fererice was found here when the perchlorate titration was carried out in the pressure of 0.05M chlorate. Since no precipit,ate is formed when equal volumes of 0.1M tetraphenylstibonium and 0.1M chlorate are mixed, the solubility of the chlorate is a t least 0.05M, greater than that of tetraphenylstibonium chloride. The titration should be unaffected by concentrations of chlorate 0.551 or higher. I n a study of t’he polarographic reduction of tetraphenylstibonium ion (8) it was found that in a Clark and Lubs phosphate buffer of pH 6.5 (total phosphate = 0.0551), a tetraphenylstibonium phosphate of undetermined composition precipitates when the tetraphenylstibonium ion concentration exceeds 0.0053M. Thus phosphate concentrations not too much higher than 0.05 to 0.1M can be tolerat’ed in this titration. Tetraphenylstibonium hydroxide has (7). a solubility product of 1.2 X This is comparable to the value of 3.5 x 10-8 reported for tetraphenylstibonium perchlorate. Thus, titrations must be carried out, in acidic or neutral solutions. There is no objection to working in unbuffered dilute acid or neutral solution, since the first step of tet,raphenylstibonium reduction does not involve hydrogen ion. If a buffer is employed, it must be chosen with care, since the tetraphenylstibonium salts of
most carboxylic acids are sparingly soluble in water ( 2 ) . No systematic tests were made for cationic interferences. However, two classes of cations are expected to interfere: those cations which give polarographic diffusion currents at the titration potential and those which form anionic complexes in the supporting electrolyte. Shinagawa, Matsuo, and Okashita (10) have shown that anionic complexes of heavy metals, including those of mercury, bismuth, and cadmium, precipitate tetraphenylstibonium. The titrations show a definite negative bias. The reason for this systematic error probably lies in the method of standardization of the tetraphenylstibonium sulfate titrant solutions. Because the perchlorate has a relatively high solubility product, it is difficult to avoid weighing losses. Our standardization procedure involved the precipitation of aliquots of titrant and collection of approximately 100-mg. quantities of tetraphenylstibonium perchlorate. At this level, small washing losses can contribute appreciably to a negative error in the apparent concentration of a tetraphenylstibonium solution. Affsprung and May (2) standardized tetraphenylstibonium sulfate by back titrating the excess acid used to dissolve the hydroxide. They report purity by neutralization of 98% after repeated recrystallizations of the hydroxide. Im-
purities may remain after these recrystallizations. Until further work is done on standardization procedures for tetraphenylstibonium salts, standardization by a method which approximates the titration conditions is the safest course. LITERATURE CITED
( 1 ) Affsprung, H. E., Archer, V. S., ANAL. CHEM.35, 976 (1963). (2) AffsDrunz.. H. E.. Mav. H. E.. Ibid.. 32, 11-64 (T660). ( 3 ) Armstrong, G. W., Gill, H. H., Rolf, I
” I
K. F., “Treatise on Analytical Chemistry,” I. M. Kolthoff and P. J. Elving, eds., Part 11, Vol. 7, Interscience, Kew York, 1961. (4) Fritz, J. S., Abbink, J. E., Campbell, P. A., ANAL.CHEM.36, 2123 (1964). (5) Kerry, H. A., “Perchlorates, The$ Pro erties, Manufacture and Uses, J. Schumacher, ed., Reinhold, New York, 1960. ( 6 ) Lineane. J. J.. I N D .ENG. CHEM.. ANA; ED: 16, 329 (1944). ( 7 ) Moffett, K. D., Simmler, J. A., Potrate, H. A., ANAL.CHEM.28, 1356
8.
~
(1956). (8) Morris, M. D., McKinney, P. S., Woodbury, E. C., J . Electroanal. Chem., in nrms r-
(gj‘Nezu, H., Bunsaki Kagaku 10, 561 (1961); C . A . 56. 26f (1962). (10) Shinagawa, M., -Matsuo, H., Okashita, H., Ibid., 7 , 219 (1958); C . A . 54, 3025e (1960). (11) Willard, H. H., Perkins, L. R., ANAL.CHEM.25, 1634 (1953). RECEIVEDfor review March 5, 1965. Accepted May 11, 1965. Division of Analytical Chemistry, 149th Meeting, ACS, Detroit, Mich., April 1965.
Measurement of Proton Relaxation Times with a High Resolution Nuclear Magnetic Resonance Spectrometer Progressive Saturation Method ANTHONY
L.
VAN GEET’ and DAVID N. HUME
Department o f Chemistry and laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Mass. Details are given of experimental techniques whereby proton relaxation times may be measured with a high resolution nuclear magnetic resonance spectrometer. The transverse relaxation time, TL is determined by linewidth measurements, and m 2 by progressive saturation. The effect of an inhomogeneous RF field on progressive saturation measurements i s considered; the results are not affected. The spectrometer used operates by the side-band modulation method; the steady-state response is not affected by the modulation. Progressive saturation is performed on the peak height as well as the integral-e.g, the area under the peak-and in homogeneous as well
as inhomogeneous magnetic fields. These methods give the same relaxation times for aqueous solutions of copper sulfate.
I
past few years, high resolution nuclear magnetic resonance (NMR) spectrometers have become widely available. As a result, proton N M R spect r a based on chemical shifts are now extensively used in the determination of structure and in qualitative and quantitative analysis of mixtures of organic compounds. By comparison, very little attention has been given to possible applications of relaxation time measurements in organic chemistry ( 9 ) ,although this technique has proved exceedingly N THE
valuable in the study of paramagnetic transition metal ion complexes, and in the measurement of proton exchange between ligands and solvent, for example (3). I n organic N M R spectra, each peak will usually have a different relaxation time. The relaxation of a given proton is affected by the molecular motion of the neighboring protons. This motion causes a rapidly fluctuating magnetic field, and interaction with this field produces relaxation. The contribution to the relaxation is proportional to the inverse sixth power of the distance, so Present address, Department of Chemistry, State University of New York at Buffalo, Buffalo, N . Y. VOL. 37, NO. 8, JULY 1965
979
only the nearest neighbors need to be considered. Some of these nearest neighbors belong to the same molecule; others belong to other molecules. The first give rise to intramolecular, and the others to intermolecular relaxation. Intramolecular relaxation is caused by rotation of the molecule or a group of the molecule, while intermolecular relaxation is usually dominated by the translational diffusion of the molecules with respect to each other. The effects of intra- and intermolecular relaxation are additive. By extrapolating the relaxation time to infinite dilution, one obtains the intramolecular relaxation time. While intra- and intermolecular relaxation are often dominated by the dipolar coupling described above, other relaxation mechanisms are important in some cases. One of these mechanisms is anisotropic shielding. I n this case the screening constant depends on the orientation of the molecule with respect to the magnetic field. Rotation of the molecule causes a fluctuation of the field a t the nucleus, contributing to relaxation. Relaxation by anisotropic shielding depends on the strength of the magnetic field. Scalar coupling of the protons via the bonding electrons gives rise to spin-spin splitting, but does not contribute significantly to the relaxation. However, if paramagnetic species are present, scalar coupling between the unpaired electron and a proton may be important. This interaction causes hyperfine splitting in electron spin resonance spectra. Study of relaxation times should provide information about the degree of association in liquids and their solutions, and also about proton exchange in these solutions. The addition of paramagnetic substances such as copper and nickel salts to solutions of organic compounds increases the chemical shifts and affects the proton relaxation times. Relaxation studies can, therefore, be used to obtain information about chemical interactions and complex formation. Two relaxation times, the spin-lattice, or longitudinal, T1,and the spin-spin, or transverse, T 2 ,are distinguishable. The former is proportional to the half time required for a perturbed system of nuclei to reach a condition of thermal equilibrium. The latter corresponds to the half time of the kinetically firstorder decay of X - Y magnetization of a group of nuclei precessing in phase about the 2 axis of a common magnetic field. Although the physical theory of the relaxation processes is complicated, the experimental determination of the relaxation times is relatively straightforward. If proton exchange occurs, one may find that the longitudinal relaxation of the magnetic moment can no longer be
980
ANALYTICAL CHEMISTRY
described by a single relaxation time, Tl. If the exchange occurs between two sites, the relaxation is described by the sum of two exponential terms. Often, one of these exponentials dominates strongly, and then a single exponential adequately describes the relaxation (7'). This paper shows that proton relaxation times, both longitudinal and transverse, may readily be determined with the widely used Varian A-60 NMR spectrometer, either without modification or with a very slight modification which does not affect the usefulness of the instrument in its regular applications. In comparison with more versatile and costly instruments such as the Varian HR-60, the A-60 has the advantage of simplicity and speed of operation while giving comparable reproducibility and accuracy. THEORY
OF SIDE-BAND MODULATION METHOD
I n a high resolution spectrometer, the sample is subjected to a modulating field of audio-frequency in addition to the R F field. The signal is extracted by a phase-sensitive detector of audio-frequency. This detector is more stable and easier to construct than the troublesome R F phase-sensitive detector. In the A-60, the NMR signal is induced in the same coil that is used to subject the sample to the radio-frequency field, H1, of frequency, v = 60 megacycles. The modulating current sweeps the main magnetic field, H o (14,100 gauss) , through the resonance 5000 times a second ( u , = 5000) with an amplitude H , =0.12 gauss. The effect of the modulation is that in addition to the usual resonance a t Ho = w / y , resonances are also found (2) at
Ho
= (U f w,)/Y
=
~ T ( Vf
n~,)/y
Of these resonances, only the first upper side band is detected in the A-60:
HO =
(W
+ wm)/r
(1)
or AW -
urn=
0
with AU = THO-
LO
(2)
The resonances a t n = 0 and n = 2 fall outside the spectrum range of the A-60, where they cannot interfere. The NMR signal from the sample is amplified and diode-detected in the sample receiver. Primas has solved the Bloch equations for the present case (11). Assuming slow passage-that is, y dHo/dt 5 seconds), the line width is determined by the inhomogeneity. Equation 10 may be corrected for the inhomogeneity line width U R / ~ : Width.
Tz
= l/H(U,,Z
-
URiZ)
(16)
The instrument used was a Varian A-60 (Varian Associates, Palo Alto, Calif.). Its inhomogeneity line width, U R / Z (also called the resolution), was usually about 0.6 c.p.s. Accordingly, relaxation times longer than 500 milliseconds could not be determined accurately by this method. If T z becomes smaller than 1 millisecond, deviations are to be expected because the condition 1/Tz I., Pound, R. V.)Phys. Rec. 73, 679(1948). (5) Carr, H. Y., Purcell, E . AI,, Ibzd., 94, 630 (1954). (6) Ernst, R., Tarian Associates. Palo Alto, Calif.; private communication. 1964. ( 7 ) Luz, Z., Rleiboom, S., J . Chem. Phys. 40, 2686 (1964). (8) Meiboom, S., Gill, D., Reo. Sei. Instr. 29, 688 (1958). (9) Xederbragt, G. W., Reilly, C. A., J . Chem. Phys. 24, 1110 (1956). (10) Pople, J. A,, Schneider, W. G., Bernstein, H. J., “High Re;olution Nuclear hlagnetic Resonance, p. 82, McGraw-Hill, New York, 1959. (11) Primas, H., Helv. Phys. 9cla 31, 17 (1958). (12) Van Geet, A. L., Hume, U. N., Inorg. Chem. 3 , 523 (1964). (13) Williams, R. B., Ann. S. I’. Acad. Scz. 70, 890 (1958).
RECEIVED for review August 4, 1964. Resubmitted February 23, 1965. Accepted May 5, 1965. Work supported in part by the Cnited States Atomic Energy Commission under Contract A T (30-1)-905.
Measurement of Proton Relaxation Times with a High Reso Iutio n Nuclea r M a gnetic Resona nce Spectrometer Direct Method ANTHONY L. V A N GEET Department of Chemistry, State University o f New York at Buffalo; Buffa/o; N. Y. DAVID N. HUME Department of Chemistry and laboratory for Nuclear Science; Massachusetts Institute o f Technology, Cambridge, Mass.
Details are given of an experimental technique whereby the proton relaxation time, TI, may b e measured with a high resolution nuclear magnetic resonance spectrometer, using the direct method. The method is best suited for relaxation times between 50 milliseconds and 25 seconds. A theoretical study of the method i s made. The Bloch equations are solved under the simplifying assumption of negligible saturation (YHI TI-^). The result shows that a simple exponential signal recovery of time constant T I occurs only if the magnetic field i s sufficiently inhomogeneous Tn-’).
P
ROTOP:
nuclear magnetic resonance
(KMR) spectra are widely used in
structure determination and in qualitative and quantitative analysis of organic compounds. By comparison, much less attention has been given to relaxation time measurements (13) with this instrument. The transverse relaxation time, TB,follows from the line width, of course, but relaxation times longer than about 1 second cannot be determined accurately in this way because of limited resolution. This paper shows the longitudinal relaxation time, TI, may readily be determined by the direct method (If).
I n spite of its simplicity, the direct method has not found wide application (3, 6). I n its simplest form, the sample is introduced into the magnetic field and one observes the signal growing in. I t is not necessary to introduce the sample physically into the magnetic field. Instead, the sample may be saturated by the application of a sufficiently strong R F field, HI,so y HI >> ( T I T z ) - ” * . When the amplitude of the RF field is suddenly reduced to a nonsaturating value, the ISAIR signal (v-mode) recovers exponentially with a time constant which is essentialll- T1. VOL. 37, NO. 8, JULY 1965
983
