Table 11. Dependence of the Prediction Ability on the Dimension of the Decision Vectora Dimension of the decision vector No. of training vectors N o , of test vector Wrong answers Prediction ability, %
4
11
21
51
101
151
201
251
110
100
106
100
105
107
107
106
442
452
446
452
447
445
445
446
104 76.4
0 100
0 100
Dimension of the decision vector is n
12 97.2
12 97.3
5 98.9
14 96.8
7 98.4
+ 1taking n from Equation 1.
dure was completed the obtained decision vector W was used to classify the remainder of vectors and 75-100% correct answers (depending on the dimension of vector W) were obtained. The results are collected in Table 11. The number of iterations required for training did not exceed 151 in any case. Although the prediction ability is very good, the fact that both anomeric configurations R, and Ra are represented with only 252 and 300 spectra may not be overlooked. For more accurate or finer grade coverage of the peak regions in the NMR spectra of R, or Rp patterns, many more vectors should be used. For example, by simulating NMR spectra of 4 shifts and coupling constants with only 5 different values of each item, we get about 10 million patterns. Furthermore, the prediction ability was not tested as yet on real spectra. However, this work is in progress and will allow the final verification of the practical value of the method. Apart from this shortcoming, we believe that the method itself is highly selective for problems of this kind and it could be of great help in tracing the anomeric configuration of ribofuranosides, especially in the nucleoside se-
ries, irrespective of the type of the blocking groups used during the reaction. LITERATURE CITED (1)J. L. Imbach, J. L. Barascut, E. L. Karn. and C. T. Tapiero, Tetrahedron Led., 129 (1974). (2) J. D. Stevens and H. G. Fletcher, J. Org. Chem., 33, 1799 (1968). (3)C. Altona and M. Sandaralingarn, J. Am. Chem. SOC.,95, 2338 (1973). (4)C. Giessner-Pattre and E. Pullman, J. Theor. Bo/., 40, 144 (1973). (5) T. L. lsenhour and P. C. Jurs, Anal. Chem., 43 (lo),20 A (1971). (6)J. E. Justice and T. L. isenhour. Anal. Chem., 46, 223 (1974). (7)E. R. Kowalski, P. C. Jurs, and T. L. Isenhour, Anal. Chem., 41, 1945 (1969). (8)R. W. Lindell and P. C. Jurs, Appl. Spectrosc., 27, 371 (1973). (9)D.R. Preuss and P. C. Jurs, Anal. Chem., 46, 726 (1974). (10)B. R. Kowalski and C. A. Reilly, J. Phys. Chem., 75, 1402 (1971). (11)R. E. Carhart and C. Djerassi. J. Chem. SOC., Perkin Trans. //, 1753 (1973). (12)C. L. Wilkins, R. C. Williams, T. R. Brunner, and P. J. McCambie. J. Am. Chem. Soc., 96, 4182 (1974). (13)E. R. Kowalski and C. F. Bender, J. Am. Chem. SOC.,96,916 (1974).
RECEIVEDfor review October 21, 1974. Accepted February 18, 1975. Financial support of the Boris KidriE Fund is gratefully acknowledged.
Simplified Method of Calibrating Thermometric Nuclear Magnetic Resonance Standards M. L. Kaplan, F. A. Bovey, and H. N. Cheng Bell Laboratories, Murray Hill, N.J. 07974
One of the more difficult aspects of performing reliable rate measurements by nuclear magnetic resonance techniques is the determination of true sample temperatures. Various methods, including the placement of a thermocouple in the probe or in the temperature regulating gas flow, suffer from the inherent defect that recalibration is often necessary, especially when probe geometry or gas flow rates are changed (1 ). Perhaps the most generally used mode of temperature measurement depends on a secondary standard with a temperature-dependent chemical shift covering a wide temperature range. These criteria are met by the hydroxyl proton in methanol for temperatures below ambient, and by the hydroxyl protons in ethylene glycol for high temperature work. Although, in principle, accurate measurements can be made with these compounds, the standardization of chemical shift as a function of temperature has relied upon some thermocouple method, such as those mentioned above.
Various authors have reported the calibration of these secondary standards. For example, when a methanol sample was calibrated, the thermocouple was placed in a capillary inside a nonspinning sample tube also containing a capillary of methanol ( 2 ) .Large vertical temperature gradients were observed which made thermocouple placement critical. Accuracy was also significantly limited by broadening of the spectral lines due to introduction of the thermocouple. More sophisticated apparatus, which included a specially designed static thermistor probe, permitted the sample tube to be spun during temperature measurements ( 3 ) .The same author has reported on measurements with a spinning thermistor ( 4 ) but states that the static thermistor is more accurate ( 5 ) . Still others have utilized a melting point method for calibrating a t 100 MHz, both ethylene glycol and methanol standards supplied by the manufacturer of their spectromANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
1703
eter (6). In their method, a liquid giving a lock signal was placed in the outer jacket of a coaxial tube assembly while a melting point standard was put into the inner part. In the NMR probe, the temperature of the tube was raised to the melting point of the standard compound, when its signal could be observed (more than an hour was required for thermal equilibrium to be reached). The coaxial tube was replaced by the ethylene glycol or methanol standard and the hydroxyl proton chemical shift measured. Curiously, only the results for the ethylene glycol standard resembled any published calibration curve (7). The methanol calibration differs considerably from all accepted values. The inconsistencies found here may be due to changes in heating gas flow caused by slight differences in diameters of the ethylene glycol and coaxial tubes. Clearly, a reinvestigation of this technique, because of its simplicity, was in order. DESCRIPTION OF METHOD The method which we report here obviates the need for specialized temperature measuring devices and eliminates many of the objections connected with thermocouple techniques. I t is based on the melting point characteristics of pure organic solids. To calibrate the ethylene glycol standard, a series of compounds, each containing a t least one sharp absorption line, were purified by usual techniques (recrystallization, sublimation, etc.). The corrected melting point of each compound was determined to within f 0 . 2 "C. The only special requirement for these measurements is that the NMR spectrometer which is used have an oscilloscope for the observation of spectral lines. The powdered organic solid was packed into the central part of a coaxial sample tube and ethylene glycol was placed in the outer portion to provide good heat transfer. The sample was inserted into an NMR probe with a variable temperature accessory and then heated to slightly above the melting point of the solid. While still solid, no absorption lines for standard compounds were visible. Upon liquefaction, the spectrum of the neat material was apparent. The magnetic field homogeneity was tuned on the melting point standard. The temperature was then lowered while observing the absorption line of the melting point standard on the oscilloscope. As the compound froze, the line disappeared. The temperature was then raised in 0.5-1.0 "C steps until the appearance on the scope of a broad line which was indicative of a partially melted standard compound. At this point, the absorption lines of the ethylene glycol were recorded and their positions measured to f 0 . 2 Hz with the aid of a frequency counter. Each measurement was repeated several times. Direct reading of the line positions from the chart paper gave similar results although, because of the nonlinearity of the sweep-width calibration, the accuracy was probably less reliable. EXPERIMENTAL Compound Preparation. All the solid compounds used were commercially available and were purified as follows: p-dichlorobenzene, sublimation; cyclododecane, commercially zone refined; 2'-hydrox~-4',5'-dimethyl acetophenone, used as is; hexamethylcyclohexanetrione-1,3,5, p-dibromobenzene, p-diacetylbenzene, p diiodobenzene, 1,2,4,5-tetrachlorobenzene, and hexamethylbenzene were all recrystallized. In general, no major changes were noted in melting points on purification; however, the range over which the solids melted did narrow. The latter became our criterion for purity. Reagent grade ethylene glycol was used without further purification. No acid was added to sharpen up resonance lines as this was found unnecessary for our measurements. Freshly opened bottles of glycol with a nominal water content of 0.06% were used. Melting Point Determination. Melting points were determined on a Leitz binocular microscope fitted with a Mettler FP-52 heated stage. The melting point corrections were obtained with 1704
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
Table I. Temperature Measurements with Different Ethylene Glycol Calibrations At',
Varian,
HZ
95 60 30
OC
30.7 88.6 138.3
V a n G e e t , "c
Neumanpd Jonas, C
This, work, C
31.8 91.1 142.0
32.7 91.8 142.6
30.8 90.5 141.6
Table 11. R a t e Parameters for the Internal Rotation of N,N-Dimethylformamide, Calculated from the D a t a in Ref. 9 Varian
h euman and Jonas
Van Geet
This work
E,
20.5 20.4 20.3 20.1 (kcal /mole)o A (sec-l)a 3.4 x lo1* 2.5 x 10I2 2.2 x lo1* 1.9 x 10l2 122.2 121.7 119.0 122.8 T, 21.2 21.2 21 .o 21.2 AG+, (kcal /mole)c UTaken from standard Arrhenius plot, k = A e c E a XT. COalescence temperature Free energy of activation at the coalescence temperature Fisher Scientific Co. T-418, Ther-Metric Standards. The heating rate used in all cases was 0.2 "C/min. All compounds exhibited a melting range of 0.5 "C or less, with most melting over 0.3 "C. No significant differences were observed on remelting any sample. The corrected melting points, where the last bit of solid just melts are given below. Compound
OC
p-Dichlorobenzene C yclododecane 2 -Hydroxy -4I , 5'-dime thy1acetophenone Hexamethycyclohexanetrione1,355 p-Dibromobenzene p-Diacetylbenzene p-Diiodobenzene 1,2,4,5-Tetrachlorobenzene Hexamethylbenzene
53.3 60.7 71.1 80.2 87.6 112.9 129.5 140.0 165.5
Nuclear Magnetic Resonance Measurements. A JEOL-C6OHL spectrometer was used in conjunction with a JES-VT-3 variable temperature controller. Frequency measurements of the ethylene glycol lines (in Hz) were performed with a Hewlett-Packard, Model 5302A, 50 MHz Universal Counter. Commercial coaxial sample tubes were used (Wilmad Glass Co.): inner tube dimensions, 190-mm length, 2.97-mm o.d., and 1.95-mm i.d.; outer tube dimensions, 178-mm length, 5.0-mm 0.d. and 4.20-mm i.d.
RESULTS A N D DISCUSSION
A plot of the separation of the ethylene glycol NMR absorption lines ( A u ) as a function of temperature ("C) gave a straight line fit. Least-squares analysis of the data resulted in an equation of the form:
T "C = -1.704 Av
+ 192.7
(1)
The root mean square deviation of the temperature was &0.9 "C. The equations for the calibration of ethylene glycol as determined by some other laboratories may provide some insight into the magnitude of the errors in kinetic measurements resulting only from variations in techniques of temperature determinations. These equations are:
+ 192.8
Van Geet ( 3 )
T "C = -1.695 Au
Neuman and Jonas (3,8)
T "C = -1.691 Au
(3)
Varian ( 7 )
T " C = -1.656
(4)
+ 193.8 AU + 188.0
(2)
When arbitrary ethylene glycol line separations at the low, middle, and high temperature ranges were substituted in the four equations, the results in Table I were obtained. It is evident that at higher temperatures major differences occur and variations as large as 4 ‘C were observed among the different methods. These differences are rather significant since in the literature Equations 2, 3, and 4 have all been used to a certain extent in the calculation of kinetic parameters, and these differences may show up as systematic errors in the rate parameters. A sample calculation based on the literature values for the internal rotation of N,N-dimethylformamide is given in Table 11. The deviations, though not grotesque, are large enough to be annoying, In view of the painstaking experimental and computational work needed to derive accurate rate data, such obvious systematic errors are certainly unwarranted, and should be minimized, especially in regard to accurate temperature measurements. This, no doubt, may be accom-
plished if NMR kinetic measurements are performed in coaxial tubes with a calibrated temperature standard in the outer jacket. LITERATURE CITED (1) A. Allerhand. H. S. Gutowsky, J. Jonas, and R. A. Meinzer, J. Am. Chern. SOC., 88, 3185 (1966). (2) R. Duerst and A. Merbach, Rev. Sa‘.lnstrum., 38, 1896 (1965). (3) A. L. Van Geet, Anal. Chem., 40, 2227 (1966): Professor Van Geet has informed us that he has further refined his published equation, giving a result with which our data agree even more closely. His most recent results ( T OC = -1.705 Au 193.2) were presented at the Tenth Experimental NMR Conference, Mellon Institute, Pittsburgh, Pa., February 1969. (4) A. L. Van Geet, Rev. Sci. lnstrum., 40, 1914 (1968). (5) A. L. Van Geet, Anal. Chem., 42, 679 (1970). (6) 0. Yamamoto and M. Yanagisawa, Anal. Chem., 42, 1483 (1970). (7) Varian Associates, Palo Alto, Calif. 94303, Publication No. 87-202-006. (8) R. C . Neuman and V. Jonas, J. Am. Chem. Soc.,90, 1970 (1968). (9) M. Rabinovitz and A. Pines, J. Am. Chern. SOC.,91, 1588 (1969).
+
RECEIVEDfor review March 26, 1975. Accepted May 15, 1975.
Diffusion Cell for the Preparation of Dilute Vapor Concentrations Antonio H. Miguel and David F. S. Natusch School of Chemical Sciences, University of Illinois, Urbana, Ill. 6 180 1
One of the more difficult problems associated with analytical investigations of air pollutants involves the generation of known constant concentrations of gases and vapors. Most commonly such standard concentrations are required for calibrating instruments which operate in the parts-permillion (pprn) range, for use in diagnostic studies of analytical methodology, or for providing a constant source for experimental investigations of control processes ( I , 2). In all cases, it is desirable to have a continuously flowing gas stream in order to minimize errors due to adsorption on glassware and to provide large quantities of the gas mixture (3,4 ) . Permeation devices offer a simple method of preparing low concentrations of gaseous materials in the range of 0.001 to 100 ppm, depending on the thickness of the walls, the length and temperature of the tube, and the flow rate of the diluent gas ( 5 ) .A variety of gases, liquids, and solids have been permeated through Teflon, PTFE, and F E P to produce low concentrations of these materials in air or other gases (6-11). A dynamic dilution device which can be used for the production of gases in the 10- to 1000-ppm range has been described by Axelrod et al. (12). The simplest procedure for generating standard vapor concentrations is based on achieving either saturation conditions or a known rate of vapor diffusion into a diluent gas stream. Several devices based on these principles have been described in the literature (13-16) and their operating characteristics have been presented in a comprehensive article by Altshuller and Cohen ( 17). In this paper, we describe the construction, operation, and evaluation of a simple diffusion cell which can be used to obtain large amounts of a standard vapor ranging in concentration from a few ppm to several thousand ppm. Its main advantages over comparable devices are improved flow geometry which allows very precise calculations of experimental diffusion rates from theoretical diffusion coefficients, ease of operation over a wide range of concentrations, and the ability to maintain constant vapor concentrations over prolonged operating periods.
EXPERIMENTAL Apparatus. The diffusion cell (Figure 1) was constructed from Pyrex tubing, 8.0 cm long and 3-cm 0.d. The diffusion tube, D, which contains the liquid sample, was made from Kimax tubing, 8.0 cm long and 1.1-cm i.d. The diffusion tube holder, E, is an internally threaded glass connector (Ace Glass Catalog No. 7644-15) with a Teflon bushing and “0” ring (Ace Glass Catalog No. 750627). The diluent gas enters the cell via tube A . Its flow through the diffusion cell is controlled by a 4-mm Teflon valve, E , and is delivered t o the cell chamber, C, through a capillary, F , which is 2 cm long and 1.0-mm i.d. The diluent gas flow rate is monitored by a calibrated flow meter (Brooks Instrument Division No. R-2-15-B) situated between the Teflon valve, B, and the diluent gas supply. The standard vapor mixture leaves the cell through tube H, and can be sampled for analysis through a septum sealing tube, G. Where very low vapor concentrations are required, secondary dilution can be employed by introducing the gas mixture from tube H, into a second diluent gas stream. The whole device is enclosed in an insulated box equipped with an air circulating fan and a 100-watt lamp which is operated by a proportional heater controller (Texas Instruments, Inc. Bulletin No. DL-S 7211595, May 1974). This controller is capable of maintaining the cell temperature constant within f0.5 “C (long term). The temperature can be maintained to within fO.10 “C (short
Figure 1. T h e diffusion cell ( A ) Diluent gas inlet, ( B ) diluent flow rate control valve, ( C ) mixing chamber, (D)diffusion tube, ( E ) diffusion tube holder, (4diluent delivery tube, (G)sampling port, (.cl) vapor mixture outlet ANALYTICAL CHEMISTRY, VOL. 4 7 , NO. 9 , AUGUST 1975
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