A Study of the Static Nuclear Magnetic Resonance Method for Determining Diamagnetic Susceptibilities and a General Method for Its Use John L. Deutsch,l Andrew C. Lawson, and Stephen M. Poling Department of Chemistry, Pomona College, Claremont, Calif. 91 713
THEEXPERIMENTAL METHODS for measuring volume susceptibilities of diamagnetic liquids and solutions using NMR have already been described (1-6) and a complete theoretical analysis has been given (7). The necessity for using volume susceptibilities when correcting chemical shifts obtained using an external reference has been described (7-10). The static NMR method has a number of attractive features: it has a precision of about 1% (3) and an accuracy not equal to classical methods or the spinning NMR method (2, 4 , 3,but sufficiently good for making external reference susceptibility corrections; it is reasonably rapid; it requires small samples (0.1-0.2 ml); it utilizes a commercially available NMR concentric tube; and it gives simple and easily interpreted spectra. Previous uses of the concentric tube technique, spinning and static, have limited the compounds measured to those which have no NMR spectrum or a very simple one. It is the purpose of this discussion to describe how diamagnetic volume susceptibilities of any liquid or solution (no matter how complex its NMR spectrum) may be measured by the static NMR technique. The static NMR technique has been described by several authors (1, 3, 9, 10). One sample is placed in the annular section of a coaxial NMR cell consisting of a cylindrical sample tube held rigidly within a standard NMR tube by a set of precision mechanical spacers. Another sample is placed in the central sample tube. When the tube is not spinning the annular sample experiences a nonuniform magnetic field and as a result the resonance signal of the annular sample is split into two peaks. The splitting, 6 v in sec-l, is given by the following expression (10)
where v a is the frequency of the r.f. field; XI, XZ, and x 3 are, respectively, the volume susceptibilities of the central sample, (1) C. A. Reilly, H. H. McConnell, and R. G. Meisenheimer, Phys. Rec., 98, 264(A), (1955). (2) K. Frei and H. J. Bernstein, J . Chem. Phys., 37, 1891 (1962). (3) D. C. Douglass and A. Fratiello, Ibid., 39, 3161 (1963). (4) L. N. Mulay and M. Haverbusch, Reu. Sci. Znstr., 35, 756 (1964). (5) L. N. Mulay and I. L. Mulay, ANAL.CHEM., 38, 501 R (1966). (6) L. N. Mulay, “Magnetic Susceptibility,” Interscience, New York, 1963, p 1801. (7) J. R. Zimmerman and M. R. Foster, J . Plrys. Chem., 61, 282 (1957). (8) A. A. Bothner-By and R. E. Glick, J . Chem. Phys., 26, 1647 (1957). (9) M. G. Marin, G. Paulett, and M. E. Hobbs, J . Phys. Chem., 60, 1594 (1956). (10) A. Fratiello and D. C. Douglass, J. Chem. Phys., 39, 2017 (1963).
210 -
”y,o/o’,
,
,
,
,
0.8
0.9
1.0
1.1
40
30 0.3
0.4
0.5
0.6
0.7
1
x’, Figure 1. Graphs of Equation 3 for reference compounds TMS and CH3COOH
the glass, and the annular sample; a, b, and rare, respectively, the inner radius of the central tube, the outer radius of the central tube, and the mean radius of the annular region. This expression can be simplified to 6~ = Axl’
+ Bx3’ + C
(2)
where x’ = -lo6 x, and A , B, and C are constants characteristic of the sample cell and which vary slightly with orientation of the tube in the probe, or with field homogeneity. It is possible to make measurements either by placing the fixed reference in the annular region and the sample of unknown susceptibility in the central tube or vice versa. The former method is the more useful, because unknown susceptibility samples with no proton resonance spectrum or a very complicated one can be used. (With the cells used by these authors, it is easier to change samples with a given reference if the unknown sample is in the central tube). Thus to make this method as general as possible, the fixed sample or reference sample is placed in the annular region of Present address, Department of Chemistry, State University College, Geneseo, N. Y. 14454 VOL 40, NO. 4, APRIL 1968
839
Sample tube
Table I. Summary of Results Central sample Benzene and bromoform
518
Annular sample Calibration compounds’
518
TMS
Calibration compounds
519
CFICOOH
Calibration compounds
519
CF3COOH
Calibration compounds Calibration compounds Calibration compounds
Equation and correlation coefficient 196.58 xi’ - 361.26 ~ r = 0.9967 6~ 192.44 x i ’ - 21.49 r = 0.9998 6~ = 101.84 XI’ - 4.133 r = 0.9999 6~ = 101.49 X I ’- 3.72, r = 0.9998 6~ = 101.07xl’ - 5.637 r = 1.oooO 6~ = 99.55 X I ’ 0.974 r = 0.9999 6~
=
+ 176.49
3 ’
+
This is an example of compounds of different x o being placed in the annulus and a fixed sample placed in the central tube. For this equation the data for C6H6and CHBr3 in the central tube were combined. 0
the cell. Then, because x3’ is a constant and not necessarily known, Equation 2 reduces to
6~
=
Axl’
+ C’
(3)
where C’ is a new constant. In order to determine x u for a compound or a solution, the values of A and C’ must be evaluated from tube geometry or found experimentally. Because x 3 or x 3 ’ is not always known and because geometry is not always perfect, A and C’ are best determined experimentally by measuring 6 v for a series of compounds of various known x 0 . The volume susceptibility of any sample can then be found directly from a measurement of 6v, using a calibrated coaxial cell. There are three requirements which should be met by the reference sample. (1) The NMR spectrum of the reference sample must be a single peak or it must have an isolated single peak, the sharper the reference peak the easier the measurements and the greater the accuracy and precision. (2) The position of the single reference peak should be outside the normal NMR spectral region. (3) Although the volume susceptibility of the reference sample need not be known, it should be chosen such that for 0.2 < xO’ < 1.5 6 v is never zero. When the first two requirements are met, the third can be satisfied experimentally if necessary. The actual dimensions of the coaxial cell should be chosen so as to give a strong reference signal and the largest possible value of the constant A in Equation 3. As the volume of the annulus increases, the strength of the reference absorption peak increases, and the magnitude of A (the slope of the straight line represented by Equation 3) decreases. Thus the coaxial cell is chosen for a given reference compound so that an easily measurable reference doublet with large splitting is obtained with a minimum volume for the annular region, thus maximizing A . One feature of the static NMR method which disturbs the uninitiated worker is the asymmetry of the line shape of the reference doublet. This can be corrected by adjustment of the field homogeneity controls (see ref. 3). As not only the line shape but the splitting, 6v, is affected by the homogeneity it is most important that great care be given to this parameter. The homogeneity is adjusted so that the sharpest, most symmetric doublet is obtained. Rotation of the tube from one fixed position to another should have little or no effect. If the doublet line shape is symmetric for one fixed position and the symmetry deteriorates when the tube is rotated (this is 840
ANALYTICAL CHEMISTRY
usually caused by slight asymmetry in the tube geometry) the tube can be marked so that whenever it is used it is placed in the probe with exactly the same alignment of its inner and outer sections to the field direction. To make a volume susceptibility measurement using a calibrated tube, the tube is placed in the probe, taking care, if necessary, to align it with respect to the field. The splitting of a standard sample of known xu is adjusted using homogeneity controls until 6 v and the line shape are identical with that obtained for the standard sample during calibration measurements. The unknown sample is then exchanged for the standard sample and the splitting measured. The volume susceptibility, xu, is calculated using Equation 3. The authors used Wilmad tubes No. 518 and No. 519 (Wilmad Glass Co., Buena, N. J., Bulletin 5006). Some common compounds which were found to meet the first two requirements of a reference compound were H3PO4, CH3COOH, CFICOOH, and TMS. The latter three were the only ones which satisfied the third requirement. The followwere found ing compounds and their respective - x u X convenient for calibrating tubes with CF3COOH,CH3COOH, and TMS as the reference: nitromethane (0.391), methanol (0.530), n-pentane (0.5472), toluene (0.6179), carbon tetrachloride (0.691), chloroform (0.740), iodobenzene (0.826), bromoform (0.948), and di-iodomethane (1.156). TMS worked well as a reference in tube No. 518; however, both acetic acids required the larger annular volume of tube NO. 519 to give absorption peaks of sufficient strength. Data on all reference samples were fitted to Equation 3 by regression analysis using an IBM 360/30 computer. Typical results and correlation coefficients, r , are given in Table I. Figure 1 shows graphs of Equation 3 for the reference compounds TMS and CH3COOH; the circles are experimental points for the calibrating compounds. ACKNOWLEDGMENT The authors thank Edna W. Deutsch for carrying out the regression analyses, and Anthony Van Geet for critically reading the manuscript. RECEIVED for review July 28,1967. Accepted January 2,1968. Two of the authors, A. C. Lawson and S. M. Poling, acknowledge the support of the National Science Foundation from which they received NSF-URP grants.
