STUDY 0? EENDEREE [RTE—WE. QGYATEQN EN SOME $UBST'ETU'FED AMIDES BY NUCLEAR MAGNETIC RESONANCE SF‘EC‘FR-G‘WGFY "flint: Ear {he Dogma (3&3 DE. D. EXCEEGAN STATE UMVEESIIT‘L’ JflmmmémflvutVmeflmey 1960 11-15614 0;. MICHIGAN. STATE UNIVERSITY OF AGRICULTURE AND APPHTD SCIENCE DEPARTMENT OF CHEMISTRY EAST LANSING, MICHIGAN STUDY OF HINDERED INTERNAL ROTATION IN SOME SUBSTITUTED AMIDES BY NUCLEAR MAGNETIC RESONANCE- SPECTROSCOPY BY Jame 5 Calvin Woodbrey A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1960 a - ~ .( f ., '3 i? ~~*’ Q s" it 2 fl} (‘4‘ .{PI ,.ut In M emo riam MARJORIE MABELLE HEWES ii ACKNOWLEDGMENTS It is with sincere appreciation that I acknowledge the counsel of Professor M. T. Rogers under whose direction this investigation was conducted. ‘ I also wish to express my gratitude to Doctor P. T. . Narasimham for many informative discussions during the early phases of this research; toMr. Forrest Hood for fabricating the glassware; to the UnionICarbide Corporation for a fellowship, and to the National Science‘Foundation for grants subsidizing part of this research. To Connie, my wife, who patiently gave encouragement and self sacrifice in order that I might complete this phase of my education, I offer my everlasting appreciation. ************** iii VITA James Clavin Woodbrey candidate for the degree of Doctor of Philosophy Dissertation: Study of Hindered Internal Rotation in' Some Substituted . Amides by Nuclear Magnetic Resonance Spectroscopy Outline of Studies Major: Physical Chemistry Minor: Physics and Organic Chemistry Biographical: Born, October 16, 1934,- Sebago Lake, Maine Undergraduate Studies: B.’ S. ,- Chemistry, The University of Maine, Orono, Maine, 1956. Professional Affiliations: American Chemical Society The Society of Sigma Xi Tau Beta Pi ' Sigma Pi Sigma iv STUDY OF HINDERED INTERNAL, ROTATION IN SOME - SUBSTITUTED AMIDES BY NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY BY James Calvin Woodbrey AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Departrn ent of Chemi st ry 1960 Approved ABSTRACT A Varian high-resolution nuclear‘magnetic resonance spectrom- eter was used for observing proton and fluorine magnetic resonance spectra of several symmetrically N, N-disubstituted amides over a wide range of temperatures. Apparatus for controlling sample temperatures at high or low values was constructed. Also, coils for electrically shimming the applied magnetic field were constructed. The use of these coils was essential to the observation of high- resolution fluorine magnetic resonance spectra at the applied radio- frequency 60. 000 mcs. Theoretical methods for relating the rate of internal rotation about the central C-N bond of the substituted amides to various components of resonance line shapes were considered. Three of these methods were applied experimentally to the study of the phenomenon of hindered internal rotation. Of the three-methods used, only one was well adapted to the study of hindered internal rotation about the central C-N bond of the symmetrically N, N-disubstituted amides used in this work. This method relates the ratio of maximum to central minimum absorption intensities of a symmetrical resonance doublet to the rate of internal. rotation. The energy barrier and frequency factor, for each internal rotation studied, were calculated from the experimental temperature dependence of the rate of internal rotation. The experimental errors were much lower than those previously reported for similar studies. ‘ ‘ The phenomenon of hindered internal rotation about the central C-N bond of the following pure liquid amides was studied: N, N-di- methylformamide; N, N-dimethylacetamide; N, N—dimethylprOpionamide; N, N- dimethyltrichloroacetamide; N, N- dimethyltrifluoroacetamide; N, N-dimethylacrylamide; and N, N- dimethylcarbamyl chloride, The internal rotation about the C-N bond of N, N- dimethylbenzamide was studied for a. solution of the amide in dibromomethane. ~ Similar studies were made for a solution of N, N-dibenzylacetamide in dibromo- methane, and for a solution of this amide in carbon tetrachloride. The apparent rates of internal rotation about the central C-N bond of ethyl-N, N- dimethylcarbamate, and about the central C-N bond of methyl-N, N-bis-(trifluoromethyl)-carbamate, were too fast to be detected, even at quite low temperatures. In addition, the presence of hindered internal rotation about the central C-N bond of N, N-bis-(trifluoromethyl)-trifluoroacetamide could not be detected. The origin, of the barrier to internal rotation about the C—N bond of the amide group is attributed to the existence of partial C=N bond character, which arises from resonance between valence bond structures. Some possible explanations for the exceptionally high barrier observed for N, N-dimethylformamide are the following: a small amount of intermolecular association of the pure liquid, the nonexistence of contributing resonance structures that would suppress the partial double bond character of the central C-N bond, and the possibility of the barriers for all the other amides being suppressed by transition states which involve excited electronic states. The low-barrier compounds were compared with N, N-dfiethylacetamide. The values of the energy barriers for these compounds were explained in terms’ of contributing resonance structures which suppress the double bond character of the central C-'N bond. For most of the internal rotations studied, the experimental 1 frequency factors were from about 105 to 107 sec.‘ These low values were attributed to low transmission coefficients. vii The phenomenon of hindered internal rotation about the central C-N bond of N, N—dimethylpropionamide was studied for several solutions of the amide in dibromomethane and in carbon tetrachloride. The con- centration dependence of the barrier to internal rotation for the amide in dibromomethane solutions suggests the possible existence of a specific solvent-solute interaction. When the amide was diluted with carbon tetrachloride, the barrier was observed to decrease markedly. This decrease is attributed to the dissociation of the slightly associated pure liquid amide upon dilution. Similar effects were observed for solutions of N, N-dimethylcarbamyl chloride in dibromomethane and in carbon tetrachloride. The apparent very rapid internal rotations about the central C-N bond of ethyl-N, N~dimethylcarbamate, and about the central C-N bond of methyl-N, N-bis~(trifluoromethyl)—carbamate, are attributed to a low energy barrier for the internal rotations. These compounds have important resonance structures which tend to suppress the double bond character of the central C-N bond. viii ' TABLE OF CONTENTS INTRODUCTION . . ........... EXPERIMENTAL . . . . . . . . "Spectrometer . . . . . . . . . . Probe mounting . . . . . Modifications for Observing Spectra at High or Low Temperatures. . . . . . . . . . . . Vacuum-jacketed receiver coil inserts . . . . Sample spirming . . . . . . . Temperature control . . . . Temperature measurement ............. Current Shims . .......... Resolution... ..... Materials Used . ‘. . . . . . . . . . Preparation of Samples . . . . Rotations o o o o o o o o g Determination of Energy Barriers for Hindered Internal HISTORICAL REVIEW . ........... . ......... THEORETICAL BACKGROUND ................. Method I . .............. . ..... MethOdII......... MethodIII........ External Chemical Shifts. . . . . . Calculation of Errors in the Energy Barriers and Frequency Factors . . . . . . . RESULTS................. High-resolutionSpectra . . . . . . . . N, N-Dimethylformamide. . . . . . . . ..... N, N-Dimethylacetamide . . . . . ......... N, N— Dimethylpropionamide . ........... N,N-Dimethyltrichloroacetamide . . ..... . N, N-Dimethyltrifluoroacetamide . . . ...... N, N— Dim ethylac rylamide N, N-Dimethylbenzamide N, N- Dibenzylacetamide . . ix 0 9 -N, N-Dimethylcarbamyl chloride. . ..... . . Page 12 54 54 55 56 59 60 61 64 66 69 69 72 73 74- 76 78 83 83 85 85 85 87 87 89 89 92 92 95 95 TABLE OF CONTENTS - Continued Ethyl-N,N-dimethylcarbamate . . . . . . . . . N, N-Bis- (trifluoromethy1)-trifluo roacetamide. Methyl-N, N-bis-(trifluoromethyl)-carbamate . Hindered Internal Rotation. . . . ....... . N, N-Dimethylformamide. . . . . . . . . . . . N, N-Dimethylacetamide . . . . . . . . .. . N, N-Dimethylpropionamide . . . . . . . . .. . N, N-Dimethyltrichloroacetamide . . . . . . . N, N-Dimethyltrifluoroacetamide . . . . . . N, N-Dimethylacrylamide. . . . ....... . N, N-Dimethylbenzamide . ‘. . . . . . . . . . . N, N-Dimethylcarbamyl chloride . . . . . . . . N, N-Dibenzylacetamide ............. DISCUSSION..... ..... ..... Methods for Obtaining Energy Barriers and Fre- quency Factors for Hindered Internal Molecular Rotations by High- resolution Nuclear Magnetic Resonance ................. . . . Results. . . ...... _ ..... . . . . . . .‘ ..... . SIJMMARY O ..... O O O O O O O O O BIBLIOGRAPHY .......... . . ..... . . Page 98 98 98 100 100 100 100 115 115 115 115 115 142 162 162 168 176 179 TABLE I. II. HI. IV. V. VI. VII . VIII . LIST OF TABLES Page Electric Moments and Dielectric Constants for Some Primary and N-Substituted Amides. . . . . . 9 Summary of Some Early NMR Results for the Hindered Internal Rotation in N, N- Dimethyl- formamide (DMF) and N, N-Dimethylacetamide (DMA)..... ......... 11 Some Physical Constants for Materials Used. . . . 70 Proton Chemical Shifts for Some Solutions of N,,N-DimethylprOPionamide. . . . . . . ...... .90 Proton Chemical Shifts for some Solutions of N, N-Dimethylcarbamyl Chloride. . . . ..... . 96 Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethylformamide, Method 111. . ..... . 103 Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N—Dimethylformamide, Method 11. . . . . . . . 104 Temperature Dependence Of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethylformamide, According to Gutowsky and Holm (5,6), Method 11. . . . . ......... 105 IX. Temperature Dependence of the Rate of Internal X. Rotation About the Central C-N Bond of N, N-Dimethylacetamide, Method 111. . . . . . . . . 111 Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethylacetamide, According to Gutowsky and Holm (5, 6), Method 11. ..... . ...... . 112 LIST OF TABLES - Continued TABLE Page XI. Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethylpropionamide, Method 111 . . . . . . 116 XH. Temperature Dependencies of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethylpropionamide in Dibromomethane 'Solutions, MethOdIII. . . . . . . . . . . . . . . .117 ‘ XIII. Temperature Dependencies of the Rate of Internal Rotation About the Central ‘C-N Bond of N, N- Dimethylpropionamide in Carbon Tetra- Chloride Solutions, Method 111 . . . . . . . . . . . 120 XIV. Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethyltrichloroacetamide, Method 111. . . 132 XV. Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethyltrifluoroacetamide, Method 111. . . 136 ‘XVI. Temperature Dependence of the Rate of Internal RotationAbout the Central C-N Bond of N, N-Dimethylacrylamide, Method 111. . . . . . . 138 XVII. Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethylbenzamide (36. 34 Mole Per Cent in Dibromomethane), Method III. . . . I. . . . . . . 140 XVIII. Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N-Dimethylcarbamyl Chloride, Method III. . . 143 XIX. Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of AN, N-Dimethylcarbamyl Chloride in Dibromo- methane Solutions, Method 111. . . . . . . .‘ . . . 144 LIST OF TABLES - Continued TAB LE XX. Temperature Dependencies of the Rate of Internal XXI. Rotation About the Central C-N Bond of N, N-Dirnethylcarbamyl Chloride in Carbon Tetra- chloride Solutions, Method 111. . . . . . . . . . . Temperature Dependence of the Rate of Internal Rotation About the Central C-N Bond of N, N—Dibenzylacetamide (38. 09 Mole Per Cent in Dibromomethane), Method III. . . . . . ..... XXII. Temperature Dependence of the Rate of Internal Rotation About the Central C—N Bond of N, N-Dibenzylacetamide (38. 29 Mole Per Cent in Carbon Tetrachloride), Method 111. . . ...... XXIII. Values of Ea, A, AFlge. z and TC for Hindered Internal Rotation About the Central C-N Bond of Some Symmetrically N, N-Disubstituted Amides as Determined by Proton Magnetic Resonance Spectroscopy. . . . . . ._ ............. xiii Page 146 156 158 160 LIST OF FIGURES FIGURE Page 1. Resonance formulae for amides. . . ...... ‘. . 3 2. Structural formula for the amide group in peptides 10. 11. and related substances. . . . . . . . . . . .. . . . Structural formula and dipole moment for formamide..... ..... Representation of unsaturated and "slow-passage" NMR line Shapes. O O C O O O O O O O O O O O O O I O . The effect of overlap of two equally intense reson- ance lines on their apparent separation, as a function of line width 2/Tz. . . . . . . . . . . . . . . Cross sectional drawing or probe body, vacuum- jacketed receiver coil insert, upper chamber, and mounting plate and tube. . . . . . . . . . . . . . . . The RF probe, some accessories for controlling temperature, and the probe mounting. . . . . . . . Diagram of circuit used for monitoring and measur- ing sample temperatures. . . . . . . . . .' . . . .. . Diagram of shim coils and circuits ...... . . . Solid curve: ratio of maximum to central minimum intensities, r, for two equally intense absorption lines as a function of exchange rate 1/2 '2: . Dashed curve: observed separation five of two equally intense absorption lines, relative to the observed separation in the absence of exchange 6 v, as a function of exchange rate. . . . . . . . . . . . . . . H1 magnetic resonance Spectrum of HCON(CH3)Z. . . 24 48 57 63 65 67 82 86 LIST OF FIGURES - Continued FIGURE 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. H1 magnetic resonance spectrum of CH3CON(CH3)2. Hlmagnetic resonance spectrum of CH3CHZCON (CH3)2 000000000000 o 000000000000 Hl magnetic resonance spectrum of CC13CON(CH3)2 F‘9 magnetic resonance spectrum of CF3CON(CH3)Z H1 magnetic resonance spectrum of CF3CON(CH3)Z Hl magnetic resonance spectrum of CH2 2 CHCON R—C + \ \. Nu-H 1|\I-H l H H A B Figure 1. Resonance formulae for amides. He empirically estimated the resonance energy to be about 21 kcal./ mole'l, and the basicity constantfor the amide group to be of the order of 10-20. Such a high resonance energy suggests restricted (or partially restricted) rotation about the C-N bond, whereas the small basicity constant merely confirms the fact that most amides fail to form stable salts. Because N-methylacetamide is the simplest peptide molecule, a great number of investigations have dealt with physical and chemical properties of this and similar molecules (references 8 through 15 and many others). Mizushima and collaborators have used dielectric measurements and Raman, infrared, and ultraviolet spectroscopy to interpret the structure N-methylacetamide (16). They estimated the resonance energy for this molecule to be about 16 kcal. /mole. Their measurements provided evidence that nearly all the molecules exist in the mconfiguration over the temperature range: ca. 25—950C. Also, the data indicated that intermolecular hydrogen bonding causes considerable chain-like association of the trans amide in carbon tetra- chloride solution. Mizushima has also shown that hindered internal rotation about the CuN bond in amides is an important consideration in theories pertaining to the structure of protein molecules (17). Cannon has made extensive infrared absorption measurements for a number of amides in carbon tetrachloride/chloroform and carbon tetrachloride/anhydrous hydrogen chloride solutions (18). When diluted with carbon tetrachloride, the N-H absorption band for N- ethylacetamide shifted to higher frequencies. This shift was attributed to depolymer- ization upon dilution. From the infrared spectra Of N- ethylacetamide in the mixed solvents, it was concluded that this amide is much less associated in chloroform than in carbon tetrachloride solutions. When N, N—diethylacetamide and N, N-dimethylacetamide were diluted with various mixtures Of carbon tetrachloride and chloroform, frequency shifts for the CzO absorption band were observed for both dilution and changes in solvent. These changes were attributed to changes in the dielectric constant of the solution; association due to hydrogen bonding being assumed negligible for these compounds. The infrared spectra of N- ethylacetamide in solutions of carbon tetrachloride plus anhydrous hydrogen chloride indicated that protonation of this amide occurs at the nitrogen atom: CH3CONHZCZH5. Finally, Cannon concluded that the C=O group of secondary amides readily forms hydrogen bonds with proton donating molecules, whereas the N—H group is inert (somewhat doubtful), neither donating nor accepting a proton for hydrogen bond formation. The question as to whether amides preferentially protonate at the oxygen atom or at the nitrogen atom has been the subject of several investigations. From infrared absorption measurements of crystalline urea nitrate, Davies and Hopkins have concluded that urea preferentially + protonates at the nitrogen atom: HZNCONH3 (19). Based upon similar spectral measurements in the infrared and ultraviolet regions, Spinner has concluded that the salts of urea, thiourea, and acetamide are also preferentially protonated at the nitrogen atom: HZNCONH3, HZNCSNHg, and CH3CONH3 (20). However, Goldfarb, (33: al. , have interpreted their ultraviolet spectral measurements on several amides in sulfuric acid solutions as evidence for preferential protonation at the oxygen atom: HOCRNHR <———-> HOCRIi-IHR. (21). Fraenkel and Niemann have observed the NMR Spectra of several N— substituted amides in acidic solutions, from which they concluded that amides preferentially protonate at the oxygen atom (22). Berger, Loewenstein, and Meiboom have studied the protolysis kinetics of N-methylacetamide in aqueous solutions using a high-resolution PMR technique (23). They found the protolysis reaction to be both acid and base catalyzed, the reaction rate being proportional to the amide concentration and the hydrogen ion concentration. The data indicated that protonation at the oxygen atom is preferred, but that an equilibrium exists between N- and O- protonated ions. Also, they found that acidification Of N, N-dimethylacetamide reduced the energy barrier to internal rotation about the central C-N bond to the extent that "free rotation” occurs (obviously, the authors mean free rotation on the NMR time scale—-their spectrometer frequency was 31. 65 mcs. ). These workers attributed this reduction in the energy barrier to the minor N-protonation, thus leading to destruction of the partial O-C=N character. Takeda and Stejskal have confirmed the PMR studies of the protolysis kinetics of N, N-dimethylacetamide, and they have extended the work to the investigation of the similar protolysis kinetics of N, N-dimethylformamide (24). In these protolysis studies, the kinetic equation of major importance may be written as k1A + (RCOHNHCH3) + H20, (1) RCONHCH3 + (H,O)+ sz where the reported equilibrium values Of kIA are as follows: 380 i 40 sec. ”M“ at 23 a: 2°C. (23) and 200 a 70 sec. "M“ at 25°C. (24) for Namethylacetamide and 10 :I: 3 sec. “'IM”1 at 250C. for Namethylformamide (24). Spinner has recently made an unsuccessful attempt to explain the apparent contradiction between infrared Spectral results which have been interpreted as evidence for preferential protonation of amides at the nitrogen atom (18, 19, 20), and NMR data that have shown that preferential protonation takes place at the oxygen atom (22, 23, 24). As Spinner pointed out, the internal rotation about the C~N bond in acetammonium type ions (e. g. CH3CONH3) is not "free. " Rather, such internal rotations are probably hindered by energy barriers of about one to three kcal. /mole (i. e. , energy barriers of about the same magnitudes as those inhibiting internal rotations of methyl groups). However, the frequencies of internal rotations (or torsional oscillations) with such small energy barriers are too great to be detected by existing NMR techniques. Spinner has suggested that the NMR doublet observed for the N-methyl group of N-methylacetamide in highly acidic solutions, [(CH3CONHCH3)H]+, is due to chemical nonequivalence Of the protons on the N-methyl group, resulting from hindered internal rotations about the C-N-C bonds. This suggestion is 119‘. correct. Chemical non- equivalence of the type suggested by Spinner would lead to an unsymmetri- cal 2:1 doublet. Such a doublet is not Observed. Indeed, the Observed symmetrical doublet has been shown to be the result of spin- Spin coupling and not chemical shift differences (23). Corey and collaborators have determined the structure of the amide group in a number of peptides and related substances (26). Their resultsgbased on several X-ray struCture determinations, are shown in‘Figure 2. In this structure, the value of the O=C-N bond angle is about the same as the tetrahedral value 125016'. The central C-N bond Figure 2. Structural formula for the amide group in peptides ' and related substances. distance, 1. 32 X, is 0.13 X shorter than the normal C-N bond dis- tance. This is evidence for about 40 per cent contribution of the resonance structure analogous to B of Figure 1 (27). Kurland and Wilson have reported the structure and dipole moment of formamide, as determined by microwave spectroscopy (28, 29). They found this molecule to be planar, thus proving that the resonance structure analogous to B of Figure 1 is a major contributor to the normal state of the molecule. The structure and dipole moment of formamide are diagramed in Figure 3. As expected, the C-N bond distance is appreciably shorter than the normal CAN bond distance. This confirms the ,I=3.714a .06D H 3‘. . 002 Ho Figure 3. Structural formula and dipole moment for formamide. _ + - existence of considerable O-C=N bond character. Pauling has suggested that in addition to the normally expected O-C=N contribution, the C-N bond in amides might have some contribution of multiple bonds involving the p orbitals normal to the plane Of the group (30). Electric moments and dielectric constantS'have been measured for numerous primary and N— substituted amides. These data are tabulated in Table I. From the electric moments Of several halogen— substituted benzamides, Bates and Hobbs have shown that the amide group moment is oriented at an angle of about 700 to the C-aC bond between the aromatic ring carbon atom and the carbon atom of the amide group (31). Using high-resolution PMR at the Spectrometer frequencies v0 , 30 and 40 mos. , Phillips proved that the doublet PMR structure for N, N-dimethylformamide and N, N-dimethylacetamide was due to the chemical nonequivalence of the protons of the two N-methyl groups (39). This confirmed unequivocally the existence of highly hindered internal- rotation about the central CwN bond in these amides. Also, he found evidence that the compounds N-methylformamide and N-methylacetamide exist in only one configuration. ' The PMR studies ‘by Phillips were confirmed later by Gutowsky and Holm (5,6). Using PMR at the spectrometer frequency 17. 735 mcs., they also observed that when N, N-dimethylformamide and N, N-dimethyl- acetamide were heated, the two N-methyl resonances coalesced to a single line. This coalescence was attributed to thermal enhancement of the internal rotation about the central C-N bond. They related the temperature dependence of the internal chemical shift between the two N-methyl resonance lines to the rate of the internal rotation. From the eXperimental temperature dependencies Of these chemical shifts for N. N—dimethylformamide and N, N-dimethylacetamide, they were able to estimate the following: energy barriers Ea, frequency factors A, the temperatures at which the chemical shifts coalesced to zero .coflmcfifiz vamp o>d30n OMS Om damnmmu * $3 33 Sam nEOE/560...an :3 m .m anamzoovamo :3 e axamzoow :3 as .m :3 e: .m amzooemsoamVa :3 36 :3 Sim NEZOOJISOsmén :3 3.... :3 and .mzooflaofim :3 $.m :3 3.... smzoofiac:o-8 mm am“ :3 $5 NE,HOO...E..O :3 mm .m :3 es .... ...mzoomoaxamonv- :3 S .m .ENOTZOOEAO-” :3 £5 :3 $4.. amzoofaoé $3 Rem: max: _ nmomzoosmao :3 mm: :3 and Nmzoomaso $3 :3 me .m :3 on .m Ammaovzooamo 33 3:; 5.3 ....m 8.3 :3 and Ammovzooamo :3 5 .m aTania/HOMES 33 A .3: 3: mm .s ...:omzousmo .553 was mm om .M :3 as. .mzooamo $3 33 Sam em 3.? sxamovzoom 33 it: mat ”momzoom :3 LR... .. :3 .3: $3 .3: - 3:10.46: £3 85 :3 $5 Nmzoom .mom .Uomm .Uoom .wom 6:383 .wmm ocoucmn. .w .ucmumcoo QCOOOHOAQ .803 80.3». CGDOQEOU . . .Q .1 .Q .1 .LIHI. 1.Hal(l. .7 H ”mamas. mHQHHZ/w QHHDHHBmmDm ..Z Q73». >m<§HmQ MEOm mOh mHZ_ . The value Of T1 is a measure of the difference between the excess population and its equilibrium value, and it varies with the type of nucleus and its environment. » For this reason T1 measures the extent of spin-lattice interactions. Here, the lattice is considered as any degree of freedom that may give rise to local fluctuating magnetic fields; some examples are electron spins, electron orbital motions, and fluctuating electric fields arising from nuclear electric quadrupole moments. Liquids of low viscosity tend to have small values of T1, about 10-2 to 102 seconds; solids may have T, as large as several days; and paramagnetic substances may have values of T, as small as 10" seconds. The quantum-mechanical treatment of NMR absorption predicts extremely sharp absorption lines. This arises from the use of the Dirac 6 function in calculating transition probabilities. In reality, the absorption lines are broadened because of various factors. Therefore, in the quantum-mechanical formulation, an arbitrary line-- shape function g (v) is introduced to account for the line broadening. The form of g (v) is such that it is proportional to the absorption intensity at any frequency v. In addition, it is usually convenient to normalize g (v); i. e. , co f g (v) dv = 1. (9) 0 There are about six factors which may cause broadening of NMR absorption lines; these are Spin-lattice relaxation, magnetic dipole interactions, electric quadrupole moments, applied field inhomogeneity, and spontaneous emission. Because of the possibility of spontaneous emission, the line width of any spectrOSCOpic transition may have a lower limit determined by 16 the finite lifetime of the upper state (49). For the case of nuclear spin transitions this possible cause of line broadening was shown to be negligible compared to the broadening due to other factors (50). The finite lifetimes of both states are Of more importance, since other atomic and Inolecular degrees Of freedom may induce transitions between them. This is the always-present spinwlattice relaxation men- tioned earlier. The broadening caused by this type of relaxation is estimated from the uncertainty principle to be of the order 1/T‘x. Although Spinelattice relaxation may occur by many mechanisms, frequently the most important is that of direct interaction of neighboring dipoles. This interaction depends upon the dipoleudipole distances and their relative orientations so that energy may be transferred to the Spin system from translational and rotational degrees of freedom. In some highly viscous liquids and in solids, where nuclei stay in similar relative positions for a long enough time, interactions of magnetic dipoles lead to greater line broadening than given by the spin- lattice relaxation time. In such cases, it is necessary to treat nuclei as being in all the local magnetic fields of neighboring dipoles. When broad- ening due to Spin-lattice relaxation is minor compared to direct dipole- dipole interactions, another characteristic time constant T; is usually defined. The convenient definition of T2 is in terms of the line-shape function g (v): T2 5 i" [g(V)]max, . (10) Here the factor 1/2 is introduced to make this definition Of T2 consistent with that of Bloch's definition to be mentioned later. Because the inter- action of nuclear magnetic dipoles is the predominant cause of line broadening in many solids, T2 is often called the Spin- spin relaxation time. When molecules rotate and tumble rapidly, as in fluids of low viscosity, the local magnetic fields become averaged and only 17 spin-lattice relaxation remains. In these cases T! and T2 are equivalent, or very nearly so, and only one time constant need be employed. Line broadening may be increased by the presence of nuclei of Spin I > 1/2. These nuclei may have electric quadrupole moments which interact with fluctuating electric field gradients. AS mentioned earlier, this is another Spin-lattice relaxation mechanism. The widths of absorption lines due to nuclei in fluids of low viscosity are frequently determined by inhomogeneities in the applied static magnetic field He over the volume of the sample. This is an instrumental limitation and really leads to the superposition Of absorptions due to molecules in different regions of the sample. Consideration of the cla ssical equation Of motion for a magnetic dipole in a magnetic field reveals much information about the nature of resonance absorption. The nuclear magnet experiences a torque it A 1:1, which by Newtonian mechanics must equal the rate of change of angular momentum ”L . The nuclear magnetic moment and the angular momentum are collinear. Their ratio is defined by the scalar 7, called the magneto- 0: yric or gyromagnetic ratio. The classical equation Of motion may then be written as ' P 1 : —-—“"' : (.1 A H . (11) W 7 W “II Equation (11) represents the precession Of the magnetic dipole u about the field H with angular frequency “59', where 2 : — ‘Y 21 (12) The angular frequency Of nuclear precession is called the Larmor angular or precessional frequency. For an applied field of several kilogauss, most nuclei have a Larmor angular frequency of the order 18 of a few megacycles per second, or in the radio frequency (RF) range. If the total applied field is a constant 510, then in a coordinate system rotating with the Larmor angular frequency—71:10 the magnetic moment H is stationary. That is, in the rotating frame, the effect of the applied field £3140 is reduced to zero. In addition to HO, consider the application of a field of constant magnitude H1, which ”is rotating about and perpen- dicular to the direction of M130. If the angular frequency of 1:1, is different from that of the Larmor angular frequency, then E1 will be rotating in the rotating frame. The applied rotating field H, exerts a torque )3; A 1:11 on the nuclear dipole, tending to turn its moment to the plane perpendicular to £10 . When 1:11 is moving in the rotating frame, the torque E A 1:11 varies rapidly, and the result will be a slight wobbling perturbation. of the steady precessional motion of the dipole 31° When H1 is stationary in the rotating frame, that is, when 1:11 is rotating with the Larmor precessional frequency, then it acts as a stationary field and the torque .1“: A “1:11, remaining in the same direction for a long time, will affect large oscillations in the angle betweenit and Ho . When the angular frequency of ~11, is varied through the Larmor angular frequency, the oscillations will be largest at the Larmor frequency and will show themselves as a resonance phenomenon. ~A similar resonance will occur if £11 is in a fixed direction but varies sinusoidally in magnitude with a frequency in the vicinity of the Larmor value. Such a variation can be resolved into two fields rotating with equal angular frequencies in opposite directions, the phases being appropriate. The'component rotating in the direction Opposite to the Larmor precessional frequency will have very little effect on the resonance. In his original formulation of the behavior of nuclear magnetic moments in variable magnetic fields, Bloch used a set of phenomenological equations for the variation of the components of the total nuclear magnetic moment per unit volume (51). These important equations are the bases for the discussion of the time dependent phenomena to be considered later. l9 Summing equation (11) over unit volume, one may write M=7MAH, (13) M where M is the macroscopic moment in unit volume. Equation (12) does not allow for the relaxation effects already mentioned, so it must be modified by addition of appropriate damping terms. The component Mz approaches an equilibrium value, which is the product of the volume susceptibility, equation (6), and the field Hz = Hit). The rate of approach to equilibrium is governed by the spin-lattice relaxation time according to the equation ‘ Mz - Mo M 2: - —-————_ . 14 Because T1 is the time—constant determining relaxation of the magnetic zation in the direction parallel to the large static magnetic field Ho, it is called the longitudinal relaxation time. The solution of equation (13) shows that the component of M perpendicular to H0 rotates about the z-axis with the Larmor angular frequency. However, because of fluctuations and relaxation effects, the individual nuclei will get out of phase, and the components Mx and My will decay to zero. Similar to the longitudinal relaxation, Bloch assumed this transverse relaxation to be an exponential decay with the characteristic time-constant T3. The equations of relaxation for the x and y -compqnents are then sz ' Mx/th (15) My = - My/Tz. (16) The time constant T; is called the transverse relaxation time. 20 The complete equations of motion for the magnetization vector in unit volume are obtained by adding the right-hand sides of equations (14), (15) and (16) to that of equation (13). In the NMR experiment, the vector liof equation (13) takes on the components szHl coswt — —H, sinwt (17) *< I Hz:Ho Thus the complete Bloch equations are . . Mx MX : ’y (MYHO + Mz H1 s1n u) t) - T: (18) . _ Mz 1 My - 7(MZH1 cos 6.) t - MxHo) — ,—I,—Z— ( 9) . M _ Mz = 7(--MXH1 sin .5 t - MyH, cos ... t)- fi—M-l. (20) 1 In substances of high viscosity the locations (not directions) of nuclear spins may remain essentially fixed for long times. The spin- lattice relaxation time T1 is then very large, and M2 changes only slowly. If the range of local fields due to neighboring nuclei is 6 H, the nuclei will be precessing at angular frequencies which cover the range 7 (6H). As a result, individual nuclei will get out Of phase in a time 1/'y(6 H) and the amplitude of Mx or My will decay in a time T2 ‘3 1 / 7(6 H). Under the above conditions the decay of Mx and My will be very rapid while that of M2 will be very slow. Herein the reason for the t_w_q time constants T1 and T2 is explained. The equivalence of the constant Tz, as introduced by Bloch, to that defined earlier will become apparent with the final solutions of the Bloch phenomenological equations (18), (19), and (20). ..- 21 In fluids of low viscosity where molecular motions are rapid, the local magnetic fields due to neighboring nuclei become averaged to a very narrow range of values. In this case T1 and T3 are essentially the same, and in the absence of any paramagnetic materials the nuclear resonance lines are very narrow. This permits the resolution of very closely Spaced resonance lines. The whole field of high-resolution NMR spectroscopy falls into this last mentioned class, and only systems belonging to this class are of interest in this present work. At this point, it is worth noting that the nonequivalence of T1 and Tzin liquids may frequently be used to measure the rate of molecular tumbling, self diffusion or intermolecular exchange of nuclei. In order to obtain quantitative relationships between the shape of an NMR signal and the values of the relaxation times T1 and T2, it is desirable to solve the Bloch equations. These equations, (18), (19) and (20), are simplified by transforming to a set of coordinates rotating with frequency—w about the z—axis. The new components of M, u and U" , are called the in-phase and out-of—phase components respectively of the RF magnetization Mrf. Since all the components of M in the new frame are orthogonal, the RF magnetization is conveniently written as the complex number Mrf = u + i7f' (21) The transformations from the rotating frame to the Cartesian frame are sz ucoswt-Vsinwt (22) My 2-71. sinw t - 2!“ cos wt, (23) and the inverse transformations are 22 uzchoswt-Mysinwt (24) If: 'Mx sin to t - My C08 00 t . (25) The Bloch equations in the new rotating frame are then written as ZZ+—2(—'-+ A0020 (26) T2 ‘ 2f 'U’+—,-r—-ZLAw+w1Mz=O (27) Z Mz+ M_Z_____'I"' Mo -U‘wl= 0: (28) l where A w 2 too - to = 7 H0 - to and ml = 1' H1. Equations (26), (27) and (28) are a. set of coupled linear differential equations with constant coefficients and are readily solved. The steady-state solutions of these equations are obtained by setting 22, 'U' and lfdz all equal to zero. The steady— state solutions are (01 T22 A u) 2 2‘ M0 1 + T;2 sz+ (012?sz ( 9) T V: _ “I 2 M0 1+ TZZAeZ+wlTT1TZ (30) 1+ TZ 7' MZ=M0 Z A“ (31) 1 + T22 A (02 + (012 T,Tz The rate of absorption of energy per unit volume is given by. -MK Hx, which is proportional to U", the out-of-phase component of the RF magnetization vector. Under conditions of "slow—passage, " e. g. , when the field H0 is varied slowly through resonance at constant to so'that 1.4 E 7}" 5 M2 '5 O, the rate of absorption of energy is proportional to ‘U’ of equation (30). If the magnitude of the oscillating field is small so that yzleTsz << 1 , (32) 23 then the rate of absorption of energy becomes prOportional to 2 T; 1+ T22 A (.02 ’ (33) which gives the form of the line-shape function g (v), 2 T g M = z (34) 1+ 4 E2 T} (wo-v)z Function (33) describes a Lorentzian or damped oscillator curve. Its peak value is given by [g (v)]ma_x. : 2 T2 ’ (35) which is identical with the earlier definition of T2; see equation (10). Returning to equation (30), one notes that at the resonant frequency, the denominator becomes 1 + wlleTz. This quantity is called the saturation factor. When it becomes greater than unity, the resonance is said to be saturated, or partially so, and the line shape is no longer correctly approximated by equation (34). Under suitable experimental conditions, it is possible to observe 26, the in-phase component of the RF magnetization vector. This is known as the dispersion mode and under conditions of "slow-passage, " the line shape function is proportional to equation (29). When saturation is negligible, i. e. when 'ylelleTz << 1, the dispersion mode line shape function is V0 - V 1+ 4 11%,} (v0 - v)2 (36) The forms of the absorption and dispersion modes, under conditions of "slow-passage" and negligible saturation, are shown in Figure 4. 24 (a) (13) f ' O O (vo-v) ———> (v.0—v)-—-> \/ Figure 4. Representation of unsaturated and "slow-passage" NMR line shapes for: (a) the absorption V—mode and (b) the dispersion ’lL omode. From equations (34) and (35) it can easily be shown that the width of the absorption 1.” -mode curve is 1/11 T3 at one-half maximum intensity. The value l/sz is called the natural line width, since it is the line width in the absence of "fast passage, " saturation, chemical exchange and other complicating factors. Similarly, the natural line width for the dispersion mode, the width from minimum to maximum, is l/Tr «F?— T;. In the above, only the features of a single isolated NMR line have been considered: When a spectrum has multiple resonance lines, the form of each line may frequently be represented by the Bloch equations, and under conditions of "slow-passage" and negligible saturation, by the Lorentzian curve. The Bloch equations, as discussed above, do not correctly represent the form of a spectral line when overlapped with another spectral line. Overlap, i. e. when the separation between lines is of the same order of magnitude as the natural line widths, is very common. The most important parameters derivable from high-resolution NMR spectra are obtained from experimentally measured frequency 25 separations and relative intensities. These two measured quantities are influenced, especially in regions of overlap, by the shapes of individual resonance lines. The theoretical background for resonance line shapes enables one to apply corrections to the apparent measured values of frequency separations and relative intensities. Of more importance in this present work is the influence of time-dependent processes upon the parameters determining resonance line shapes. Before consideration of this problem, it seems beneficial to discuss briefly the two most important causes for multiple line high-resolution NMR Spectra. These are chemical shift and electron coupled nuclear spin- spin interactions. As mentioned earlier, nuclear dipole—dipole and quadrupole moment interactions cause extensive broadening of (resonance lines. The effect of these two types of interactions upon the nature of the resonance spectrum depend upon the environment of the nuclei under observation. The existence of either of these two types of interactions usually causes such extensive broadening that resolution of closely Spaced lines becomes impossible. In the realm of high- resolution NMR spectroscopy, another environmental effect becomes extremely important. This effect is called the chemical shift, and its cause is magnetic shielding of nuclei by electrons. An atom or molecule acquires a diamagnetic moment when placed in a strong magnetic field. The moment results from the induction of orbital motions of the electrons. These electron motions constitute magnetically effective currents within the molecule or atoms which also act on the nuclei. These induCed currents are proportional to the applied field Ho, so the secondary field will also be proportional to H0. The local magnetic field at the position of the nucleus will be given by . Hlocal = H0 (1 ' 0' 1, (37) where 0‘ is called the screenirg constant. 26 Electron screening brings the nuclear Zeeman levels closer together so that the energy (resonance frequency) for a transition between states will be lower than for an unscreened nucleus. If the experiment is performed by varying Ho through resonance at constant frequency, the applied field necessary for resonance of a screened nucleus will be larger than that needed for an unscreened nucleus if, as is nonnally the case, the screen constant 0" is positive. Because the distribution of electrons in molecules may vary markedly with the nature of the chemical bonds, it is not surprising that strong applied magnetic fields cause differences in the electron screening of chemically different nuclei of the same species. The result of these differences in screening is that nuclei of a common Species but of chemically different groups will resonate at the various applied fields that are characteristic of each individual chemical group. The field separation of two such resonance peaks is referred to as the chemical shift. The closely related "Knight shift" in metals was first observed in 1949 (52), and chemical shifts for N“, F”, and HI nuclei were first observed by Proctor and Yu (53), Dickinson (54), and Linstr'om (55) and Thomas (56) respectively. Since these early observations, many theoretical consider- ations have been made concerning the nature of electron screening of nuclei. An excellent review of these works is given in Chapter 7 of reference 48. Chemical shift separations may be expressed either in units of magnetic field or in frequency units. The two systems of units are readily converted by use of the Larmor resonance condition, equation (12). From this and equation (37) it is apparent that the chemical shift is proportional to the applied field. Reported values of chemical shift separations must necessarily be accompanied by the values of the applied fields or resonant frequencies used in their measurements. Therefore, it is convenient to express chemical Shifts in terms of the dimensionless unit defined by 27 _ H-Hr Hr . (38) where H is the resonance field of the signal being measured at a fixed frequency and Hr is the corresponding value for a second resonance signal. The separation of resonance signals is usually most easily measured in frequency units by the well-known side-band technique (57), or the "Wiggle-beat" method (58, 59, 60). The chemical shift is then easily expressed as 5 : l’_Z_.‘.’_I_‘_ , (39) ”I where v is the resonant frequency of the signal being measured and vr is the corresponding value for a reference signal. Usually v1. is very nearly equal to the spectrometer frequency. Since both these frequencies are usually very much greater than v - vr, equation (39) may be rewritten as 6 : LLLE. . (40) ”o In this present work, the symbol 6 will be reserved for the purpose of expressing chemical shifts with respect to some stated reference signal in units of ppm, i. e. , values of 6 will be calculated by use of equation (40). For convenience, however, the symbols 6v and 66.: will be used to express the frequency separations of chemically shifted resonance lines in units of cps and radians per second respectively. The appropriate values of v0 and too will necessarily accompany all reported values of 6v and 6w respectively. In early NMR experiments on liquids it was found that many sub- stances show more resonance lines than required by simple considerations of the number of chemically nonequivalent nuclei (61,62, 63). Many mole- cules gave symmetrical doublets, triplets, quartets, etc. , and the frequency separations of the multiplet components were found to be 28 independent of the applied field H'o. On the basis of these early experi- ments, Gutowsky, McCall, and Slichter (64) and Hahn and Maxwell (65) proposed that the multiplets arise from the indirect interaction of neighboring nuclear Spins. They proposed that the energy of this type of interaction was proportional to the "dot" product 11 - “14', where l1 and ~11) are the nuclear Spin vectors of the two magnetically active but chemically different nuclei i and j reSpectively. The constant of proportionality, Jij = in, is called the nuclear Spin- spin coupling constant and is usually given in the energy units of Planck's constant; i. e. , in units of cps. In some special cases, Spin- spin coupling may occur between chemically equivalent nuclei. The independence of spin- spin coupling of the applied field may be qualitatively understood with the assumption that the magnetic fields responsible for the interaction arise within the molecule itself. A simple example of spin— spin coupling is provided by the molecule acetaldehyde, in which there are three chemically equivalent protons A, each of spin 1:: 1/2, and one other chemically different proton B of spin I = 1/2. The multiplet of the resonance of the three protons A will arise only from Spin- spin interaction with proton B. Interaction with C1?. or 016 each of I = 0 is impossible, and any interaction with the one per cent natural abundance of C13 of 1: 1/2 is of such low intensity that it may be neglected in the present consideration. Therefore, the resonance of the three A protons is a symmetrical doublet because the B proton has two spin states. Similarly, proton B will "see" all the possible Spins states of three A protons. The energy of the proton B transition will depend only on the sum of the Spin components of the three A protons Z IAz' Since IAz = :1: 1/2, this sum can take the values 3/2, 1/2, -l/2, ~3/2. Therefore, the proton B signal is split into a symmetrical quartet with relative intensities 1:3:3: l. 29 For the case of a set of ni chemically equivalent nuclei of type i interacting with nj chemically equivalent nuclei of type j such that Jij/ ) vi- vj) << 1, thej signal has 2 niIi + 1 components and thei Signal has 2ndj + 1 components. The relative intensities of the compon- ents within each symmetrical multiplet will be given by the corresponding binomial coefficients. These simple rules are probably always valid when nuclei of different elements interact; for in such cases the "chemical shifts" are much larger than the largest values of J yet measured. However, for the case of interaction of nuclei of a common species, there are countless examples of the situation in which the chemical shift and coupling constant are of the same order of magnitude. In situations of this type, the simple rules given above are no longer valid. When the chemical shift and corresponding coupling (constant are of the same order of magnitude, the transition frequencies and relative intensities no longer fall into any simple regular pattern. Indeed, the number of observable transitions may be much greater than that predicted by the above simple rules. The nature of spin- spin coupling has been theoretically investigated by several authors. All but the most recent of these works are discussed in Chapter 8 of reference 48. Also, the general analysis of most of the easier spin systems, having coupling constants comparable in magnitude to the correSponding chemical shifts, is discussed in Chapter 6 of reference 48. NMR spectra that are complicated by Spin- spin interactions fre- quently may be simplified by the method of double irradiation, which was originally demonstrated by Bloch (66). The method consists of the saturation of one chemical group of nuclei while observing the NMR spectrum of another group of nuclei. This experiment is applicable only when the ratio of the chemical shift to the correSponding spin-spin coupling constant is very large. The saturation of one group leads to very fast 30 transitions between the possible states of nuclei in that group, so that the nuclei in the group become effectively decoupled from the nuclei in the other group being observed. The theory of double irradiation, also called spin decoupling, has been given by Bloom and Shoolery (67), and some very good experimental examples have been given by Anderson (68). ~ From the previous discussion, it is apparent that the shapes of all NMR Signals are influenced to some extent by the motions of nuclei or "lattice" of the material under observation. These effects provide methods for studying a large number of rate processes in the solid, liquid, and gas phases. The first theoretical and experimental analysis of such an effect was given by Bloembergen, Purcell, and Pound (50). They proved that “lattice" motions were an important mechanism for spin—lattice relaxation and for narrowing NMR absorption lines. Their treatment is well adapted to the study of rates of certain types of "lattice" motions in solids and viscous liquids. In these cases, the occurrence of rate processes may cause narrowing of resonance lines which are otherwise broadened by direct nuclear dipole—dipole interactions. The work of Bloembergen, Purcell and Pound is only one example of the large number of broad-line NMR investigations of rate processes. The narrowing observed in these broad-line NMR works are, in principle, the same as the observed effects of rate processes upon the narrow lines encountered in the high-resolution NMR spectra of liquids and gases. However, because of the obvious basic differences between the characteristics of these two types of spectra, the observed effects of rates processes manifest themselves in quite different ways. As a result, the mathematical methods for relating rates of kinetic processes to line-Shape parameters are also different. Only high-resolution spectra of some non-paramagnetic liquids are encountered in the work reported in this thesis. Therefore, the theory discussed in the remainder of this section is usually best adapted to high-resolution type spectra. 31 If a magnetically active nucleus (I 7! 0) kinetically experiences different magnetic environments separated by resonance frequencies Av, the resolution of the NMR signals for that nucleus at each magnetic environment is possible only if the lifetime 2’ of the nucleus at each environment is greater than N 1/2 1T Av. This is a statement of the uncertainty principle, from which it is apparent that kinetic processes may cause coalescence of multiple line spectra. The first quantitative formulation of such coalescence was given by Gutowsky, McCall, and Slichter (69). They derived equations which quantitatively related the coalescence of spin-spin coupling multiplets to the rates of random fluctuations in the Spin coordinates of the coupled nuclei. These equa- tions served as an argument for the nonexistence of F19_p31 Spin- Spin coupling in some fluorinated phosPhorus compounds. Although these authors did not use their equations for any actual calculations of rates, their theory was the basis for many later applications {references 5, 6, 12, 13, 40, 70 through 81, and others). According to Gutowsky and collaborators (69, 70, 5, 6), two NMR lines A and B may be considered as arising from: (a) two magnetically different Sites A and B having X - NMR positions differing by a frequency 60.) or (b) the spin- spin interaction of the X nuclei with one other chemically nonequivalent nucleus Y of spin I = '1‘: where JXY = 6:». Here, X represents the nuclei being observed. The molecule N, N-dimethyl- acetamide is an example of case (a) above. The protons of the two N-methyl groups constitute the X nuclei, the protons of one of these methyl groups (say gig = A) is chemically nonequivalent to the other N-methyl group (Eggs = B). The trimethylammonium ion is an example of case (b) above. Here, the protons of the three methyl groups constitute the X nuclei. The magnetic resonance of these protons is Split into two lines A and B by the equivale+nt Spin- Spin coupling of all X nuclei with a Y nucleus of spin I = 1;." the N - H proton. In making the definitions 32 described above, one must keep the facts in mind-mthat spi.n-- spin coupling constants J are field invarient, whereas chemical shifts 66.) are proportional to the applied static magnetic field. Choosing the average field Hy of the resonance lines A and B as a reference, the line shapes for these lines may be represented by the Bloch equations (26, 27 and 28). The resonance frequency for one X resonance line, say A, may be taken as 7 Ho + OLD/Z . The other X resonance line B will then be at 7 H0 .- 353 . Thus, for line A, equations (26), (27), and (28) must have all values of Au replaced by Aw + 552—“ , and for line B, all values of Am must be replaced by Aw - £29- . This modifi- cation of the Bloch equations is equivalent to adding descrete quantum states (the descrete values 1: if) to classical equations of motion. Such a treatment provides a Simple way of taking into account the Spin- Spin coupling or chemical shift differences reSponsible for the existence of the two resonance lines. If magnetically different sites cause chemical shift differences among the X nuclei, then any additional multiplicity in the resonance arising from spin- spin coupling among the X nuclei at these sites may, in principle, be taken into account. If the magnitude H1 of the applied radiofrequency (RF) magnetic field is small, so that z 2 z 2 7 H1 TIATZA <<1>> ‘Y H1 TIBTZB , (41) then saturation of the resonance lines A and B due to X nuclei is negligible. If, in addition, the experimental conditions are those of "slow-passage, " then from equation (31) it is apparent that M = M0 . i (42) Using equations (26), (27) and (28) with the modifications described above, and using the notation of equation (21), the equations of motion for the 33 RF magnetizations of the X nuclei, MA and MB, may be written as ’ 1 MA+ [ -T—— --1 (Am ‘1'?” MA 2 ~21 “1M0 , (43a) 2 .. M + [ l- »-i (Au) .. 12)] M ’ ~10.) M (43b) B T2 2. B ‘ ‘ ° ’ - respectively. In equations (43a and b) it is assumed the natural line width of A, l/n TzA: is equal to that of line B, l/n T213; or TzA 7': TZB : T2. (44) This restriction will not be made in a later simplified treatment. Applying the Laplace transformation to equation (43:), the trans- formation of variables being (a) the time t to time s and (b) the RF magnetization MA to mA, one obtains iwlMo . MA( 0+) - 4 s(s+aA) s + aA ( 5) mA = In this last equation, MA(O+) is the RF magnetization of X nuclei for line A at the arbitrary time t equal to zero, and “A is defined for convenienc e a s 1 6 (1A: T2 - i (Aw+—2—w—). (46a) Also, for convenience, a. B is defined as 1 . 5 0.3: T2 .1 (Aw— -—2‘-*’-—). (463) A solution of equation (433) may be obtained from the inverse Laplace transformation of equation (45). This solution is given by the theory of residues as 34 MA(t) : ‘11‘CD1M0 651: + -ILUIMO 8 St + s + GA 3 __> 0 s s —-> — “A st MA(0+) e 5‘9 — (1 A -iw M - o. t — t = ...—If. (1- e AH MA(O+) e “A . (47) A similar solution in MB(O+) and o. B may be obtained for MB(t). Now consider three cases in which effective random exchange of nuclei will tend to remove the degeneracy causing the existence of the two resonance lines A and B. One case is that of effective random exchange of X nuclei between two chemically different sites A and B. A second case is that of effective random exchange of a Y nucleus (1 = 1/2) between- two (or more) environments with X-Y spin- spin coupling occurring in only one of the environments available to Y. A third case is that of effective random exchange of X nuclei between two (or more) enviromnents with X-Y spin- spin coupling (IY = 1/2) occurring in only one of the environments available to X, namely, the environment being observed. In all three cases, the nuclei causing the twofold degeneracy (the two resonance lines A and B) experience effective random fluctuations in their Spin coordinates. Therefore, although the three cases are chemically and/or physically different, they are mathematically equivalent in that the same equations may be applied in all three cases. To conserve Space, the remaining derivations will be discussed in terms of the nomenclature of the first case mentioned above (i. e. , in terms of effective random exchange of X nuclei between the two chemically different sites A and B). Suppose now that some kinetic process effectively causes random exchange of X nuclei between sites A and B, and consider the effect of such a process upon the appropriate simultaneous solutions of equation (47) and the similar one for MB(t). Assume the kinetic process may be represented by 35 e l)! ’1‘ ' * * a): >:= where NA and NB are the number of labelled X nuclei at sites A and B at time t, reSpectively. Since the kinetic process is one of exchange, the following useful equations may be written. kAPA = kBPB (49) 3A:_1__: 3L and tBe—_L= 3::— (so) kA PB k13 pA In these latter equations, PA and PB are the fractions of X nuclei at sites A and B at time t, respectively, kA and k3 are the specific first—order rate constants for the equilibrium exchange of X nuclei between sites A and B, IA and TB are the mean lifetimes of X nuclei at sites A and B, respectively, and t is defined for convenience as TA 2’ B [t = W— . (51) A B The probability that a given X nucleus will have stayed at site A a time between t and t + dt is given by the exponential factor tA-l exp(-t/tA)dt. The value of MA for those X nuclei with MA equal to MA (0+) at time t equal to zero, when averaged over the exchange, is, given by < MA > = I tA-l exp(-t/ZA)MA(t)dt o '-' MA(0+) _ iwiMo [KIA (52) 1+0. A’tA 1+ 0. AKA . A similar equation in MB(0¢), (1B, and t B may be obtained for < MB>. , + Thus far, only X nuclei with given values of MA (0+) and MB(O ) have been considered. Since different X nuclei may have different values 36 of MA(0+) and MB(0+), it is necessary to average equation (51) and the similar one for < MB > over all possible "initial states" MA(O+) and MB(O+). To obtain these averages, it is assumed that the RF magnetization M, summed overall X nuclei, is not affected by the kinetic process. Such an assumption imposes the boundary condition that the average value of MA(O+) must equal the average value of MB at the time of an exchange of an X nucleus between sites A and B. Since the exchange is random, i. e. , an event is as likely at any one time as at any other time, the average value of MB at the time of an exchange must be equal ' to the value of MB at any time t, namely < MB >. Therefore, the following equations may be written, -+ — — t MA(0 ) =- < MB > and < M'A > = MB(O ) (53) Substituting equations (53) into equation (52) and into the Similar one for < MB >, and simultaneously solving the two resulting equations, leads to the following relationships. (M > :3 -iwlM0 (1+ aBZB)(1+ eAtA)-1 (543) - TA+(1+°'AZ’A)Z’B = -iw1Mo (54.2) (1+ .A YAHH aB “Cm-1 The RF magnetization M, summed over all X nuclei and averaged over the exchange and "initial states," is given by the weighted sum: M=BA<fiA> +pB <17IB>. (55) Using equations (50), (54a) and (54b), equation (55) may be written in the form: 37 MLMMO (KNEE) + 2., ZB< aApB+ aB pA) (56, (1+ eAZA)(1+ (132,3) -1 Equation (56) is the same as equations (3) and (18) of references (5) and (67), respectively. This equation expresses the total RF magnetization for all X nuclei as a function of the rate constants for an effective random kinetic exchange of X nuclei between two sites A and B. The RF magnetization is a complex number. The real part of M gives the dispersion mode shape function u in terms of the rate constants, and the imaginary part of M gives the absorption mode shape function V in terms of the rate constants. In principle, equation (56) is only applicable to a doublet-type resonance structure having a common natural line width for each line. The importance of this restriction will be considered later. Although the method described above provides an illustrative back- ground for the calculation of more complex line-shape functions in terms of rate constants, an easier method has been formulated by McConnell (82). His formulation will now be applied to the "two-site" problem solved above. In the following treatment of the problem the restriction of equation (44), that TLA 2' TzBa will be removed and the final solution will be that for the more generalized "two-site"problem. Also, certain approximatiom that were implicit in the earlier solution of the problem will be pointed out. The Bloch equations (26), (27), and (28) are modified to the following: . HA 16B + A = - + -— ~ 57 B 7AA. 7,213+ AwBVB= - + -—— (58) 38 V - A 74 = - + -—— - M 59 A (”A A 22A TB (‘91 ZA ( ) 7f u VB VA (6 ) - Aw — - + w M 0 B B 1 z B ’szB 1A B MZA _ ..., VA: 29% - MZA + MzB (61) 1A tlA 73B MzB ' “’1 VB = MOB ' MZB + MZA , (62) T13 1’13 TA where 1 1 1 —-—- = -——-— + —— , (63) Tm TIA ZA 1 1 1 —— : + —--— ’ (64) [ZZA TZA 27A similarly for LB and $213, and AwA=wA-oo, (65) AwB = “’B - w . (66) In the last two equations, “A and “’B are the resonance frequencies for X nuclei at sites A and B, reSpectively, and o.) is the angular frequency of the applied RF field. All other symbols in equations (57) through (62) are the same as before. The Bloch equations, as just modified, are written to obey the kinetic equations (48) through (51) used in the earlier treatment. The reasoning behind the above modification can be seen by comparing equations (57) and (64) with equation (26). Equation (57) 39 differs from equation (26) by the addition of two terms, - RA/ 2A and 193/13, to the right hand side. The first term, - 2(A/ Z A: accounts for the transfer of u magnetization out of site A to site B. The second term accounts for the transfer of M magnetization from site B to site A. The same type of modification leads to equations (58) through (6 2). The Bloch equations resulting from the type of modification just described require approximations not imposed on the ordinary Bloch equations. It must be assumed that any magnetic environment of X nuclei other than A and B (e. g. an "activated complex"), is short lived so as to produce no change in the magnetization components as the X nuclei are effectively exchanged between A and B. Also, it is required that Tm, TZA, TIB, and TZB be independent of 2’ A and ’t’B. This last requirement is most easily realized when TA > (TIA: TZB, TlB’ T213) < 1:13; i. e. , when the X nuclear relaxations are of high frequency compared to ZA'I and/or t B”. In addition, the relaxations of the X nuclear magnetizations at site A must be independent, except for the kinetic exchange effects, of those at site B. It should be noted that all the above restrictions are implied for the solution of the "two-site" problem described earlier. Even with all the above restrictions, equations (57) through (62), along with obvious extensions to multiple-site systems and to multiple resonance experiments, may be used to study a large number of kinetic problems. Although the set of coupled differential equations (57) through (62) may be applied to the important case of kinetic processes as observed by "rapid-passage" transient experiments (83), the easiest problems to solve are those for the case of "slow-passage, " so that 74A: 7413 '5 VA 2' VB = MZA = MZB = o. (67) 40 In this case, equations (57) through (62) become a complete set of ordinary simultaneous linear equations in six unknowns. In many cases of interest these equations may easily be solved in closed form, and they can always be solved numerically in the most general case. With negligible saturation the total z magnetization Mz becomes unaffected by kinetic processes, i. e. , M M M2: MZA+MZB=MO=MOA+MOB: Pr = p33. (68) The RF magnetization, summed over all X nuclei, is written as M: 71+ iv' = MA+MB= 71A+iVA+ uB+i2fB. (69) Equations (50), 63), (64), (68), (69) and (57) through (60) are then easily transformed to M: -iwiMo 'zJA‘L tB+ ZA TB(PB 511+ PA L3B) , 70 (1+rA BA)(1+rBBB)-1 ‘) where 9A and [3 B are defined for convenience as )3 1 1A (3 1 iA (71) = — -- (,0 ’ = " w s A TZA A B TZB B Equations (56) and (70) are equivalent except for the restriction of equation (44) being implied in the former case. Choosing the average resonance frequency 7 H0 of (DA and toB as a reference, then AwA and A613 may be written as 6 329—, A0013: Ate-ii, (72) AwA;Aw+ 2 respectively, where 661 is equal to “A - LOB. Upon rationalizing equation (70), the real part gives the dispersion 2!. -mode shape function in terms of the rate constants, and the imaginary part gives the absorption V-mode 41 shape function in terms of the rate constants. These functions may be written as —e,M, {OP-[1 PHI-’13- + BA-)] R} T2 TzB 26 = Z A 1 (73) P + R2 “wlMo {p [1+"C(£B +2A.):| + QR} V. - TZA TzB ‘ (74) ‘ P2 + R2 The quantities P, Q, R, and S are defined for convenience as P: ————-Ad+(-—-—) +——-—+ -—=s-'?.’Ad, (75) It [TZATZB 2 ] T2B TzA 6w ' Q = 2: [A00 - '2— (PA “‘ 1313)] i (76) 1 1 “C a... 1 1 R=Aw 1+ “(:(——+ ) + ( --——)+ i. TzA TZB ] 7- TZB TZA 66.) P P 7- ( A - B) . (77) For practical applications of equations (73) and (74), the parameters 6w, TZA, TZB, PA' and FE must be known. A family of line shapes, corres- ponding to a set of rate constants, may then be generated by calculating u. and/or 7f— over the desired range of values for A6). The experimental rate constants may then be taken as those values giving a calculated line- shape function best matching the experimental line shape. Such a method is obviously very time-consuming, and it is seldom applied to high- resolution type Spectra. More direct methods of evaluating the rate constants consist in relating the rate constants to measurable components of the line-shape functions. The following are some of the more useful 42 components: frequency separations of absorption maxima, frequency separations of dispersion intensity nulls, ratios of maximum to central minimum absorption intensities, widths of one-half maximum intensity for absorption lines, and frequency separations of maximum and minimum dispersion intensities. The equations for some of these components, as they pertain to the ”two-site" problem, will now be derived. In equation (74), 66.) is the frequency separation, in the absence of any kinetic processes, between the resonance absorptions for X nuclei at sites A and B. In equation (73), 660 is the same value when measured as the frequency separation between dispersion intensity nulls. In both cases, the line shape functions depend upon the frequency scale Aw, which was arbitrarily taken as zero for the frequency (OJA + ”Bl/2' At this time only the more useful absorption 71' -mode, equation (74), will be considered. The values of ZAw for which V of equation (74) is maximized will give the observed frequency separation 6t.)e in terms of the rate constants. The values of A6.) corresponding to maxima and minima in V are given by the solutions of the equation obtained when the derivative dV(Aw) /d(Aw) is set equal to zero, or since P2 + R2 51 :1: 00 and “IMO 7! 0, o. e (p2 + R6372?)— [Vii/[1:9] _ [1%351] dag») (PZ+R"‘) = 2 ’tzA Aws + 37:2B A004 + 4.th A63 + (Bo-1611:3716)2 + 2(CD-AF) A0.) + (CE — BF), (78) where A tz(:‘:A+ %” (79> B—tzde(—B—-pA), (80) 43 C = 2" 12512 [I ‘ (PA‘PBV' +78] + T213213 [1 + PAZ+ sz + PB PA 1 1 A Z’( T2A+ :12; :l + ’ziPAPB (m + 11:23,) + ‘78-; (81) D: 1+'t(—l—+ 1) Z-ZZS, (82) TZA TZB . .j— 1 1 E: 660 (D‘I'ZTS) [pA-pB + 2’( TZB- m)] , (83) E2 _1 ‘ F: 52+ 7 (n+2Z’S). (84) Equation (78) should always have a solution in each limit Ace—9 :L- 00 . These solutions correSpond to minima in the absorption intensity at the "wings" of the 'U' -mode shape function. ' When "C —--> 0 (i. e. , for very rapid exchange) equation (74) has only one maximum. From equation (78), the frequency position of this maximum is given by A... = 9-53— (pB - p.) (85) Therefore, for very fast exchange, the X nuclear resonance is coalesced to one line, and equation (78) has two imaginary solutions. When z —-—>00 it is important to note that, in general, equation (78) does not have solutions at :1: —-;—°— . Because the natural line widths, vv l/TZA and N l/TZB, may be comparable in magnitude to 661, the observed separation 66.)e = 2Aw in the absence of exchange may be less than the true value 66.). Indeed, if TzA and TzB are small enough, then resolution of the two resonance lines is both experimentally and theo- retically impossible. This phenomenon results from the overlap of resonance lines. Correction for this effect is made conveniently by letting 2 At.) = 6we——> 2 Ado, = 86,, as t ——> so in equation (78). 44 The result may be written as P P B PA 66. A B 661 PB PA 2 1 l ,_ T213 TzA [ °° TzATzB TzB TZA] A PB 1 l 6.6 3 (-— —) (-—z- - --z-) (--) + TzA TzB TZB T 3 P P z 4 1 1 1 7' 2 A — B ) 3A.»; Aw” z + ( + ) Ami. + TzA T2B TzATzB TzA T213 T2A T213 1 B FA 1 l (50.) PA +p__B) __,__T 2864 + (——1 —-.—1) - o (86) T21), TzB TzA T213 °° T213.z TzA . Equation (86) may be used to correct for the overlap of any two Lo renztian line shapes . Q. In some systems, the overlap effect is negligible and the restriction that 1 1 — << (500 >> —— (87) TZA TZB . . . . 1 1 may be imposed on equation (78) (1. e. , all terms 1n —— and /or TzA T213 may be neglected). Such a restriction enables one to write equation (78) as 45 Z 2tZAe3+[1-2t2(i§—]Ad+(6A-pB)-§Z9—=o (88) or ,5 = 2[ 6606+ 6w (PA'PBH . (89) 6608 ((5002 - 6wez) When PA = pB, YA = TB = 2 t , the restriction of equation (44) may often be a valid one. Imposing these restrictions enables one to write equation (78) as 4 t -5 Z t 3 "C ZZZ 7f: A.._+z't s(1+ T2 )Aw + (1+—f;)(1+-.-r-;-) - ts(2+ 3t)] sAw=O, (90) T2 and equation (86) as 66) l 16 4 4 -— z —— '-—-—' I I 2 1 ( 5w.» ) i 4—3—{2 [(1'sz as)4 + (Tzéweo) + :l + 1 4 .5. (91 - (T250941: )z ’ ) where s in equation (90), derived from S of equation (75), may be written as 1 7: 6w 5: T2 + T,2 + “2 )2 (92) Equations (90) and (91) are the same as equations (5) and (8) respectively of Gutowsky and Holm (5), who derived them from equation (56). Equation (90) always has one solution at Am 2 0. This solution corresponds 46 to a maximum in U for small 1’ (i. e. , fast exchange) and a minimum in V" for large t (i. e. , slow exchange). The other four solutions of equation (90) are given'by l T 1 666 T z 4 T 4 1 1 A»: 1[-s( 7— + 7%) =t s7 (-—Z-Hf§‘r+ 75—22— +7—)T:J 2'. (93) There Should always be a solution in each limit Adi—9 aw ; these correspond to the "wings" of the absorption lines. When the exchange is slow, the remaining two solutions give the maxima in the absorption mode. These two solutions are imaginary when the exchange is fast. Since the dispersion u -mode is similar in appearance to the derivative of the absorption V—mode, the position of a resonance dis- persion line is .taken as that of zero intensity dispersion. For the "two-site" exchange problem the frequency separation of these diSpersion intensity nulls in terms of the rate constants may easily be found by setting 16 of equation (73) equal to zero. When the restrictions pA :: PB (I’A = 71B = 2 t ) and that of equation (44) are imposed, the above procedure yields the following equation. 6 12Ad3+{—1—[2+3—]-7¢2(—“—)2+1} szo (94) T2 T2 2 The solution at Aw = 0 corresponds to the frequency position of the central minimum absorption for slow exchange, and to the position of the coalesced dispersion line for the case of fast exchange. For this last case the remaining two solutions of equation (94) are imaginary. The two non-zero solutions of equation (94) may be written as J]. I 1 2 1 5we—ZAw-i26w z-W[-—T—zz+fiz+-ET]. (95) The equation for overlap corrections is obtained by letting 2 A6.) 2 6618—9 2Aw°° = 66650 as '2: ——->°Oin equation (95). The result 47 may be written as (60) )zi‘rl+ 2 6w (Swan w T_zz . (96) These overlap corrections for the dispersion mode may be very much larger than for the absorption mode. The large difference in these overlap effects is apparent from the plots of equations (92) and (96) shown in Figure 5. When overlap effects are negligible, imposing the restriction of inequality (87) upon equation (93) yields the following simple relationships between the separation of absorption maxima and the rate constants: if 2’68. >«/2 66.18 _ ZAw _ 2 (6w)-( 6w )-i~[lm'tzéwz (97) 6we=2Aw=0 fittings/2 This result is the same as equations (6) and (60) of references (5) and (84), respectively. Imposing the restriction of inequality (87) on equation (95) gives a similar Simple relationship between the separation of dispersion lines and the rate constants. 66:6 _ 2A0.) _ J 4 . (6w)-( (mks l-tT—r—éw 1f t6e>2 (98) 6608 = 0 if 7:66): 2 The ratio r of maximum to central minimum intensities for the absorption 'U" -mode may easily be related to the rate constants in the region of intermediate rates of exchange. For the "two-site" problem having negligible overlap and each line of common intensity, the V—mode 6w/6ww 48 6 ) I l T 1 r l I T I °5- 1. 008_ ,' a 7 / I / I / 8 I / 3 I // t0 __ .— 4... \ 1.004 / / __ 0O / / / / / / l. 000 L 1 17 / 0 0 O 2 0.4 0.6 / 3 o / / / / / Z— / - / / / / / / —- / / / / / / / / / / 0 —- -' ’ — 1 1 1 1 1 0.0 0.2 0.4 0.6 0.8 1.0 2 /T26w Figure 5. The effect of overlap of two equally intense resonance lines on their apparent separation, as a function of line width Z/Tz. The observed separation is 6mm and the separation corrected for overlap is 661. V—mode: curves. solid curves, dispersion u. -mode: Absorption dashed 49 shape function is easily obtained from equation (74) by imposing the restriction that pA = PB and that equation (87) be valid. The result, written in frequency units of cps, may be written as ' 2 v- 0C 95‘5” /4 8 .~ (99) 2 4+2 (AC-‘17:— - 'Csz)+Aw For this particular case, the frequency positions of the maxima and minima in V are given by equations‘(97) and (90), reSpectively. These frequency positions may be expressed by 6v 5 1W . Avmax.“ 2 fl-W 1f 26V>Nj 2 /ZTI’ (1003.) Av = Oif Tév > \(2/ 2n (100b) min. From equations (99, 100?; and b), the values of Vmax and Vmin. may be written as I 'C3 6v2 Vmax. QC I101) “C 7‘6 v2 - 1/4 n2 and Wm... 0"- 1 /“" “C 61” I102) respectively. The rate constants, in terms of r 274.113,}, /V‘min. , may be written as i :1: — 1 1 rs. = 2": . [r s (r2 - r)? )T. (103) For the case in which PA = pB, the rate constants kA = kB are equal to l/ZZ . In this case, the rate constants are most easily evaluated in terms of the quantity Z6 v. Since 6 v is a constant for a given system, the classical Arrhenius-type rate equation (4) may be written as 50 6v E __i_______ 2A) + 2.303 RT ’ (104) 10810 ( 7: 5V) = 10810 ( where R is the molar gas constant, A is the frequency factor for the kinetic process, and Ea is the energy barrier (more precisely, the experimental activation energy) inhibiting the kinetic process. From the value of 6v and the temperature dependence of "C 6 v, the quantities A and Ea are conveniently evaluated from the intercept and slope, respectively, of the straight line plot of loglo ( '2: 6 v) versus l/T. Assuming the validity of the absolute rate equation (85), the free energy T of activation AF for the kinetic process may be calculated from AFT : 2. 303 RT logm (31%;) . (105) Grunwald, Loewenstein and Meiboom have observed the effect of direct chemical exchange upon the absorption U" -mode for a symmetrical spin- spin quartet (74). Using the approach of Gutowsky, McCall, and Slichter (69), they formulated the "four-line” problem having pA = PB = 1/8 and pB = PC = 3/8 with AwA = -AwD = 3AwB= ~3ch referred to the average resonance frequency 7H0 = (toA + wD)/ 2 = (“B + wc) /2. Their treatment assumed TzA = TZB = Tzc = TzD = T2, but it did not necessarily exclude overlap effects. In the region of intermediate rates of exchange they related the rate constants to the ratio of maximum to central minimum intensities. The effects of rates of kinetic processes upon this ratio were calculated numerically for various degrees of overlap. The results of their numerical calculations were presented in graphical form. In the region of fast exchange rates, they related the rate constants to the full line-width at one-half maximum intensity for the coalesced quartet. Numerical calculations, similar to those in the previous case, were made, and these results also were presented in graphical form. 51 In addition to the "four-line" problem just mentioned, Loewenstein and Meiboom have made similar numerical calculations for spin- spin 1:1 doublets (this is the same as the "two-site" problem discussed earlier) and spin-spin 1:2:1 triplets (the "three-line" problem) (75). The results of these numerical calculations were presented in graphical form. They may be used to account for overlap effects, whereas equation (103), which also applies to the case of a spin- spin 1:1 doublet, is only valid in the event of negligible overlap effects. In the region of fast exchange rates, another method for evaluating the rate constants for a symmetrical "two-line" (or "two-site") problem has been demonstrated by Takeda and Stejskal (24). These authors have related the rate constants to the ratio of I, the maximum absorption intensity of the coalesced doublet at the exchange rate 1/2'23 , to lo, the maximum absorption intensity for the same line when '2: -—9 0. This relationship may be written as Z + 1 __ = o 1 I0 2 + 1 + T2600 ( 06) T660 T260.) 4 This equation is not restricted to cases of negligible overlap, but theoretically it is restricted to cases where TZA = TZB = T2. In addition to the methods thus far discussed, Piette and Anderson have derived the equation of motion for the RF magnetization, summed over all X nuclei, for a system experiencing effective X nuclear random exchange among any number of magnetic sites (81). This more generalized equation, which may be applied to a Spectrum containing any number of lines, may be written as 2“, P.) . J :I-il—Jr + iij M = - MM, . (107) T; + i ij § pl" 1 TI? 4'1ij 52 where l l 1 Equation (107) is the same as one derived by Arnold (72), only he assumed that all sz were equal. From equation (107), Piette and Anderson were able to obtain approximate expansions which related the rate constants to the line—widths at one-half maximum intensity. One expansion is valid in the region of slow exchange rates (i. e. , when I wi - “’j I Tj' >> 1 for any i and j). This expansion may be written as 1 + (1 -Pj) (TTAV): sz—J- t 1 (109) where (11 A v) is the measured line-widthof the jth resonance line at one-half maximum intensity in units of rps. For cases that may be kinetically represented by equations (48) through (51) with Z’A = Z B’ equation, (109) may conveniently be substituted into the Arrhenius-type rate equation to yield Ea . 2. 303 RT logiol (wAv) - -1— logic [2A(1- p,-1] (110) sz The other expansion derived by Piette and Anderson is valid in the region of fast exchange rates (i. e. , when I “Ii - wj I T' <> T2, T' ‘2" T2, and Iwi - ij T2 << 1 ). As before, when equation (111) is applied to kinetic problems correctly represented by equations (48) through (51) with TA = tB’ it may be substituted into the Arrhenius—type rate equation to yield T2 Ea V 1°g1° “““ITZ' 1]: “gm (T‘H m- A (113) Although the quite general expansions of Piette and Anderson are not valid in the region of intermediate rates of exchange, they should be extremely helpful in the studies of multiple-line spectra. An earlier statement was made that only systems free of para- magnetic substances would be considered. However, it is pertinent to point out that many of these methods are easily adapted to paramagnetic systems. A very good example of such an adaptation is the treatment of electron exchange reactions as given by McConnell and Berger (85). They used the original formulation of Gutowsky, McCall and Slichter (64) to relate the rate of rapid electron exchange between a diamagnetic site and a paramagnetic site to the line-width for the X nuclear magnetic resonance at the diamagnetic site. One other important fact should be mentioned. The theory presented in this section really overlooks many minor subtleties that actually exist in any_r_e_3._l_ system. Several very rigorous mathematical considerations have dealt with the effects of kinetic processes upon NMR line shapes (references 84, and 89 through 94). In particular, these works have thoroughly examined the whole general field of nuclear magnetic relaxa- tions. However, there is no cause for alarm. For, although these more profound mathematical treatments have given a better understanding of the true complexities of anyfiaL system, they confirm the important general predictions derived in this section from the simple Bloch equations. EXPERIMENTAL Spe ct romete r The Spectra were obtained with a high-resolution nuclear- induction type NMR spectrometer, Varian Associates (VA) Model V-4300-2. A VA Model V-4301C fixed-frequency RF unit and a. VA Model V-4331A RF probe were used to obtain NMR Spectra at the fixed frequency 40. 000 mcs. The frequency was measured with a Collins Type 51J-4 RF receiver against the National Bureau of Standards (NBS) Station WWV. The VA Model V-4301C RF unit utilizes amplitude detection. A VA Model V~4311 fixed—frequency RF unit and a VA modified Model V-4331A RF probe were used to obtain NMR spectra at the fixed frequency 60. 000 mcs. , also measured with the Collins receiver against NBS Station WWV. The VA Model V-43ll RF unit utilizes phase-sensitive detection. The 60 mcs. probe was modified so that it, and the Model V~43ll RF unit, could be used with or without the simultaneous usage of the VA Model V-4320 Spin decoupler. The spin decoupler was capable of transmitting 56.44 or 4. 33 mcs. at power levels correSponding to various degrees of NMR saturation. The static magnetic field was obtained with a VA twelve-inch electromagnet, Model V-4012A-HR, and associated regulated magnet power supply, VA modified Model V-2100A. A field-reversing mechanism was installed in the magnet power supply. This provided a way for cycling the applied large magnetic field to higher homogeneity. I A VA model VK-3513 field trimmer was bolted to the yoke of the electro- magnet. This also provided a way for obtaining higher homogeneity in the applied large magnetic field. 54 55 Several features were included to insure overall stability for the system. The applied large magnetic field was stabilized with a VA Model VK—3506 magnetic flux stabilizer. Stabilization of the 117 volt A. C. (single-phase) input to the regulated magnet power supply was accomp— lished with the use of a Raytheon Model VR-6115 voltage stabilizer. The 117 volt'A. C. (Single-phase) inputs to all other Spectrometer and accessory circuits were regulated with a Sorensen Model 1000 S A. C. voltage regulator. Distilled water, used for cooling the electromagnet, was recycled through a refrigerated copper tank. The temperature of the water at the output of this tank was regulated at 18. 0 :1: 0. 15°C. A commercial air-conditioning unit regulated the ambient room tempera- ture. Air temperature in the region of the magnet was normally stabilized to better than :1: 20C. Since overheating of the electromagnet windings may lead to their destruction, two precautionary steps were taken. The usual safety switch in the cooling-water line was set to turn off the current in the electromagnet when the water pressure dropped below a safe value. This switch is of importance in the event of a water- line plug or a malfunction in the recycling pump. In addition, a "thermoregulating” switch was placed in the water tank and wired in series with the pressure switch just mentioned. The "thermoregulating" switch was set so that the current in the electromagnet would be turned off automatically when the water temperature exceeded 95°F. This last precaution is of extreme importance in the event of a malfunction in the refrigeration unit. Modifications for Observing Spectra at High or Low Temperatures To use the VA RF probes for observing high-resolution NMR spectra of samples at high or low temperatures, several requirements must be fulfilled. Due to limitations in the homogeneity of the static magnetic 56 field, spinning samples of small volume must, as usual, be surrounded by a small receiver coil. The temperature of the samples must be regulated precisely at the desired high or low value over long periods of time. Also, the sample must be thermally insulated from the RF probe. This last requirement is necessary because excessive heating or cooling of the RF probes may damage some of their vital components. Heating or cooling of the RF probes may also induce thermal gradients in the nearby magnet pole faces. Such thermal gradients cause undesir- able inhomogeneities in the static magnetic field. Therefore, devices were constructed that would enable one to fulfill the above requirements. Vacuum—jacketed receiver coil inserts —- Two vacuum-jacketed receiver coil inserts were made to plug into the VA Model V-4331A RF probes. Except for the number of turns in the receiver coils, the two inserts were identical. The design for their construction was, in some ways, similar to that used by Shoolery and Roberts (95). One insert had six turns of No. 40 pure copper wire and was used at the RF 40. 000 mcs. The other insert had three turns of the same kind of wire and was used at 60. 000 mcs. The vacuum envelope, made of cylindrical Pyrex tubing, provided the necessary thermal insulation between the sample and the RF probe (see Figure 6). A female standard taper, sealed into the top of the envelope, supported a male standard taper sealed to a cylindrical inner tube. This inner tube extended coaxially in the vacuum envelope, down to within about two millimeters from the inner bottom of the envelope. A small Teflon cup was cemented inside the bottom of the inner tube. This cup served as a bearing for Spinning sample tubes (about 5 mm. od. ). The receiver coil was wound and cemented on the outside of the inner tube, about three-eighths of an inch above the top of the Teflon cup. The receiver coil lead wires were insulated with Teflon and brought out Figure 6 -- Cross sectional drawing of probe body, vacuum-jacketed receiver coil insert, upper chamber, and mounting plate and tube. Pyrex glass - A = 12 mm. od. , B :2 24 mm. od. , 21 mm. id. , C :. inner tube, 9 mm. od. , 7 mm. id. , D = 14 mm. od., 11. 6 mm. id. , E : 18.6 mm. od., 16.2mm. id., F = 19 mm. od., Cr: 8 mm. od., H 2 .sample tube, 0.192 :1: . 002 in. 0d. , 0. 1604 in. id., straight within :1: 0.003in., I = 12/5 ball joints, J = 12/30 standard tapers, K = flared handle; Teflon - L 2 Split rings, M : bearing, N = gasket, O = spinning collet, P = insulator; brass — Q»: 4‘40 screws, R 2 6—32 screws, S = RF coaxial connector; ceramix — T 2: mounting plug; pure copper - U = receiver coils and leads; V = vacuum envelope; aluminum - W = VA air- driven NMR sample-spinning turbine, X = centering plate for air-driven turbine, .2. 5 x1. 5 x 0. 25 in. , Y 2 upper chamber, outside 5 x 2.75 x 1. 5 in. , inside 4.5 x 2. 25 x1. 25 in. , Z = VA Model V—4331A RF probe l_)__o_d_y_, a : mounting plate, 5. 25 x 1. 5 x O. 5 in. slotted for b : mounting tube, outside 20 x 0.75 x 0.75 in. , c : mounting bolt, 3748 — 24; filtered air - d = turbine input, e = turbine exit, f = input heating _o_r_ cooling, g = input heating or cooling, room temperature, h 2 exit heating and cooling; i = thermocouple junction. 57 58 through a small hole in the bottom of the vacuum envelope. The ends of the lead wires were soldered to a brass RF coaxial connector. This connector and its ceramic mounting plug were cemented onto the bottom of the vacuum envelope. All cementing was done with Shell No. 828 Epon resin and a pyromellitic dianhydride-maleic anhydride catalyst mixture. Twenty grams of resin was heated to 700 C. , a finely divided mixture of 3. 4 grams of dianhydride and 5. 6 grams of anhydride was added to the resin slowly while stirring. Then the resin-catalyst mixture was stirred at 900C. until polymerization just started (this required about 30 minutes). At this point, the mixture was cooled to room temperature and applied to the parts to be cemented together. After application, the resin was annealed at 800C. and at 20 degree intervals up to 220°C. (at least two hours per temperature interval). 50 that dry air could be used for heating or cooling the samples, a side-arm delivery tube was sealed through the vacuum enve10pe, just below the female standard taper. Also, two holes, about 0. 084 inch in diameter, were drilled through the inner tube about one-half way between the receiver coils and the Teflon cup. The temperature controlled air entering the Side arm would then flow down around the outside of the inner tube, through the holes at the bottom, up around the sample tube, and then out the top of the insert. To adjust the RF coupling of the receiver coil to the transmitter coils, it was necessary to be able to turn the inner tube and male standard taper. For this purpose, a flared Pyrex handle was sealed to the top of the male standard taper. Before the vacuum-jacketed inserts were assembled, all the Pyrex glassware was annealed in a furnace. (The jackets were thoroughly cleaned and twice silvered, from the top, down to about three-quarters of an inch above the ultimate levels of the receiver coils. The jackets were evacuated and sealed off at pressures less than 10"7 mm. Hg at about 59 5000C. Each insert was then assembled according to the following procedure. (A) To remove all ferromagnetic surface impurities, _a_l_l_ parts were soaked in concentrated hydrochloric acid, rinsed, and then thoroughly dried at 1100C. (B) The receiver coil was wound on the inner tube, clamped firmly in place, cemented, and annealed. (C) The lead wires were insulated with Teflon tape, cemented to the outside of the inner tube, and annealed. (D) A small amount of high-temperature silicon grease was applied to the male standard taper, and the receiver coil lead wires were drawn out through the hole in the bottom of the vacuum envelope while the inner tube was inserted in place. (E) The lead- wire ends were threaded through two small holes in the ceramic mounting plug. (F) This plug was cemented to the bottom of the vacuum envelope, aligned, and then annealed. (G) The coaxial connector was inserted into the ceramic plug with resin. (H) The lead wires were soldered to the connector, the center post of the connector was cemented in place, and then the resin was annealed. The two vacuumwjacketed receiver coil inserts, assembled in the manner just described, did not break during temperature cycles between -1000 and + 2200C. An insert, when placed into the probe, was held firmly in position by means of a Teflon ring around the outside of the vacuum envelope (see Figure 6). Sample Spinning -- An aluminum upper chamber was constructed to fit on the top of each RF probe (see Figure 6). A Teflon gasket was inserted between the probe and upper chamber, and the chamber was made fast with two small brass screws. Among other functions, the upper chamber served as a mounting for a VA air-driven NMR sample-spinning turbine. An aluminum plate on the cover of the upper chamber was threaded to receive the turbine. The plate was fastened to the cover with two brass screws. By using oversized screw holes in the plate, 60 the turbine could be centered so that sample tubes would Spin freely and rapidly. The cover was made to fit the top of the upper chamber closely. This allowed removal and replacement of the cover, plate and turbine as a unit, without disturbing the alignment of the turbine. A hole, 0. 25 in. in diameter, was drilled through the cover so that a sample tube could be lowered into the receiver coil insert directly below. In order to obtain sufficiently free and rapid Spinning, the sample tubes had to be extremely straight and well balanced. Therefore, custom-manufactured sample tubes were used (96). These Pyrex glass tubes had the following dimensions--0. 192 :1: . 002 in. 0d. , 0.1604 in.. id. , straight within 0. 003 in. , hemispherical bottoms. A small amount of friction between the Spinning sample tube bottom and the Teflon bearing would turn the inner tube in the receiver coil insert. This slight turning was highly undesirable because it caused detuning of the RF coupling between the receiver coil and the transmitter coils. Detuning was prevented by demobilizing the inner tube of the receiver coil insert. This was accomplished by carefully forcing small cork wedges between the side edges of the flared handle at the top of the insert and the walls of the upper chamber. Probe mounting —- The RF probe was bolted on top of a horizontal mounting plate and tube. The mounting tube was bolted to the probe mounting post. Then the applied field could be mapped, in the usual way, with the RF probe. Also, the RF probe could be moved in and out of the applied field. With the RF probe located at the center of the applied field gap, one end of the aluminum mounting tube extended well out of the field gap. The out-of-field end of this tube was used for supporting lead wires, cables and other necessary accessories. 61 Temperature control -- The sample temperature was regulated by passing temperature and flow- rate controlled air through the vacuum jacketed receiver coil insert. At very low or high sample temperatures, the air escaping from the top of the insert caused the upper chamber and RF probe to deviate markedly from room temperature. Thermal conduction through the bottom of the receiver coil insert also caused the RF probe to deviate from room temperature. These difficulties were eliminated by passing room-temperature air into the tuning hole at the bottom of the RF probe whence it flowed through the probe body to the bottom of the insert, up around the outside of the vacuum envelope, through the split Teflon ring and into the upper chamber. This prevented heating or cooling of the probe due to thermal conduction through the bottom of the receiver coil insert. In addition, a Pyrex tube was fitted through the front of the upper chamber.. One end of this tube was placed near the top of the receiver coil insert, just below the cover on the upper chamber. The other end was connected to a flexible rubber hose, which led to the intake of an air blower. In this way, the air escaping from the top of the insert, and some room-temperature air, was removed from the upper chamber. The air which was used for spinning, heating and cooling was taken from a pressure reduction gauge attached to a compressed air line. To prevent contamination of the RF probe and insert the air was filtered. After filtering, the air was split into three flow- rate controlled streams. The flow rate of one stream, used for sample spinning, was controlled with the usual needle valve on the Spectrometer. The flow rate of another stream, used for maintaining the probe at room temperature, was controlled with an adjustable gate-type valve. The flow rate of the third air stream, used for regulating the sample temperature, was controlled with a needle valve, a pressure reduction gauge, another needle valve, and a small adjustable leak (series connection in the order 62 mentioned). For low temperature measurements, this last stream of air was dried with a cold trap and a calcium chloride drying tower. The trap and tower were connected into the line immediately following the series of flow—rate-control valves. Drying was sufficient to prevent harmful frosting at low temperatures. Both the cold trap and drying tower were by-passed for high temperature measurements. After controlling the flow rate (and drying when necessary), the air for controlling the sample temperature was led into a heat exchanger. For low temperatures, a coil of copper tubing immersed in a liquid air or a dry ice and solvent bath was used as a heat exchanger. In this case, the cooled air was led through silvered and vacuum-jacketed delivery tubes to the input at the front of the upper chamber. For high temperature measurements, a coil of resistance wire, carrying an adjustable current from a powerstat, was used as the heat exchanger. The resistance wire was wound onto an asbestosucovered Pyrex finger which fit into the silvered and vacuum-jacketed delivery tube located at the input to front of the upper chamber (see Figure 7). The sample temperature was controlled at low values by adjusting the flow rate of dry air and the temperature of the bath in which the coil of copper tubing was immersed. The sample temperature was controlled at high values by regulating the flow rate of air and the current flowing through the coil of resistance wire. For sample temperatures above 1500C. , a preheater with adjust- able dissipation (zero to 500 watts) was placed in the air line just before the coil of resistance wire. To prevent the receiver coil insert from moving while mapping the field, it was necessary that the delivery tube at the input to the upper chamber be held firmly in place. This was done by clamping the silvered and vacuum-jacketed delivery tube to the aluminum mounting tube (see Figure 7). The delivery tube was clamped so that it exerted a steady inward force against the input to the upper chamber. In this way, the Pyrex ball-joint connections were also held firmly together without the use of clamps. darts.» mcmcdfimm iofimgmm my...“ oh :6. mo €193 n O 34...... mcflooc WILIM wa....._.¢oc.. mo .336 M Z ...»poo. oQOuQ or: on has shenamcanoFEOOH mo 629: o- 2 .oFceaHoQEoH 6386...,» Mo HobcoU some 95m ....0 Banana .1. 1H .oamsoooEpcaS oat .HoH no.3? ps3 pouoEHm u M JcoEoHo mcflmofl oat. Howe mow?» puma u h Toma: .>.po>..:op pas nomcrcoxo urea pouoxodfltflfissosay n H .umom 933308 638.958.. n m .9300. wcflcdoa n .033.» WGECSOE n .3813 933305 n H .onoum mm n O .uonamflo Momma .1. O .ocfipdu madcaamtoHQEMm n m .633 63856 u an, .msflcdoa oQOHm ogu paw .ousuduomaou wcfifioupcoo no“ moanOmmooom @80m .0393 mm 6:9 é. oudwfim 63 64 Temperature measurement -- The sample temperature was monitored with a copper-constantan thermocouple (No. 30 wire) in conjunction with an adjustable bucking voltage, a Leeds and Northrup Model 9835-B D. C. microvolt amplifier, and a Brown Model Y153XlOV-X6 strip chart recorder. The measuring-junction lead wires of the thermocouple were cemented into a sideuarm double—ball-joint adapter as shown in Figure 6. The measuring junction was then threaded into the side arm of the receiver coil insert and down between the vacuum envelope and the inner tube of the insert. The junction was finally located about one-half inch above the receiver coil. The E.M. F. of the measuring junction, versus a reference junction at 00C. , was monitored with a circuit as diagramed in Figure 8. The pure c0pper wires from the measuring and reference junctions were connected to the Input 1 as labelled in Figure 8. With this circuit, the temperature could be measured to d: 0. 020C. and monitored to changes of less than :1: 0. 0020C. In practice, the temperature was adjusted to the desired value, measured, and then monitored for deviations from the measured value. The deflection of the linear recorder scale (zero to 12 mv.) was calibrated in microvolts per inch for all setting of the scale multiplier of the D. C. microvolt amplifier. These calibrations were made by applying known mic rovoltages to Input 1. The known micro- voltages were obtained from a constant-current controller and two Leeds and Northrup standard resistors, one ohm and one kilohm. The thermo- couple was calibrated, while connected to Input 1, at the temperatures of the equilibria for carbon dioxide sublimation, melting pure ice, sodium sulfate-sodium sulfate pentahydrate transition, and boiling pure water. The temperature - E. M. F. calibrations were in agreement (within :t 0. 040C.) with literature values (111.). Therefore, the literature data were used in constructing the working E.M. F. versus temperature curves. From the slopes of these curves, the recorder scale defection was then 65 D. C. Recorder r Amplifier O—r Input III ~00 v—ooao——o InputI :— 0—1 O T 1L (i) 6 % Potenti- Input 11 I: 1* Q ‘ Ometer O i.) [“‘771\J_'—’\t} X W 0.1megohm 15 megohm 1.5 volts each Figure 8. Diagram of circuit used for monitoring and measuring sample tempe rature s . 66 calibrated in degrees per inch for each setting of the scale multiplier of the D. C. amplifier. Calibrations were made at ten degree intervals. Sample temperatures could be controlled for long periods of time to about :1: 0.10C. in the region zero to 100°C. In the regions -100 to zero 0C. and 100 to 2200 C. , sample temperatures could be controlled to about :1: 0. 50C. Current Shims For a field gap of 1.75 inches between the magnet pole faces, applied fields greater than 15. 5 kilogauss could be obtained with the electromagnet and regulated magnet power supply. However, at these higher values of the applied field, properly cycled, "flat, " and homo- geneous fields could not be obtained. To obtain high—resolution fluorine magnetic resonance spectra at the RF 60. 000 mcs. (an applied field of about 14. 979 kilogauss), shim coils were constructed to give the necessary homogeneity. The shim coils consisted of a pair of figure-eight coils and two pairs of concentric circular coils. The diameter of the figure-eight coils was about 2. 25 inches. Each pair of circular coils had one coil _ four inches in diameter and the other coil 1. 5 inches in diameter. Each pair of concentric circular coils was fastened with celluloid tape to separate sheets of stiff paper backing. A figure-eight coil was taped over each pair of circular coils so that the center of the figure-eight coil coincided with the common axis of the circular coils. Each figure-eight coil was wound so that D. C. in the two loops would flow in opposite senses (see Figure 9). The loOpS were made with six turns of No. 40 pure copper wire. Each circular coil was made with ten turns of the same kind of wire. 67 i .3; co . e *0 ' 9 32 R: :_:-__:-__B '. .11.. R4 4., _ 010101 0’ 0 Figure 9. Diagram of shim coils and circuits. Ammeters -A, to 200 ma. , A; = 0 to 100 ma.; helipots -R1 = 70’ohms, R; = R3 = l kilohm; R. = 200 ohms; B = battery of Edison cells, ca. 15 volts; C = dry cells, 1. 5 volts. Connections between all points having common numbers are omitted. : 68 The paper~backed coils were taped to either side of the RF probe, figureo-eights in a vertical position, so that the axis of the circular coils passed through the center of the receiver coil inside the probe. Since the sides of the RF probe were parallel, the Helmholtz condition was obtained for the two circular coils of large diameter, and for the two of small diameter. Each pair of circular coils was so connected that D. C. in the coil of large diameter would always flow in the Opposite sense to that in the coil of small diameter. The steady voltage for the D. C. in the circular coils was obtained from a battery of Edison cells. The direction of this D. C. could be reversed, and the magnitude of the current was adjustable. The magnitude of the D. C. flowing in the circular coils could also be divided between the coils of large and of small diameters. The steady voltage for the D. C. in the figure-eight coils was obtained from three dry cells connected in parallel. The direction of this current could be reversed, and its magnitude was adjustable. The shim coils were used only when observing high-resolution ‘fluorine magnetic resonance at the RF 60. 000 mcs. The circular coils were used to flatten the undercycled ("dome-shaped") static magnetic field. The flattening was accomplished by choosing the direction of D. C. in the small circular coils such that the magnetic field at the sample 1 produced by these coils would be in opposition to the applied large'mag- netic field. The magnetic field at the sample produced by the large circular coils would then be in the same direction-as the applied large magnetic field. The D. C. was divided between small and large circular coils so that a null field due to all the circular coils was produced at the sample. After the field at the sample due to the circular coils had been nullified, the degree of shaping could easily behadjusted by varying the total amount of current flowing in the circular coils. The effective field at the sample was usually undercycled for currents below about 69 120 milliamperes. Very "flat" (usually very homogeneous) effective fields at the sample were obtained for current values in the region about 120 to 175 milliamperes. For larger current values, the effective field was usually overcycled ("dish- shaped"). Occasionally the inhomogeneity along the vertical y-axis could be removed more easily by using the figure-eight shim coils than by shimming the electromagnet. Spinning of the sample usually caused sufficient averaging of the inhomogeneity along the horizontal x-axis. The necessary D. C. in the figure-eight coils was only from zero to ten milliamperes. For this reason, the figure-eight coils probably would have been much more useful had each loop contained only one turn of wire. A coil of one turn per loop could have been wound much more symmetrically than the coils having six turns per loop. Resolution With the apparatus described above, the limits of resolution at the RF 60. 000 mcs. were approximately as follows: protons - 0. 2 cps, 0. 0033 ppm, or 0.047 milligauss; F19 - 0. 5 cps, 0. 0083 ppm, or 0.124 milligauss. The limits of resolution (but not the intensities) at the RF 40. 000 mcs. were slightly better than at 60. 000 mcs. Materials Used The materials for which data were obtained are tabulated in Table III. Physical constants listed as "observed" in this table are for the materials used in the preparation of samples. The observed values may be compared with the tabulated literature values. The amide N, N-dimethyltrifluoroacetamide was prepared by allow— ing trifluoroacetic anhydride to react with anhydrous dimethylamine (the molar ratio of anhydride to amine was 2:1). The anhydride was added v..||.lI11 .bIIIrIiuII.“ |.In1.r..h. Liraglrn‘nuut; u A a“. :‘l. ‘ lull. ‘5.’.lll'\ili‘:l. ..I ..l 0.1.11“! _n.nm.v.—- Mb~d<-V-u.~.-.pom£O -..:IIIIII - - .-I ..- . .. I . I 1.1.3 QMWD wlnsmandJZ MOrIH mHZANEmZOU stUHmtwmnm ”Np/HOW :HMJm;,|xi-x|’-F], (116) 1 where b is the least-squared slope, E is the average value of the n values of l/T, t is a constant for converting the standard error in the slope to the region of 90 percent confidence (the value of t depends upon the number of points n), and 0" is given by 2 '1’. Z . 0' -[§y,-a§v1—b§xiv,]/n-zg (117) In equation (117), a is the least-squared intercept. The limits of 90 percent confidence in A were calculated from _ 1 it0’[2_3xiz/n EIXi-Xlz]? 1 . (6v/Z)lO-a 1 . (118) This function assumes that the error in A due to the error in the measurement of 6 v is small compared to the error in A introduced by the error in a. This assumption was valid in every case. RESULTS High- resolution Spectra ‘ All the spectra shown in this thesis were obtained at theuradio— frequency 60. 000 mcs. and with the linear sweep field "increasing from left to right. Positions of proton magnetic resonance lines are given with reSpect to the resonance position of the ring protons of toluene which was used as an external reference. Positions of fluorine magnetic resonance lines are given with respect to the resonance position of the fluorine nuclei of l, l-dibromo-l, l, 2, Z-tetrafluoroethane whichwas used as an external reference. Frequency displacements to the right (the high-field side) of the reference positions are arbitrarily taken as positive, whereas those to the left (the low-field side) are taken as negative . N, N-Dimethylformamide - The high- resolution proton resonance Spectrum of pure'N, N-dimethylformamide is shown in Figure 11. The magnetic resonance of the aldehyde proton consists of an unresolved multiplet centered at 571.4; cps. Theoretically this multiplet consists of ten equally- spaced (0. 28 cps) lines with relative intensities 3:10: 20:33:40:40:33:20:10:3. The doublet centered at 232. 3 cps is due to the magnetic resonance of the protons of one ’N-methyl group, whereas the doublet centered at 241. 7 cps is due to theproton resonance of the other N-methyl group. The splitting of the low-field doublet is 0. 28 cps, and that of the high-field doublet is G. 56 .cps. The (shift between the two doublets is very large comparedto the effective natural line width of either partially resolved doublet. The gain used while recording the low-field multiplet was much larger than that used while recording the high-field doublets. 85 86 mmo . m atom m .omm w .m.o~ 7 J - AI cm £50.33 13.388 mo Tasman ”monoumwou .0095...” u. :88 08.8 n s. .Anmovzoonmo _ mo 8.950on monGOmoH ofloawmfi .m .NH ondwfim who ~.H¢~ m.~m~ v.Hs- “ u b q u 1 ..1 t M 668.33 fimcumuxm mo aamgm u monopomou .0 03 u a :88 80.3 n s. .anmovzoom mo guuoomm oquGOmou oflocmma LA .: ondmfim 87 N, N‘Dirnethylacetamide :_ The protonmagnetic resonance spectrum of pure N, N-dimethylacetamideis shown in‘Figure 12. The lines at 205. 7 and 216. 3 cps are due to the proton resonance of the two nonequivalent N-methyl groups. The resonance of the protons of the C-methyl group is located at 261. 5 cps. Very weak and nonequivalent Spin- spin coupling of the protons of the C-methyl group with the protons of each N-methyl group causes the effective natural line width of the high-field N-methyl proton resOnance to be slightly broader than that of the low-field N-methyl proton resonance line. N, N-Dimethylpr0pionamide - The proton magnetic resonance spectrum of pure N, N-dimethylpropionamide is shown in Figure 13. The proton resonance due to one N-methyl group is located at 225. 2 cps, whereas that of the other N-methyl groupis located at 234.4 cps- The effective natural line width of the high-field N-methyl proton resonance is slightly broader than that of the low-field .N-methyl proton resonance. The difference is caused by the very. weak and nonequivalent spin- spin coupling of the methylene protons with the protons of each N-methyl group. The effective natural line width of each N-methyl proton resonance is small compared to the chemical shift between the lines. The quartet between 25f). 9 and 272. 5 cps arises from the resonance of the methylene protons, whereas the triplet between 338. 8 and 348.3 cps is due to the resonance of the methyl protons of the ethyl group. The triplet and quartet structures are the result of spin- spin coupling between the methylene and methyl protons of the ethyl group. Each component of the quartet and triplet is split into a multiplet. These small Splittings also result'from the Spin- Spin coupling between the methylene and methyl protons 'of the ethyl group. At lower applied fields, where JCH3CHZ becomes comparable in magnitude to v CH3” v CHZ' the true complexity of the "ethyl spectrum" would become much more apparent than that revealed in Figure 13. 88 m8 mam: oz»? Al cm 435.33 39883 mo Htwqmgm ”oodouomou . .Uow.omu n a . .oma Geode n NammDvZODnHUU mo Euomam seademoH 0.33%ch am «l 039me was 93% wamm m .NZ a. omm ... .3...” ~.m- _ . . 6:033 39388 mo Kasai .mocouomoh ..0 o.m hull n :88 ooo ...8 ... s. .xnmovzoonmonmo mo €5.30on mocdcomou 33¢de "E .2 $de 89 The doublet, quartet and triplet shown in'Figure 13 were each recorded at slightly different gains. The proton resonance spectra of the solutions of N, N- dimethylpropionamide in dibromomethane and in carbon tetrachloride were all essentially the same as that shown in ‘Figure 13. The pertinent NMR data for these solutions are tabulated in Table' IV. N, N-Dimetlgltrichloroacetamide - The proton magnetic resonance spectrum of pure N, N-dimethyltrichloroacetamide is shown in‘Figure 14. The line at 132. 9 cps is due to the proton resonance of one N-methyl group, and the line at 150. 5 cps arises from the proton resonance of the other N-methyl group. The natural line widths of both» lines are about the same, and these widths are negligible compared to the chemical shift between the lines. N, N-Dirnethyltrifluoroacetam‘ide - The high-re solution fluorine magnetic resonance spectrum of pureN, N-dimethyltrifluoroacetamide is shown in-Figure 15. The multiplet structure arises from the non- equivalent spin- spin coupling of the three fluorine nuclei with the protons of each N-methyl group, Theoretically this spectrum consists often equally-spaced (0. 7 cps) lines with relative intensities 3:10:20:33:40:40: 33:20: 10:3. .1 The observed Spectrum is in agreement with the theoretical one. The high- resolution proton magnetic resonance spectrum of pure ‘N, N-dimethyltrifluoroacetamide is shown in-Figure 16. The quartet between 215. 2 and 219.4 cps is due to the resonance of the protons of one N-methyl group, (whereas the quartet between 223. 7 and 225. 8 cps is due to the proton resonance of the other N-methyl group. The quartet structures are the result of nonequivalent spin- Spin coupling of the three fluorine nuclei with the protons of each N-methyl group. The splitting in thevlow-field quartet is 1. 4 cps, and that in the highéfield quartet is 0.7 cps. 90 .mmdo gods cm was N .N. gonna mm? NEUMEUH mo 051.5 93. 620.33 Hounouxo mo mcouonm ME.” 05 o» 65.3.30.” ohm mumEm 30.686440 * m 66- 004.6 m: 4. 66 6 .64.6 400 5o 44 o 4.6.. 6.. 6 .8 4. £6 6 .3 .6 400 6 66 64.6- .666 M464. o$6 O$6 Joo .666 m 66- 68 4. E36 .8 6 .8 6 62.. .5440 .4 .2 o 4%. Jo 6 ...? 6 :N 6 o: 6 :3. 4.638 .4 6... 4. 6m. .66 6 62. 6 .66 6 .6... 6 6o 4 .545 6 .2. 4.6...- 64.6 .644. 666 04.4.6 ...:4 NHmnmo .066 66...- N3.6 :64. .36 N64.6 .24 36340 £66 66...- C36 :64. .36 4.66 464 Numumo 64.6 666- £66 N664. 4.2.6, 64.6 1, 2: . U0 . H can . Sam 8mm unozom vodka .mmUm. .nmUe .NAnEUVZe Just/How o unmouonm 302 h l . illl (II I! *MQHEdaonnHOMnHAVmBHv/HHQIZ .2 MO wZOHHDAOm HEOM MOh mfiham AH MAmaqu 91 mmo m.m.- . ....MNN «5.: . . NAME Ala: .2833 #93968 HO Tannin “0068.630." . .UOmN n u :38. 8o .8 ... ,5 ....muvzoomho mo Shauna engagemou 030:de «E A: 93$er 3... 66 4. .6 4. . . ....1... ...... ..mamUHmfio ngofino ”monouvmou ..Uomm u u :86 8o .3 u s. ....muvzoommo mo guuummm 00:936.?“ oflmcwdfi $.m .mfl muflmwh 92 N, N-Dimethylacrylamide - The high resolution proton magnetic resonance spectrum of pure‘N, N-dinnethylacrylamide is shown in . Figure 17. The resonance line at 215. 3 cps is due to the proton resonance . of one N-methyl group, whereas the line at 224. 8 cps is due to the proton resonance of the other N-methyl group. The effective natural line widths of these two lines are about the same. This indicates that the spin of the tertiary proton of the vinyl group is coupled very weakly and equivalently with the Spins of the protons of each N-methyl group. The effective natural line widths of the two N-methyl proton resonance lines are small compared to the chemical shift between the lines. The proton resonancenof the vinyl groupis located between -25. 7 and 68. 6 cps. The gain used while recording this portion of the spectrum was much higher than that used while recording the proton resonance of the two N-methyl groups. The‘proton resonance of the vinyl group shown in Figure ”is indicative of the complexity of NMR. spectra when the magnitudes of spin- spin coupling constants are comparable to the corres- ponding internal chemical shifts. The "vinyl spectrum" is of the type (ABC)? and although the complete solutions for the. analysis of such a spectrum may, in principle, be given in closed form, the solutions are more simply'arrived at by numerical calculations. The "vinyl spectrum" of N, N-dim ethylacrylamide is similar to the "vinyl spectrum" of styrene '(105). N, N-Dimethylbenzamide - The proton magnetic resonance spectrum of 36. 34 mole percent N, N-dimethylbenzamide in dibromomethane is shown in Figure 18. The peak at -60. 7 cps is due to the proton resonance of the phenyl group, and the peak at 81. 6 cps is due to the proton resonance of the solvent dibromomethane. The lineat 202. 9 cps arises from one * , ‘ An ABC- -type spectrum is the spectrum of a system having three non- equivalent nuclear spins, the three internal chemical shifts and the three coupling constants being of the same order of magnitude. 93 moo w.¢- 6.6mm . AI cm .9853» Hdcnouxo mo Tasman "ouaonomou :86 ooo .8 .... ... ....movzoomo n .66 mo 5.3.30on 0043:0on 032“on L1H .3 ousmwh who m.mm ozvm. m.m~ o; MAE: mmu c.wo m v.wm_ @6m mdN aim «2w... . 5mm- “ a J— . w a u . _ w a m w Al. on .0 0mm "u 94 {It}: {i 1W I.” 42.8.33 18:0me HQ 3559 "oucmuvmmu .6093. "a :38 98.3 n... ....mumu aw Ammoioommoo E353 208 .m .0... mo gnuummm vonAHOmuu 33¢de LA .3 mafimwm mac m.wH~ m.oo~ : All cm .9533 H9333... mo i323 ”mononomon . ..Uom .vNu n u :38. coo .8 u s. .Anmuvzoufio mo 8.93023 causeway 03¢:de um .oH mndmfw ago in: odom oéw v.09. n J- h AI om 95 N-methyl proton resonance, whereas the line at 212. 1 cps is due to the other N-methyl proton resonance. The natural line widths of the two N—methyl proton resonances are small compared to the chemical shift between the two lines. N, N—Dimethylcarbamyl chloride - The proton magnetic resonance spectrum of pure N, N-dimethylcarbamyl chloride is shown in Figure 19. One line is due to the proton resonance of one N-methyl group, and the other line is due to the proton resonance of the other N-methyl group. The natural line widths of the two lines are small compared to the chemical shift between the two lines. 2 The proton resonance spectra of the solutions of N, N-dimethyl- carbamyl chloride in dibromomethane and in carbon tetrachloride were all essentially the same as that shown in Figure 19. The pertinent NMR data for these solutions are tabulated in Table V. N, N-Dibenzylacetamide - The proton magnetic resonance spectrum of 38. 09 mole percent N, N-dibenzylacetamide is shown in 'Figure 20. The large peak at -42. 3 cps is due to the proton resonance of the two phenyl groups, and the peak at 100. 1 cps is due to the proton resonance of the solvent dibromomethane. The peak at 266. 4 cps arises from the proton resonance of the methyl group. The line at 117. 0 cps is due to the proton resonance of one methylene group, and the line at 129. 0 cps is due to the proton resonance of the other N-methyl group. Due to very weak Spin- spin coupling between the ring and the methylene protons of each benzyl group, the proton resonance lines for each methylene group are broadened slightly. ~ However, the effective natural line widths of these lines are still small compared to the chemical shift between the two lines. The proton resonance Spectrum of 38. 29 mole percent N, N-di- benzylacetamide in carbon tetrachloride is shown in Figure 21. This spectrum is essentially the same as the one shown in Figure 20. TABLE V PROTON CHEMICAL SHIFTS FOR SOME SOLUTIONS OF N, N- DIMETHYLCARBAMYL CHLORIDE Mole Per cent 6 solvent, 6 N(CH3)2, . Amide _ Solvent ppm ppm t, 0C. 100 3-496 3.603 -24. 2 90.03 CHzBrZ 1.388 3.415 3.522 -Z4.5 63.44 CHzBrZ 1.253 3.209 3-314 . -24.5 40.93 CHzBrz 1.107 3.048 3.152 -23.7 10. 72 CHZBrz .903 z. 804 z. 906 -22. 2 71.35 CCl, 3.499 3.518 -20.2 40.08 CC14 3.322 3.444 -20.2 10.98 CCL, 3.219 3.34, -19.7 9,: Chemical shifts are relative to the ring protons of external toluene. 97 mmo oonm 0.3.4 H.N.NH Ném — _ _ _ _ q 1...: fl .% T ...... .9353”. Hmnnooxowofwnoflm 5285mm“: ..Uom.m.. u :88. ooo .oo n s. .400 E Ammommooozoonmo 38 So 3065 am .mm mo 55.30QO songbook 9.305me "E .HN oa5mfim m m ovflocN o.m- 0.5: H.o_oH m.~.¢u a PI: d a - Al M i- v M a TE .9353» Hmcuofino mo 3593 Hoocouomou ..U 0N.m.. u a . .mocu ooo.oo u o: . m .NymNmofi fimommooozoonmo 2.8 So 208 oo .wm mo 5.55:0on ooddGOmmn ofluoamme LA .om ou5mfim 98 Ethyl-N, N-dimethLlcarbamate - The-proton magnetic resonance spectrum‘ of pure ethyl-N, N-dimethylcarbamate is shown in‘Figure 22. The quartet between 148. 3 and 168. 7 cps and the triplet between 325. 2 and 338. 8 cps are due to the proton resonance of the ethyl group. The narrow line at 229. 5 cps is due to the proton resonance of the two equivalent N-methyl groups. The gain used while recording this line was less than that used while recording the quartet. and triplet. The proton resonance of the two N-methyl groupsiwas observed to be a single narrow line in the temperature region from room temperature down to the freezing point. N, N-Bis-(triflugromethylktrifluoroacetamide - The fluorine magnetic resonance spectrum of pure N, N-bis-(trifluoromethyl)—trifluoro- acetamide is shown in Figure 23. The quartet between -323. ‘7 and -306.. 7 cps arises from the fluorine resonance of the two equivalent N- trifluoromethyl groups, whereas-:the septet between 685. 0 and 718. 6 cps arises from the fluorine resonance of the C-trifluoromethyl group. The gain used while recording the septet was much greater than that used while recording the quartet. The splittings in the quartet 3.32 septet are about 5.6 cps. The spectrum for the septet consists of seven equally spaced lines with relative intensities 1:6:15:20:15:6:1. The observed septet is in agreement with the theoretical one. The spectrum of the quartet did not change in thetemperature region from room temperature down, to the freezing point . fiethyI-N, N-bis—(trifluo romethyl)-carbamate - The. proton magnetic resonance spectrum of pure methyl-‘N, N-bis: (trifluoromethyl)-carbamate consists of a single narrow line. The external chemical shift, relative to the proton resonance of the ring protons of toluene, is 2.. 843 ppm. The fluorine resonance was observed to be a single narrow line in the temperature region from room temperature down to the freezing point. The external chemical shift, relative to the fluorine resonance of 1, l-dibromo- 1, 1,2, 2, -tetrafluoroethane, is -5. 260 ppm. 99 moo o.m:. 5:2. oooo ooo? 53? n r a t. n n n t. .. T n l 1 0.. 4| om .Hmohuummhu 355303 ”00505305 . ..U 0mm n a :88 ooo .oo u e. 5150200550 mo 555.3023 005d50m05 0305mm55 Sh .mm 055m?» ago mono ~.m~m momm od.,: m .3; P c b p . m w w w a 9.. om 65033 355038 mo 15059 “00505305 . .0 0mm n u :88 ooo.oo n s. .Anm0ozooommno mo 55555005? 005d50m05 0305me um .NN 055mrm 100 Hinde red Internal Rotation >N, N-Dimethylformamide -‘ The hindered internal rotation about the central C-N bond of N, N-dimethylformamide was studied by Methods'II and III. Some of'the spectra, from which data were obtained by Method 111, are shown in Figure 24. The experimental data obtained by Method 111 are tabulated in Table VI, and the experimental data , obtained by Method II are tabulated in Table VII. For comparison, the I data obtained by Gutowsky and Holm '(5, 6), who studied the internal , rotation in this compound by Method 11,- are tabulated inTable VIII. The data obtained by Method-III are plotted as logm(4 «2 "C 6 v) against 103/T in‘Figure 25, and a similar plot for the data obtained by Method 11 is shoWn in Figure 26. , For comparison, a somewhat similar plot of the data obtained by Gutowsky and Holm is. shown in Figure 27. N, N-Dime thylacetamide - The hindered internal rotation of pure N, N-dimethylacetamide was studied by Method 111. . Some of the spectra, from‘ which data were obtained, are shown in-Figure'ZB. The experi- mental data are tabulated in Table :IX and plotted as logio(4 Wt 61») against 103/T in Figure 29. For comparison the data obtained by Gutowsky and Holm (5, 6), who studied this compound by Method 11, are tabulated in Table X and plotted in Figure 30. N, N- Dimethylpropionamide - The hindered internal rotation about the central C-N bond of pure‘N, N-dimethylproPionamide was studied by Method 111. In addition, the phenomenon was also studied for the follow- ing concentrations (mole per cent) of amide .(a) in dibromomethane: 84. 7,, 68. 88, 58. Co, 40.57, 22. 17, and 10. 14; and (b) in carbon tetra- chloride: 69. 3.; 39. 9;, and 11. 07,; The experimental data for the pure liquid amide, the solutions of amide and dibromomethane, and the solu- tions of amide and carbon tetrachloride are tabulated in Tables XI, XII, and~XIII, respectively. These data are plotted as logm(41rzr 6v) 101 Allow .oufiumuomgou >uo>o um madam o5 >304.“me «on who? 93mm novuooou pad moan.” moo»; 05H. :01an ooo .oe n 3» .moudomHomEou odowumcr um opwfimgofiifiogvnz .Z 5 manoum 35mg 05 mo muuoomm ooamnomou 3qume Gouounm t"' "" |"" o O o . 00 N vNH t . o . o o o o2 .0 03.52 .0 .3 enema @- 0:; 102 Allow .0 03.63 ‘l‘ll’ o O. 001:: o M. OoeoE 003.3280 .wN 0.5%th . h. ooemfl 103 TABLE VI TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL c-N BOND OF HCON(CH3)2. METHOD 111 v0 = 60.000 mcs., 6v = 9.43 4 .20 cps at 25°C. ~t,AoC. 103/T, (OIL) r log10(4 Trz'tév) 144.26 4 .104 2. 3957 1.141 4 .002* 1.0425 4 .0005“ 143.60 4 .01 2.3994 . 1.166 4 .017 1.0515 4 .0060 140.43 4 .10 2.4178 1.474 4 .036 1.1305 4.0060 135.47 4 .08 2.4472 2.451 4 .030 1.2675 4.0030 130.90 4 .13 2.4749 3.528 4 .060 1.3552 4 .0040 124.20 4 .40 2.5166 7.562 4 .071 1.5310 4 .0023 123.79 4.40 2.5192 7.507 4 .060 1.5295 4 .0020 :5: The error given is the average dev1ation from the average of five measurements. TABLE VII 104 TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL . ROTATION ABOUT THE CENTRAL C-N BOND OF HCON(CH3)2, METHOD II ' v, = 60.000 mcs., 6v = 9.43 4.20 cpsat 25°C. o t, 'C. 103/ T, (°K.) 1' 1°810(4'rrz 7: 6V) 131.76 4 ,12* 128.72 :1: . 10 122.81 4 .21 121.48 4 . 12 115.86 :I: .16 113.124 .18 107. 18 :1: . 10 NNNNNNN .4696 .4883 .5254 .5340 .5706 .5888 .6292 5.49 a: .92* 7.41 4 .60 , 8.074 .97 8.244.38 8.584 .36 9.004 .69 ~9. 16 4 .27 ' 1. 0395 4 .0443* 1.1557 4 .0713 1. 2350 4 . 1280 1.2620 4 .0790 1.. 3295 4 . 1145 1.4665 4 .1915 1.5615 4 .1393 * _ The error given IS the average dev1ation from the average of 81x measurements. 105 TABLE VIII TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF . HCON(CH3)2. ACCORDING To GUTOWSKY AND HOLM(5, 6), METHOD II ’ v0 =.- 17.735 mcs., 6v = 3.24 4.05 cps at -37.2°C., . Tz=0.88:l:.19cps r A w—v '— ~— t,°C. 103/ T, (0K.) 6ve, cps log‘o(;6vr) 95.8414 2.7100 1.904.104 -.31664.0130* 93.8 4 1 2.7248 2.014.10 -.3034 4 .0134 89.3 41 2.7586 2.10 4 .05 -.2753 4 .0143 87.3 41 2.7739 2.45 4 .10 -. 1784 4 .0303 85.8 4 1 2.7855 2.20 4 . 10 -.2606 4 .0147 81.34 1 2.8209 2.454.10 -.17844.0303 74.0 41 2.8818 2.64 4 . 19 -.0993 4 .0605 70.8 4 1 2.9070 2.75 4 . 10 -.0286 4 .0704 51.841 3.0769 2.944.19 .16054.1457 49.3 41 3.1008 3.06 4 .14 .2984 4 .1758 —37.241 3,204.05 r 17 4: The error given is the standard deviation from the average of about ten measurements. 106 T T I I 00 1. 5— T 1.47 w _ O '5: “(3 3° 1. 3— '— r; S: S (D on .9. 1 2 Figure 25. Plot of 1.0310(4172 ‘t: 6v) 4 ' against 103/T for pure HCON(CH3)2, Method 111. Ea = 18.3 4 0. 9 kcal. /mole . A =T(2 to 50) x 1010 sec. “'1 A172... ,_ = 22. l‘kca1./mole ° Tc = 421.6° K. v0 = 60.000 mcs. 1.1.. 6v=9.43:L-.20 cpsat25°C. - 0 O 1.0 l 4 l ' l 2.40 2.44 2.48 2452‘ 103/T, (°K.) --v°‘u‘-.. 1.6 1.4 1.2 1.0 107 l 1 ~ Figure 26. Plot of logm(41rz"C 6v) against 103/ T for pure'HCON(CH3)z, Method 11. EaL = 14.3 4 2.8 kcal./mole A = (2 to 130) x 10'3 mac."1 AFz”. 2 = 19.6 kcal. /mole fl Tc = 410.7°K. 6v = 9.43 4 .20 cps at 25° C. 1 1 2. 2.5 2.6 2.7 103/T- l°1<.1 0.4 0.2 0.0 -o.4 108 Figure 27. Plot of log1°( 'Clév) against IO/T for pure HCON(CI-I3)z, according to Gutowsky and Holm (5, 6), Method ‘II. .EaL = 6.7 42.9 kcal./mole A = (1 to 1100) x 103sec". AF298.Z = 18. 0 kcal. /mole TC = 279. 3° K. we: 17.735 mcs. o " 6v = 3.244 .05 cps at -37.2 C. l l z. 7 2.9 3.1 103/T, (°K.) 109 Alucm .0u5u0u0m50u >u0>0 0.0 05.00 05 4:40.88 no: 0H0? 050m u0vuoo0u was 003.” @0030 0:8 .008 ooo do n... a: .m0u30u0980u 053.405 um 03503003443312 .2 no 09993 350812 043 .«o 0.30090 00:044—000.” 03048.05 Gouounm I‘."’ .3 charm ’ / l "” II / .I .0644 .3 C = . o . Os c 3 0644.3 .Uom~ 2 110 Allcm . p. 06644 . v. 0643. 60.95300 . m .. 004.3. .3 684E 111 TABLE IX TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL . ROTATION ABOUT THE CENTRAL C~N BOND OF CH3CON(CH3)2.. METHOD III v0 = 60.000 mcs., 6v = 10.55 4 .34 cps at -27.6°C. t, °C. 103/T, (°K.) r . r. ’ p . _ 163.0(41721160) 84.97 4 .334 2.7923 ’ 1.029 4 .0054 .. 9890 4 .0035* 79.57 4.10 2.8350 . ' 1. 287 4.023 1.0880 4 .0033 74.454 .01 ' 2.8768 1.743 4 .‘023- 1.1787 4 .0015 66.43 4 .09 2.9447 3.4014 .025, 1.3467 4 .0014 62.66 4.09 2.9778 4.3614 .027 1.4053 4 .0065 1.5180 4 .0055 57.96 4 .04 ' 3.0201 7.145 4 .238 V r 4 The error given 18 the average deVIation from the average of five measurements. 112 TABLE X TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF CH3CON(CH3),,. ACCORDING To GUTOWSKY AND HOLM (5, 6), METHOD 11 v0 = 17.735 mcs., 6v = 3.91 4. 14 cps at —24.2°C., T2 = 1.134 .25 cps W t, C. 103/T, (°K.) ave,cps ‘ log10(’t6v) 49.3 4 1* , 3.1008 1.56 4 ,. 11* 91.4794 4 .0090»: 48.0 41 3.1133 2.14 4.21 {—.4317 4 .0292 46.5 41 3.1279 2.45 4 . 14 —.3892 4 .0321 43,34 1 3.1596 2.784.11 -.32964 .0366 39.8 41 3.1949 3.25 4 . 14 -.1962 4 .0644 37.341 3.2206 3.454.14 -.09934 .1140 33.8 41 3.2573 3.48 4 .18 -.0770 4 .1363 29.8 41 3.3003 3.63 4.14 -.0555 4 .3010 19.8 41 3.4130 3.77 4 .11‘ +.2980 4 .2757 -24.241 4.0161 3.894.14 :1: The error given is the standard deviation from the average of about ten measurements. 10g10(4TTz 2: 6V) 1.4 1.2 1.0 113 0 Figure 29. Plot of log10(41'rz't 6v) against 103/ T for pure CH3CON(CH3)2, Method 111. Ea: 10.5} 0.5 kcalL/‘mole , “ A =T(3 to 33) x 1.07 sec. 71 AF298.2 = 17.4 kcal./mole TC=369.4°K.' - v0 = 60. 000 mcs. 60.: 10.55 4 .34 cps at 427.690 2. 103/T, (°K.) logw( t 5V) 114 7 l I l 0.4 r' 4 0.2 — _ 0.0 _ _. -.., _ / y _ Figure 30. P101: 61163,,“ 6v) against 103/T for pure CH3CON(CH3)2, according to Gutowsky and Holm (5, 6), Method II. Ea = 11.44 1.2 kcal./mole. A, - (6 to 170) x 107 sec". . -0.4 17 _ r AFm,z .. 1‘7. 3 kcal. /m61e -4 TC = 273. 0 K. v0: 17.735 mcs. o 6v = 3.91:1: .14 cps at -24.2 C. l I l I 3.1 3. 2 3. 3 3. 4 103/T. (°K.) 115 against 103/T in Figures 31 through 40. The concentration dependencies of the energy barrier Ea, for the solutions of amide in dibromomethane andfor the solutions of amide in carbon tetrachloride, are shown in ‘ Figure 41. N, NaDimethyltrichloroacetamide - The hindered internal rotation about the central C—N bond of pure N, N- dimethyltrichloroacetamide was studied by Method III. The experimental data are tabulated in Table XIV and plotted as 1.0310(4 «3'2: 6v) against 103/T in-Figure 42. N, N—Dimethyltrifluoroacetamide - The hindered interval rotation about the central C-N bond of pure N, N-dimethyltrifluoroacetamide was . studied by Method 111. The proton-fluorine spin- spin interactions were decoupled by the double irradiation technique. ~ Some of the spectra, from which data were obtained, are 'shown in Figure 43. The experi- mental data are tabulated in Table XV and plotted as logm(4 nz'Zév) against 103/T in Figure 44. N, N-Dimethylacrylamide - The internal rotation about the central C-‘-N bond of N, N-dimethylacrylamide was studied by Method 111. The experimental data are tabulated in Table XVI and plotted as logm(4 Irz'L’bv) against 103 /T in Figure 45. N, N-Dimethylbenzamide - The hindered internal about the central C--N bond of N, N-dimethylbenzamide (36.34 mole per cent in dibromo- methane) was studied by Method III. The experimental data are tabulated in Table XVII and plotted as logm(4IIz 26v) against 103/T in‘ Figure 46. N, N—Dimethylcarbamyl chloride - The hindered internal rotation about the central C-N bond of pure‘N, N-dimethylcarbamyl chloride was studied by Method 111. In addition, the phenomenon was studied for the following concentrations (mole per cent) of amide (a) in dibromomethane: 90. 03, 63.44, 40. 93, and 10. 73; and (b) in carbon tetrachloride: 71. 35, TAB LE XI 116 TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THEKCENTRAL C-N BOND OF N, N- DIMETI-IYLPROPIONAMIDE, METHOD III . ,v0 = 60.000 mcs., 0v 2 9. 18 i. 17 cps at -27.5°C. L 1' . ,1,o_g10(4 177‘ 2: 6 v) , t,°c, 103/T, (°K.) 56.264 .054 3.0356 55.83 4.05 3.0396 52.44 4 .16 3.0713 50.48 4 .08 3.0899 50.44 4.09 3.0902 47.26 4.04 3.1209 44.65 4.14 3.1465 39.27 4 .14 3.2007 34.014.16 3.2555 1.094 4.0044 1.095 4 .006 1.410 4 .014 1.623 4 .020 1.702 :1: .025 2. 163 4 .027 2.495 4 ,111' 3.597 :1: .185 5.896 :1: .134 [1.0244 4.00191‘ 1.0248 4 .0025 1. 1165 4 .0027 1.1589 4 .0038 1.1720 4 .0040 1.2362 4 .0035 1.2720 :1: .0116 1.3600 4 .0126 1.4745 4 .0053 W The error given is the average deviation from the average of five measurements. TABLE XII 117 TEMPERATURE DEPENDENCIES OF THE RATE OF INTERNAL . ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIMETHYLPROPIONAMIDE IN DIBROMOMETHANE SOLUTIONS,- METHOD III v0 = 60. 000 mcs. (a) 84.71 mole per cent amide, 6v = 8.88:1: . 20 cps at -26.80C. ‘1. . t, C. 103/T, (°K.) r 16g,o(4457:6v) 56.04 4 .114 3.0395 1.081 4 .006* 1.0172 4 .0005* 55.13 4 .06 3.0461 1.041 4 .005 1.0285 4 .0347 52.59 4 .23 3.0698 1.3214 .038 1.0957 4 .0089 49.94 4 .13 3.0950 1.591 4 .008 1.1530 4 .0012 49.86 4.14 3.0958 1.635 4 .012 1.1608 4 .0019 46.78 4 .05 3. 1256 2. 282 4 .073 1.2491 4 .0078 44.72 4 . 26 3.1458 2. 644 4 .073 1. 2862 4 .0068 39.29 4.09 3. 2005 4. 143 4 .251 1.3933 4 .0149 34.14 4.06 3. 2541 6.024 4 . 177 1.4794 4 .0063 (b) 68.88 mole per cent amide, 6v = 8.55 :l:. 21 cps at -26.8°C. 56.07 4 .05 ' 54.95 :1: .13 52.514 .11 50. 50. 47. 44. 591 044 044 834 39.814 33. 984 .07 .14 .04 .06 .11 .09 1.083 4 .009 1. 102 4 .002 1.348 4 .019 1.620 4 .008 1.643 4 .017 2.254 4 .073 .. 2.480 4 .054 4.088 4 .060 6.538 4 .308 1.0191 4 .0034 1.0271 4 .0003 1.1022 4.0040 1.1580 4 .0012 1.1622 4 .0029 1.2463 4 .0081 1.2704 4 .0057 1.3903 4 .0035 1.49814 .0112 Continued TABLE XII - Continued 118 t,°C. 103 /T, PK.) 1‘ 19,810“ "2'1: 5 V) ._ (c) 58. 00 mole’p'eur cent amide, 60 = 8. 24 :1: .19 Cps 34-21406. 56. 55. 52. 50. 50. 47. 45. 39. 39. 36. 34 56 55 55 52 50 50 47 46 39 35 204.09 904.05 914.11 554.06 364.11 414.07 594.12 674.05 644.24 444.07 .184.24 3.0356 3.0390 3.0668 3.0892 3.0910 3.1194 3.1373 3.1966 ‘ 3. 1969 3. 2300 3. 2537 1.0794 .008 1.075 4 .004 1.356 4 .005 1.598 4 .009 1.605 4.018 2.136 4 .065 2. 467 4.046 3.997 4 .140 3.671 4 .127 6.147 4 .009 6.4514 .280 f 1.0180 4 .0042 1.0159 4 .0021 1.1040 4 .0012 p 1.1545 4 .0017 1.1555 4 .0034 1.2327 :1: .0081 1. 2692 4 . 0044 1. 3847 :1: . 0028 1. 3647 :1: .0082 1. 4840 :I: .0005 1.4950 4 .0102 (d) 40. 57 mole per cent amide, 6v = 7.45 4 .25 cps at -26.4°C. .61 4.09 .974 .10 .904 .08 .474_.07 .194 .13 .164.08 .654 .09 .124.06 .904 .09 .004.21 3.0324 3.0383 3.0389 3.0710, 3.0926 3.0929 3. 1171 3. 1320 3. 1943 3.2451 1.0294 .005 1.0594 .004 1.0594 .004 1.286 4 .020 1.505 4 .008 1.551 4 .010 2.077 4 .035 2.155 4 .018 3.5194 .082 5.133 4 .253 . 9890 4 . 0045 1.0078 4 .0026 1.0078 4 .0026 1.0872 4 .0051 1.1370 4 .0016 1.1456 4 .0017 1.2253 4 .0045 1. 2350 4 . 0022 1.3547 4 .0057 1.4427 4 .0107 Continued 119 TABLE XII - Continued t, °c. 103/T, (°K.) r 16mm «2?: a v) (e) 22. 17 mole per cent amide, 6v = 6.42 4 . 13 cps at ~24. 0°C. 57. 30 4 .09 3.0261 1.000 4 .004 .9856 4 .0039 52.33 4 .05 3.0723 7 1.2414 .012 1.0755 4 .0035 50.82 4 . 18 3.0866 ‘ 1. 334 4.012 1.0988 4 .0019 49.47 4 .09 3.0995 1.4914 .023 1.1342 4 .0052 47. 17 4.14 3.1218 1.691 4 .056 1. 1702 4 .0097 45.714 .12 3. 1361 1.879 4.023 1.1990 4 .0035 39.914 .08 3. 1942 3.017 4 .063 1.3182 4 .0054 34. 96 4 .06 3.2455 4.685 4 .065 1.4215 4 .0031 (f) 10.1., mole per cent amide, 6v = 5.77 4 .26 cps at -23.8°C. 51.284 .06 3.0822 1.5164.007 1.13954.0007 46.99 4 .07 3.1235 2.005 4 .003 1.2160 4 .0005 42.45 4 . 05 3. 1685 2. 328 4 .048 1.2542 4 .0050' 39.25 4.05 3. 2009 2.772 4 .063 1.2977 4 .0038 36.55 4 .02 3.2288 3.5014 .024 1.3538 4 .0015 36. 32 4 . 11 3. 2312 3.395 4 .072 1.3462 4 .0050 34.23 4 .02 3. 2532 3.8814 .013 1.3780 4 .0007 30. 08 4 .04 3. 2977 4.738 4 .065 1.4242 4 .0033 4 The error given 18 the average deV1at10n from the average of five measurements. 120 TABLE XIII TEMPERATURE DEPENDENCIES OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-‘-N BOND OF N, N—DIMETHYLPROPIONAMIDE IN CARBON TETRACHLORIDE SOLUTIONS, METHOD 111 v0 = 60. 000 mcs. (a) 69. 34 mole per cent amide, 6v = 9. 59 i . 18 cps at -24. 0°C. 44L J O t, c. 103/T, (°K.) ‘ r ._ 16g1'0(4 n22; 6v) 51. 38 4 .9054- 3.0813 1.140 4 .003* 1.0420: .0015»: 47.02 4.07 3.1232 1.531 4 .016 1.1420 4 .0030 42.47 4.05 3.1683 1.964 4 .019 1.2105 4 .0037 39.56 4 . 02 3.1978 2.527 4 .026 1.2752 4.0025 36.76 4.04 3.2260 3.138 4 .027 1.3277 4 .0020 34.84 4 .05 3. 2468 3.544 4 .037 1. 3565 4 .0035 36. 34. 29. 26. 18. 12. .(b) 39. 94 mole per cent amide, 6v = 9.69 4.13 cps at -24. 0°C.. 34. 29. 26. 24. 18. 14. 27 4 .. 05 3.2528 . - 1.061 4 .005 1.0090 4 .0025 94 4 . 02 3. 2992 1. 310 4' .009 1.0935 4 .0025 104 .05 3.3416 1.6964_.007 1.17104.0015 47 4 . 24 3.3599 1.780 4 .008 1.1845 4 .0010 68 4 .02 3.4265 2.744 4 .045 1.2952 4 .0032 07 4 .15 3.4815 4.056 4 .028 1. 3882 4 .0018 (c) 11.07 mole per cent amide, 6v = 9.65 4 . 15 cps at -23.8°C.’ 69 4 . 03 3.2274 1. 108 4 .027 1.0303 4 .0097 94 4 .09 3. 2457 1. 209 4 .008 1.0655 4 .0030 97 4 .05 3.2989 1.544 4 .011 1. 1445 4 .0020 544 .12 3.3367 1.9134 .026 1.2035 4 .0035 66 4 . 25 3.4269 3.052 4 .062 1.3210 4 .0047 73 4 . 12 3.4978 4.385 4 . 177 1.4065 4 .0090 * . The error given 18 the average demation from the average of five measurements. -'OLU \ .42 .34 .26 .18 .10 .02 @ Figure 31. Plot of 163,0(4 énz'ta v) against 0 103/T for pure C2H5C0N(CH3)Z, Method 111. E3 = 9. 240. 8 kcal/mole A =T(8 to 26) x 106 sec."-1 AFM, 2 = 16.7 kcal/mole Tc = 334.4°K v0 = 60. 000 mcs. 6v: 9.18417 cps at-27.5°C. - 3. 02 3.10 3.18 3.26 103/T, PK.) 1°810(4 "2 t 45V) 1 1. 122 .48?- .16"' 1.00 32— Figure 32. Plot of 1.0810(411’zt5 v) against 103/T for 84. 7‘ mole per cent C2H5CON(CH3)Z in aCHzBrz, Method 111. Ea = 10. 1 i=0. 9 kcal./mole A a} (2 to‘90) x 107 sec". AF298,2 = 16.7 kcal./mole TC = 333.0°K. v0 = 60. 000 mcs. 6v = 8.88 4 .20 cps at -26.8°C. l l l —1 3.04 3.12 3.20 3.28 103/T. (°K.‘) 123 1.32— logm(4 177‘ Z: 6v) Figure 33. Plot of 1ogm(41rz'?.'6 v) against 103 /T for 68. 83 mole per cent .CzH5CON(CH3)Z in Q CHzBrz, Method 111. ' o Ea = 10.34 0. 9 kcal./mole ' A =T(3 to 93) x 107 sec.‘1 Arm 2 = 16.8 kcal./mole Tc = 333.1 0K. V0 = 60. 000 mcs. (iv = 8.55 4 .21 cps at -26.8°C. 1.00 - 124 1.48 — — .3 1. 32 — - h . N1: 3‘, 6'5 .9. 1 '16 — '— ’ Figure 34. Plot of log10(4 172 ‘C 61:) against 1 10’ /T for 58. 00 mole per cent CZHSCON(CH3)2 J in CHzBrz, Method 111. ) Ea=10. 24 08kca1/m01e 1.00.. _ 7 -7 A - (2 to 85) x 10 sec.‘ ArmJ = 16.8 kcal./mole TC = 333. 3 °K. v0 = 60. 000 mcs. =8 24 4.19cpsat 23. 4°C. 3.02 3.10 3.18, 3.26 ' 103/T (°K.) ‘7“ A log10(4 "2 t 6 V) 125 I I r IQ 1.40 *- _. O 1. 32 " __ 1. 24 —— O .3 O 1. 16 — .. O 0 Figure 35. Plot of logm(4 112 'Z: 6 v) against 103 /Tfor 40. 57. mole per cent CZHSCON(CH3) _ in CHzBrz, Method 111. Ea = 9. 9 =1: 0. 9 kcal./mole 1 08 O A =T(2 to 50) x 107 sec'.‘ ' " AFm,, = 16.8 kcal./mole - TC = 332. 7° K. V0 3 60. 000 mCS. O 60': 7.454 .25 cps at -26.4 c. 1.01:) - __ 1 1 1 1 3.00 3.08 3. 16 3.24 103/T. (°K.) logw(4 117‘ 2’ 0 v) 1. 40 .32 .24 .16 .08 .00 126 ° for 22. 1., mole per cent C3H5C50N(CH3)Z in 0 Figure 36. Plot of logm(4 02756 v) against 103/I CHzBrz, Method III. , Ea = 9.1 4 0. 2 kcal./mole A = (8 to 13) x 106 sec?1 Ad,“ = 16.8 kcal./mole v0 = 60. 000 mcs. 6v = 6.42 4.13 cps at -24.0° c. 1 l L 3. 00 3.08 3. 16 3.24 103/T, (°K.) A A ‘— iii 103.0(4 Trz 2’ 6 v) 127 1140-— 1.32 1.24 1.16 1.08 3. 04 , Figure 37. Plot of log10(4 ‘n'z’Zf 6 v) against 103/ T for 10. 14 mole per cent C2 HSCON(CHa)z in CHzBrZ, Method III. Ea. = 7.140.8 kcal./mole A :1 (2 to 44) x 105 sec."1 AFzgsJ = 16. 7 kcal./mole TC = 337. 3°K v0 = 60. 000 mcs. 6v = 5.77 $.26 cps at —23.8°C.' 1 1 1 3. 12 3.20 3. 103/T, (°K.) —1 10 1.1 1.D 128 "‘84 = 9. 59 4.18 cps at 21.0%. 1 Figure 38. Plot of log1o(4 177‘ ”C 6 v) against 103/T for 69. 34 mole per cent CszCON(CH3)z in CC]... Method 111. ' . Ea = 8. 6:1: 0. 6 kcal. /mole A =T(4 tolz) 4106 sec:‘ AFzga. 2 = 16. 5 kcal. /m01e TC = 333. 00c. v0 = 60. 000 mcs. A . 10 3.20 3.30 103/T. (°K.) logm(4 Trz 2’6 v) 1.4 1.3 1.2 1.0 128 .7 Figure 38. Plot of logm(4 «2 "C 5 v) against 103/T for 69. 34 mole per cent C2H5CON(CH3)Z in CC1,, Method III. I , Ea = 8.64 0.6 kcal./mole A = (4 t012)x106 sec:1 AFI98. 2 = 16. 5 kcal. /mole TC = 333. 0°C. v0 = 60. 000 mcs. ‘ "6v = 9. 59 i . 18 cps at -24. 0°C. J l . 10 3.20 3.30 103/T. (°K.) 0.- (.3 ‘ 1.09.“. 10g10(4 772 2’ 6 v) 129 I I 1, 40- T l. 32- l . 24— O 1 161— Figure 39. Plot of log1o(4 1T?- ’2: 5 v) against 103/1' 1, 0 s— for 39. 9, mole per cent c2141.,c301xuc143)z in-ccn. Method IIL ‘ Ea: 7. 5 4 0. 5 kcal. /mole A =T(4 to 26) x 105scc?l AF298.2 = 15. 9 kcal./mOIC TC = 311. 30K. v0 = 60. 000 mcs. 0 6V = 9.69 4. 13 cps at -24.0 C. LOG- l l 1 l 3.26 3.34 3.42 3.50 103/r, (°K.) 1081M4 "2 2: 6 v) 130 I I I I 1.40 b 1. 32 ” O 1. 24 - O 1 16L Figure 40. Plot of log10(4 177‘ ”C 6 v) against 103/T for 11. 07 mole per cent Cal-15CON(CH3)2 in CC14, Method 111. 1 C) Ea. = 6. 3 4 0. 5 kcal./mole ' 8_ A = (2 to 32) x 105 sec."1 AFZ98.Z :5 16.0 kcal. /m01€ TC = 316.4 0K. V0 '3 60.000 mCS. 6v = 9.65 4 .15 cps at -23.8° c. 1.00 - I 4 l .24 3.32 3.40 1 3.48 103/T, (0 K.) Ea, kcal. /m61e ll 10 \O 00 131 I T I I r I ,/’.V—_€'> \ // <> \ \(o) _ _ /<.) \ / \\ \ / \ 4% 11 / / / I. / I / r // “ / 9.3 g III __ I I - / 1 I g I l l l I l 0 20 40 60 80 100 Mole Per Cent Amide Figure 41. Concentration dependencies of the energy barrier Ea for internal rotation about the central C-N bond of . N, N-dimethylproPionamide in: (a) dibromomethane solutions - -® - - -O- -, and (b) carbon tetra- chloride solutions {3 B . 132 TABLE XIV TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIMETHYLTRICHLOROACETA’MIDE, METHOD 111 v0 =60.000 mcs., 6v =17.514.22 cps at -26.8°C. H"— 4* t, °C. 103/T,(°K.) r . 16g,o(4 "at 6v) 1.0. 28 4 . 24* 3.5306 1.149 4 .0134 1.0450 4 .0050»: 8.60 4 .03 3.5491 1.308 4.005 1.0932 4 .0010. 5.95 4 .05 3.5828 1.6414 .009 1.1620 4 .0014 3.43 4 .45 3.6155 2.239 4 .032 1. 2447 4.0035 -o.45 4 .05 3.6669 3.394 4 .031 1.3467 4 .0016 -4.07 4 .05 3.7162 5.377 4 .108 1.4532 4 .0048 The error given is the average deviation from the average of five measurements. 1°810(4 172 t 6 V) 133 1.36_ 1.28— 1.2%.. 1.12%- Figure 42. Plot of 16g,0(4 172 z 6 v) against 103/1" for pure CCI3CON(CH3)Z, Method 111. Ea. 7; 10.0 :1: .4 kcal./ mole A :T(8 to 17) x 108 sec:1 AF”... 2 = 14.9 kcal. /mole TC = 287.0 °K. v0 = 60. 000 mcs. 6v = 17.51 4.22 cps at -26.8°C. 3.52 3.60 3.68 103/T, (°K.) 134 6.353th83 >uo>o pd 088m 03... 438.88 «0: one? wcwmmfiovuooou pad mofimu @6026 03H. .moa mmvém ”Bond Ho snoooswoumofipmH m . .mofi ooo .oc n 6: .moudfimuomgo» an“? poudnfiudm mm? 00995.43.” 030:me Sh 04.3. magnate um upwgmuoomououflfiuugfiogpIZ .2 mo .930on ooGdGOmou 3qude Gouounm ‘|” .. .o. . u. . b. 064 ms oom 2. Use 3 .2. enema .068 2 135 podGflGoO .24 oudmfim 66.4.44 .0 64.4.64 ‘ 66.4.8 66.4.3 .064}: TABLE XV 136 TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N- DIIVIETHYLTRIFLUOROACETAMIDE, METHOD III 7 v0 = 60.000 mcs., 6v = 7.48 4 .30 cps at 21.4°c. 1‘ 10810“ “z I: <5 V) t, c. 10%“, (°K.) 89.87 4 .114 2.7546 86.48 4.06 2.7806 82.54 4 .07 2.8113 79.62 4 .07 2.8346 76.47 4 .04 2.8602 75.40 4 .04 2.8689 70.21 4 . 15 2.9123 62.07 4.11 2.9830 1.0664 .008* 1.221 4 .014 1.527 4 .023 1.843 4 .011 2.324 4 .012 2.426 4 .041 3.513 4 .069 5.822 4 .185 1.0115 4 .0040* 1.0695 4 .0043 1.1414 4 .0041 1.1932 4 .0018 1.2622 4 .0030 1.2648 4 .0042 1.3542 4 .0048 1.4805 4 .0020 a): The error given is the average deviation from the average of five measurements. 1081o(4 "2 Z 6 V) 137 1.48 ” 1. 32— 1. 16 I— Figure 44. Plot of logm(41rz "C 6v) against 103 /T for pure CF3CON(CH3)Z, Method 111. G) E =3 9.5 :1: 0.7 kcal./ mole 1.004 a 6 —1 A =I(3 to 54) x 10 sec. AF298.2 = 17. 6 kcal./mole TC = 367.0°K. V0 = 60. 000 mCS. 6v = 7.48 4 .30 cps at 21.4 °c. I L l I 2. 76 2.84 2. 92 3.00 103/T, (°K.) TABLE XVI 138 TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIMETHYLACRYLAMIDE, METHOD III v0 = 60.000 mcs., 6v = 9.46 4.21 cps at 4.3°c. =44====L m t,°C. 103/T, (°K.) r log10(4 172 z 6v) 39.20 4 .07»: 3. 2014 1.180 4.006* 1.05760 4 .0020* V_ 38.-33 4 .04 3. 2104 1.199 4 .004 1.0625 4 .0009 35.934 .02 3.2353 1.3134.001 1.09464 .0002 33.90 4.02 3.2567 1.571 4.006 1.1495 4 .0005 27.214 .12 3.3292 2.285 4 .039 1.2497 4.0038 25.04 4.02 3. 3535 2.4994 .016 1.2728 4.0002 The error given is the average deviation from the average of five measurements. 1°810(4 "2 Z“ 5 V) l. 139 103/ T, (°K.) T I I 26 — O 22 - 1.18 - Q 1 14_ Figure 45. Plot oflog10(41rz’2: 6v) against 103/T for pure CH3 = CHCON(CH3)Z, Method 111. Ea = 6.8 4 0. 9 kcal. /mole A =T(2 to 13) x 105 sec:1 1 10 _ 01me2 = 16.1 kcal./mole TC = 319.4014. v0 = 60. 000 mcs. 6v = 9.46 4 .21 cps at 4.3°c. 1. 06 I I 4 I 3. 22 3. 26 3. 30 3. 34 140 TABLE XVII TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIMETHYLBENZAMIDE (36. 34 MOLE PER CENT IN DIBROMOMETHANE), METHOD III v0 = 60.000 mcs. , 46v = 9. 22 4.18 cps at -26.6°C. t, c. 103 /T, (°K.) r 1og,o(4 n3 7: 6v) 9.91 4 .024 3.5327 1.010 4 .0034 .9720 4 .0035* 9.15 4.15 3.5422 1.040 4.004 .9965 4.0027 6.66 4.05 3.5737 1. 206 4 .009 1.0650 4.0027 5.80 4 .05 3.5847 1.289 4 .012 1.0883 4 .0034 2.81 4 .45 3.6236 1.5054 .006 1.1368 4.0012 -2.04 4.16 3.6884 2.369 4 .071 1. 2586 4 .0076 -3.974 .10 3.7148 2.9444.025 1.31224 .0020 -11.764.11 3.8256 5.6514.096 1.46524.0035 The error given is the average deviation from the average of five measurements. 10810(4 "z t <5 V) 141 Figure 46. Plot of log10(4 172 ’t 6 v) against 103/T for 36. 34 mole per cent C6H5CON(CH3)zin CHzBrz, Method III. Ea = 7.7 :1: 0.6 kcal./mole A =I(4 to 17) x 106 sec."1 AF298_ 2 = 15. 5 kcal. /mole TC = 285.0°K. v0 = 60. 000 mcs. 6v = 9.22 4.18 cps at -26.6°C. J I L 3.56 3.64 3.72 3.80 103/T. (°K.) 142 40. 0.8, and 10. 9,, . The experimental data for the pure liquid amide, the ' solutions of amide and dibromomethane, and the solutions of amide and carbon tetrachloride are tabulated in Tables XVIII,~ XIX, and XX, respectively. These data are plotted as log10(41rz ’t 6 v) against 103/T in Figures 47 through 54. The concentration dependencies of the energy barrier Ea, for the ‘solutions of amide in dibromomethane and for the solutions of amide in carbon tetrachloride, are shown in . Figure 55. ‘ N, N—Dibenzylacetamide - The hindered internal rotation about the central C-N bond of N, N-dibenzylacetamide (38. 09 mole per cent in dibromomethane) was studied by Method III. The experimental data are tabulated in Table XXI and plotted as logm(4 n2 "C 6v) against 103/T in' Figure 56. In addition, the phenomenon was studied for the amide in carbon tetrachloride solution (38. 29 mole per cent amide). These data are tabulated in Table XXII and plotted as log10(4 172 '2: 6v) against 103/T in Figure 57. The values of Ea: A, APE”. z and Tc for hindered internal rotation, about the central C—N bond of the amides studied, are tabulated in Table XXIII. 143 TABLE XVIII TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIMETHYLCARBAMYL CHLORIDE, METHOD 111 v0 = 60.000 mcs., 6v = 6.46:. .13 cps at -24.2°c. O t, (1.103 T, (°K.) r log1§(4 fizz 6v) 47. 13 :l: .06* 3.1222 1.103 :t .003* 1.0383 :1: .0009* 42.40 :1: .07 3.1690 1.406 :1: .017 1.1155 i .0040 39. 94 :l: . 20 3.1939 1.586 :1: .014 1.1523 :1: .0022 33.21 :1: .06 3.2640 2.566 :1: .025 1. 2788 :i: .0024 29.94 :I: .02 3. 2992 2.953 :1: .029 . 1.3130 :5 .0023 24.18 :1: .10 3. 3632‘ 4.580 :1: . 069 1.4162 :1: .0035 The error given is the average deviation from the average of five measurements. 144 TABLE XIX TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N—DIMETHYLCARBAMYL CHLORIDE IN DIBROMO- METHANE SOLUTIONS, METHOD III v0 = 60.000 mcs. (a) 90.03 mole per cent amide, 6v 2 6.45:1: . 29 cps at -24. 50C. ° 103 . t, _‘C. T, (°K.) r log10(4 «2 2' 6 v) 47. 27 4.044 3.1208 1.124 4 .0034 1.0362 4 .0008* 42.33 4.09 3.1697 1.448 4 _. 008 1.1252 4.0016 38,654.05 3.2071 1.8104.010 1.18894.0013 34.56 4.02 3.2497 2.486 4.018 1.2710 4.0017 32.07 4.02 3.2762 2.070 4 .062 1. 3224 4.0048 26.03 4.05 3. 3424 4.820 4 .050 1.4285 4.0025 (b) 63.44 mole per cent amide, 6v -‘-‘-' 6.27 :1: .20 at -24. Sec. 47.37 4.09 3.1198 1.149 4 .002 1.0450 4.0010 42.314.02 3.1700 1.5114 .007 1.1480 4.0015 38.65 4.05 3.2071 1.905 4.017 1. 2022 4.0025 34.60 4.04 3. 2493 2.605 4 .029 1.2825 4.0027 33.14 4 .10 3.2648 3.157 4 .036 1.3290 4.0030 28.42 4.02 3.3159 4. 9594 .040 1.4351 4.0016 (c) 40. 92 mole per cent amide, 6 v = 6. 25 :1: . 20 cps at --23. 7°C. 47.24 :1: .05 3. 1211 1.147 4 .004 1.0445 4 .0015 42.22 4 .02 3. 1708 1.4514 .006 1.1260 4 .0010 38.654.05 3.2071 1.9094.006 1.20284 .0007 34.64 4 .05 3. 2499 2.7714 .033 1.2977 4 .0022 32.514.05 3.2715 2.9954 .056 1.31654.0045 26.49 4 .05 3.3372 5. 238 4 . 150 1.4472 4 .0055 Continued TABLE XIX - Continued 145 t, C. 103 /T, (°K.) 1‘ 16gm(4 «2 “C. 6v) (d) 10.72 mole per cent amide, 6v 2 6.08:1: . 15 cps at -22. 20C. 47.03 4 .05 42.26 :1: .07 38.69 :1: .05 32.30 4 .02 29.82 4 .02 24.35 :1: .02 3.1231 3.1704 3.2067 3.3005 3.3005 3.3612 1.130 4 .012 1.372 :1: .009 1.632 4 .012 3.289 4 .045 3.289 4 .045 4.332 4 .088 1. 0380 i . 0050 l. 1078 :1: .0032 l. 1602 :1: .0021 1. 3393 :1: .0034 1. 3393 :1: .0034 1.4042 :1: .0040 ’1‘ . . . . . The error given is the average dev1ation from the average of five measurements. TABLE XX TEMPERATURE DEPENDENCIES OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIMETHYLCARBAMYL CHLORIDE IN CARBON TETRACHLORIDE SOLUTIONS, METHOD 111 v0 = 60. 000 mcs. (a) 71. 34 mole per cent amide, 6v = 7.18 4 .20 cps at -20. 2°C. 146 —.nfi t, C. 103/ T, (°K.) r log10(4 wz’L’6v) 47.04 4=.09* 3.1231 1.107 4 .0024 1.0292 4.00104 42.37 4.06 3.1693 1.388 4.006 1.1115 4 .0013 38.504 .05 3.2086 1.7194 .013 1.17484 .0022 33.12 4.02 3. 2650 2.416 4.032 1.2637 4 .0033 29.84 4.02 3.3003 2.739 4 .033 1.2947 4 .0030 25.85 4 .02 3.3444 3.719 4 .031 1.3679 4 .0020 (b) 40.08 mole per cent amide, 6v = 7. 34 :1: .20 cps at -20. 2°C. 1.024 4 .002 1.255 4 .009 1.569 4 .017 2.106 4 .034 2.780 4 .018 3.0814 .028 47.194 .09 42.194 .05 37.24 4 .05 30.96 4 .07 27.514 .05 25.014 .02 (c)10.93 38.60 4 .02 36.644 .05 34.76 4 .04 29.87 4 .05 25.20 4 .02 16.21 4 .03 3.1216 3.1711 3.2217 3.2882 3.3259 3.3538 3.2076 3. 2279 3,2476 3.3000 3. 3517 3.4558 1.111 4 .003 1.206 4 .020 1.308 4 .011 1.731 4.026 2.206 4 .079 4. 343 4 .033 .9850 4 .0010 1.0795 4 .0022 1.1490 4 .0030 1. 2290 4 . 0042 1. 2985' 4 . 0015 1. 3232 4 .0022 mole per cent amide, 6 v = 7. 33 4 . 25 cps at -19.7OC. 1.0312 4 .0012 1.065 4 .0055 1.9032 4 .0025 1.1768 4 .0042 1.2410 4 .0085 1.4043 4.0017 The error given is the average deviation from the average of five measurements. loglo“f 1T- (, O V) 1 1. 34 1. 1. .42 .10 147 26 02 Figure 47. Plot of logm(4 177‘ ”C 6v) against 103 /T for pure C1CON(CH3)2, Method 111. Ea = 7. 2 4 0. 5 kcal./mole A = (4 to 10) x 105 sec.’1 AF298.7_ = 16. 5 kcal. /mole TC = 326.5°K. v0 = 60. 000 mcs. 6v 4 6.46 4 .13 cps at -24. 2°C. 1 l J .14 3.22 3.30 , 3.38 103/T, (°K.) 10g10(4 1r" L 0v) 148 l l T 1.40- 1. 32.. o O 1. 24_ O 1 16— 0 Figure 48. Plot 16g,0(4 n3 t 6v) against 103/T for 90. 03 mole per cent C1CON(CH3)2 in CHzBrz, Method 111. 1.08— Ea = 8. 2 4 0.4 kcal./mole A = (2 to 26) x 105 sec."l AF 98.; = 16. 5 kcal./mole TC = 325.60K. 0 v0: 60.0001ncs. 6v = 6.45 4 .29 cps at -24.5°c. 1.00 1 1 l 1 .12 3.20 3.28 3.36 103/T. (°K.) logm(4 772 z 6v) 1.44 1.36 1.28 1.20 1.04 Figure 49. Plot of logm(41rz 28v) against 103/T for 63.4., mole per cent C1CON(CH3)Z in CHzBrz, Method 111. Ea = 9. 0 4 0.9 kcal./mole 'A = (4 to 19) x 106 sec.-1 AFzge. 2 = 16. 6 kcal. /mole TC = 325.5°K. v0 = 60. 000 mcs. 6v = 6.27 4 .20 cps at -24.5°c. l l .10 3.18 3.26 3. 103/Ta (0K0) 34 150 1.30:. 3‘ to 20 Ni: 3‘5 1.22 55 3 1.14 0 Figure 50. Plot of log10(4777‘ 'Z 6v) against 103/T for 40. 92 mole per cent C1CON(CH3)2 in CHzBrz, Method 111. Ea = 8.6 40.7 kcal./mole A = (3 to 64) x 10" sec.-1 AFLNJ = 16.6 kcal./mole TC = 3.25. 50K. V0 3 60.000 mCS. 6v = 6.25 4.20 cps at -23.7°c. l l 3.12 3. 20 103/T, (°K.) 3.28 3.36 151 1081014 “2 ’0’ 5") Figure 51. Plot of log10(41rz't 6v) against 103/T for, 10. 72 mole per cent ClCON(CH3)z in CHzBrz, Method 111. I Ea = 7. 3 4 0.8 kcal./mole A = (3 to 103)x105 sec." ' AFZE8.2 : 16. 5 kcal./mole ‘ TC = 325.8 °K. v0 = 60.000 mcs. 6v = 6.08 :1: . 15 cps at -22.2°C. 1 l l l .14 3.22 3.30 3.38 103/T, (°K.) 1°810(4 "2 2’ 5V) 152 r 1.40 “ a 1.32 4 _ o O 1.24 ._ .. 1.16 4 4 Figure 52. Plot oiiogmm n27: 6v) against 103 /T for 71. 35 mole per cent C1CON(CH3)Z in cc1.,, Method 111. Ea = 6. 9 d: 0. 7 kcal./mole 1.08— A: (2 to 40)x 105 sec.-‘ __ AF,1§,,2 = 16.4 kcal. /mOIe TC = 326.5 °K. v0 = 60. 000 mcs. . 6v 4 7.18 4.20 cps at -20.2°c. 1.00 _ 4 l L 3.10 .18 3. 26 .34 103/T. (°K.) 10810(4 172 Z” 6v) 153 I I r 1. 32 ‘ G O 1. 24 - O 1.16 *- O 1. 08 4 Figure 53. Plot of log10(4 173 t 61:) against 103/T for 40. 08 mole per cent C1CON(CH3)Z in CClg, Method 111. Ea = 6.6 .4 0.7 kcal./mole A =T(2 to 36) x 105 sec.-1 AF298.2 = 16.3 kcal. /mole TC = 323.8°K. 1.00 v0: 60.000 mcs. 6v: 7.344 .20 cps at -20.20C. 1 l l 3. 10 .18 3.26 3.34 103/T. (°K.) 10g‘0(4 772 2,’ 6 v) 1 1. 1. 154 .40 32 08 1.00 Figure 54. Plot of logm(4 112 7: 612) against 103/T'for 10. 98 mole per cent C1CON(CH3)2 in CC14, Method 111. Ea= 6.8 4 0. 3 kcal./mole A =,r (4 to 7) x 105 sec. -‘ 2117298., = 13. 2 kcal. /rn61e TC = 317.4 K. v0 = 60.000 mcs. 6v = 7.33 4.25 cps at -19.7°c. 3.20 3.28 3.36 3.42 103/T, (°K.) Ea, kcal./mole 155 1 l l 1 1 l 9. 5 — -—1 9. 0 '— / / ’ JD‘ \ \ _ / \ / / \ / \ /<-> \ 8. 5 — / \ ... / \ / / 9\ / \ 8.0 — / \ - / \ / \ / 1 / \ 7. 5 — 1 j t/ ‘ / 1-5 / / 7. 0 _ / " / 1| //E‘P / [n./ I 7/’ [-1 6. 5 — _ 6.0 ’ 1 1 I 1 L 7 0 20 40 60 80 100 Mole per cent amide Figure 55. Concentration dependencies of the energy barrier Ea for internal rotation about the central C-N bond of N, N- dimethylcarbamyl chloride in: (a) dibromomethane solutions - - - O—- - -G—----, and (b) carbon tetra- chloride solutions 1:} E] TABLE XXI 156 TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIBENZYLACETAMIDE (38. 09 MOLE PER CENT IN DIBROMOMETHANE), METHOD 111 v0 = 60.000 mcs., 6v =.- 12.02 4 . 14 cps at -5.2°c. t, c. 103/T, (°K.) r 16g10 (4n ’2: 6v) 65.54 4 .09* 2.9525 1.068 4 .0054 1.0125 4 .0035* 58.59 4.07 3.0143 1.403 4.008 1.1150 4 .0018 51.96 4 .06 3.0758 1.995 4 .014 1.2146 4.0019 47.10 4.04 3. 1225 2.976 4.029 1.3147 4.0025 44.27 4.05 3.1503 3.128 4.039 1.3268 4.0032 40. 97 4.02 3.1834 3.986 4 .030 1.3842 4.0018 37.944 .04 3.2144 4.8354 .131' 1.42924 .0060 The error given is the average deviation from the average of five measurements. 1.40 157 Figure 56. Plot of 16g,0(4 1721’ 6v) against 103/T for 38. 09 mole per cent CH3CO(C6H5CHZ)2 in CHzBrz, MethOd III. 1'08 Ea = 7. 3 4 0.7 kcal./mole — A = (4 to 12) x 105 sec.-1 AF298, 2 = 16. 5 kcal./mole TC = 343.70K. v0 = 60.000 mcs. C 6v 212.02 4 .14 cps at -5.2 C. o 1.00 — 1 L l l 2.96 3.04 3.12 3.20 103/T, (°K.) TABLE XXII 158 TEMPERATURE DEPENDENCE OF THE RATE OF INTERNAL ROTATION ABOUT THE CENTRAL C-N BOND OF N, N-DIBENZYLACETAMIDE (38. 29 MOLE PER CENT IN CARBON TETRACHLORIDE), METHOD 111 v0 4 60.000 mcs., 6v 4 9.79 4 .22 cps at -5.8°C. t, °C. 103/T, (°'K.) 16g,o(4 n 2t 5 v) 55.72 4 . 10* 52.13 4 .05 47.11 4 .07 42.54 4 .02 36.83 4 .07 34.34 4 .02 31.87 4 .37 3.0406 3.0742 3.1224 3.1676 3.2259 3.2520 3.2784 1.077 4 .009* 1.185 4 .012 1.5654 .017 1.9894 .030 2.416 4 .012 3.164 4.010 3.393 4 .056 10 ...a 0169 :1: . 0036* .0580 4 .0034 .1482 4 .0030 .2138 4 .0037 . 2638 4 .0010 .3297 4 .0008 . 3475 4 .0042 * . . The error given is the average deviation from the average of five measurements. 10g10(4 172 Z 6") 1. .28 .20 .12 04 159 Figure 57. Plot of 16g,0(4 1:3 “C 6v) against 103/T for 38. 29 mole per cent CH3CON(C5H5CHZ)2 in CC14, 0 Method 111. Ea: 6.4 4 0.7 kcal. /mole A = (1 to 28) x 105 sec”. '- AFzng. 2 = 16. 3 kcal. /mole TC = 334. 50K. v0 = 60. 000 mcs. 6v 2 9.79 4 .22 cps at -5.8°c. 3. 04 3.12 3.20 3.28 103/T, (0K) 160 @045qu00 4.2... 2 .2 ...2 x 2 8 3 a .o n 4.6 2: Ammovzoomousmo o .43 c .2 42 x 44m 8 2 To ... m .a 02 Aamovzoonho o .5... a .2 M2 6. A: 8 a m .o 4 22 o2 Aamovzoomoo o .2m 0 .2 m2 x a... 8 3 m .o. n. m c :00 so .: Ammovzoommno 3: a .2 ...2 2 SN 8 i m .o 4 m .4 :00 .22 24204200426 0.4mm m .2 .2 x .2 8 .3 2o 4 2m :00 44 .46 samovzoonmso m .smm s .2 m2 4 $4 8 3 4.0 4 2 .4. 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MOM and 55030 mumgfi 03H. ** * m .42 m .2 m2 4 EN 8 3 2o 4 4.4 :00 $4. .2 ~A~m0£00504m0 n .34 m .2 m2 4 .2 8 2 N. .o 4 m 4. 4.53.20 .5 .2. 24.204242400004220 4.2m N .2 42 x C 8 i m .o 4 m .o :00 mm. .2 2442020020 234 m .2 ...2 x 3m 8 3 p .o 42.0 :00 MWo .2. 24420020020 m .2; «.2 42 x 84 8 .0 p .o 4 ... .o :00 mm .2. 24420020020 22.4 22. . 42 x 82 8 3 2o 4 m .0. 3.4.2.20 ~22 24420020020 m .2... o .2 .02 4 A3 3 3 n .o 4 o .m ~4m~m0 4m. .2. 2420020020 m .mmm 22 .02 x 2 3 2 a .o 4 o .o N5430 44.3 24420020020 0 .mmm ... .2 .02 4 ANN 3 3 «to 4 N .m N.2320 4o .2. 2.2002020 m .2... m .2 ...2 x .2 3 i m .o 4 N .4 02 2420:3020 o .22 m .2 .02 x E 3 i c .o 4 2. .p #0420 4m .3 244602004240 0 .08. «Jodi .Hdux 1000*;4 0HOE\ .Hdox unoséom Sig 280 00mg 4 ...th 40 .8m 23“ 00232.50 .. :HXN Hdmdwh. 162 DISC USSION Methods for Obtaining Energy Barriers and Frequency Factors for Hindered Internal Molecular Rotations by High- resolution Nuclear Magnetic Resonance In the Theoretical Background of this thesis, several NMR methods for obtaining energy barriers and frequency factors for hindered internal molecular rotations were introduced. Attempts were made to use three of these methods to study the phenomenon of hindered internal rotation about the central C-N bond of some symmetric- ally N, N- disubstituted amides. The first method used, Method 1, was not well suited to the study of hindered internal rotation about the central C-N bond of N, N-dimethylpropionamide. This method relates changes in resonance line widths to the rate of the kinetic process being studied. For N, N-dimethylpropionamide, the magnitudes of the changes in the line widths of the two N-methyl proton resonances with the rate of internal rotation are determined by the chemical shift between the N-methyl proton resonances in the absence of internal rotation. For N, N-dimethylpropionamide, this chemical shift is only about 7.5 cps (at v0 = 60.000 mcs.). One equation of Method 1, equation (110), is valid only in the region of slow rate processes. This equation relates the kinetic broadening of resonance line widths to the rate of the process. For N, N-dimethylpropionamide the region over which equation (110) is valid corresponds to changes in the N-methyl proton resonance line widths from about 0. 6 to 2. 0 cps. , Since the line widths were measurable only to an accuracy of about :1: O. 3 cps, the rates calculated from equation (110) were very unreliable. The other equation of Method 1, equation (113), is valid only in the region of very fast rate processes. This equation relates the kinetic 163 narrowing of the line width of the coalesced resonance peak to the rate of the process. For N, N-dimethylpropionamide the region over which equation (113) is valid corresponds to changes in the coalesced N-methyl proton resonance line width from about 3 to 0. 8 cps. Again, because of the inherent errors in line-width measurements, the rates calculated from equation (113) were very unreliable. Similar errors should be expected when Method I is applied to most of the other symmetrically N, N-disubstituted amides. Since the chemical shift in the absence of internal rotation about the central C-N bond of N, N-dimethyltrichloroacetamide is about 17. 5 cps (at v0 = 60. 000 mes. ), Method 1 would probably yield fairly reliable rates of internal rotation for this compound. Piettle and Anderson used Method I for studying the hindered internal rotation about the O-N bond of some alkyl nitrites (81). ‘For these compounds, the chemical shift between the resonances of the o.--protons of the cis and tra___n_s alkyl nitrites, in the absence of internal rotation, was about 43 cps (at v0 = 40 mos). Therefore, for the alkyl nitrites the regions over which equations (110) and (113) were valid corresponded to changes in line widths that were very large compared to the experi- mental error in the line—width measurements. For such systems, one should expect Method I to yield quite accurate values for the rates of internal rotations. Piette and Anderson found that in the region of slow rates of internal rotation about the O-N bond of the alkyl nitrites, equation (110) yielded unreliable values for the energy barriers. However, in the region of very fast internal rotations, they found that equation (113) yielded values for the energy barriers having errors of about 2. kcal. /mole. More accurate values for the energy barriers to hindered internal rotations about the O-N bond of alkyl nitrites would probably be obtained by using Method I and an applied 164 radiofrequency of 60. 000 mcs. At this higher frequency, the chemical shift between the resonances of the o.-»protons of the cis and trans isomers, in the absence of internal rotation, would be about 22. cps larger than the chemical shift which was observed at 40 mcs. This larger chemical shift would correspond to more pronounced changes in line widths due to rotational averaging. A second method, Method 11, was used to obtain the energy barrier and frequency factor for hindered internal rotation about the central C-N bond of N, N-dimethylformamide. For this compound, Method 11 relates the observed frequency separation of the two N~methyl proton resonances to the rate of the internal rotation. The chemical shift between these resonances in the absence of internal rotation is about 9.4 cps (at Va 2 60. 000 mcs. ). Since effective natural line widths from about 0. 3 to 0. 6 cps were observed for the two resonance lines, corrections due to the effect of overlap on the apparent separation of the two peaks were much smaller than the experimental errors in the measurements of the peak separations (see Figure 5). Therefore, the overlap corrections were neglected. Method 11 was originally proposed by Gutowsky and Holm (5, 6), who used it to study hindered internal rotation about the central C—N bond of N, N-dimethylformamide and N, Nudimethylacetamide. Their measurements were made at the applied radiofrequency 17. 735 mcs. , where the chemical shift between the N—methyl proton resonances of N, N-dimethylformamide in the absence of internal rotation was about 3. Z cps. - Since effective natural line widths of about 2. 3 cps were observed, corrections due to the effect of overlap on the apparent separation of the two peaks were very important (see Figure 5). For N, N-dimethylformamide, Gutowsky and Holm obtained 7 a: 3 kcal. /mole and from 103 to 107 sec.‘1 for the energy barrier and fre- quency factor, respectively. These authors suggested that more 165 precise values should be obtained by using higher applied radiofre- quencies. At higher frequencies, the chemical shift between the N-methyl proton resonances in the absence of internal. rotation would be proportionately larger, and providing that the experimental errors would be no worse, more precise results would be obtained. The use of Method 11 in this present work yielded 14. 3 :l: 2. 8 kcal. /mole and (Z to 130) x 108 sec:'1 for the energy barrier and frequency factor, respectively, for hindered internal rotation about the central CdN bond of N, N-dimethylformamide. Although the data were obtained at the radiofrequency 60. 000 mcs. , these results are not significantly more precise than those obtained by Gutowsky and Holm. Just as the chemical shift between the two N-methyl proton resonances in the absence of internal rotation is about 3.4 times greater at 60. 000 mcs. than at 17. 735 mcs. , the errors in the Ameasurements of the separations between the two peaks in the presence of internal rotation are also greater. The increased chemical shift leads to increased broadening due to rotational averag- ing. - Since the tops of broad absorption peaks are quite flat, the frequency positions of the maxima of such absorption peaks are dif- ficult to determine precisely. This difficulty seriously effects results obtained from the use of Method 11. In the region of very slow rotational rates, where the broadening of the resonance lines due to rotational averaging is small, the change in the separation between resonance peaks is very insensitive to large changes in rotational rates. Therefore, in the region where the separation between resonance peaks can be measured most accurately, the dependence of the separation upon rotational rate is too small for accurately determin- ing changes in rate. This dependence of the separation of resonance peaks upon the rate of rotation is clearly shown in Figure 10. In the region of faster rotational rates, where broadening of the resonance 166 lines is large, the separation between peaks is very sensitive to changes in rate. 80, in the region where the separation between resonance peaks is very sensitive to changes in rate, the measure- ments of frequency separations are subject to large error. Frequency positions of broad NMR lines are best determined by use of the dispersion '14. -mode, which is very sensitive to changes in the slope of the absorption V—mode. However, the effects of overlap on the apparent separation of dispersion modes may be extremely important (see‘ Figure 5). Because of errors in the ‘measurements of effective natural line widths, overlap corrections are, in general, subject to large errors. Therefore, no serious attempts were‘made to measure the separations of the N-methyl proton dis- persion lines for N, N-dimethylformamide. The third method, Method 111, was used to study the hindered internal rotation about the central C—N bond of most of the symmetric- ally N, N-disubstituted amides used in this work. For an N, N-dimethyl amide, this method relates the ratio of maximum to central minimum intensities for the chemical-shift doublet of the two N-methyl proton resonances, to the rate of internal rotation about the central C—‘N bond of the amide. For all the amides studied by Methodlll, the effects of overlap upon the ratios of maximum to central minimum intensities were estimated, from equations (74), (91), and (93), . to be negligible compared to the errors in the measurements of the intensity ratios. Therefore, no overlap corrections were made. Since changes in the intensity ratios were more pronounced than changes in line widths and frequency separations, and since the ratios could be measured quite precisely, the results obtained from the use of Method 111 were more accurate than those obtained by either Method I or II. The dependence of the intensity ratio upon the rate 167 of internal rotation is clearly shown in Figure 10. The ratios could be measured most accurately in the region of fast internal rotations, (i. e. , in the region of small ratios). In this region, large changes in the rate correspond to small changes in the ratio. The errors in the ratio measurements were largest in the region of slow internal rotations (i. e. , in the region of large ratios). In this region, small fluctuations in the base line have pronounced effects upon the observed ratios. However, large changes in the intensity ratios in this. region correspond to only small changes in rate (see‘Figure 10). For the hindered internal rotations studied in this work, Method III had the disadvantage that it was applicable only over temperature ranges of about 25 degrees. As mentioned in the theoretical back- ground of this thesis, Takeda and Stejskal (24) have recently developed an NMR method for Smeasuring the rates of exchange reactions in the region of very fast exchange rates. Their method should be applicable - to the study of hindered internal rotation about the central C-JN bond of most of the amides used in this present work. By using Method 111 and the method recently proposed by Takeda and Stejskal, one should be able to obtain experimental .rates for the internal rotation over temperature ranges of about 50 degrees. Providing the errors in the rates as determined by the method of Takeda and Stejskal were no worse than those in the rates determined by Method 111, the larger temperature range would markedly decrease the errors in the energy barriers and frequency factors. 168 Results The energy barrier hindering internal rotation about the central C-N bond of pure N, N-dimethylformamide is 18. 3 e 0.9 kcal. /mole in height. This value was obtained by Method III. The actual error in the value 14. 3 kcal. /mole, as obtained by Method 11, is probably much larger than the estimated error of 2. 8 kcal. /mole given in Figure 26 and Table XXIII. As described in the Experimental section of this thesis, the errors were calculated from the set of points obtained when several measurements were averaged at each of several temperatures. The deviations from these averages were not considered when the errors were calculated. Figure 26 shows that such deviations are very large for data obtained by Method 11. In view of such large deviations, the linearity of the resultant averages is quite surprising. The error in the energy barrier ob- tained by Methodll would probably be much larger than 2. 8 kcal. /mole, if one included the deviations from average values in the error calcu- lations. Figures 27 and 30 show that the data obtained by Gutowsky and Holmi (5, 6) contain similar errors. These authors reported the value 7 i=3 kcal. /mole for the energy barrier hindering internal rotation about the central C-N bond of N, N-dimethylformamide. Their estimated error was confirmed when calculated from their data by the'method described in the Experimental section of this thesis. Therefore, an estimated error of a: 3 kcal. /mole for the measurements of Gutowsky and Holm on N, N- dimethylformamide does not include the large deviations from average values and should, therefore, be regarded as too optimistic. The high value 18. 3 :f: O. 9 kcal. /mole, obtained by Method 111, is supported by the high value (about 20 kcal. /mole) reported earlier (41). 169 It is supported also by the high value (about 18 kcal. /mole)* for the energy barrier hindering internal rotation about the C-iN bond of formamide. Assuming that the central C-N bond of N, N-dilnethyl- formamide contains about 40 per cent CPN character (29), a barrier height of 18. 2 kcal. /mole may be estimated from the difference between the C=N bond energy, 94 kcal. /mole (113), and the C~N bond energy, 48. 6 kcal. /mole (113). The energy barrier hindering internal rotation about the central C—N bond of N, N-dimethylacetamide is 10.5 a. 5 kcal. /mole. This value was obtained by Method IH, and it is in agreement with the value 12 i 2 kcal. /mole reported by Gutowsky and Holm (5, 6). It should be noted that the barrier for N, Nudimethylacetamide is about 7. 8 kcal. / mole lower than that for N, N-dimethylformamide. Usually, N, N-dialkyl amides are considered to be only very slightly associated (18, 22, 36). However, a small amount of association, involving the slightly acidic aldehyde hydrogen atom of N, N-dimethylformamide, may be responsu- ible for the higher barrier for this compound. Determination of the barrier for N, N-dimethylformamide as a function of concentration in several solvents would probably give definitive information concerning the effects due to association. Barriers for rotation about the C-N bond 1"This value was obtained by W. G- Schneider from NMR measurements on N15 labelled formamide. His estimate of the energy barrier was . revealed in a footnote of a recent article by Costain and-Dowling (112). These authors have re- -examined the microwave Spectrum of formamide. Their results show that the dihedral angle between the H' NC plane and the NCO plane, and between the H"NC plane and the NCH plane are 7 :1: 5o . and 12 :I: 50 ,respectively. The hydrogen designated in H' is cis to the oxygen atom, and the one designated as H" is cis to the aldelfyB—e hydrogen atom. Although these angles are small, they 3.1-16w significant non- »planarity at the nitrogen atom. Previous to the work of Costain and Dowling, the microwave Spectrum of formamide had been interpreted on the basis of a completely planar structure for the molecule (28, 29). 170 in amides are much larger than observed barriers for internal rotations in ethane, amines, alcohols, and ketones, which are about one to three kcal. /mole (3). The extra height of the barrier for rotation about the C-iN bond in amides is attributed to partial double bond character of the C-N bond. Resonance between structures I and II have been shown to be important (27, 28, 29, 112). 1"" H H .Q\C +/ / \ / \ H H H H I II :6 \ .. \C—N The contribution of II has been estimated as about 40 per cent (29). ~ In acetamide, where additional structures such as 111 (hyperconjugation) may contribute (106), the double bond character of the central C—N bond would be somewhat reduced. 3.6- H \C*1-\-,/ H\C/ \H / H H+ 111 An alternative explanation of the large difference between the barriers for N, N-dimethylformamide and N, N-dimethylacetamide may belthat the transition state for internal rotation about the central C-N bond of the latter molecule involves an excited electronic state of the molecule. If the energy surface of an excited state crOsses that for the normal state, the barrier _a_n_d_ frequency factor for internal rotation may be markedly suppressed (107, 108). - Such an explanation for the 171 large difference between the barriers for these apparently similar molecules seems somewhat doubtful. However, this explanation, as it pertains to the large differences among the barriers and frequency factors for internal rotation about the C=C bond of ethylene and its derivatives, seems to be fairly well accepted (107, 108, 109). The energy barrier hindering internal rotation about the central C-N bond of pure N, N-dimethylpropionamide is 9.. 2 :h 0. 8 kcal. /mole. The small difference between this value and that for N, N-dimethyl- acetamide is equal to the sum of the experimental errors involved. Since the reported errors are those for'90 percent confidence, the small difference between the two barriers may be regarded as signifi- cant with probably at least 50 per cent confidence. The magnitude of the difference (1. 3 kcal. /mole) is about what one would predict on the basis of the additional suppression of the energy barrier due to the difference between the hyperconjugative resonance of the C-methyl group of N, N-dimethylacetamide and that of the ethyl group of N, N- dim ethylp ropionamide . The values of the barriers hindering internal rotation about the central C-N bond of N, N-dimethyltrichloroacetamide and N, N-dim ethyl— trifluoroacetamide are 10. 0 :1: 0. 5 kcal. /mole and 9. 5 i=1: 0. 7 kcal. /mole, respectively. .As expected, these values are about the same as that for N, N-dimethylacetamide. If there is any significant difference among the three values it is probably due to inductive effects of the more electronegative halogen atoms, which would be expected to in Crease the barrier height. I I The barrier hindering internal rotation about the central C-N bond of N, N-dimethylacrylamide is 6. 8 i 0. 9 kcal. /mole. This value is significantly lower than that for N, N-dimethylacetamide. The difference (about 3. 7 kcal. /mole) between these two barrier heights is attributed to the contribution of the resonance structure, 172 IV which is in competition with the contribution of the structure similar to‘II above. The low value, 7. Z :0. 5 kcal. /mole, for the barrier hindering internal rotation about the central C—Nbond of N, N- dimethyl- carbamyl chloride is attributed to the contribution of the resonance' . . structure V. :9\ ../CH3 /C —— N\ +61 _ , CH, V Similarly, the low barrier height, 7. 7 :L- 0.6 kcal. /mole, for N, N-dimethylbenzamide (36. 3‘ mole per cent in dibromomethane) is attributed to the contributions of the resonance structures VI, VII, and VIII. =6" :0 :o " \ ‘ J/CH3 " \ H /CH3 "\ H/C;I"I3 \ c—N . C—N , c—N + // .CH. // \CH. ' // \CHs Q 0* v1 + - v11 , vlll It should be noted, however, that the energy barrier was obtained for this compound dissolved in dibromomethane solution. The effect of the solvent upon the barrier height may be‘ significant. 173 The proton resonances due to the two N-methyl groups of ethyl-- 'N, N-dimethylcarbamate were observed to consist of a single narrow line, even at quite low temperatures. This observation is explained in terms of one phenomenon, which plays a dual role in causing the coalescence of the two resonances. For the protons of the two N-methyl groups to have different chemical shifts, the environmental shielding of the protons of each N-methyl group must be different. For ethyl-N, N-dimethylcarbamate, such differences in shielding would have to result from differences in the electron densities around the two oxygen atoms. However, resonance between the two structures IX and X .. : H O\ --/CH3 C.)\ “‘/C 3 C—N C— N- .. / \ ..// \ V CH,CH,—o, CH3 CH3CHz—O+ CH3 IX X tends to make the electron densities around the two oxygen atoms about the same. The importance of this resonance should be apparent from the estimated large resonance energy, 24 kcal./mole (110), associated with it. Therefore, one role of the above resonance is to cause the protons of each N-methyl group to have similar chemical shifts. Thesecond effect would be to suppress the contribution of the resonance structure analogous to II. This effect reduces the barrier to internal rotation about the central C-aN bond so that the rate of rotation would be too large to "see" on the NMR time scale. - Similar arguments explain the failure to detect hindered internal rotation about the central C-N bond of methyl-N, N-bis-(trifluoromethyl)- carbamate. The failure to detect hindered internal rotation about the central C-N bond of N, N-bis-(trifluoromethyl)-trifluoroacetarnide is quite surprising. - Since the barrier for this molecule would be 174 expected to be at least as large as that for N, N~dimethyltrifluor~ acetamide, one is led to conclude that the chemical shift between the two N-trifluoromethyl groups in the absence of internal rotation is very small. The barrier to internal rotation about the central C-N bond of N, N-dimethylprOpionamide was observed to decrease from 9. 2 :1: O. 8 kcal. /mole for the pure liquid to a low value of 6. 3 i O. 5 kcal. / mole for 11. 07 mole per cent amide in carbon tetrachloride solution (see Figure 41). This decrease in the barrier is probably due to dissociation of. the slightly associated pure liquid amide when diluted, and to the change in the dielectric constant of the solution upon dilution. Figure 41 shows that most of the observed changes in the barrier, when the amide was diluted with dibromomethane, were within the experimental errors involved. However, the values ob- tained suggest that when the amide is diluted with dibromomethane, the barrier rises to a maximum of about 10. 3 kcal. /mole at about 66 mole per cent amide, and then falls to the low value of about 7. l kcal. / mole at about 10 mole per cent amide. These effects are attributed to a specific interaction, which involves two molecules of amide and one molecule of solvent. The actual existence of these effects are supported to some degree by the similar results observed for solu— tions of N, N-dimethylcarbamyl chloride in carbon tetrachloride and in dibromomethane (see Figure 55). Although these results should not, of course, be regarded as conclusive evidence for specific solvent-solute interactions, they certainly serve as an incentive to search for more pronounced effects in solutions of substituted amides in other solvents. The following energy barriers for hindered internal rotation about the central C-N bond of N, Nudibenzylacetamide were obtained: 175 38. 09 mole per cent amide in dibromomethane, 7. 3 d: 0.7 kcal. /mole; 38. 29 mole per cent amide in carbon tetrachloride, 6. 4 :1: 0. 7 kcal. / mole. These values probably contain significant contributions due to solvent effects. 2 ._ The experimental frequency factors for the internal rotations studied vary from very low values of about 105 sec:1 to higher values 1 The highest frequency factor, about 1010 sec.", of about 107 sec.- was obtained for N, N-dimethylformamide. It should be noticed that the experimental frequency factors, obtained from the Arrhenius-type rate equation, are much lower than the normal value kT/h predicted by the simple theory of absolute reaction rates. It is not surprising, therefore, that the calculated free-energies of activation, shown in Table XXIII, do not agree with the experimental energies of activation. Since small entropies of, activation are expected for internal rotations (108), the low experimental frequency factors may be explained in terms of the more general theory of absolute reaction rates; i. e. , in terms of low transmission coefficients. 176 SUMMARY A Varian high- resolution nuclear magnetic resonance spectrom- eter was used for observing proton and fluorine magnetic resonance spectra of several symmetrically N, N-disubstituted amides over a wide range of temperatures. Apparatus for controlling sample temperatures at high or low values was constructed. Also, coils for electrically shimming the applied magnetic field were constructed. The use of these coils Was essential to the observation of high- resolution fluorine magnetic resonance spectra at the applied radio- I frequency 60. 000 mcs. Theoretical methods for relating the rate of internal rotation about the central C-N bond of the substituted amides to various components of resonance line shapes were considered. Three of these methods were applied experimentally to the study of the phenom- enon of hindered internal rotation. Of the three methods used, only one was well adapted to the study of hindered internal rotation about the central C-N bond of the symmetrically N, N-disubstituted amides used in this work. This method relates the ratio of maximum to central minimum absorption intensities of a symmetrical resonance doublet to the rate of internal rotation. The energy barrier and frequency factor, for each internal rotation studied, were calculated from the experimental temperature dependence of the rate of internal rotation. The experimental errors were‘much» lower than those previously reported for similar studies. The phenomenon of hindered internal rotation about the central C-N bond of the followingpure liquid amides was studied: N, N-di- methylformamide; N, N-dimethylacetamide; N, N-dimethylpropionamide; 177 N, N- dimethyltrichloroacetamide; N, N- dimethyltrifluoroacetamide; N, N-dimethylacrylamide; and N, N- dime thylcarbamyl chloride. The internal rotation about the C-‘-N bond of N, N-dimethylbenzamide was studied for a solution of the amide in dibromomethane. - Similar studies were made for a solution of N, N-dibenzylacetamide in dibromomethane, and for a solution of this amide. in carbon tetra- chloride. 2 The apparent rates of internal rotation about the central C-N bond of ethyl-N, N-dimethylcarbamate, and about the central C-N bond of methyl-N, N-bis-(trifluoromethyl)-carbamate, were too fast to be detected, even at quite low temperatures. In addition, the presence of hindered internal rotation about the central C-N bond of N, N-bis-(trifluoromethyl)-trifluoroacetamide could not be detected. The origin of the barrier to internal rotation about the C-N bond of the amide group is attributed to the existence of partial C=N bond character, which arises from resonance between valence bond structures. Some possible explanations for the exceptionally high barrier observed for N, N-dimethylformamide are the following: a small amount of intermolecular association of the pure liquid, the nonexistence of contributing resonance structures that would suppress the partial double bond character of the central C-N bond, and the possibility of the barriers for all the other amides being suppressed by transition states which involve excited electronic states. The low-barrier compounds were compared with N, N-dimethylactamide. The values of the energy barriers for these compounds were explained in terms of contributing resonance structures which suppress the double bond character ‘of the central C-N bond. For most of the internal rotations studied, the experimental frequency factors were from about 105 to 107 sec?1 These low values were attributed to low transmission coefficients. 178 The phenomenon of hindered internal rotation about the central C-N bond of N, N- dimethylpropionamide was studied for several solutions of the amide in dibromomethane and in carbon tetrachloride. The con- centration dependence of the barrier to internal rotation for the amide in dibromomethane solutions suggests the possible existence of a specific solvent-solute interaction. When the amide was diluted with carbon tetrachloride, the barrier was observed to decrease markedly. 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