Anal. Chem. 1980, 52, 567-569
567
CORRESPONDENCE Correction to Static Tube Nuclear Magnetic Resonance Method for Determination of Magnetic Susceptibilities of Solutes in Solution THEORY A theoretical treatment of the magnetic shielding variation in a coaxial XMR tube has been given by Zimmerman and Foster (8) and the following discussion is based on these authors' approach. A cross-sectional view of the coaxial system is shown in Figure 1. The regions numbered 1 t o 5 refer, respectively, to the paramagnetic solution, the glass (of the inner tube), the reference material, the glass (of the outer tube), and the air. Zimmerman and Foster (8) have shown that in region 3, the annulus containing the reference compound, the magnetic field strength H 3 a t any point is a function of both the distance r from the origin and the angle 0 which the vector joining that point to the origin makes with the direction of the applied magnetic field strength Ho, and is given by
Sir: Magnetic susceptibilities of substances iri solution have been measured successfully for several years by the technique proposed by Evans ( I ) . T h e method involves placing t h e solution of a paramagnetic material and a reference compound in the outer cavity of a concentric NMR tube while the pure solvent and reference compound are in the inner cavity. The magnetic susceptibility of the paramagnetic material is then calculated from the measured difference in chemical shift of the reference material in the two cavities. While the method is sensitive and quite reliable for many paramagnetic solutes, it does suffer from a number of theoretical and technical disadvantages. One particular disadvantage is the line broadening experienced by the reference material in the inner cavity which limits t h e accuracy of chemical shift measurement. Another serious limitation of the method is t h a t it is not strictly valid for paramagnetic species which can induce contact or dipolar shifts in the reference nuclei. Such shifts commonly occur whenever there is appreciable association between the paramagnetic solute and the diamagnetic reference compound. Additionally, the spinning of concentric cavity tubes, which is essential for accurate measurements of chemical shift differences, can often produce quite strong modulation side-bands unless the very highest precision tubes are used. Such side-bands can often interfere with the bands being measured. Most of these problems appear to be circumvented with the static sample method described by Engel, Halpern, and Bienenfeld ( 2 ) . Their method uses a concentric NMR tube similar t o t h a t of the Evans method but in this case the solution of t h e paramagnetic material is placed in the inner cavity and the chosen pure reference material contained in the outer cavity. When the tube is stationary in the NMR probe, the reference material in the outer cavity experiences a n inhomogeneous magnetic field and its signal is split into a doublet. In 1955 Reilly, McConnell, and Meisenheimer ( 3 ) proposed t h a t this splitting. Au, is given by
H d H o = 1- YAP3 - PJ [ a , ' ( ~ ,-
~
CLJ + a 2 * ( y l-j ~ ~ ) l ( c 2oQs / 2 r 2 ) (2)
Now the relative permeability, p is defined as
1+ 4ffx
p =
where
x is magnetic susceptibility.
H J H o = 1 - 274x3
-
47r[aI2(x2-
XJ
Equation 2 then becomes
-
xl) + a 2 2 ( ~-: 1xJ](cos
2 0 / 2 r 2 ) (4)
which can be written more simply .as
H3/Ho= A
+ ( B cos 2 0 ) / r 2
(5)
where A = 1 - 27r(x3- x5)and B = - - 2 i r [ ~ ~-' xl) ( ~ ~+ a 2 2 ( ~ 3 - X2)l.
Considering the first quadrant (0" I 0I 90O) of Figure 1, the maximum and minimum value of H 3 will occur when r = a , and A = 0" and 90",respectively; i.e.
H3 (max)/Ho = A H 3 (min)/Ho = A
where uo is the operating frequency of the NMR spectrometer, the magnetic susceptibilities xl,x2, and x 3 refer to the unknown, t h e glass, and the diamagnetic reference material respectively, and a , b, and r are geometric shape factors of t h e concentric tube. Parameter a is t h e inner radius of the inner cavity, b is the outer radius of the inner tube. and r is t h e mean radius of the annulus. We wish to show that this expression, which is reproduced in a number of standard NMR textbooks (4-7) is incorrect. Over the past 20 years or so, this equation has been widely used as the basis for measuring diamagnetic susceptibilities. However, for such measurements only the fact that the line splitting Au is proportional to xl, the magnetic susceptibility of t h e unknown, is required. No exact knowledge of the geometric factors is necessary. However, for paramagnetic susceptibilities, the correct geometric factors of the coaxial tube system are required and we wish to show that Equation 1 is incorrect in this respect. 0003-2700/80/0352-0567S01 0010
(3)
+ B/ag2
(6)
B/az2
(7)
.-
Nuclei experiencing these magnetic field strengths will contribute to the highest and lowest field wings of the doublet absorption signal. When 0 = 45O, cos 28 = 0 and H : , ( 4 5 ' ) / H 0 = A ; in other words, all molecules lying on the 45' vector experience the same magnetic field strength; Le., H 3 is independent of r. For all other vectors H 3 will vary with the distance r. T h e two absorption maxima in the measured doublet signal will c w respond to values of H , which are experienced by the maximum numbers of nuclei in the reference material. These maximum numbers will correspond to the magnetic field contour lines of maximum length in the annulus. T h e field strength contour map has been calculated for the concentric tubes used in these experiments and is shown in Figure 2. Numerical details for the contour lines shown in Figure 2 are given in Table I. Commencing from the 45" line (line 1 , Figure 2 ) , it will be seen t h a t the contour lines (each representing constant H , C
1980 American Chemical Society
568
ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980 Y
Y
4
A
t ,
4
4
+X
-
Figure 1. Coaxial NMR tube system showing the regions 1-5 (see text)
It is preferable t o change Equation 8 in two important respects, (i) to take account of the fact that observable magnetic properties depend on t h e magnetic flux density B rather than H (where B = p H ) and (ii) t o convert t h e equation from its unrationalized CGS form above to SI form using t h e relationship p = 1 + x. T h e resulting Equation 9 is A& (abt. max)/B, , - =
Table I. Magnetic Field Strength Distribution i n t h e Annulus of a Coaxial NMR Tubea line/ H IH, pointa (= A + B cos 2 0 / r 2 ) 1 2 3 4
A
A + 10.12B A + 22.59B A + 41.11 B A + 96.86B A - 10.12B A - 22.59 B A -~ 4 1 . 1 1 B A - 96.86 B
5b
6 7 8 9C
0 /degrees
e(a.)
o(a3)
45 43.1 38.3 32.5 0 46.9 51.7 57.5 90
45 36.6 0 0
Bo Figure 2. Distribution of magnetic field strength in the annulus of a coaxial NMR tube system with dimensions a , = 0.0635cm, a 2 = 0.1016 c m , and a 3 = 0.2104 cm
(sJ[ 5) (XI -
53.4 90
+
(x2 -
$1
.I(
(9)
These new expressions (Equations 8 and 9) will now be tested using some common inorganic materials.
90
a See Figure 2. Point of maximum H , / H , . of minimum H,IH,.
I.(
' Point
values) increase in length until they meet the x or 3 axes after which they decrease in length until they reach t h e points of maximum and minimum H 3 values. It will be seen t h a t the longest contour lines (lines 3 a n d 7 , Figure 2) pass through the points r = a3,0 = 0' or 90'. In other words, t h e magnetic field strengths corresponding t o the two absorption maxima of t h e observed doublet are
H , (abt. m a x ) / H , = A f B / a ? *
EXPERIMENTAL Apparatus. All NMR spectra were recorded using a JEOL MH-100 spectrometer operating a t 100 MHz for 'H studies. Concentric cavity sample tubes were obtained from Wilmad Glass Company, Buena, N.J. The inner cavity tubes were of type 520-2 and were used with outer tubes of type 506-PP. The geometric shape factors for such an arrangement were as follows: a, (inside radius of inner tube) = 0.0635 f 0.0005 cm; a2 (outside radius of inner tube) = 0.1016 f 0.0005 cm; and a3 (outside radius of the annulus) = 0.2104 f 0.0005 cm. Reagents. Fresh commercial samples of cobalt(I1) chloride hexahydrate, iron(II1) chloride, nickel(I1j chloride hexahydrate and nickel(I1) nitrate hexahydrate were used without further purification. AnalaR grades of methanol, ethanol, and acetone were used as solvents. Chloroform (BDH spectroscopy grade) was used as the reference signal.
Table 11. Experimental Values of Magnetic Susceptibilities Using t h e Static Tube N h l R hlethod (
paramagnetic solute CoC1;6HI0 FeCl NiCl ;6H1 0 Ni( NO ,);6H.O
so 1vent
{ {
McOH EtOH Mr,CO MeOH EtOH Mr,CO MeOH MrOH
;-: (.I, dm I'
/A
mol
1158. 20 1128. 4 8 1142 I 1649 1649 * 1685. 487: 485d
37 31
12 21 13 15
intercept, HZ
10'%41u, d m ' mol-'
1 O"\a, dm'mol-
21.0 12.0 25.0 12.5 17.6 27.6 14.0 12.5
1 0 . 1 2 : 0.17 9 . 8 5 - 0.42 9.98 0.32 1 4 . 4 1 : 0.27 11.41 i 0.10 14.72 i 0.18 4 . 2 5 ' 0.11 4.24 + 0 . 1 3
1 2 7 . 2 : 2.1 123.8 5.3 1 2 5 . 4 4.0 181.1 - 3.4 181.1 - 1 . 3 185.0.2 . 3 53.4 1.d 53.3 * 1.6
1
2
1
'
i o 4 @ , lit.
1 0 4 ~ ~
10.28 I 0 . 1 7 10.01 i 0.43 10.14 + 0.32 32.36 1 0 . 6 1 3 2 . 3 6 .c 0 . 2 3 33.06 I 0.41 4 . 2 9 I 0.11 3.76 .i 0.11
9.87
}
30.20 4.28 3.81
Molar magnetic susceptibility, unrationalized CGS-EMU system. Molar magnetic susceptibility, SI system. = \a,f~/iV w h e w ,J =: density and M = molar mass of material. Converted t o SI values f r o m CGS values in "Handbook of Chemistry and Physics", 52nd ed., T h e Chemical R u b b e r Company, Cleveland, Ohio 441 2 8 .
' Magnetic susceptibility, SI system.
Anal. Chem. 1980, 5 2 , 569-572
Procedure. The magnitude of the splitting of the chloroform signal was measured as accurately as possible on a suitably expanded chart scale and, in most cases, was based on the average of four values for the four positions of the tube differing by 90" rotations about the vertical axis. In general, the splitting was found to vary by no more than 3% on rotating the tube. The NMR probe temperature was ca. 25 "C for all the measurements. For each paramagnetic substance studied, five different concentrations of the solute in the range 0.05 to 0.25 mol dm-3 were used.
RESULTS AND DISCUSSION Graphs of the chloroform signal splittings vs. the molar concentration of the paramagnetic solution were plotted and yielded good straight lines with small positive intercepts (see Table 11), corresponding to the residual splitting of the chloroform reference signal which will arise due to the diamagnetic susceptibilities of the pure solvent, chloroform, and t h e glass. T h e results of linear regression analyses of the experimental points are given in Table 11. Following Engel e t al. ( 2 ) it can be shown that for dilute solutions of a paramagnetic material Equation 8 leads to the following expression for molar magnetic susceptibility, x h f ,
569
presence of some hydrated FeC1, i n the sample used. T h e hydrated salt (Le., FeCl3.6H20)is known t o have a higher magnetic susceptibility than the anhydrous salt. The results show no obvious dependence on t h e nature of the solvent suggesting t h a t solute-solvent interactions do not appear to affect solution paramagnetic susceptibilities in the concentration range here chosen for their measurement. I t should be noted that the intercepts of the graphs should be constant for a given solvent and reference material. The values in Table I1 approximately support this and indicate that for methanol the intercept (Le., the residual splitting of the reference material due to the diamagnetic susceptibilities of the reference compound, the solvent, and the glass) has an average value of 15.0 Hz whereas for ethanol and acetone the values are 14.8 and 26.3 respectively. Our results show that the NMR static tube method is undoubtedly a convenient and accurate method for determining paramagnetic susceptibilities in solution. While its accuracy is a t least comparable to that of the more well known Evans method ( I ) ,the static tube method is more versatile than the latter from the point of view of choice of suitable solvents and reference materials.
ACKNOWLEDGMENT The corresponding equation in SI units is obtained by omitting . 10 differs from the correall the factors of 4 ~ Equation sponding one of Engel e t al. ( 2 ) by the factor
( 1 + 41x5)( 1 4793
+
)2:
~
($2
which is, numerically equal to 1.82 for the tubes used in these experiments. This inevitably brings into question the K~ (Le., ,ypvI) values quoted by Engel e t al. These cannot have been calculated from their listed values of the graphical slopes ( A l v / l c ) using their version of Equation 10 with r replacing a3. I t would appear that either these authors have based their calculations on different ( A l v / l c ) values or they have used the correct expression for xhl (Le. Equation 10) without stating
so. Table I1 lists some values of X M and y, based on Equation 10 and compares them with literature values obtained by classical methods. It will be seen that the agreement is excellent, as it is within the experimental errors of the NMR values in all cases except t h a t of FeCl,. Here the somewhat higher NMR values are thought most likely to be due to the
We thank Christine A. Carrick and A. J. Wybrow for many of the experimental measurements.
LITERATURE CITED (1) Evans, D. F. J . Chem. SOC. 1959, 2003. (2) Engei, R. E.; Halpern, D.; Bienenfeld, S. Anal. Chem. 1973, 45, 367. (3) Reilly, C. A,; McConneli, H. M.: Meisenheimer, R. E. Phys. Rev. 1955, 98,264. (4) Pople, J. A,; Schneider, W. G.; Bernstein, H. J. "High Resolution Nuclear Magnetic Resonance", McGraw-Hill: New York, 1959; p 79. (5) Emsley, J. W.; Feeney, J.; Sutcliffe, L.. H. "High Resolution Nuclear Magnetic Resonance Spectroscopy", Volume 1; Pergamon Press: Oxford, 1965; p 262. (6) Becker, E. D. "High Resolution NMR, Theory and Chemical Applications", Academic Press: New York, 1969; p 49. (7) McFarlane, W.; White, R. F. M. "Techniques of High Resolution Nuclear Magnetic Resonance Spectroscopy", Butterworth & Co.. Ltd.: London, 1972: p 81. (8) Zimmerman, J. R.: Foster, M. R. J . Phys. Chem. 1957, 61, 282.
Keith G. Orre_ll* Vladimir Sik Department of Chemistry, T h e University Stocker Road, Exeter, Devon, England RECEIVED for review July 18, 1979. Accepted November 8, 1979.
Estimation of Proton NMR Chemical Shifts from Carbon Peak Heights in Variable Frequency Proton-Carbon Off-Resonance Decoupling Experiment s Sir: Coherent, medium-power, off-resonance decoupling of 'H nuclei, while observing 13C, yields coupled 13C NMR spectra with reduced magnitudes of the spin couplings to 'H; the effective values are essentially proportional t o the decoupler offset from the exact proton resonance ( I ) . By systematic variation of the irradiation frequency, it is thus possible to construct a cross-correlation map between directly bonded proton and carbon resonances. Such a dual assign0003-2700/80/0352-0569$01 0010
ment procedure will greatly reduce signal assignment ambiguities in both spectra. Alternatively, beforehand knowledge of proton shifts will be of great value when attempting to analyze a strongly coupled proton spectrum through iterative computer simulation. Although such spectra contain a large amount of detailed structural information (related to 'H-'H couplings and 'H shifts), chemists rarely attempt to go through the necessary computer analysis procedure for the evaluation 1980 American Chemical Society
