Anal. Chem. 1990, 62, 1665-1671
quirement for application of the technique. However, considering the biological function of enzymes this requirement is not limiting, and the technique should be applicable to a wide range of enzyme systems. Theoretical analysis of the relationship between the measured signal and the kinetic parameters has shown that the primary experimental parameter to consider is the net difference in specific rotation for the reactant(s) and product(s). In support of this, it was demonstrated that the glucose concentration did not affect either the magnitude of the signal or the noise. Polarimetric measurement of glucose oxidase activity provided values that were in good agreement with those obtained with accepted analytical procedures. A mass limit of detection of 34 fmol of glucose oxidase was demonstrated by using the polarimetric system, and the system response has been shown to be linear with enzyme concentration over 4 orders of magnitude. A1though this LOD is impressive, significant improvements can be expected when procedures are implemented to buffer the system from the effect of temperature variations. Registry No. Glucose oxidase, 9001-37-0.
LITERATURE CITED Lucy, C. A.; Cantweli, F. F. Anal. Chem. 1989, 6 7 , 101-107. Sandifer, J. R. Anal. Chem. 1989, 6 1 , 2341-2347. GolsharrShirazl, S.; (kriochon, G. Anal. Chem. 1988, 60, 2364-2374. , Mottola, H. A. Kinetic Aspects of Analytical Chemistry; Wiley: New York, 1986; Chapter 5. (5) Ashour, M. B. A.; Gee, S. J.; Hammock, B. D. Anal. Biochem. 1987, 766, 353-360. ~
1065
(6) Urbanke, C. Methods Enzym. Anal. 1983, 7 , 326-340. (7) Taguchi, H.; Ishihara, N.; Okumura, K.; Simabayashi, Y. Anal. Chim. Act8 1900, 228, 159-162. (8) Wang, J.; Wu, L.-H.; Lu, 2.; Li, R.; Sanchez, J. Anal. Chim. Acta 1990, 228, 251-257. (9) Gaal, F. F. An8&Sf (London) 1987, 772, 739. (10) Wllklnson, J. H. The Prnciples and Practice of LXsgnostlc Enzymology; Year Book Medical Publishers: Chicago, 1976; pp 494-502. (11) Bobbitt, D. R.; Yeung, E. S. Anal. Chem. 1984, 5 6 , 15-77-1581, (12) Bobbitt, D. R.; Yeung, E. S.Anal. Chem. 1985, 5 7 , 271-274. (13) Yeung. E. S.; Steenhoek. L. E.; Woodruff, S. D.; Kuo, J. C. Anal. Chem. 1980, 5 2 , 1399. (14) Bobbitt, D. R. Ph.D. Thesis, Iowa State University, 1985. (15) Bright, H. J.; Appleby, M. J. Blol. Chem. 1989, 244, 3625-3634. (16) Ainsworth, S. Steady-State Enzymc Kinetics; University Park Press: Baltimore, 1977; p 31. (17) Boyer, P. D.; Lardy, H.; Myrback, K. The Enzymes; Academic Press: New York, 1963; Voi. 7, pp 567-586. (18) Castellan. G. W. Physical Chemistry; Addison-Wesley: Reading, MA. 1983; pp 311-312.(19) Shao, Y. Y.; Rice, P. D.; Bobbitt, D. R. Anal. Chim. Acta 1989, 227, 239-247 - - - .. .
(20) Pardue, H. L.; Burke, M. F.; Jones, D. 0. J. Chem. Educ. 1987, 4 4 , 684-689. (21) Pardue, H. L.; Simon, R. K.; Maimstadt, H. V. Anal. Chem. 1984, 36, 735-737. (22) Rutan, S. C.;Fitzpatrick, C. P.; Skoug, J. W.; Weiser, W. E.; Pardue, H. L. Anal. Chim. Acta. 1989, 224, 243-262. (23) Campi, G. L.; Ingle, Jr., J. D. Anal. Chim. Acta 1989, 224, 275-288.
RECE~VED for review March 21,1990. Accepted April 30,1990. Support for this work is acknowledged from the donors of the Petroleum Research Fund, administered by the American Chemical Society, and from the Camille and Henry Dreyfus Foundation through a Teacher-Scholar Fellowship (D.R.B.).
Bulbed Capillary External Referencing Method for Proton Nuclear Magnetic Resonance Spectroscopy Kozo Momoki* 10 Shirahata-higashi-cho, Kanagawa-ku, Yokohama-shi, 221, Japan Yoshiyuki Fukazawa
Industrial Research Institute of Kanagawa Prefecture, 31 73 Shouwamachi, Kanazawa-ku, Yokohama-shi, 236, Japan
Through fundamental reanalyses of the external referencing system and the chemical shift equation, an entirely new referencing method using a new buibed capillary reference tube device Is derlved. The device was initially for a dlrect diamagnetic correction needing no susceptiblilty and geometry factor values to be theoretlcally performed on the spectrum. Then, the same devke method was straightforwardly developed to eventually glve the first bias-free or true chemlcal shlfts,,,,a’ unequlvocai to samples In NMR with accuracles estlmated as high as f0.004-0.009 ppm In addition to high preclslons obtained as 0.004-0.009 ppm. Thus, we could reasonably Introduce “accuracy”, by analogy to instrumental analysis cases, for the first time into NMR that has been governed only by experlmental precislons. Therefore, by comparison, the usual external referencing shifts relative to the TMS cyllnder reference are reasonably found as showing preclslons as high as 0.004-0.005 ppm but accuracies as poor as a mere -0.24-0.8 ppm. Slmilariy, the usual Internal referencing shifts are suggested to have as unexpectedly poor accuracies as -0.3-+OS ppm by solute-solvent effects, reasonable for the sample sdutlons. The new method can be carried out with simple procedures under practically moderate experimental conditions. Unique theoretical and technical features of the method are discussed in detail.
Several years ago when we were restudying the characteristic ‘HNMR spectra of ion-exchange resins immersed in water (1-4), a question was raised concerning the diamagnetic correction (DC) for external referencing (ER). Although DC had been theoretically required as important (5,6),only one of nearly 30 papers (3) studying ion-exchange resin spectra with ER did not perform DC. Even that one (3)in a brief note could not show the practicality or effectiveness of DC in their ER measurements. A literature study of this point also revealed that no practical DC technique had yet been established for any other sample systems probably because of technical difficulties against its theoretical importance. Instead, most ‘H chemical shifts had been measured with internal referencing (7), which needed no DC (6) to be used more easily. Thus, the DC problem in ER seemed to have been neglected and left practically unsolved since the advent of NMR. However, we had actual ion-exchange resin samples that could not be measured without ER, where a practical DC technique was urgently needed. Therefore, to search for an usable method, we began to restudy the DC problem from theoretically considering why observed ER shifts had to be actually corrected. In this course, we noticed that DC had usually been called a “susceptibility correction (SC)” (6,8), meaning that the correction was to be done only by evaluating
0003-2700/90/0362-1665$02.50/00 1990 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990
Ho
Ho
-
(A)
(81
(C)
Lorentz cavity __+
I -
Ho
Ho
(B)
Figure 1. Diamagnetic polarizations in the usual external referencing system using a reference cylinder inserted in a cylindrical sample.
Figure 2. Determination of unknown x, using known der-sphere pair system from eq 3: (A) ref 21; (B) ref
unknown susceptibilities, and that this understanding as SC might be questionable for establishing a practical DC method. Namely, the fundamental ER shift equation is written (6) as
(6) has always been accompanied with g,, = 2a, but such qualitative comments are not enough as g,, is 0.6% smaller than 2a even a t a large L I D = 20 (19). Thus, many actual ER might have been performed unnoticely at g, < 2a and g < 2x/3. Also, the idealized eq 1could not be obtained unless both sample and reference cylinders are ideally given a strict g,, = 2a a t L I D > 40-50 (19) in Figure 1. Therefore, g, # 2a and g # 2 ~ / may 3 be more probable in actual ER measurements. This sounds as if we are introducing another difficulty into performing the actual DC, since nonideal ( # 2a/3) g and unknown xs have to be corrected as two unknown parameters for obtaining b,, in eq 1. However, what is needed for DC is not necessarily a separate g and x,, but a combined DCT as a whole may be taken as a lone unknown parameter in eq 1. The present paper deals with a new reference device for obtaining an unknown DCT as a whole simply on the spectrum. However, the ER spectrum measured with our device is soon found as directly giving not only DCT but also 6,, in eq 1 a t the same time. Furthermore, actual DCT and 6,, obtained thus on the spectrum are still nonideal (g # 2a/3). Our same device method could easily be developed to give a simple process to normalize these nonideal values to idealized (g = 2a/3) ones. Our final results are idealized chemical shifts that are entirely new in NMR but will be shown to be easily obtained most reasonably and accurately. Thus, we propose our new device method as a most reasonable, practical, and accurate ER technique. Experimental Approach To Directly Obtain DCT as a Whole. The form of DCT in eq 1 can be analyzed as
&cor
( P P ~ =) [(Hr- Hs)/Hr +
&cy
- gsp)(xs - x r ) l X
lo6 = bobs + g(xs - x r ) (1) where the subscripts r and s refer to reference and sample, respectively, (gcy- gsp)(x,- xr) and g(x, - x,) are diamagnetic correction terms (DCT), and x represents a volume diamagnetic susceptibility (VDS)originally given a IO4 cgs emu/cm3 unit. In such b (ppm) equations, x can be assumed as representing VDS X lo6. In this paper, x values are taken from the compilation (9)given a cgs emu/g unit by multiplying the density at 25.0 "C (10, 11). Thus, all the x values in the paper are at 25.0 "C in accord with our NMR measurements. In the present study, the magnetic field is applied perpendicularly to the sample tube. The usual understanding of DC as SC is based on the following: a geometry (or shape) factor g can be a priori taken as ideal 2 ~ / so 3 that xs must be a lone unknown parameter in DCT in eq 1 to be evaluated and corrected (6,8). This g = 2 ~ / comes 3 from the ideal g,, (for a cylinder shape) = 2a and g,, (for a sphere shape) = 4a/3 (6). In the late 1950s, Bothner-by (12,131 suggested that actualg might not be 2a/3, but he showed only a rough estimation from his experimental data without further investigations. For SC, the determinations of unknown xs have been tried with NMR techniques (3, 5 , 8, 14-17) but without practical success. We also questioned the g = 2r/3, especially for actual ER measurements. Thus, from magnetism (18), we reanalyzed the usual ER system with sample and reference cylinders (Figure 1B) and became assured that the DCT to be involved could be written as in eq 1 but only under approximations and idealizations. For example, all the cylindrical boundary shapes a-f in Figure 1B should be manufactured and set strictly parallel to each other and strictly perpendicular to the applied field. Only such strict conditions are fulfilled, Figure 1B can be reduced to Figure 1A + lC, where combining two equations each for Figure 1A or 1C gives rise to eq 1. Still, equational approximations in combining the two equations are needed to deduce a DCT form similar to that in eq 1. These approximations and idealizations could easily cause actual g to be somewhat different from 2a/3. More directly, however, g,, = 2a in g = 2a/3 may be questionable in most actual ER measurements. Although geometry factors represent diamagnetic polarizations on containers' boundary shapes (Figure l),only g,, = 4 s / 3 can be defined unequivocally as the polarizations only on spheres can be isotropic regardless of diameter. Those on the other shapes are all anisotropic, where g, cannot be defined without defining its dimensions. Therefore, a comment as 'for a cylinder of length ( L )large compared with the diameter(D)"
DCT = gcy(xs - xr) - g s p ( x s
-
XI)
xi in a cylin22.
(2)
The first term of the right-hand side suggests the presence of a cylindrical boundary between a sample and reference, while the second term a spherical boundary. Therefore, DCT may be directly obtained by constructing and simultaneously measuring such two states with NMR. This type of experiment has been in fact carried out but only for the NMR determinations of paramagnetic (20) or diamagnetic (21, 22) susceptibilities. In Figure 2A (21), a substance i(xJ in g, and g,, forms is placed in another j(x,) and measured with NMR, where two i peaks are obtained on the spectrum, giving (3) '1,Cy - ' 1 , S P = " I = @Cy - g,p)(x] - XI) g(x, - XI) Thus, if xl (or x,) is known, unknown x, (or x,)can readily be evaluated under g = 2 ~ / by 3 measuring A& A cylindersphere connected device (Figure 2B) was also reported as successful (22). We paid special attention to Figure 2B. Since they intended to merely measure unknown x,, they used water (21) or bromoform (22) as the known x,. However, if an ER sample is
ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1. 1990 I
P
1667
E cap o :Sphere part 0 .:Cylinder part
5mmp Sample tube
P f FE thread
Capillary II
74
1 m m g Capillary 2.5mmg Sphere 0
Flgure 3.
taken as j with the reference as i in Figure 2B, a new ER system in which DCT in eq 1 is given as A& directly on the spectrum will be obtained, as &,cy
5 Peak height ( 0 ,n ) or area(. . m )
Bulbed capillary device and sample tube arrangement.
- &,sp =
A 4 = @cy
- gsp)(Xs
Figure 4. Peak heights or areas of the TMS sphere and cylinder parts measured at varied heights of a bulbed capillary. bbdh
- XI) = g ( x s - XI) =
DCT
10
a)
(4)
(CH,)2co xbulh > X l M S
from eq 3 for the case.
EXPERIMENTAL SECTION New Bulbed Capillary Reference Device. We designed and self-fabricated a new cylinder-phere connected reference device called "bulbed capillary" by us (Figure 3). A 2.5-mm-0.d. sphere bulb is blown at one end of a 1-mm-0.d. capillary (used as a 5-rL microdispenser, Drummond Scientific Co., PA) to be fitted to the usual 5-mm-0.d. NMR sample tube. TMS is drawn in up to no less than 5 cm long in the cylinder part to hold ,g = 2a at L I D k 50 (29) at least for the reference tube. The other end of the capillary is also sealed at about 7 cm long. Height Adjustment of the Device in the Receiver Coil. Since the receiver coil shows a vertical sensitivity distribution sensible to our tiny device, the height position of the device has to be adjusted and fixed in the receiver coil for the ER measurement. The accessories shown in Figure 3 are for easy but precise manipulations required for the device. By pulling the PTFE thread up and down, the bulbed capillary can be moved up and down easily and smoothly to take any height positions in the sample tube. The device can easily be fixed at any height positions by fastening the thread to the top of the sample tube with the PE cap. The preselection of an appropriate height position of the device in the receiver coil can be made by simulation in the sample tube placed in a sample holder usually supplied by NMR instrument manufacturers. Our holder was a PVC cylinder and had a vertical opening of 5 X 30 mm for observing the inside. The holder had also a height mark at almost a midheight of the opening to designate the center height of the receiver coil in our NMR instrument. We newly cut open another opening of a similar size at the opposite side of the cylindrical holder so that the device in the sample tube in the holder could be seen on a line passing through the both openings from the outside. Then, on the inner surface of the holder, we pasted a thin sheet of a transparent plastic millimeter scale toward the outside on the original opening and a thin A1 mirror plate toward the inside on the new opening. By observing from the original opening side the sphere part to be matched with its image on the mirror, we could easily read the device's height position at the midheight of the sphere part to a millimeter. Similarly, the height of the device can be adjusted and fixed at any selected positions quite easily but precisely to a millimeter. Selection of an Appropriate Height Position of the Device. Figure 4 shows the variations of our TMS peak heights or areas obtained by varying the height position of a typical bulbed capillary. In Figure 4, the zero height is taken at the receiver coil's designated center height with the minus signs for the lower heights. The sphere peak height plots seen as almost symmetrical eventually give the coil's vertical sensitivity distribution, where the sensitivity maximum height is shown as already displaced
dbulh
JI X l /lo
c
6
'
$
I Q
b
*
77 Spectrum of (a) acetone or (b) water as the bulk sample measured with the bulbed capillary method. The TMS,cy peak is always smaller than the TMS,sp peak in a pair on any spectrum. The x values are given in the text. Flgure 5.
downward by 2 mm from the designated center height of the receiver coil. The smaller cylinder peak heights due to the smaller diameter are measured only below the sensitivity maximum height. The two TMS peaks have to be simultaneously measured for our method merely in the lower receiver coil's region. By considering also their peak height ratios, we decided to take a -5 mm as the most appropriate height position for this bulbed capillary. We similarly checked several bulbed capillaries self-fabricated differently but used for the present study. All these capillaries showed the same -5-mm height position as most appropriate for our instrument. NMR Measurement. Our spectra are measured with a JEOL PS-100 (100 MHz, CW) at 25.0 i 0.5 OC and a bulbed capillary fixed at the -5-mm height position. The sample head is made to come at not lower than the TMS head in a 5 mm-0.d. sample tube. d values are measured five times and averaged. Chemicals. TMS of Merck was used throughout. Water was deionized and distilled. Benzene and cyclohexane were of Dotite Primasol-99(99% purity, Dojindo Labs, Kumamoto, Japan). Chloroform and bromoform of reagent grade were extracted with water to remove the stabilizers, distilled, and dried. Acetone and carbon tetrachloride were of reagent grade and only dried. Bulbed Capillary ER Method as a Direct DC Technique. Figure 5 shows our typical bulbed capillary ER spectra of acetone and water each as a bulk sample, where DCT is directly obtained as (5) A h s = cy - d ~ M S , a p= d x b u l k - X W ) from eq 4. The characteristic TMS peak pairs are clearly distinguishable in Figure 5, since the sp peak appears always taller
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990
than the cy peak in a pair because of their given dimensions. Also, in accord with eq 5, the sp peak comes at a higher field in acetone while at a lower field in water than the cy peak in each pair, due to xacetone> XTMS > xwaWr.The cy-sp separation is smaller in acetone than in water, corresponding to their x differences as seen later. Thus, our spectrum directly gives DCT as A~TMS,which can be inserted into eq 1to calculate 6, without knowing or evaluating the g or x values. However, the deduction of 6, can be performed readily on the same bulbed capillary spectrum as in Figure 5 even and 6b,& peaks without deriving DCT on the way. Namely, b,w on our spectrum are essentially the same as TMS cylinder reference and bulk sample peaks, respectively, in the usual ER method. Therefore, 6obs in eq 1 can be written as boba,cy, representing an observed sample shift relative t o the TMS cylinder reference peak as dbulk - 6TMS,cy in absolute ppm shift notations. Thus, eq 1 can be 6cor = 8oba.cy + AbTMS = (abulk - dTMS,cy) + (XTMS,cy - XTMS,sp) = 6bulk - 6TMS,~p- 6oba,sp (6) where 6oba,sp refers to an observed bulk sample shift relative to our 6TMS,sp peak as the new reference peak. Equation 6 shows that a DC-performed b,, shift can be obtained , ~ ~ peak. directly on our spectrum, giving a new ~ T M S reference Thus, our bulbed capillary ER method is indicated as offering an entirely new direct DC technique, needing no g and x values. Normalization to Idealized Chemical Shifts. We measured some samples with different self-fabricatedbulbed capillaries but obtained merely different 6cor values for an identical sample, making the new ER method as still unusable. We studied reasons for such different ,6 and noticed that different capillaries actually gave different nonideal A6TMS for the same sample to yield different 6obsap in eq 6. For this point, we realized that the nonideal A6TMS by capillaries can be expressed as a function of only X b d k in rewriting eq 5, as (7) AdTMS = axbulk + b since acual g may be nonideal but can be given definitely for each capillary while xTMSis given definitely, regardless of capillaries. The values of a and b are decided by a capillary but are variable from a capillary to another, yielding different A6Ws for the same Xbulk sample by different capillaries. The situation could be ensured by drawing A ~ T M Svs Xbulk calibration lines for six different capillaries with use of the following seven calibration standards with known X b d k in parentheses: acetone (-0.456), benzene (-0.617), cyclohexane (-0.623), carbon tetrachloride (-0.685), water (-0.719),chloroform (-0.731), and bromoform (-0.936). Figure 6 shows the results, where each capillary gives its own line with a good linearity but that is considerably different from the others by varied a and b as exvalues ~ for the same Xbulk have t o pected. Thus, different A ~ T M be expected by different capillaries. The values of actual g are represented by those of a given in Figure 6 as obviously nonideal and variable for all the capillaries tested. Therefore, we cannot still attain unequivocal chemical shifts for samples without controlling such variabilities by actual capillaries. However, we realized that we could expect the unequivocal 3 xTMS = -0.547, as "ideal" line by giving g = 2 ~ / and A6"TMS = (2"/3)(Xbu]k + 0.547) = 2.094Xbdk + 1.145 (8) The ideal line is also shown with a broken line in Figure 6 in which our actual lines are seen as obviously nonideal lines considerably different from the ideal line. Now, it is obvious that if a xb& is given in eq 8 a Adoms value is obtained unequivocally for the sample, giving the unequivocal in eq 1, as remarked in eq 6, as sample shift 6O,,, However, this A ~ O T M S can be deduced from experimetnal A~TMS, in normalizing nonideal lines to the ideal line, by a mathematical normalization performed by simply eliminating Xb& between eqs 7 and 8. as A ~ * T M S= (2.094/a)(A6TMs - b ) f 1.145 (10) Thus, A6'TMS can readily be derived from A6TMS, if a and b are a priori determined for each capillary and inserted into eq 9 to
1
2 3
4 5 6 ,---
Xbulk
Flgure 6. Ab,,
(xlO6)(cgi
1.963 1.981 1.812 1.936 1.851 1,869 2.094
1.030 1.023 0402 0.943 0.900 0.870 1.145
rmu/cm9
xbu*
vs calibration lines in eq 7 measured with six different capillaries set at a definite height position fixed in the receiver coil. The broken line shows the ideal line in eq 8.
obtain 6",,,. Practically, the normalization term A6",,, is useful, as Mono,= A~"TMS - Abms = (2.094/a - 1)AaTMS - 2.094b/a + 1.145 (11) for finally deriving 6°c,,, from eqs 6 and 9, as &"cor = dots,sp + A6Onor
(12)
bo,, is our final result of the new bulbed capillary ER method to be obtained as the unequivocally idealized chemical shift for
the sample. The entirely new 6O, shift, which cannot be obtained without our new technique, has profound meanings for NMR and chemistry, as will be discussed.
RESULTS Precisions and Accuracies. The effectiveness of our new technique, especially of the normalization process, was quite impressive as shown in Table I. In Table I, the chemical shifts and their standard deviations of the above six calibration standards as the samples measured with the six different capillaries used in Figure 6 are summarized. The shift values shown for each sample are those averaged among the six capillaries with the standard deviations given in parentheses. In Table I, the first line shows the conventional ER shifts measured from each bTMS,cy reference peak on our spectra, where the shifts are obtained as very precise but without DC. The shifts in the second line are those DC performed in eq 6 but still unnormalized, showing deviations as large as 0.03-0.04 ppm. Their normalization terms (eq 11) are in the third line to show also deviations of 0.03-0.04 ppm. However, the fourth line, giving our new normalized 6°cor shifts, shows that the normalizations by simply adding (eq 12) these two values in the second and third lines surprisingly reduce the deviations of 0.03-0.04 ppm to a mere 0.004-0.009 ppm. Thus, our normalization process is shown to be quite effective in giving very precise boco, values. Furthermore, however, the fact that the deviations of 0.03-0.04 ppm among quite different (Figure 6) capillaries are actually reduced to a mere 0.004-0.009 ppm strongly suggests that these boc,, values in the fourth line are obtained also as accurate to nearly &0.004-0.009 ppm or as almost bias-free. Therefore, our 6O,, can be taken as the bias-free unequivocal chemical shifts for these typical samples with accuracies estimated as 10.004-0.009 ppm. Accordingly, the accuracies of the conventional ER shifts (first line) can be estimated by their differences from our bias-free 6°co, shifts (fourth line) to be -0.2-+0.8 ppm (fifth line) as very poor not to be ne-
ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990
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Table I. Chemical Shifts and Standard Deviations (in Parentheses)/ of the Six Calibration Standards in Figure 6 Measured as the Bulk Samples with the Six Different Capillaries Also in Figure 6 sample
ob,,; ~0b.W
A80ngrC 6O,,
6ob8,ey
- gam:
CHBr8
CHC13
7.931 (4) 7.099 (33) 0.019 (31) 7.115 (6) +0.816
7.757 (5) 7.317 (29) 0.057 (35) 7.373 (9) +0.384
C6H6
6.879 (4) 6.644 (41) 0.078 (37) 6.722 (9) +0.157
5.206 (4) 4.794 (36) 0.060 (35) 4.853 (4) +0.353
1.631 (5) 1.390 (35) 0.079 (38) 1.469 (5) +0.144
1.849 (4) 1.931 (43) 0.111 (43) 2.042 (8) -0.193
The conventional ER shift measured relative to each TMS,cy peak on our bulbed capillary spectrum. *The DC performed but unnormalized shift in eq 6 measured from each TMS,sp peak. cThe normalization term in eq 11. dThe DC performed and normalized shift in eq 12. ‘The bias of the conventional ER shift without DC estimated from our bias-free 6O,, shift. /The standard deviations in parentheses are those among the six different capillaries showing quite different calibration lines in Figure 6 for these chemical shift measurement. (I
glected as small. Since the first line shows quite high precisions (0.004-0.005ppm) for the same shifts, a good example that high precisions do not assure high accuracies is clearly illustrated. Another reasonable point of our 6O, shifts more than 6ob,cy shifts is suggested also in Table I. Bromoform comes at a lower field than chloroform in 6obs,cy shifts, contrary to the electronegativity shift order expected for Br and C1, while at a higher field in 6O,, shifts in the right order. Thus, chemical shift studies may be performed more reasonably with 6°co, shifts. Such high quality data as in Table I have not been reported.
DISCUSSION I. The proposed method is an entirely new ER technique with a simple reference device and easy procedures not only to perform a direct DC but to finally obtain new bias-free 6O, shifts unequivocal to samples. Since our 6”,, shifts do not need x values, the method is not for the usual SC (6,8) studies. 11. The new method is for ER, which seems to have been disliked by some as “not an easy technique” (23). However, this comment came obviously from a different understanding of the ER system from ours and cannot be applied to the present method. In fact, the above comment was followed (23) by discussion on the difficulties in susceptibilities, but our ER does not need y , values as above. Also, the geometry of the sample was required to be rigorously controlled with high-precision sample tubes, ultrahigh-precision reference capillary tubes, careful centering of reference capillaries, exact repositioning of the two tubes, and so on (23). However, such impractically rigorous experimental requirements are not necessary for our ER as mentioned. The criterion for these requirements was high precision without a word for accuracy (231, where high-precision data could be thought as obtained only by rigorously giving ideal experimental conditions for eq 1. We contrarily found, through reanalyses of the ER system, that eq 1 was in fact an approximated and idealized equation that might hardly be attained experimentally. Thus, rather than relying on experimental rigorousness, we set practically moderate experimental conditions. Instead, we tried to add a simple data-handling process in a final stage to obtain high precisions by normalizing experimental nonidealities to idealities (eqs 7-12). This attempt was successful far beyond expectation in obtaining not only high precisions but also high accuracies in Table I, which eventually shows also the practicality of our new ER method with moderate experimental conditions. Thus, our ER is new and cannot be criticized with the above older understanding. 111. In fact, no paper dealing with “accuracy” as a criterion for chemical shift data or referencing methods has yet appeared, only those with “precision” (23). Nevertheless, we could estimate accuracies in Table I.
Our standpoint comes by analogy to instrumental analysis cases, since how to evaluate chemical shifts is analytically the same as how to determine analyte concentrations. Also, in instrumental analysis, it is well-known that experimental precision does not mean accuracy. To estimate accuracies, analysts usually measure standard reference materials (SRMs) issued by the National Institute of Stanards and Technology (the former NBS) with their method and compare obtained concentrations with SRMs’ values. Since the SRMs’ values are taken as the “true” values in an implicit agreement among them, accuracies meaning biases from the true values can be estimated from differences between measured and SRMs’ values. However, we have no “true” chemical shift values and we cannot obtain biases in NMR by comparing measured and true shift values, suggesting a main reason why accuracies have not been discussed in NMR. We could nevertheless estimate accuracies by returning to how NIST assigns the SRMs’ true values. They measure the same SRM sample with several different analytical methods. If thus-obtained values agree within a reasonably high precision among the different methods, the agreed values can be assumed as bias-free or true for the sample and used for assigning the SRMs’ value. Correspondingly, we measured 6”,,, values of six typical samples with six different capillaries. Thereby, the capillaries already gave quite different calibration lines from each other in Figure 6 to yield 6obs,sp with precisions as poor as 0.03-0.04 ppm, but still resulted in eventually producing 6O, that agreed with precisions as high as 0.004-0.009 ppm in Table I. Thus, by analogy to the SRM case, we concluded that we did different measurements of the same samples and still obtained agreed 6°co, meant as almost bias-free or true with accuracies estimated as also high as *0.004-0.009 ppm. However, our bias-free 6°co, is also understandable theoretically by referring to the nonnegligible biases in dobs,cy shifts as -0.2-+OB ppm, given also in Table I. Most of these biases in the usual ER shifts relative to the TMS cylinder reference come understandably from uncorrected diamagnetic effects (DCT), but the latter could easily be removed by newly taking bobs,sp on the spectra (eq 6). The remaining minor biases coming primarily from experimental nonidealities by our moderate conditions could also be eliminated almost completely through the new normalization process (eqs 7-12). Thus, our 6°co, shifts must be theoretically and experimentally bias-free or true chemical shifts unequivocal to samples, for the first time in NMR. Also, accuracies come into NMR, making NMR chemical shifts really quantitative not just qualitative as before. NMR should and can now search for accurate shifts more than previously precise shifts. IV. Two more technical features support our easy but accurate 6°,0, shifts. First, we could simply realize a sphere reference that has sometimes been tried as being more reasonable than the usual cylinder reference but without success (24). Only our reanalyses of the ER system and eq 1 (Figures
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1 and 2) should be noted for our success against their failure. They tried to give only a sphere peak and failed, whereas we succeeded by giving sphere and cylinder peaks a t the same time. Our sphere part can then represent the Lorentz cavity in the reference phase (Figure 1)and give a new sphere reference peak naturally used for a direct DC without x and g values (eq 6). 6 = 0 ppm should now be at the TMS sphere peak and not the cylinder peak. Second, we used seven Xbu]k standards for drawing the calibration lines (Figure 6) that were the used for the normalizations (eqs 7-12). Therefore, the accuracies of O6, shifts had to be governed heavily by those of the X b u k values taken, where Table I suggested that the values were taken also accurately. However, a more positive meaning of using X b d k for 6°,0, cannot be ignored. 6 and x are linearly connected originally in eq 1 so that each can be substituted for the other, where a x standard can be a subreference for 6. Thus, in our normalization process, seven new subreferenced 6 values besides 6TMS.aD= 0 ppm are eventually given on the 6 scale by the Xbulk standards at their ~ T M S , ,peaks ~ through A ~ T M S(eq 5 ) , resulting in giving the higher accuracy ,O,6 values in Table I. This reminds us of pH measurements. The “one-point referencing” using only a pH standard gives less accurate pH values than the “multipoints referencing” using several differnt pH standards. Analogously in NMR, the usual ER using only a TMS reference is just a “one-point referencing”, giving less accurate or rather qualitative shifts even if the DC problem is avoided. Our method eventually using TMS and seven d subreferences is the first “multipoints referencing” in NMR naturally giving the higher accuracy 6.O,,, These new features may not easily be expected with other techniques, making our method quite unique and invaluable for NMR. V. We obtained the first bias-free or true chemical shifts unequivocal to samples in NMR, meaning that the same samples should be given the same 6,°, values regardless of instruments or referencings. The present method is developed with our lone instrument in which the magnetic field is applied perpendicularly to the sample tubes. However, newer instruments using superconducting magnets in which the field is applied longitudinally are now more in use. Even to such instruments, our same bulbed capillary and procedures will be applicable in principle by only changing g,, to 0 so that g becomes - 4 ~ 1 3 . We will check that point when we obtain a newer instrument. Others are also hoped to check with their instruments. As for other referencing methods, our bias-free 6°,0, shifts can be used rather for checking others’ biases as shown in shifts. Comparisons with internal Table I for the usual referencing (IR) shifts are most interesting, since the bulbed capillary even if in the IR sample solution is indifferent to the solution. Therefore, by placing a bulbed capillary in an IR sample solution, we can measure the IR shift while independently obtaining 6°,0, shifts of the IR sample solute and reference peaks for the direct comparisons. In this manner, we measured the usual IR solutions composed of 1-2 vol 70 sample solute, 1 vol % TMS, and CCl, added as the balance. The results were surprising in that IR was quite problematic. The biggest problem was that since IR shifts could not be obtained for pure solutes, solvent effects if any in such IR mixture solute solutions could not be detected with IR by comparing pure and mixture solute shifts. In contrast, our ,O 6, shifts can be measured for either pure or mixture solutes, where we can obtain bias-free solvent effect data from differences between pure and mixture solute shifts. Furthermore, our method can measure solvent effects in IR solutions on sample solute and reference peaks independently.
Thus, in the above IR solutions, we found that solvent effects primarily by CCl, were in fact so large and variable on different solutes including even the reference TMS against expectation (23)that the IR shifts could hardly represent these pure solutes. The biases of the mixture solute shift in the above IR solutions from our pure solute shifts for the same sample solutes amounted also to a nonnegligible -0.3-+0.5 PPm. Similar measurements of binary mixtures give new quantitative data showing solvent effects on solutes and solute effects on solvents to always occur simultaneously. Such solutesolvent effects are characteristic by each solute-solvent combination, not by each solute or solvent alone. Thus, our method can be used for new solute-solvent effect studies by giving entirely new data. These details will be reported in a succeeding paper (25). VI. Thus, entirely new ,O6, shifts are methodologically deduced as bias-free or true chemical shifts unequivocal to samples and experimentally obtained with high precisions and accuracies. Therefore, the new method will affect NMR considerably. However, the validity of our method or data should be checked further by other instruments and laboratories. Also, many more solutes and samples should be measured with our method for checking its applicability. In addition to methodological checks, chemical checks on what our new 6Oc0, shifts really mean for chemistry will also be necessary. For chemical checks, solute-solvent effect studies with new 6,O,, data will especially be useful (25). With methodological and chemical checks performed further for many more solutes and samples, the bulbed capillary ER method will newly be established as the most reasonable, accurate, and practical referencing technique for NMR, contributing also to chemistry.
CONCLUSION Through fundamental reanalyses of the external referencing system (Figures 1and 2) and the chemical shift equation (eq 11, an entirely new referencing technique using only a new bulbed capillary reference tube device (Figure 3) is developed. As the result, the first idealized bias-free or true chemical shifts 6°,0, (eq 9) unequivocal to samples in NMR could finally be obtained with accuracies estimated as high as ~0.004-0.009 ppm in addition to precisions as high as 0.004-0.009 ppm (Table I). The biggest achievement of this study is that we could thus bring “accuracy” by this new 6O,, shift with our new practical method for the first time to NMR, which had been governed almost exclusively by only “precision” (23). How we could reasonably attain to accuracy is discussed in detail (Discussion, subsection 111). A good example that precision does not mean accuracy is clearly illustrated in Table I for the usual external referencing shifts relative to the TMS cylinder reference. Their high precisions are given as 0.004-0.005 ppm against their accuracies estimated as poor as -0.2-+0.8 ppm, reasonably coming mostly from uncorrected diamagnetic effects. External referencing has been taken as “not an easy technique” because of ideal experimental conditions thought to necessitate high precisions (23). However, our new external referencing is derived from a different standpoint and can be performed with simple procedures under practically moderate conditions (Discussion, subsection 11). Our high accuracies are technically supported especially by new sphere reference and multipoints referencing features that are newly introduced by the bulbed capillary device (Discussion, subsection IV).A simple mathematical normalization (eqs 7-12) added as a data-handling process is another key point for our high precisions and accuracies. Our new bias-free 6O, shifts can be used even for revealing unexpected defects of internal referencing by giving new
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bias-free solute-solvent effect data, which will be useful also for new solution chemistry studies (Discussion, subsection V). Thus, our new bulbed capillary method will be established as the most reasonable, accurate, and practical referencing technique for NMR contributing also to chemistry.
ACKNOWLEDGMENT K.M. greatly thanks Prof. Naonori Miyata, a fellow physicist formerly at Yokohama National University, for his invaluable discussions given on magnetism in this paper. LITERATURE CITED Gordon, J. E. J . Phys. Chem. 1962, 66, 1150-1158. Creekmore, R. W.; Reilley, C. N. Anal. Chem. 1970, 42, 570-575. Weiner, P. H.; Howery, D. G. Can. J . Chem. 1971, 49, 2913-2916. Walton, H. F. Anal. Chem. 1972, 44, 256R. Zimmerman, J. R.; Foster, M. R. J . Phys. Chem. 1957, 67, 282-289. Pople, J. A.; Schneider, W. 0.:Bernstein, H. J. High Resolution Nuclear Magnetic Resonance; McGraw-Hill: New York, 1959; pp 80-81. Tiers, G. V. D. J . Phys. Chem. 1958, 6 2 , 1151-1152. Becker. E. D. High Resolution NMR, Theory and Chemical Applications, 2nd ed.; Academic Press: New York, 1980; pp 38-39, 50-51. In the Japanese translation by: Saito, H.; Shinto, H. Tokyo Kagaku . . Dojin: Tokyo, 1983. Sechste Auflage , 10 teil; Springer-Verlag: Berlin, Landolt-Bornstein, 1967. International Critical Tables; McGraw-Hill: New York, 1928.
Tables of the API Research Project 44; Carnegie Press: Pittsburgh, 1953. Bothner-by, A. A.; Glick, R. E. J . Chem. Phys. 1957, 26, 1647-1650. Bothner-by, A. A.; Naar-Colin, C. J . Am. Chem. SOC. 1956, 80, 1728-1733. Reilly, C. A.; McConnell, H. M.; Meisenheimer, R. G. Phys. Rev. 1955, 98, 264. Deutsch, J. L.; Lawson, A. C.;Poling, S. M. Anal. Chem. 1968, 4 0 , 839-840. Spanier, R. F.; Vladimiroff, T.; Malinowski, E. R. J . Chem. Phys., 1966, 4 5 , 4355-4356. Malinowski, E. R.; Weiner, P. H. J . Am. Chem. SOC. 1970, 92, 4 193-4 197. Weiss, A.; Wine, H. Magnetochemie-Grundlagen und Anwendung; Verlag Chemie GmbH: Weinheim/Bergstr, 1973; pp 41-45. In the Japanese translation by: Sorai. M. Misuzu Shoten: Yokyo, 1980. Bozorth, R. M. Ferromagnetism;Van Nostrand: New York, 1951; pp 845-849. Feher, G.; Knight, W. D. Rev. Sci. Instrum. 1955, 2 6 , 293-294. Frei, K.; Bernstein, H. J. J . Chem. Phys. 1962, 3 7 , 1891-1892. Muiay, L. M.; Haverbusch, M. Rev. Sci. Instrum. 1964, 35, 756-757. Rummens, F. H. A. van der Waals forces in NMR intermolecular shielding effects (NMR Basic Principles and Progress); Springer-Verlag: Berlin, 1975; Vol. IO, Chapter 15. Frost, D. J.; Hail, G. E. Mol. Phys. 1966, IO, 191-200. Momoki, K.: Fukazawa. Y. Unpublished work.
RECEIVED for review November 9, 1989. Accepted April 6, 1990.
Titration of Nitroxide Free Radicals by Nuclear Magnetic Relaxometry Robert N. Muller,*?’Yves Van Haverbeke,’ Pierre A. Bonnet,2 Jean-Pierre Chapat,2and Patrick Vallet’ Department of Organic Chemistry a n d NMR Laboratory, University of Mons, B-7000 Mons, Belgium, and URA CNRS 11 11, Laboratory of Pharmaceutical Organic Chemistry, University of Montpellier, F-30460 Montpellier, France
An alternative to electron spin resonance spectroscopy is proposed for the quantitathre analysis of nitroxlde free radicals In solutlon. The method is based on the chemical reduction of the Paramagnetic compounds followed by NMR measurements of the longitudinal relaxatlon rate of the solvent protons. This titration of the nitroxldes has been carried out in ethanollc solutions by reactlon with known amounts of phenylhydrarlne. The Paramagnetic fractlon of the solvent relaxation rate is precisely related to the concentration of the free radical which can be measured without prior knowledge of Its specific Influence on the protons relaxation rate (relaxlvlty). Oxygen has to be ellmlnated from the solutions In order to avoid reoxldatlon of the hydroxylamlne formed. The preclslon of the method, tested on 11 diversely subsHuted derivatives of piperidine-l-oxyl,pyrrolldlne-I-oxyl, and 3-oxazolldlne-l-oxyl, offers a precision of about 3 % .
INTRODUCTION Nitroxide free radicals have received a great deal of attention in biomedical magnetic resonance because of their potential uses as contrast agents for imaging (1-3)and as probes for pharmacokinetics ( 4 ) or cellular redox state (5-8). A knowledge of the absolute concentration of these compounds is often required, as for instance when their efficiency (or ”relaxivity”) as magnetic resonance imaging contrast agents University of Mons. University of Montpellier.
is to be assessed. The calculation of relaxivity requires a determination of the concentration of the paramagnetic compounds in solution. When isolation and weighing of the pure compound are not achievable, the quantitation of it in solution is usually performed by double integration of the first derivative ESR spectrum. This kind of quantitation requires the production of standard solutions of known concentration and has a precision of about 5%. Other methods have been proposed such as titration of the iodine formed by reaction of the nitroxides with potassium iodide (9) or measurement of the volume of nitrogen produced when they react with phenylhydrazine (eq 1) (IO). In the course of this chemical \
2N-0’
/
+ CGHbNHNH2
+
\ 2N-OH /
-
+ CGH,+ N,
(1)
reduction, the paramagnetic center is transformed into a diamagnetic N-hydroxylamine functional group (10,11). A new analytical procedure based on this quenching of the paramagnetism can thus be proposed. Provided that the reaction is complete and of known stoichiometry, a true “relaxometric titration” can easily be achieved by monitoring the proton relaxation rate of the solvent as a function of the amount of phenylhydrazine added.
EXPERIMENTAL SECTION Reagenh. The Tempo (I), Tempamine (II), Tempo1 (III),and methyl-7-doxylstearate nitroxides (X) (Table I) are commercially available (Janssens, Beerse, Belgium and Aldrich, Brussels, Belgium). The 4-carboxytempo (IV) and the doxy1 (XI) were synthesized by the procedures described by Rauckman et al. (12) and Keana et al. (13), respectively. 4-Ethoxytempo (V) was
0003-2700/90/0362-1671$02.50/00 1990 American Chemical Society
