Pulsed Nuclear Magnetic Resonance Measurement of Relaxation Times in Ion-Exchange Resins W. J. Blaedel, L. E. Brower, T. L. James,l and J. H. Noggle2 Department of Chemistry, University of Wisconsin, Madison, Wis. 53706 Pulsed nuclear magnetic resonance (NMR) techniques have been used to measure longitudinal and transverse relaxation times (TI and T2) for water protons and for sodium ion in a sulfonic acid ion exchanger in the sodium form. Cross-linking ranged from 2 to 12%, and moisture content ranged from fully swollen to less than one water per exchange site. Cross-linking affects rl and r2 for water protons only slightly. For water contents above 6 moles of water per exchange site, rl and r2 became independent of water content, indicating a water-like environment for the water protons. Below 6 moles of water per exchange site, the relaxation times indicate that the water is structured.
NUCLEAR MAGNETIC RESONANCE (NMR) techniques have been used to investigate the interactions of nuclei with their environments. The interaction of ions in solution, the arrangement of solvent molecules surrounding ions, and the diffusion of ions and molecules have been studied by NMR methods (1-3). These methods are being applied to other environments including solid surfaces (4) and ion-exchange materials. NMR studies of the interactions among counter ion, exchange site, and solvent in ion-exchange resins have been made primarily by continuous wave measurements of chemical shift effects. The use of the chemical shift of protons to investigate and characterize ion-exchange resins was described in papers by Gordon (5); Dinius, Emerson, and Choppin (6); and devilliers and Parrish (7). Papers published by Creekmore and Reilley (8) and by Gough, Sharma, and Subramanian (9) described determinations of hydration numbers of ions in ion-exchange resins by measurement of the temperature-dependent chemical shift of water protons within the resin. Creekmore and Reilley have also described a double resonance technique for measuring both longitudinal relaxation time (Tl) for water protons in the resin, and the exchange rate of water between the resin and the exterior solution (10). In the present work, pulsed NMR techniques are applied to the measurement of relaxation times (TI and T2)in ion exchange resins of various water contents and cross linkages. 1 Present address, Celanese Corporation, Corpus Christi, Texas. Present address, Chemistry Department, University of Delaware, Newark, Del. 19711. _
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(1) J. F. Hinton and E. S . Amis, Chem. Reu., 67,367 (1967). ( 2 ) C. Deverell, Progr. N M R Spectrosc., 4, Chap. 4 (1969). (3) H.G. Hertz, ibid.,3, Chap. 5, (1968). (4) K. J. Packer, ibid.,Chap. 3. (5) J. E. Gordon,J. Phys. Chem., 66,1150 (1962). (6) R. H.Dinius, M. T. Emerson, and G. R. Choppin, ibid., 67, 1178 (1962). (7) J. P. deVilliers and J. R. Parrish, J. Polym. Sci., Purr A , 2, 1331 (1964). (8) R. W. Creekmore and C. N. Reilley, ANAL.CHEM.,42, 570 (1970). (9) T. E. Gough, H. D. Sharma, and N. Subramanian, Can. J. Chem.,48,917 (1970). (10) R. W. Creekmore and C. N. Reilley, ANAL.CHEM.,42, 725 (1970). 982
ANALYTICAL CHEMISTRY, VOL. 44, NO. 6, MAY 1972
EXPERIMENTAL
Resin Preparation. Dowex 50-Wion exchange resin was used in all measurements, with 200-400 mesh size and with cross-linkings of 2, 4, 8, and 12% DVB (Bio-Rad Laboratories, Richmond, Calif.). The resins were not of analytical grade so they were cleaned by a 3-cycle series of batch washes, each cycle consisting of treatment with NaOH, water, NaOHEDTA, water, HC1, and water. Each cycle was followed by thorough rinsing with triply distilled water. Routine arc emission spectrographic analysis on the cleaned sodium forms of the resin indicated the following metallic impurities to be below the following limits of detection: Fe (0.001 %); Ca (O.OOOl%); Cu (0.OOOl Mg (0.0001 %). The cleaned resins were placed in borosilicate glass tubes so that all subsequent operations could be carried out without handling or transferring the resin. The tubes were prepared by drawing IO-mm 0.d. borosilicate glass tubing to a blunt point at one end, leaving an opening of 1-2 mm. A glass wool mat pressed into the blunt end provided a base to prevent resin loss and to permit flow through the tube of solution of gas streams. The tubes were capped at both ends with rubber caps for storage. After cleaning and drying, the empty weights with caps were recorded. Resin samples ranging from 0.6 to 1.0 gram (dry weight) were added to the tubes. After filling, each tube was put through three more cleaning cycles, ending with the resin in the sodium form. The contents were then dried to constant weight with a stream of nitrogen flowing through the tube at 80 “C. The weight of dry resin in each tube was found as the difference between the filled and empty weights. Six tubes were prepared for each resin cross-linking. Of the six tubes for each cross-linking, three were used to measure the ion exchange capacity by a salt displacement and titration procedure (11). The contents of the three tubes were then reconverted to the sodium form for NMR measurement. For the capacity determination, the relative standard deviation was 0.8% (2 measurements per tube for 3 tubes having the same cross-linking). The capacities found for the sodium form of each cross-linking, when converted to capacities of the hydrogen form, agreed with the capacities listed on the resin reagent bottles. The tubes containing the resin samples formed ion exchange columns which permitted convenient change of counter ion form or of water content. Also, these same tubes could be placed directly into the NMR instrument for measurement of the relaxation times. T o prepare a tube with a desired low water content, room air was passed through the dry resin until the proper weight of water was gained, or water was removed with an air stream through the wet resin until the proper weight of water remained. After adjustment of the water weight, the contents of each tube were mixed carefully and permitted to stand with occasional mixing for 1-2 days before making relaxation rate measurements. For some tubes, relaxation rate measurements were made over a period of time (2 days), to ascertain that there was no change in relaxation rate, and that water equilibration had been achieved.
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(11) F. Helfferich, “Ion Exchange,” McGraw-Hill, New York, N.Y., 1962.
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Figure 1. Dependence of TI and T, for water protons upon water content in Dowex 50-W sodium form Instrumentation. Exploratory work with continuous wave NMR indicated that most of the line broadening observed for ion exchange resin samples was due to differences in the bulk diamagnetic susceptibility across the samples, and that such measurements would give unprecise estimates of relaxation times. Therefore, nuclear relaxation times were measured with a system consisting of a pulsed spectrometer (Nuclear Magnetic Resonance Specialties, Inc., New Kensington, Pa.) and a signal averaging system (Model 1072, Fabri-Tek Instruments, Inc., Madison, Wis.). Combined with a nineinch magnet and magnet power supply (Varian Associates, Palo Alto, Calif.), the spectrometer generated the pulse sequences used and detected the resulting signal from the sample. The signal was further amplified and passed to the signal averager, where it was digitized, averaged, and stored for readout to either an oscilloscope or an X-Y recorder. All measurements of amplitudes of free induction decay and spin echo signals were obtained from X-Y recorder data, and pulse times and separations were measured with an electronic counter (Model 5245L, Hewlett-Packard Co., Palo Alto, Calif.). Relaxation Time Measurement. The general treatment of NMR and spin-echo techniques is given in many works (12-14). Relaxation time measurements were made by pulse techniques at the normal equilibrium probe temperatures for the instrument (24-28 "C for 23Na and 19-23 "C for IH), and at one observation frequency of 15004 KHz. Signal averaging was done on almost all measurements, but was necessary only for the short sodium counter ion relaxation times. The longitudinal relaxation time (TI) was measured with the 180-90" pulse sequence, and the transverse relaxation time (T2)for times above 1 msec was measured by a CarrPurcell 90-180" pulse sequence (15). For TZ relaxation (12) A. Carrington and A. D. McLachlan, "Introduction to Magnetic Resonance," Harper and Row, New York, N.Y., 1967. (13) A. Abragam, "The Principles of Nuclear Magnetism," Oxford Claredon Press, 1961. (14) E. L. Hahn, Phys. Ret?.,80,580 (1950). (15) H. Y .Carr and E. M. Purcell, ibid.,94,630 (1954).
.
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Figure 2. Dependence of TI for sodium counter ions upon water content in Dowex 50-W
times from 0.1 to 20 msec, the width of a single free induction decay following a single 90" pulse was measured at the highest magnetic field homogeneity. The transverse relaxation time (TJ was calculated from the measured value (Tzm)after correction for the contribution from field inhomogeneity. The correction (Tzc)was found by measuring the decay signal from Z3Na in saturated NaCl solution and from IH in water. For 23Na,T2ewas 15.5 msec, and for 'H, Tzowas 21.6 msec. For single 90" pulse experiments, it was assumed that
For T2 values above 2 msec, where the field inhomogeneity correction is significant, the corrected values of TZ agree with those measured directly by the Carr-Purcell pulse sequence. Since the time required for recovery of the receiver from saturation was around 0.03 msec, the lowest measurable relaxation time was around 0.1 msec. All values for TI and T2were calculated by linear regression analysis (Stat 6 program, 300 Series Program Library, Wang Laboratories, Tewksbury, Mass.). The internal resin environment can be varied from dry (solid-like) to fully swollen (solution-like) simply by varying the water content, so water content was chosen as the experimentally controlled variable. T I and Tz for both 2aNa(counter ion) and 1H (in water) were measured for four crosslinkings of Dowex 50-W, and at water contents ranging from almost dry to fully swollen. The results are presented in Figures 1 to 4, which are plots of TI or T2 us. water content. Water contents are expressed in terms of mole ratio, r . r =
moles of H 2 0 moles of ion exchange sites
(2)
For comparison purposes, a more conventional scale of the concentration of ion exchange sites is also given in terms of molality, f i (11). of ion exchange sites _ _0.018 - = moles - _ m -(3) kilograms of H 2 0 r ANALYTICAL CHEMISTRY, VOL. 44, NO. 6, MAY 1972
983
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RESULTS AND DISCUSSION
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Figure 4. Dependence of Tl and T2 for sodium counter ions upon water content in 8 % cross-linked Dowex 50-W. (Data from Figures 2 and 3) A log scale of relaxation time is used because the data extend over 3 orders of magnitude. Weighing caused negligible errors in the calculated water contents of the resin samples. However, processing of the tubes to adjust the water content caused small losses, which in turn resulted in errors in the calculated water contents. These losses were estimated for a number of tubes by redetermining the dry weight of resin in each after several processings over 10 months of measurement, and comparing with the original dry weight. The average error in r was estimated as 0.04 over all samples measured, which is very small on the scales of Figures 1 to 4. Several sources contribute to errors in relaxation times. The standard deviation of the calculator program was around 3z relative. Twenty-four measurements of TI for the six samples in the 4 % cross-linked series at a water contents around r = 1 gave a relative standard deviation of about 7 %. 984
ANALYTICAL CHEMISTRY, VOL. 44, NO. 6 , MAY 1972
Proton Relaxation. For water protons in Figure I , TI and TZare each quite independent of cross-linking, except for small differences a t high water contents. Cross-linking affects the water proton relaxation rates only slightly, which would be expected if the waters are associated principally with the ion exchange site and its counter ion. Above r = 6, TI and TZfor water protons diverge and appear t o approach values independent of the water concentration, indicating a water-like environment for the water protons. The average TI of 0.5 sec from Figure 1 compares favorably with the value of 0.46 sec determined by Creekmore and Reilley (10). If the protons behaved as in water solution, Tl and Tz should be equal. To determine what process might be contributing t o shortening T, a t high water contents, TZ was measured as a function of T (the Carr-Purcell pulse separation time). A plot of 1/T2over the range 3-12 sec-l cs. 7 * yielded roughly a straight line, indicating a contribution to TZby diffusion of water inside the resin. This was for the 8 crosslinked resin with r = 11 water molecules per site. However, the correlation of this line was poor, and the 1/T2 intercept was not equal t o l/Tl, showing the presence of other contributions t o T2, such as exchange. Below r = 6 in Figure 1, the relaxation of protons corresponds t o water with restricted motion. The minimum in TI with the lack of a minimum in Tz indicates an increase in correlation time ( T ~ )of the motion of the proton environment as the water content is reduced. The mechanism of dipolar relaxation in water predicts such a minimum as r Cis increased, and predicts further that T2/Tlis 1 : 6 at the minimum (4). Experimentally, the minimum in Ti comes around r = 2, and the experimental value of TZ/Tlis around 1 : 5, in passable agreement with the theoretical. Confirmation of this behavior was not checked at other observation frequencies. 2aNa Relaxation. Figures 2 to 4 show relaxation times (TI and T,) for the 23Na nucleus present in the sodium form of the resin. The relaxation mechanism of the Na nucleus in water solution depends on the fact that Na has a quadrupole moment which can couple with fluctuating electric field gradients near the nucleus. This relaxation mechanism is more efficient than the magnetic dipole-dipole coupling which determines proton relaxation, and the observed Na relaxation times are shorter. Relaxation times below r = 2 were too short for accurate measurements. Above r = 6, both Tl and TZshow strong dependences upon cross-linking (Figures 2 and 3). The increase in Ti and T, with decreasing cross-linking agrees with the decrease in 23Na line widths reported by Creekmore and Reilley (8). Relaxation times for both 12 and 8 % cross-linked resins appear t o level off after the resin is fully swollen. Measurements above the fully swollen limits of the 4 and 2% cross-linked resins were not made. T, and TZappear t o remain separate and different over the measured range of water contents for the 8 % cross-linked resin [Figure 4), and this applies also to the other cross-linkings studied. T, was measured with changing Carr-Purcell pulse separation time ( T ) , but plots of 1/Tz cs. either T * or 1/7 were not linear. While there is a definite dependence of TZupon T for Z3Na counter ions, the dependence is not resolvable by simple graphical tests. Below r = 6, Tl and T2 decrease with water content, with little dependence on cross-linking. From the water proton relaxation times, the correlation time appears to increase with decreasing water content, but the strength of the counter ion-site interaction may also be increasing, causing a further
bonded network of water, attached ion, and counter ion. Water added to a resin containing large amounts of water goes primarily into a water-like environment and therefore does not change the correlation time or relaxation time significantly. This work shows that the relaxation properties of ion exchange resins can be studied easily by pulsed NMR techniques, and that the relaxation times give information on the molecular structure of the resins.
distortion of electric field gradients around the Z3Na nucleus and improving the quadrupolar coupling. From the data, it is not possible to decide whether change in the correlation time or in the quadrupole coupling constant is more important in the relaxation mechanism. CONCLUSIONS
Relaxation times for both water protons and 2aNacounter ions indicate that their environment is independent of crosslinking for water contents below 6 water molecules per ion exchange site. This environment has an increased correlation time, indicating a structure which becomes more rigid as the water content decreases. This model is in agreement with that proposed by Zundel (Z6), who postulates a hydrogen-
ACKNOWLEDGMENT
Thanks are extended to M. Schwartz for assistance with the spectrometer and signal averaging system. RECEIVED for review August 30, 1971. Accepted January 6, 1972. This work was supported in part by Grant AT(11-1)1082, from the Atomic Energy Commission.
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(16) G. Zundel, “Hydration and Intermolecular Interactions,” Academic Press, New York, N.Y., 1969.
Self-Balancing Bridge for Differential Capacitance Measurements Dale H. Chidester and Ronald R. Schroeder Department of Chemistry, Wayne State Unicersity, Detroit, Mich. A self-balancing capacitance bridge has been designed and constructed utilizing electromechanical servo control of a capacitance multiplier to achieve balance. Using a 60-Hz signal of less than 10 mV peak to peak, capacitances in the range of 0.25 to 2.0 mF can be measured with a precision of +l%. Differential capacitance measurements of mercury electrodes were made using aqueous solutions of several different electrolytes and were compared with data found in the literature. A study of the adsorption of camphor at a hanging mercury drop electrode was conducted to confirm the instrument’s ability to function in systems with strongly adsorbed species.
To DATE, BRIDGE TECHNIQUES for measuring differential capacitance of mercury electrodes have been tedious and slow. Most work has been based on the techniques developed by Grahame (Z-3). Accuracy in such measurements depends on measuring the time at which a null of a capacitance bridge is achieved. The goal of this work has been to develop an automated bridge which can obtain continuous capacitance data as a function of time. THEORY OF OPERATION
A major difficulty in automating a capacitance bridge has been the lack of variable capacitors in the microfarad range and the further lack of a simple method of varying capacitance over even one order of magnitude in the microfarad region. The availability of good quality operational amplifiers has now simplified this problem and made possible the construction of capacitance multipliers which can operate over a decade range with values in the one microfarad region. Balance of the bridge is maintained by adjustment of the capacitance multiplier with an electromechanical servo system. The signal to control the servo is obtained by compar(1) D. C. Grahame, J. Amer. Chem. SOC.,63, 1207 (1941). (2) Zbid., 68, 301 (1946). (3) Zbid., 71, 2975 (1949).
ing the phase of the cell and reference signals, E, and E,, with a demodulator circuit. Figure 1 provides an overall block diagram of the instrument. The Bridge. The heart of this instrument is a modified Wien bridge circuit, one arm of which contains an electrolysis cell and the other arm contains a capacitance multiplier circuit. The condition for bridge balance (Figure l a ) is that the reference signal, E,, equals the cell signal, E,, in both amplitude and phase. Since the C,, R,, and C, portion of the circuit is electrically identical to a resistor and capacitor in series, the series resistances add algebraically, the bridge circuit can be represented by the circuit Figure l b where
and (3
From this circuit
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In the actual circuit R1 = RBIR 3 = R 4 , and R, and Rd are typically less than 100 ohms so R ,
