Determination of Hydrogen in liquids and Suspensions by Nuclear Magnetic Absorption T.
M. SHAW1 and R.
H. ELSKEN
Western Utilization Research Branch, Agricultural Research Service,
An investigation was made of the applicability of the modulation method of magnetic resonance absorption for the determination of hydrogen in various liquids and in aqueous suspensions of starch. The materials investigated contained from (1.1 to 6.7) X loz2hydrogen atoms per cc. in the liquid phase. The thermal relaxation time, TI, ranged from 0.3 to 3.7 seconds. The influence of TI on the measurements through radiofrequency saturation was eliminated by an extrapolation to zero radio-frequency magnetic field of a series of measurements at radio-frequency intensities in the range 10-4 to gauss. The precision of the measurements was limited to about 20/, by electrical noise in the spectrometer employed. The application of the magnetic absorption method for the determination of the water content of biological tissues on an absolute basis is briefly discussed.
W
ITH the development of techniques suitable for liquids
and solids, the quantitative analytical aspects of magnetic resonance absorption spectroscopy have become of great interest. Cnfortunately, of the various methods for measurement of magnetic absorption, none appears uniquely adapted for routine analysis. One method, widely used for the observation of nuclear magnetic resonance absorption, utilizes small amplitude sinusoidal modulation ( I ) , with the detector followed by a narrow-band amplifier and lock-in amplifier. A small modulation of amplitude, H,, and angular frequency, w,, is applied to the static field, Ha, as the frequency of the radiofrequency magnetic field is slowly varied through the resonance region. For a simple absorption line the observed signal, D , proportional to the slope of the absorption line, passes through the extreme values D,,, and D,,,, corresponding to the inflection points of the absorption line. It is of interest in the analytical applications of magnetic absorption to consider the usefulness of the quantity D,,, as a measure of N o , the number per cubic centimeters of sample of magnetic nuclei of the species is of interest. In the present paper the application of D, considered for the determination of hydrogen nuclei in liquids and in mixtures (suspensions) of liquids and solids in which the hydrogen nuclei of interest are contained in the liquid phase. A primary object was to determine whether N Ocan be determined accurately via Dmay in SJ stems in which radio-frequency saturation is appreciable under the conditions of measurement, and the extent of saturation is both unknown and variable with No. I t -as not the object of the present work to determine the ultimate precision of the method, but rather to explore the general performance in an analytical procedure in order to determine whether fundamental limitations exist. THEORY
For a simple absorption line described by a shape function g(r), the signal D observed in the absence of radio-frequency saturation effects (3) may be expressed as
U. S. Department of Agriculture, Albany 7 0, Calif.
parameters, r is the filling factor of the radio-frequency coil containing the sample, Y O is the frequency a t the center of the absorption line, and x0 the magnetic susceptibility given by the expression
xo
= Noyzt?21(Z
1
Present address. Southwest Research Institute, San ilntonio, Tex.
(2)
Here y is the magnetogyric ratio, Z is the nuclear spin, and T is the absolute temperature. The maximum value of D may be expressed (3) From Equations 2 and 3 it is clear that if D., is to be used in analysis as a measure of KO, the other factors must either be constant or known. The only factors which require consideration here are g( Y ) and r; y o , C, and T are either known or can be held constant, within desired limits, by a suitable choice of instrumentation and operating conditions. In general, however, g ( u ) and r are subject to relatively wide variations depending upon the physical properties of the sample. In addition, g( Y), may be heavily influenced by the homogeneity of the static applied field. Thus the use of Dma, a8 a measure of N Ois unsatisfactory except under specialized conditions. For liquids or certain other materials with relatively long 2'and intrinsic line width of the absorption so small as to be negligible compared with the artificial broadening, 6H,imposed by inhomogeneities in the static field applied to the sample, g ( v ) , may be held approximately constant by simply fixing the position of the sample in the static field and holding H , constant. Similarly for liquids or other essentially homogeneous materials, i can be maintained constant by fixing the volume and position of the sample in the radio-frequency coil. Thus for liquids and other homogeneous materials it should be possible to utilize Dmax as a measure of KO. -4further complication vhich arises in any method of observing magnetic absorption is radio-frequency saturation. In the equations given above it was assumed that the applied radio-frequency magnetic field is so neak that the Boltzmann distribution of nuclei among the energy levels is not appreciably disturbed. Actually the radio-frequency effect may be considerable, especially for systems where T I is long, and theobserved susceptibility is reduced from its maximum value. For analytical applications the effect is troublesome because in general TI varies with NO. Moreover, for analytical work it is not considered feasible to determine Tl for each specimen and thus apply a correction to the observed value of D,,, to obtain a value (D,,,)o in the absence of saturation. Thus for analytical applications a method for obtaining (Dm& without a knorledge of T 1 R-ould appear essential. Saturation effects have been thoroughly examined by others ( 1 ) and utilizing their methods in the authors' experiments with water, ethyl ether, and a 0.002-V aqueous solution of copper sulfate, it was found that the saturation followed a (1 S)-1.6 * 0.1 dependence. Bloembergen, Purcell, and Pound have shown that when
+
l / y T L< H ,
Here C is a constant for an appropriate choice of instrument
+ 1)/3kT
< bH
and w,T1
>1
the saturation parameter, S,equals yH12T1/H,, where H1 is the amplitude of the effective radio-frequency magnetic field.
1983
ANALYTICAL CHEMISTRY
1984 The effect of saturation may then be included by use of the a p proximate equation ( 3 )
Table I.
Results for Organic Liquids !Dmax)o
(4)
Froni Equation 4 it appears that a possible method to allow for the effects of saturation is to plot DmaX against Hi2 for a few values of Hi2(near Hi2 = 0) and obtain by a linear extrapolation the limiting value (Dmax)o corresponding to D,,, for S = 0. The simplicity of this procedure suggests that it may be satisfactory for routine analytical use. EXPERIMENTAL
Proton magnetic resonance absorption was investigated for the folloning systems: a group of miscellaneous organic liquids, a series of solutions of dioxane in carbon tetrachloride, and a series of suspensions of starch in water. The materials were chosen to obtain a range of NOand T I . Solutions and suspensions were prepared in volumetric flasks from weighed quantities of materials. The starch used was R commercial wheat starch containing less than 0.1 % of water-soluble materials and 9.8yo of absorbed water. Measurements xere performed a t room temperature (about 27" C.), The magnetic absorption measurements were made in a static field of strength Ho, equal to 6380 gauss, provided by a permanent magnet with poles 6 inches in diameter and a 1.75-inch gap. The proton resonance was recorded by means of a radio-frequency spectrometer of the null-balance type ( 2 ) continuously standardized by a Watkins-Pound (6) calibrator. The radio-frequency coil 11as 22 mm. in inside diameter and 29 mm. in length and was designed t o accept standard borosilicate glass test tubes which serve as containers for the test specimens. For those experiments where it mas essential t o maintain the filling factor constant, a single test tube was used. The thermal relaxation time, T I ,of the various systems investigated was determined by the saturation method ( I ) . The line width of the proton resonance was observed to be 1.7 =t0.1 kc. in all samples for a modulation amplitude, H,,, of 0.23 gauss (0.98 kc.), and urn= 2~ X 50 see.-' For each sample D,,, was determined for several values of HI gauss. Graphs of D,, vs. H12 were in the range ( 2 t o 6 ) X extrapolated linearly to HI2 = 0 to obtain (Dm&. At the lowest value of HI for which observations were made, the signal D,,, for water was approximately 100 times the noise level. At higher levels of H,, the noise decreased markedly. The effect of the noise is, of course, to decrease the precision with which D,,, can be determined. This factor appears to be the principal limitation to the precision of the remlts obtained here since the procedure used requires the use of very low radio-frequency levels in order to be able to utilize a linear extrapolation as a means of correcting for saturation effects. It has not been determined to what extent improvement is possible through the use of longer time for observations and through improvements in spectrometer design.
Table 11. Water Sample Content, KO. Wt. % 1 92.0 2 75.9 3 86.0 4 81.3 5 76.9 6 68.6 7 63.4 8 87.1
a
Ti, Sec. 2.5"
..
(Dpsx)a,
Arbitrary Units 86.56 88.5 90.0 150.0 166.5 182.0 210.0 37.5 74. .5 104,s
Results for Starch Suspensions
Density, Grams Cc. 1.029 1.096 1.050 1.072 1.095 1.135 1.157 1.045
hTo X 10-22 Cc.-i 6.33 5.55 6.04 5.81 5.63 5.20 4.90 6,Oi
TI, Sec. 0.52' 0.28 0.44 0.35 0.29 0.22 0.20
(Dmax)D,
IDmax)o x KO
Subject t o estimated error of 4 ~ 1 0 % .
b Read only t o nearest half unit.
The relaxation time, TI, was not determined for all samples. As shown in Table I, the values found for T I range from 1.1 to 3.7 seconds. Over this range the quantity ( D,,x)o/So appears to be independent of TI and demonstrates that the extrapolation procedure used to obtain (Dmax)o is satisfactory and that the intrinsic line width of the materials investigated is indeed negligible compared with the artificial width as set by magnet inhomogeneities. Figure 1 shows the values of D,,,/No for H , = 5.6 X lo-'
The results obtained for the organic liquids are summarized in Table I, which contains the values of (Dmx)0 obtained by extrapolation and values of NOfor each sample as calculated from the theoretical composition and the density according to the relation
(5)
Here nm is the number of hydrogen atoms per molecule, A ia Avogadro's number, p is the density of the liquid a t the temperatule of the observations, and M is the gram-molecular weight. To obtain Wo for the dioxane-carbon tetrachloride solutions, N o for dioxane was multiplied by the appropriate dilution factor. According to Equations 2 and 4 the values of (Dmax)o should be proportional to the values of NO. The data are in arrangement as s!iomn by the fact that the ratio (Dmax)0/Aro is approximately constant. The mean value of the ratio is 31.9 X with a standard deviation of 0.8 X 1 0 - 2 2 . The indicated error appears consistent with the observed signal-to-noise ratio, so that it may be concluded that deviations observed in the ratio (Dmex)o/No are primarily due to this source.
1022,
Arbitrary Arbitrary Units rnits 206.5b 32.6 167.0 30.1 195.0 32.3 186.5 32.1 182.0 32.3 166,s 32.0 155.0 31.6 0.46 192.0 31 6 Mean 31.8 Standard deviation 1 0 . 8
RESULTS AND DISCUSSION
N o = n,Ap/M
1022
No Arbitrary Sample Units Iodobenzene 32.0 Ethylene bromide 31.7 2.5 32.4 Ethylene chloride 1.1 31.5 E t h y l malonate n-Amyl bromide .. 30.7 E t h y l ether 3.7 31 5 Water 2.1 31.3 Dioxane, 2093, in CClr 33.3 2:h 33.0 Dioxane, 40%, in CCld 30.9 Dioxane, 60%. in CCL 145.0 32.1 Dioxane, 8070, in CClr Dioxane, 100% 2.0 184.5 32.7 Mean 31.9 Standard deviation i.O.8 a Subject to estimated error of & l o % . b Read only t o neareat half unit. No X lo-**, c c . -1 2.70 2.79 3.05 4.76 5.52 5.77 6.70 1.13 2,26 3.38 4.52 5.63
1
0 Y
I
0
2
I TI
3
4
(SECONDS1
Figure 1. Relationship between experimentally observed values of D,,,/No for HI = 5.6 X IO-' gauss and TI
V O L U M E 2 7 , NO. 1 2 , D E C E M B E R 1 9 5 5
Figure 2. Comparison of water content calculated from magnetic absorption measurements with known water content of starch suspensions
gauss plotted as a function of 7'1. The dependence on TI as calculated from Equations 2 and 4 is adjusted for best fit with the experimental points. The data are in general agreement with the approximate dependence on TI as expressed by Equation 4. The limiting value of Dmax/No for 7'1 = 0 as obtained from Figure 1 is not significantly different from the mean value of (D,,,)o/No given in Table I. Table I1 summarizes the data obtained for the aqueous starch suspensions. The water content of the suspensio?s ranged from 63 to 92%. As noted below, this range is of interest because i t corresponds to the water content of some vegetable tissues and other biological materials. The table shows values of ( determined for each suspension by the extrapolation procedure discussed above. The values of -1-0 were calculated on the assumption that the hydrogen nuclei in the starch do not contribute significantly to the observed signal. This assumption is based on the fact, established earlier (4),that the magnetic resonance line for the hydrogen nuclei in starch is broad compared with the width of the line observed here for hydrogen nuclei in liquids. The correctness of this assumption is shown by the fact that the ratio (D,)o/No shows no systematic dependence on the moisture content. The average value of (D,,,)olNo of 31.8 =k 0.8 x 10-z2 found for the starch suspensions agrees with found for the organic liquids. the mean value 31.9 3t 0.8 X The values of TI found for the starch suspensions are somewhat smaller than those for the organic liquids. As shown in Figure 1, are consistent the observed values of D,,, for H1 = 5.6 X with the shorter Tl. .hide from contributions from hydrogen nuclei in the starch, there are two other possible contributions to the magnitude of (D,,,), that should be considered. The first factor, the hydrogen nuclei in any water-soluble portion of the starch, can be dismissed because of the small (----,-
(5) Watkins, G. D., thesis, Harvard University, 1952. RECEIVED for review December 3, 1964.
Accepted April 9, 1955.
