Nuclear Magnetic Double Resonance Study of Water Movement in an Ion Exchange Resin System R. W. Creekmorel and C. N. Reilley Department of Chemistry, University of North Carolina, Chapel Hill, N . C . 27514 The rate of free exchange of water protons between the interior of an ion exchange resin and the exterior region (of an aqueous ion exchange bed) has been measured by an NMR double resonance technique. This technique, in which both the exchange rate and relaxation times are obtained, was ideally suited for this study; the conventional line shape method was not feasible because of the heterogeneous nature of the system. An exchange rate of 7.3 x lo-’ sec-’was found for the acid form of Dowex 5OW-8X (50-100 mesh). In addition, the longitudinal relaxation times for the exterior (bulk) water protons and the interior (resin) water were 2.9 and 0.45 seconds, respectively.
NUCLEAR MAGNETIC RESONANCE (NMR) has been shown to be quite useful in investigating ion exchange resins (1-6), particularly in respect to their cross-linking, internal concentrations, counterion, and heterogeneity. However, little attention has been focused on determination of time-dependent phenomena in such systems by NMR. The purpose of this investigation is to study by NMR the exchange of water in Dowex 50W resin and in addition obtain the longitudinal relaxation times ( T I )for the two types of water. For most resin suspensions, separate signals are observed for the water inside and outside the resin beads. From the various observed chemical shift differences between the two water peaks, Gordon ( 2 ) set lower limits ranging from 0.004 to 0.1 sec for the mean lifetime of water in either phase. On the other hand, the exchange was also found to be too rapid to observe by any batch deuteration technique. [Contrary to this latter finding of Gordon, Dinius et al. (3) reported an exchange lifetime of 13 sec for water in a 4% Dowex 50 (100 mesh) resin by a batch deuteration method.] Batch deuteration experiments were also attempted at this laboratory. The external water of the resin was removed by centrifugation, the resin was then placed in D20, and the time dependent NMR spectra were recorded. The exchange rate was too rapid for this technique (the exchange was essentially complete within 10 sec). Tetenbaum and Gregor (3,using a shallow-bed flow system, observed that the half life of water in Dowex 50 resins was less than 5 seconds. Usually, exchange rates are measured by NMR through analysis of line shapes (8); however, in the case of ion exPresent address, Marshall Research Laboratory, E. I. du Pont de Nemours & Company, Philadelphia, Pa. 19146 (1) J. E. Gordon, Chem. Znd. (London), 1962,267. (2) J. E. Gordon, J . Phys. Chem., 66,1150 (1962). (3) . . R. H. Dinius, M. T. Emerson, and G. R. Chotmin. _ - . ibid... 67., 1178 (1962). (4) R. H. Dinius and G. R. Chouoin. ibid.. 66. 268 (19621. ( 5 ) J. P. De Villiers and J. R. Pa&h,’J. Poly. hci., Ai,1331 (1964). (6) R. W. Creekmore and C. N. Reilley, ANAL.CHEM.,42, 570 ( 1970). (7) M. Tetenbaum and H. P. Gregor, J. Phys. Chem., 58, 1156 (1954). (8) J. A. Pople, W. G. Schneider, and H. G. Berstein, “High Resolution Nuclear Magnetic Resonance,” Chap. 10, McGraw-Hill,New York, N. Y., 1959.
change resins, the observed linewidths of the water protons depend not only on relaxation and exchange but also on resin heterogeneity and magnetic field gradients within the sample, Because of the difficulty in applying reasonable corrections for the latter effects, the lines shape approach was considered to be not feasible. Forsen and Hoffman (9, IO) have described a double resonance technique which measures moderately slow exchange rates (order of seconds) without requiring analysis of linewidths. This technique appeared ideally suited for studies of the exchange rate and relaxation times of water in an ion exchange suspension, and the results of such experiments are described here. EXPERIMENTAL
Reagents. The resin used in this study, Dowex 50W-8X, was conditioned by washing with 6N HCI followed by copious amounts of deionized distilled water. The resin beads were then allowed sufficient time to swell, and super fines were removed by decanting. Apparatus. Our experiments were conducted on a Varian HA-100 at an ambient temperature of 31 “C. The receiver gain was modified, as described by Jankowski ( I I ) , so that electronic overloading during double resonance experiments could be eliminated. The spectrum amplitude was increased to about 7000 while the gain and lock signal were reduced to less than 1 volt. The saturating field, H2, was obtained by sideband modulation using a Hewlett-Packard oscillator, Model 200 AB. Because rather large H2 fields are required in this experiment, two oscillators, A and B, were used. Oscillator A’s frequency was set downfield from any signals while oscillator B’s frequency was adjusted to match the frequency of one of two peaks. The experiments were conducted by switching oscillator A “off’ and oscillator B “on,” and vice versa, This eliminated any change in Hl (the observing sideband) while performing the experiments. The resulting decay and recovery signals were recorded on a Sanborn strip chart recorder. The reference, cyclohexane, was sealed in a 2-mm capillary and held coaxially in a 5-mm 0.d. NMR tube by Teflon (Du Pont) spacers. TRANSIENT DOUBLE RESONANCE METHOD
As a first approximation, an ion exchange suspension can be considered as a two-site case in which the water protons move reversibly between site A , which corresponds to exterior water, and site B, which corresponds to interior water (see Figure 1). In the Forsen and Hoffman experiment one of the sites, say B, is saturated with a large HZfield while the other site, A , is observed by a weak nonsaturating observing field, HI. The saturated protons at site B move to site A by an exchange process, thereby decreasing the signal in(9) S. Forsen and R. A. Hoffman, Acta. Chem. Scand., 17, 1787 (1963). (10) S. Forsen and R. A. Hoffman, J. Chem. Phys., 39, 2892 (1963). (11) W. C. Jankowski, 10th Experimental NMR Conference, Mellon Institute, Pittsburgh, Pa., 1969. ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
725
B
A
t
c
I
.
,
.
.
, . , , , . .
I
,
-tSITE A
t DOWEX 50W 8% DVB Figure 1. 100-MHz proton spectrum of water in an aqueous suspension of Dowex SOW-8X ion exchange beads Site A represents bulk water protons and site B represents protons of water inside the resin matrix. Each division represents 20 Hz
SITE 6 Figure 2. Decay and recovery signals for site A and site B Arrows pointing down indicate when the H2 field is applied to the other site and arrows pointing up indicate when the H2 field is removed. Markers in lower part of the figure are at 1-secintervals
tensity observed for site A . The rate of decrease of the signal corresponding to site A and its new equilibrium intensity are governed by both the exchange lifetime and the longitudinal relaxation time, Tl. Case I. The time dependent z-magnetization at site A after instantaneously applying a saturating field HZat site B is given by,
M s A ( f )= M,”(~)[(T~A/~A) exP(-f/Tia) -k T~A/T~AI (1) where, T I Ais the longitudinal relaxation time of site A and 7 4 is the lifetime of the proton at site A . The exponential time constant T I A is related to TIAand T A by, 1/TlA
=
+
l/Ti~
(2)
1/74
It can easily be seen that the ratio T ~ A / Tcan ~ Abe obtained from the asymptotic value of M,A( m)/M,A(O). Substituting this condition into Equation 1 gives
MzA(t)- MzA(m)= MsA(o)[(T~A/TA) exp(-f/7ia)l
(3)
and plotting the log of [M,A(t) - M 2 ( a)] us. t gives a slope of - 1 / ~ 1 A . Therefore one can calculate T I Aand T A from the asymptotic value of Mz.4(m)/MzA(0)and Equation 2, respectively. Case 11. The recovery of site A after removal of Hz from site B is more complex than the decay response since it is governed by two exponential terms as given by Equation 4,
M&)
=
M,A(O)
+ C1exp(-Xlt) + C2exp(-ht)
(4)
where
cl = MsA(0)[X2(TlA - TlA)/(hi CZ
= k‘fsA(0)
[Xl(TlA
-
71A)/(X2
- A2)TIAl
(5)
- hl)TlA]
(6)
The values of X1 and X2 are obtained by solving the following determinant :
(7) Case 111. The recovery of site A is observed after the removal of the saturating field H2 at site A . The coefficients C, and C, are given by, 726
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
cz
=
M/(O)
1 - XiTia
+ (TB/TA)TIA/(TB + T I E}) (A1
- X2)TlA
(9)
Case IV. The recovery of site A after having saturated both site A and site B simultaneously is represented by Equation 4. The coefficients C1 and C2 are given by,
c1 MzA(o)[(I cz = MzA(0)[(I
- XZTlA)/(XZ
- A1)TlAl
(10)
-
- X2)TlAI
(11)
XlTlA)/(Xl
A computer program, NMR 1, was written which calculated M , at various times for both sites and for all four cases, thereby allowing a check of the experimental results. RESULTS
Case I Experiment. The experimental decay and recovery curves for site A and for site B are shown in Figure 2. In the experiments, the sample is spun to obtain the sharpest peaks; also internal locking was used to prevent field drifting, allowing Hl to be situated at the top of the peak to be measured. This technique was also employed by Anet and Bourn (12). The observing field H I was adjusted so that a good signal-to-noise ratio was obtained but without saturation of the observed peak. Spinning was found to be an important variable in obtaining a good signal with little interference from spinning beat notes. Low spinning rates gave better results with the coaxial sample tube employed. In order to determine the minimum amount of Hz field necessary to saturate site A and site B, the following experiments were conducted. The H2 oscillator frequency is set to coincide with either the site A or site B resonance, while H1is set at the frequency of the (12) F. A. L. Anet and A. J. R. Bourn, J . Amer. Chem. SOC.,89, 760 (1967).
H2 Figure 3. Relative amplitudes of site A and site B a s a function of applied HZ(in terms of mV) Points shown have been corrected for changes in intensity of the observing field ( H l ) as HZis increased
Figure 5. Logarithmic plot of recovery of site A The curved line represents the calculated recovery curve based on the time constants listed in Table I
Table I. Time Constants Determined for Water in Dowex 5OW-8X Suspensions Site 71 (sec) Tl (sec) T (sec) 0.958 2.9 1.42 A (exterior water) 0.340 0.46 1.33 B (interior water)
1
2oh
Figure 4. Logarithmic plot of decay of site A upon sudden saturation of site B. The straight line is a least-squares line
other site. H2 is increased progressively and the decreased signal at H i is recorded after attainment of equilibrium. Changes in the base line are also compensated for. In order to determine the effect of the Hz field on the observing field HI, the H z oscillator was purposely set off resonance by 200 cps and the experiment repeated. The procedure was also repeated for the remaining site. The results obtained are graphically illustrated in Figure 3 where the H z field in terms of mV has been plotted us. signal amplitude. An Hz field of 100 mV was necessary to saturate site B while only -60 mV was necessary to saturate site A . Therefore, one can easily tell at this point that TIA > TIB. In order to compensate for the decrease in H I as 100 mV of HZis applied, a second HZoscillator was employed and set off resonance. An HZfield is then switched “on” and “of” resonance, thereby maintaining a constant H I field throughout the experiments.
In Figure 4 a plot of ln[M,A(t) - M,A( m)] us. time is given. The straight line shown is the least squares fit of the experimental data; the standard deviation of the slope was 2%. From the M,A(a)/M,A(O) ratio, a value of TIA = 2.9 =t0.1 seconds was calculated. The parameters of site B were obtained in a more indirect manner. From a knowledge of r A ,rBcan be calculated from the population ratio of site A to site B. The ratio T I ~ / Twas IB then substituted into then determined from MZB(m )/MZB(O), Equation 2. Table I summarized the values of 71, TI, and r obtained for the two sites. Case I1 Experiment. The experimental recovery curve for both site A and B are shown in Figure 2. The site B recovery was too fast to examine in any detail; therefore attention was focused on recovery for site A . Figure 5 gives a logarithmic plot of the recovery data obtained for site A after removal of H2 saturating site B. The experimental points indicate that the recovery is at later times governed by a single exponential term. Using the parameters calculated from the decay curves, the theoretical recovery curve is:
+
MZAW= MZA(O) 9.776 exp(-3.19r) - 39.108 exp(-0.798t)
(12)
From Figure 5 , it can be seen that the experimental points fit the calculated recovery curve within experimental error. In order to compensate for the Bloch-Siegert effect (13), it was necessary to decrease the experimental M,A( m ) value (10%) and adjust each subsequent point so that the experimental recovery slope is not changed. The applied H2 field causes a small displacement of all lines in the spectrum, in this case a shift of approximately 1.5 Hz was observed. Therefore if the top of a peak is measured and H z is then applied, the reso(13) A. Losche, Ann. Physik., 20, 178 (1957). ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, J U N E 1970
727
h
4
L
0.71
.\[*0.6 O L
0.4< N
d Q
2 0.21
-
-
0.2 -
u
1
0.1
2
1
t
f'
(SEC)
Figure 6. Logarithmic plot of recovery of site A after saturating site A with Hz The line drawn is the calculated recovery curve based on Table I time constants
nance position changes so that the top of the peak is displacedto one side of the applied H I . The measured magnetization, M,, is therefore a few per cent less than the actual M,. In the case of the decay signal, the displacement should be instantaneous, therefore not affecting the measured decay constants. The asymptotic M z values shown in Figure 3 were taken by scanning t o the new resonance position. Since the recovery signal calculated is based on the correct asymptotic M , value, the experimental curve starting point is expected to be shifted, but having approximately the same time constant. Case I11 Experiment. Once again only the A site has been studied because the recovery of the B site was relatively fast and good data could not be obtained. Figure 6 gives a logarithmic plot of the recovery of site A after removal of the Hz field saturating site A . In this case the process can be described primarily by a single exponential a t later times. The calculated line in Figure 6 is : M,A(t) = MSA(O)-
1.214 exp(-3.191t) - 42.286 exp(-0.798?)
(13)
Since the Bloch-Siegert effect primarily affects the asymptotic M , value, it should have no effect in this case since M , equals zero for both experimental and calculated values. Spin Echo Experiment. It was of interest to correlate the transient double resonance experiments with results obtained by spin echo measurements. Such a comparison is shown in Figure 7. The solid line given by Equation 14 represents the calculated recovery of the total magnetization (MzA MzB)from site A and site B after having saturated both sites simultaneously.
+
&IsAB(?) = MzAB(0)- 15.432 exp(-3.191?) 68.811 exp(-0.798?)
where:
(14)
+
MzAB= MSA MaB
The time constants used in obtaining the constants in this equation are calculated from the values listed in Table I. The experimental points shown were taken from a spin echo experiment using a 180-90" pulse sequence (14). It can (14) H. Y . Carr and E. M. Purcell, Phys. Rea., 94, 630 (1954).
728
(SEC)
Figure 7. Logarithmic plot of recovery of total magnetization after saturating both site A and B simultaneously
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
The line drawn represents calculated recovery of total magnetization while the experimental points were taken from a 180-90" spin echo experiment. For the calculated curve, M z A R ' - MZAB(O)- MzAe(t)/MZAB(O) while MIAB' = M p ( 0 ) - M z A B ( r ) / Z M Z A B ( O )for the spin echo results (since to +MSAB(O) the recovery is from -MzAB(0)
be seen that the spin echo experiment measures an effective TI which is composed of TU, T i B , and exchange. DISCUSSION
The recovery curves (Cases 11, 111, IV) offer a check on the validity of the time constants determined from the decay curve (Case I). The determined longitudinal relaxation time, T1a, for bulk water (not degassed) is consistent with a Tl value of 2.8 reported by Van Geet and Hume (15) for non-degassed water. This is not too surprising because the water outside the resin phase was expected to behave as pure water, thus having the same TI. The Tl value for the inside water is however, expected to be lower than T I for the outside water for the following reasons. First, the correlation time, rc would be expected to be longer because of the physical barriers of the resin matrix. Second, the resin used possesses a proton for the counterion. The proton, which exchanges very rapidly with water protons, causes the observed Tl to be a weighted average of the Tl for the counterion proton and of the TI for the water proton. If the TI for the counterion proton is small, because of its interaction with the fixed ionic group, the resultant Tl will be lowered. Such a n interaction has been suggested by other investigators (16) in studies of polystyrene sulfonic acid. And third, the water in the hydration shell of the counterion possesses a longer r c when the counterion is associated with the fixed ionic group by some coulombic interaction. A rate constant, k = 7.3 X 10-1 sec-I was found for the free exchange of water protons between internal and external phases for the Dowex 5OW-8X system studies. Although the (15) A. L. Van Geet and D. N. Hume, ANAL.CHEM.,37, 983 (1965). (16) M. Nagasawa and L. Kotin, J. Amer. Chem. SOC.,83, 1026 (1961).
determined rate constant is for proton exchange, the value should be approximately the same for the exchange of water molecules. This assumption is verified by the fact that the self-diffusion coefficients of water measured by 1*0 tracer techniques and by proton resonance are the same (17). This rate constant value is quite consistent with the estimates reported by Gordon ( 2 ) and the measurements of Tetenbaum and Gregor (7). However, the exchange time reported by Dinius appears to be longer than would be expected from our findings. The findings reported here pertain to the particular resin investigated. Changes in particle size, cross-linking, counterion, and other such variables will obviously give some(17) D. W. McCall and D. C. Douglas, J. Phys. Chem., 69, 2001
(1965).
what different results. This particular system reported in this paper was selected because of the large separation of peaks, thereby making the double resonance method possible, in addition to allowing more accurate measurements of the population ratio. The resin also had the feature of being one commonly employed in analytical work. RECEIVED for review September 30, 1969. Accepted March 10, 1970. The financial assistance provided by the University of North Carolina Materials Research Center, Contract SD-100 with the Advanced Research Projects Agency, and by the National Institutes of Health Grant GM-12598 is gratefully acknowledged. We would also like to acknowledge the National Science Foundation Grant GP-6880 for the purchase of the Varian HA-100 spectrometer used in this study.
Application of an On-Line Computer to the Automation of Analytical Experiments G . P. Hicks, A. A. Eggert, and E. C . Toren, Jr.’ Department of Medicine and Department of Chemistry, Uniuersity of Wisconsin, Madison, Wis. 53706
Traditionally, the steps in a classical analytical experiment are performed by the experimenter. Advances in on-line computer technology and digital instrumentation now make it feasible to use an on-line computer to perform many of the operations previously done by the experimenter. To aid the analytical chemist, a computer system has been designed which will control analytical instrumentation, provide on-line analysis of data for use during the experiment, and plot the experimental data with theoretical curves on a CRT and incremental plotter. This development has made it feasible to use a new graphical approach to routinely analyze data from enzyme-substrate studies.
THERESEARCH CHEMIST spends much time during a laboratory experiment performing tasks which do not require his scientific knowledge o r skills. For example, the chemist must manipulate reagents, operate equipment, and record results during the experimental procedures. Only after the completion of the experiment is adequate time usually available to reduce and analyze the experimental data so that the experimenter may employ chemical insight to draw conclusions and make decisions about further work. Because the analysis of results must usually follow the experimental procedure, the researcher may choose the wrong course of action or miss a valuable observation altogether, frequently making it necessary to repeat the entire experiment. The use of high speed digital computers in real time to perform routine experimental tasks and make defined decisions automatically should greatly enhance the ability of the chemist to apply his knowledge during each individual experiment, thereby achieving more reliable and meaningful results with less work. A typical analytical experiment may be thought of in several steps as shown by the solid boxes in Figure 1. Most previous work has emphasized the applications of computers to the On sabbatical leave from Department of Chemistry, Duke University, Durham, N. C.
steps of acquisition, reduction, and analysis of experimental data (1-5). The computerization of analytical experiments in real time has only recently become feasible with the availability of small laboratory oriented on-line computer systems. The great reduction in costs of a laboratory oriented high speed digital computer in the past five years puts the computer in the category of a “medium cost laboratory instrument.” The day is rapidly approaching when the analytical chemist can look upon the computer as just another laboratory tool. The development of related peripheral hardware, such as external logic and highly accurate incremental plotters, has also contributed to this advance. The initial applications of the online computers have usually treated the computer as a passive element in the experimental procedure to assist in data acquisition or post experimental reduction and analysis of data with little or no use of results for feedback and control during the experiment. However, it now seems practical to use the computer in real time to assist in certain other steps, such as defined decision making (6, 7), reagent mixing, and data presentation (8) in final form for permanent records and communication to other investigators. Dotted lines in Figure 1 show how the computer could be inserted into an experiment as a decision maker. While possible in principle, the real(1) R. S. Nicholson and I. Shain, ANAL.CHEM., 37, 178 (1965). (2) S . P. Perone, J. E. Harrar, F. B. Stephens, and Roger E. Anderson, ibid., 40, 899 (1968). (3) G . P. Hicks and A. A. Eggert, Clin. Chem., 14, 798 (1968). (4) P. C. Jurs, B. R. Kowalski, and T. L. Isenhour, ANAL.CHEM. 41, 21 (1969). (5) G. E. James and H. L. Pardue, ibid., p 1618. (6) E. Feigenbaum and J. Feldman, Eds., “Computers and Thought,” McGraw-Hill Book Co., New York, N. Y., 1963. (7) D. Michie, Ed., “Machine Intelligence 3,” American Elsevier Publishing Co., Inc., New York, N. Y., 1967. DP-1 Instruction Manual,” (8) Houston Instruments, ‘‘C@MPL@T Bellaire, Texas, 1968. ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
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