESINBIO-REX63
equations of Kressman and K i t ~ h e n e r . ~They concluded from this study that the slow step is particle diffusion for cations giving no chelates with the iminodiacetic group and chemical reactions for cations whicli chelate with the functional group. I n our laboratory, a study5 of the rate of exchange of the cations calcium, strontium, and magnesium was made using the same resin, but in the hydrogen form. For all these cations the exchange reaction was found to be controlled by particle diffusion. Schwarz, et al.,6 made self-exchange measurements using NaZ2,Co60, and with the same resin. Their results also indicate that the slow step in the self-exchange process is the particle diffusion mechanism. I n a more recent report, Varon and Rieman' revised their previous results and also concluded that the slow step in all cases studied was the diffusion through the particle bead. They explained their previous error by the fact that there were some inaccuracies in the capacity determinations due to hydrolysis of the sodium resin form by excessive washings. I n some further work done in. our laboratory, a careful kinetic study* was effected on the sorption of copper on the sodium form of the iminodiacetic resin and here also the rate of exchange was found to be diffusion-controlled. Although in all the studies on this resin a small concentration effect was observed, it is well established that the ion exchange on the iminodiacetic resin is controlled by particle diffusion. I n the present paper, the characteristics of the phosphonic resin Bio-Rex 63 are studied. From the literat ~ r eit, ~ is known that cations which chelate with phosphate in solution, e.g., UOz and Th, are very strongly sorbed on this resin. A comparative kinetic study was therefore effected, taking calcium and copper as nonchelatable ions: and uranyl and thorium as ions chelated by phosphate. This resin was used by Kennedy, et U Z . , ~ for analytical separations, and the selectivity order for a series of cations was determined. Persoz and RossetlO have recently studied the equilibria exchange properties of this resin and its selectivity toward bazions.
Experimental Section The resin used was Bio-Rex 63 produced by Bio-Rad Laboratories ( i e . , purified Duolite 63). The resin is of the styrene type (6% D.V.B.) and contains the phosphonic group RP(=O) (0H)z. The resin was washed with distilled water until the effluent was colorless, then washed with two column volumes of 2 N HCI. After washing the resin free of HCI, the exchanger was brought back to the sodium form by treating it with four column volumes of 1-1.5 N NaOH and water washing. This cycle was repeated twice, then the exchanger was air-dried, sieved, and
3401
separated into various mesh sizes and stored in wellstoppered bottles. Determination of the Capacity of the Exchanger. A 0.5-mg. portion of the hydrogen form of the resin was stirred with 50 ml. of 0.1 N NaOH until equilibrium was attained (no further changes occurred in the p H of the solution). The supernatant solution was filtered off and the free hydroxide titrated by 0.1 N HCl. The capacity found was 6.06 f 0.07 mequiv./g. Titration curves of the resin were constructed by Persoz and RossetlO and also by us. These experiments show clearly that the Bio-Rex 63 is a weak acid. (The pK value given by Duolite for this resin is 4-4.8, while the carboxylic resin has a value of 4-6.) The aqueous solution in which the sodium form of the resin was immersed has a p H value of 10-11. Since the phosphonic acid is weak, no exchange reactions can be realized in the hydrogen form with cations such as Fe3+, Cr3+, AI3+, U0z2+,and Th4+. This fact limits markedly the uses of the resin since a t p H values higher than 4 most of these cations hydrolyze. The capacity of the sodium form of the resin toward the cation uranyl and thorium was determined under the same conditions as for the sodium ions. The capacities found were (a) UO%2i 6.04 =I= 0.02 mequiv./g., and (b) Th4+ 5.98 f 0.05 mequiv./g. These cations are very strongly sorbed, but their elutions from the resin need further study. Kinetic Measurements. The limited bath4 technique method was used. Solutions (50-100 ml.) which were 0.003-0.02 M in the cation studied in 1 iM neutral salt were taken for each measurement. The solutions were vigorously stirred. In most cases, the concentration of the cations was kept equivalent to the resin capacity. The solutions were brought to the desired temperature in thermostats which could be regulated to =t0.1", and the weighed amount of exchanger was then added (generally 0.1 g.). At measured time intervals, the resin was rapidly separated from the solution, and the content of cation was determined. This procedure was repeated at each time interval with new fractions of resin and solutions. The radius of the resin particles was determined in two different ways : (a) microscopically; the diameters (4) T. R. E. Kressman and J. A. Kitchener, Discussions Faraday SOC., 4, 90 (1949).
(5) C. Heitner-Wirguin and G. Markovits, J . Phys. Chem., 67, 2263 (1963). (6) A. Schwarz, J. A. Marinsky, and K. S. Spiegler, ibid., 68, 918 (1964). (7) A. Varon and W. Rieman, 111, ibid., 68, 2716 (1964). (8) C. Heitner-Wirguin and N. Liebiing, unpublished results. (9) J. Kennedy and R. V. Davies, Chem. I n d . (London), 378 (1956). (10) J. Persoz and R. Rosset, Bull. SOC. chim. France, 2197 (1964).
Volume 69, h'umber 10
October 1966
3402
C. HEITNER-WIRGUIN AND V. URBACH
of 100 particles swollen in the appropriate solutions were measured and the average value was calculated; (b) the method used by Kressman and Kitchener4; determining the specific density of 500 swollen particles (in similar solutions to those used in the kinetic measurements) and calculating from it the mean value of the radius. Analytical Methods Used. 1. Uranyl was determined colorimetrically by peroxide. l 1 2. Thorium was determined by EDTA titration using xylenol orange as indicator.12 3. Copper was determined by thiosulfate titration.12 4. Calcium was determined by EDTA titration12 or colorimetrically using glyoxal bis(2-hydroxyanil). l 3
0.7 .
0.6
0.5
0.4
E‘ 0.3
0.2
Results The limited bath method was used for the kinetic measurements and the equations developed by Kressman and Kitchener4 for the first-order reaction, and those by Frost and Pearson14 for the second-order reaction. For the first case, i e . , particle diffusion, the equations are
where F is the extent of exchange, Qz is the amount of exchange in time t, Qm is the amount of exchange at equilibrium, Q0 is the amount of resin and of solute taken in each experiment (all the Q values are taken in milliequivalents), r is the radius of the resin particle in centimeters, and D is the diffusion coefficient in square centimeters per second. From this equation it can be seen that a plot of F vs. -v‘t should be a straight line if the rate of exchange is controlled by particle diffusion. From the slope (E) of this line, the diffusion coefficient of the ion examined can be evaluated. -
r Qo
-
For the second-order reaction, i.e., the chemical reaction, the equations used are
(3) If the rate of exchange is controlled by the chemical reaction, a plot of log 2 vs. t should be linear, and from its slope, S, the rate constant IC can be determined (4)
Both equations given here are valid only in the cases of equivalent concentrations of cations in solutions with the exchangeable cations on the resin. The Journal of Physical Chemistry
0 0
2.5
5.0
7.5
10.0
12.5
&sea.
Figure 1. Plots of F us. 4 for CaC12solutions in 0.1 M NaCl: 1 and 2, 0.01 and 0.02 M CaCI2, r = 0.0175 cm., 29”; 3, 0.02 M CaCL, r = 0.0131 cm., 29”; 4, 0.01 M CaCI2, r = 0.0131 cm., 29”; 5, 0.02iM CaC12, r = 0.0175 cm., 39”; 6, 0.02 M CaCI2, r = 0.0131 cm., 39”.
The exchange of calcium ions in the solution for sodium of the exchanger was studied, particularly the dependence of the rate of exchange on the particle size, concentration of the solution, and temperature. It can be seen from these graphs that the rate of exchange decreases markedly with increase in particle size and increases steeply with rising temperature. A very small concentration effect can be observed, i e . , a decrease in the rate of exchange with an increase in concentration. This effect was also previously observed in diffusioncontrolled reactions. 3,5,6 Figure 1 shows that all the plots of F us. are linear, and this leads to the conclusion that the slow step for the exchange of calcium on the phosphonated resin is diffusion through the particle. Similar plots for the exchange of copper ions were obtained and it can be concluded that the rate of exchange depends on the particle size, and practically not on the concentration of copper ions in solution.
4 i
Qm
S = 2k&o(Qo - Qm)/2.30Qm
0.1
(11) N. H. Furman, “Standard Methods of Chemical Analysis,” Vol. I, D. Van Nostrand Co., Inc., Princeton, N. J., 1962, p. 1199. (12) A. Vogel, “Quantitative Inorganic Analysis,” Longmans, Green and Co., London, 1961, pp. 358, 442. (13) A. Glasner and S. Skurnik, Israel J . Chem., 2, 363 (1965). (14) A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,’ John Wiley and Sons, Inc., New York, N. Y., 1953, p. 174.
KINETICS OF ION EXCHANGE IN THE PHOSPHONIC RESINBIO-REX63
From the experiments with calcium and copper, the respective diffusion coefficients have been evaluated, taking into consideration that the equation is valid only for the experiments with equivalent amounts of exchangeable ions in solutions to those of the exchanger. I n order to obt]ain this validity, very dilute solutions must be used. For the exchange of calcium ions a suitable colorimetric method13 was used, which gave accurate determinations of the dilute solutions used, while no appropriate method for copper was found. However, it was possible to infer the correct value of D from solutions containing higher ion concentrations. A plot of D (calculated at higher concentrations of the solution) vs. the concentration of the cation in solution gives a straight line from which the desired value of D (at the equivalent concentration point) can be extrapolated. This approach was used for the evaluation of D for the exchange of copper ions (Table I). From the values of D at two temperatures the activation energies were calculated.
3403
0.3
&
0.2
0.1
0.' 0
I
I
4
I
12 Time, min.
8
I
I
16
20
Figure 2. Rate of exchange adsorption of uranyl ion on Bio-Rex 63 from 0.003 M UOz(NO& and 1M NaCl solutions: 1, T = 0.0088 and 0.0150 em., 29'; 2, T = 0.0088 and 0.0150 em., 39".
0.08
Table I: Diffusion Data for the Exchange of Calcium and Copper on Bio-Rex 63
0.06
d Exchange reaction
T,'C;
Ca2+/Na Caz+/Na Cu2 f/Na Cuz+/Na+
29 39 29 39
+ + f
a
D X 108
E aI
cm.2 sec,-1
kcal./mole
0.705 2.25 1.24
21
M 3
0.04
0.02
15"
Evaluated from a different series of experiments.
0 0
Figure 2 shows the rate of sorption of UOzwith resin of two different particle sizes and at two temperatures. From this figure it can be seen that the rate of exchange is not dependent on the size of the particles, and that there is an increase of rate with rising temperature. From Table I1 it is clearly seen that an increase in UOz concentration increases the rate of exchange appreciably. Table 11: Influence of COS Concentration in the Solution on the Rate of Exchange t , min.
UOt, mequiv./g. sorbedfrom solutions
0.003 M 0.006 M
2
6
0.5 0.56
0.71
10
14
20
30
m
0.81 0.87 0.99 . . . 2.00 0.76 0.90 1.00 1.16 1.38 2.00
Figure 3 shows the linearity of the plots of log Z against t for two temperatures and two mesh sizes of
2
4 6 Time, min.
8
10
Figure 3. Plots of log 2 us. t for 0.003 M UOz(N03)z solutions in 1M NaCl on Bio-Rex 63: 1, T = 0.0088 and 0.0150 em., 29"; 2, r = 0.0088 and 0.0150 cm., 39".
resin, and from these slopes the rate constant k and the activation energy were calculated (Table 111). Very similar results were obtained for the exchange of thorium; ie., the rate is dependent on the concentration of thorium in solution and independent of the size of the particles (Figure 4). Some of the measurements were made a t different stirring rates, but without affecting the rate of exchange. From these experiments it can be assumed that the chemical reaction is the slow step which controls the exchange of uranyl and thorium on the phosphonated resin.
Discussion The kinetics of exchange of four cations on the phosphonated resin Bio-Rex 63 were studied, and two different types of reactions were found. I n the case of Volume 69, Number 10
October 1966
C. HEITNER-WIRGUIN AND V. URBACH
3404
tions within a limit of 8-10 mesh. Although the particale shrinkage in the uranyl and thorium form is somewhat greater than in the copper or calcium form, exact measurements showed it to be no more than 5y0 (for the same mesh size of the resin the radius of the copper 0.0006 cm., while for the thorium form was 0.0123 form the measured radius was 0.0117 f 0.0008). This difference in shrinking cannot be responsible for the different behavior of the two kinds of cations. Increased concentration of the solution considerably raises the rate of exchange; the contrary effect was observed in the case of copper and calcium. A rise in temperature increases the rate of exchange, but the increase is much smaller than in the case of the two uncomplexed cations. Changes in the rate of stirring do not affect the rate of exchange. It must be concluded from these experiments that the slow step in these reactions is the chemical reaction, and not the diffusion through the resin beads. This conclusion seems somewhat unusual since until now no exchange reactions have been known where the chemical reaction is the slow step. Even strongly chelating ions, such as copper, exchange on the chelating resin Bio-Chelex 100 (iminodiacetic group) by a diffusion-controlled mechanism. It may be assumed from these experiments that the complex formed by copper with the iminodiacetic group is labile, while the complexes formed by uranyl and thorium with the phosphonic group are inert, and therefore the chemical reaction is the slow step. It is also due to the inertness of these complexes that once these ions are sorbed it is very difficult to elute them, while copper is easily eluted from the iminodiacetic resin. The different temperature effect in the two types of exchange kinetics calls for further explanation. This difference can be seen directly from Figures 1 and 2, or from the calculated values of the activation energies (Tables I and 111). It can be assumed that the activation energies for chemically controlled exchange reactions should be higher than for diffusion-controlled reactions. In this case, the activation energies calculated for uranyl and thorium, which are in the range of 10 kcal./mole, are acceptable. The activation energies for copper and calcium are very high, and are of the same order of magnitude as those found for similar ions on Bio-Chelex 100 in the hydrogen form. Yo explanation can be given until further data are available.
*
0
10
20
30 40 Time, min.
50
70
60
80
Figure 4. Plots of log 2 us. t for 0.01 M Th(NOa)4 solutions in 1 M NaCl on Bio-Rex 63: 1, r = 0.0170 and 0.0115 em., 29'; 2, r = 0.0170 and 0.0115 cm., 39".
Table III: Rate Constants and Activation Energies for UOz and T h Ion
T,"C.
k X 108
Ea,kcal./mole
U02+
29 39 29 39
3.18 5.37 35 63
10
U022+
Th4+ Th4+
11
calcium and copper, the rate of exchange increases with decrease of the particle size of the resin, and increases considerably with an increase in temperature. An increase in concentration of the solution decreases the rate of exchange ~ l i g h t l y . ~I n these cases the exchange reaction proceeds very quickly, the half-time of reached equilibrium being of the order of 30-100 sec. according the resin particle size used. It may therefore be concluded that the exchange of copper and calcium on a phosphonated resin is diffusion-controlled, as is the case of a regular cation exchanger. From the literature it is also known that these ions form no complex with the monomeric phosphate group. The results obtained for the exchange of uranyl and thorium ions on the phosphonated resin are surprising. The exchange reactions proceed very slowly, and halftime of equilibrium is attained in 40-50 min. The rate of exchange is independent of the particle size of the resin (particles of radius 0.0878-0.169 cm. were used, and practially no changes in swelling were observed during the experiments). A particularly careful study of the particle sizes and their shrinking was made. Uniformity of particle sizes was attained by sieving the samples through standardized sieves and taking frac-
The Journal of Physical Chemistry
