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Spin echoes and chemical exchange Krakower, Earl 1966

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SPIN ECHOES AND CHEMICAL EXCHANGE by EARL KRAKOWER B.Sc, McGill University, 1960 M.Sc. , University of British Columbia, 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Che mi stry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1966. In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8 , Canada. Date The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of EARL KRAKOWER Bo Sc., =, McGill University. 1960 M . S c . j The University of B r i t i s h Columbia, 1963 TUESDAY3 AUGUST 23, 1966 AT 3i30 P.M. IN ROOM 261, CHEMISTRY BUILDING COMMITTEE IN CHARGE External Examiners J. D„ Baldeschweiler Department of Chemistry ' Stanford University Palo AltOj C a l i f o r n i a Research Supervisor; L. W» Reeves Chairman % Sydney M„ Friedman Co Froese Ds Cc Frost C. A. McDowell Ro Eo Pincock L. W. Reeves R. Co Thompson SPIN ECHOES AND CHEMICAL EXCHANGE ABSTRACT The performance of a spin echo spectrometer which i s s u i t a b l e f o r chemical exchange studies i s described,, Using the Carr-Pure e l l sequence of pulse proton T'2 values were obtained from two experiments d i f f e r i n g only i n t h e i r method of eliminating accumu-late d error i n the width of the 180° p u l s e s 0 The Meiboom-Gill method of phase s h i f t i n g the r . f . i n the f i r s t pulse i s more f l e x i b l e i n the range of puls e i n t ervals„ Following the theory of Bloom, Reeves and Wells rate constants describing the exchange process i n two molecules were measured from the dependence of T" upon the pulse i n t e r v a l . The values of the rate conr sfcants for the hindered i n t e r n a l r o t a t i o n about the N-N bond i n N.N-dimethylnitrosamine agree with pre-vious high r e s o l u t i o n studies„ A s i m i l a r spin echo study has been conducted i n order to measure the rates of i n t e r n a l r o t a t i o n about the C-N bond i n N 3N-dimethylcarbamyl c h l o r i d e . The values f o r the entropy of a c t i v a t i o n are con-s i s t e n t l y low. The p o s s i b i l i t y of systematic errors i n the spin echo method has been investigated. It i s concluded that reported values of rate constants i n magnetic resonance should be the re-su l t of a spin echo i n v e s t i g a t i o n extending over as wide a temperature range as p o s s i b l e i n a d d i t i o n to a high r e s o l u t i o n study which involves a complete t h e o r e t i c a l l i n e shape f i t to the experimental data 0 GRADUATE STUDIES F i e l d of Study: Physical Chemistry-Topics i n Physical Chemistry Topics i n Inorganic Chemistry Topics in Organic Chemistry C r y s t a l Structure Seminar Spectroscopy Chemical Physics Related Courses D i f f e r e n t i a l Equations Linear Algebra Physics J . A„ R,. Coope A„ Bree No B a r t l e t t Wo Ro Cullen H„ C. Clark Jo P. Kutney D* E. McGreer R, E. Pincock J . T r o t t e r Wo A . Bryce L„ W, Reeves Eo Jo Wells Co Reid K9 Bo Harvey Wo C. L i n D5 C. Frost Bo A. DunE.ll Dean Gage R„ Co Thompson • Mo Bloom PUBLICATIONS 1. Eo Krakower.. L„ W. Reeves and E 0 Jo Wells* Disc. F a r o Soc. 343 199 (1962) „ 2 0 E . Krakower and L. W. Reeves. Trans. Far, Soc. 59 s 2528 (1963). 3. Eo Krakower and L, W. Reeves. Spectrochimica A c t a ; 20.. 71 (1964) 0 4. K. Ho Abramsons P. 1. I n g l e f i e l d , E« Krakower and Lo W, Reeves. Can. J t Chem. 44, 1685. (1966). EARL KRAKOWER. SPIN ECHOES AND CHEMICAL EXCHANGE. Supervisor: L.W. Reeves. i ABSTRACT The performance of a spin echo spectrometer which is suitable for chemical exchange studies is described. Using the Carr-Purcell sequence of pulses, proton 1^ values were obtained from two experiments differing only in their method of eliminating accumulated error in the width of the 180° pulses. The Meiboom-Gill method of phase shifting the r.f. in the first pulse is more flexible in the range of pulse intervals. Following the theory of Bloom, Reeves and Wells, rate constants describing the exchange process in two molecules were measured from the dependence of upon the pulse interval. The values of trie-rate constants for the hindered internal rotation about the N-N bond in N, N-dimethyl-nitrosamine agree with previous high resolution studies. A similar spin echo study has been conducted in order to measure the rates of internal rotation about the C-N bond in N,N-dimethylcarbamyl chloride. The values for the entropy of activation are consistently low. The possibility of systematic errors in the spin echo method has been investigated. It is concluded that reported values of fate constants in magnetic resonance should be the result of a spin echo investigation extending over as wide a temperature range as possible in addition to a high resolution study which includes a complete theoretical line shape fit to the experimental data. i i T a b l e o f C o n t e n t s C H A P T E R P A G E I I N T R O D U C T I O N A ; R o t a t i n g C o - o r d i n a t e s 1 B . N u c l e a r R e l a x a t i o n P r o c e s s e s a n d D i f f u s i o n E f f e c t s 2 C . C h e m i c a l E x c h a n g e T h e o r y i n N u c l e a r M a g n e t i c R e s o n a n c e 9 D . H i n d e r e d I n t e r n a l R o t a t i o n a n d M o l e c u l a r C o n f o r m a t i o n 16 II E X P E R I M E N T A L A . P r e p a r a t i o n of C o m p o u n d s 21 . B . T h e S p i n E c h o S p e c t r o m e t e r 22 C . M a g n e t S y s t e m s 25 D . M e a s u r e m e n t a n d R e l i a b i l i t y 28 E . C o m p u t e r P r o g r a m s 28 III E X P E R I M E N T A L R E S U L T S 31 A . N , N - D i m e t h y l n i t r o s a m i n e 31 (i) F r e e I n d u c t i o n T a i l E x p e r i m e n t s 32 ( i i ) C a r r - P u r c e l l T r a i n s 3 3 ( i i i ) L i m i t i n g C a s e s - O f f a n d O n R e s o n a n c e 34 ( iv ) C a l c u l a t i o n o f " i i " 38 (v) A c t i v a t i o n P a r a m e t e r s 40 B . N , N - D i m e t h y l c a r b a m y l C h l o r i d e 42 (i) C a l c u l a t i o n o f ' r ^ 43 ( i i ) L i m i t i n g C a s e s 46 ( i i i ) T°, T 1 # D a t a 4 8 ( iv) A c t i v a t i o n P a r a m e t e r s 50 i i i CHAPTER IV DISCUSSION A. Experimental Consideration B. Sensitivity of the Rate Constant and Activation Parameters to Systematic Errors C. Comments on the Spin Echo Method V BIBLIOGRAPHY iv List of Illustrations Figure To follow page I Transverse Components of the Magnetic Moment Referred to Fixed Axes and Axes Rotating with the R.F. Field. 2 II The Formation of an Echo after Successive 90 and 180° Pulses. 6 III Schematic Relationship of the Magnetization Observed in a It Ty\ .. Pulse Sequence. 11 IV Transmitter Circuit 22 V Block Diagram of Receiver Circuit 2 3 VI Receiver Circuit 23 VII Generation of the Carr-Purcell Sequence 23 VIII Reference Signal Amplifier, Multiplier, Phaser and Attenuator 2 5 IX Waveforms Resulting from Frequency Multiplication Showing Respective Amplitudes 25 X Free Induction Decay for DMNA 3 2 XI Carr-Purcell Trains of the Protons in DMNA 33 XII ShortX Limit Plot for DMNA-off Resonance 3 5 XIII Short X Limit Plot for DMNA-on Resonance 35 XIV Dependence of T2(C.P). upon the Pulse Interval for DMNA ' 38 XV Activation Energy Determination for DMNA 40 XVI Dependence of T 2 upon the Pulse Interval for DMCC 43 XVII Shorty Limit Plot for DMCC 46 V Figure To follow page XVIII Temperature Dependence of T§, T 1 49 XIX Activation Energy Determination for DMCC 50 vi List of Tables Table Page I Dimethylnitrosamine-Rate Constants from r ^ kTk + ^-k ( u J ^ ) 2 II Dimethylnitrosamine-Rate Constants 37 from r^ = k - ( y ^ " ) s i n n * F 39 III Dimethylnitrosamine-Comparison of Rate Constants. 40 IV Dimethylnitrosamine-Comparison of Activation Parameters. 42 V D|methylnitrosamine-"Besfit" to r. = k - (—L.) sinh" 1 F 45 VI Rate Constant Data for Dimethylcarbamyl Chloride. 47 VII Dimethylcarbamyl chloride-Temperature Dependence of T^ . 50 VIII Dimethylcarbamyl chloride-Activation Parameters. 51 ACKNOWLEDGMENTS The Spin Echo method in Nuclear Magnetic Resonance represents a re la t ive ly new and interesting approach to the study of Chemical Exchange. In this regard I wish to thank Dr. L. W. Reeves for his helpful direction and sincere dedication to this research program. His advice has been deeply appreciated. I am grateful to Mr. P. T . Inglefield for advice and discussion regarding the construction of apparatus. The quality of this thesis has been enhanced by discussion with Mr. Inglefield who has made available to me results on similar systems. I am grateful to Dr. C. A. McDowell, for allowing me to work in the Chemistry Department and gain the experience that I now have in undergraduate teaching. Acknowledgments are accorded to Mr. K. H. Abramson and to Mr. E . Fisher for their work on the spin echo spectrometer. I am grateful to Mr. R. Wolfe and to Dr. J . Herring for help with the computer programs. I N T R O D U C T I O N CHAPTER I A) Rotating Co-Ordinates: An insight into the nature of nuclear induction (1) experiments is obtained from a consideration of the magnetic moment components referred to a rotating set of co-ordinates (2) „ In a field H, a macroscopic nuclear magnetic moment M per unit volume experiences a torque (M x H) which is equal to the rate of change K"ft — of its angular momentum. The equation of motion of a dt system in the stationary co-ordinate system i s : *(lk) = x HJ1 = KM x H (1) where # is the gyromagnetic ratio. In order to solve equation (1), it is useful to transform to a frame of reference rotating with an angular velocity with respect to the stationary frame. Then: d i ^ I dt B t = + [10 x jjj (2) "2 I where -= represents the time dependent measurement of I_ by.an observer dt in the rotating reference frame. Combining equations (1) and (2), the motion of the magnetic moment in the rotating frame is given by: ft 3-= = "cffil x (H + -=-) (3) at ~ ~~ o ' 2 Now the magnetic f i e l d H i s replaced by an effective f i e l d H e f f = ( H + f ) . For a magnetic f i e l d which i s constant i n time, He£f = 0 when observed from a frame of reference rotating withu? 0 = -TJHQ. With respect to the stationary reference frame the magnetic moment vector precesses with an angular velocity u) - - 7 f H 0 . This, i s the Larmor precession frequency of the spin in an applied magnetic f i e l d H 0 ( 3 ) . B) Nuclear Relaxation Processes and Diffusion Effects: Consider a set of nuclei placed i n a fixed magnetic f i e l d H Q acting in the z direction and also subjected to a radio frequency f i e l d applied orthogonally to H Q. The components of the Hj f i e l d rotating with an angular frequency u) are: ( H, ) = H, cos uOt 1 X 1 (4) ( H 1 ) y = -H 1 sin u>t The Bloch equations( 1 ) are now referred to a set of axes rotating with the Hj f i e l d . If u and v are the components of M directed along and perpendicular to the direction of the f i e l d , then: u = M x cos u O t - My sinudt (5) v = - M X sin u3 t - My cosuJt The transverse components of magnetization in the stationary and rotating set of co-ordinates are illustrated i n figure I. The Bloch equations(l) referred to the rotating axes are: y 3 du.+ u _ + ( u ) 0 - uO)v = 0 (6) dt T 2 ~ + ~ - (u ) 0 -u) )u + TJHjMg = 0 (7) d M ^ + M z - Mg _ ^ Q dt T x (8> The time constants and T 2 describe relaxation mechanisms which involve transitions brought about by nuclei exchanging energy with their environments and with themselves. With the application of a steady H Q f ield to a set of nuclei , at equilibrium, the population of the (21 + 1) Zeeman levels (for protons, spin 1 = 1/2) is governed by the Boltzmann factor, exp(2 /^H 0 /kT) , with the excess number in the lower states. The system is subjected to the Hi f ield and the previously attained equilibrium state is now disturbed. The process of spin lattice relaxation re-establishes the Boltzmann excess of nuclei in the lower state (4) . T^ the n is the time constant for the system to reach equilibrium. Essentially it is the time required for M z , the component of nuclear magnetization in the direction of H Q , to decay back to the equilibrium magnetization M Q . This is described by; M z = M Q (1 - 2 e " t / T l ) (9) where t is the time in which M z is sampled. In the introduction to his-paper, Bloch(l) suggested the possibili ty of observing a nuclear induction signal in the absence of the r . f . field by subjecting the system to a pulse of r . f . energy. Torrey(5) 4 considered the solutions to the Bloch equations when the r . f . f ield is suddenly applied. Methods of measuring and T2 are presented(5). The experimental effects of the free nuclear precession about a static magnetic field after the r . f . field is removed was first reported by E . L . Hahn(6). In 1950 Hahn(7) published his c lassic paper on the measurement of nuclear relaxation times by employing a pulsed field rather than a continuous radio frequency f i e l d . The effect of the rotating field Hj at the resonance frequency is to alter the direction of the bulk nuclear magnetization vector M . At equilibrium, M is parallel to the direction of H Q . When the field is applied, M wil l change its direction depending upon the duration of the pulse, and wi l l precess about the static field at the Larmor frequency. Hahn(7) referred to this signal as the FREE INDUCTION DECAY. An r . f . pulse of amplitude and duration t w wi l l rotate the magnetization vector M from the z direction with an angular velocity of 2 f H i . Adjusting and t w such that 7 f H ] t w = — the magnetization vector M w i l l be rotated into the x -y plane. The pulses are referred to as 9 0 ° pulses and immediately after the pulse, M wil l be in the v direction. The component of magnetization in the x -y plane perpendicular to H D precesses about the z direction and its amplitude decays - t / T * exponentially. The induction signal decays with a rate e ' 2 , where T2 involves the width of the line due to magnetic field inhomogeneities and includes the natural relaxation time, T ° . The effects of magnetic field inhomogeneities wi l l result in a 5 distribution of the Larmor frequenciesi£>0 usually assumed to be Gaussian. Hahn (7) has considered the behaviour of the magnetization vector M at different times in the decay process. The spin vectors—called spin isochromats—are rotated into the x-y plane by a 90° pulse. If the o pulse is applied along the x' axis in the rotating co-ordinate system, then after the removal of the iX. pulse the spin vectors are parallel to the y' axis. Since there is a distribution in the Larmor frequencies, the vectors of the spin isochromats fan out in the x'-y' plane. Considering a magnetization vector^in a region where its Larmor precession frequency is greater than the mean by A,iD , the magnitude of the spin isochromat * is reduced by e - t / / ^ 2 and the vector is at an angle of (AtO Q)t from the mean vector. In this case t is the time measured after the removal of the 90° pulse. The resultant is proportional to e " t / T 2 ^ g ( A 0 J o ) cos (A00 o)td(ALJ o). - oO g(A-U)D) represents a Gaussian distribution of the Larmor frequencies and g(AUJ 0) = ( 2 1 Y ) i / Z T 2 exp[-(Au)T 2) / 2 J . (10) At a later time % after the 90° pulse the sample is subjected to a second pulse of r.f. energy. This ft pulse, applied for twice the duration of the pulse, rotates the magnetization vectors in the plane 2 by 180°. The relative phase angle between two magnetization vectors 6 which had been increasing after the pulse now decreases. Assuming that the precession frequency of the magnetization vectors is constant, the effect of the pulse is to cause the vectors to constructively inter-fere giving rise to a signal at a time 2^ • This induced nuclear signal is referred to as the SPIN E C H O . (Figure II). Hahn(7) directly_measured T 2 by plotting the logarithm of the maximum echo amplitude versus arbitrary values of 2 X. . Hahn's T 2 values for protons in an aqueous solution of Fe ions was in good agreement with results obtained by Bloembergen(4) „ In liquids diffusion processes are not always negligible. Some of the vectors change their rate of fanning out when the molecules move in an inhomogeneous f i e l d . As a result diffusion processes attenuate the amplitude of the spin echo since the number of nuclei rephased at a time 2 t is reduced. Hahn noted and developed the theory of the "stimulated echo" which appears in company with other echoes when a third pulse is applied at a time T such that 2 t ( T <\ T 2 „ If k t 2 T ( ( T / T 1 then a plot of the logarithm of the amplitude of the stimulated echo versus T gives a measure of T\, the spin-lattice relaxation time. Bloom and Muller(8) have calculated the effect of diffusion on the stimulated echo. Carr and Purcell(9) successfully extended the work of Hahn(7) by developing a more reliable method of measuring T 2 and at the same time minimizing the effects of molecular diffusion. Their procedure 7 involved the application of a s i n g l e ^ pulse followed by a series of n/fr pulses applied at times X » 3 f , 5 t After each It pulse an echo appears and the exponential decay of the echo amplitudes is a measure of the time constant T 2 . The expression for the transverse magnetization, My'., as observed from a frame of reference rotating with the Larmor frequency is given as: My'(t) = IVbexpfVt/Tz) + ( - " u ^ D t V l Z n 2 ) ] (11) where: M D is the equilibrium magnetization. t is the time corresponding to a given echo amplitude. G i s t h e magnitude, in gauss/cm, of the magnetic field gradient. 2 D is the molecular self-diffusion constant in cm / s e c . n is the number of TT pulses applied after the initial ^ pulse. 2 It is seen from equation (11) that diffusion effects can be minimized in a Carr-Purcell experiment by applying a large number of TT pulses in a ^ , T( » Tf • • • - sequence. Carr and Purcell (9) clearly illustrated this by comparing the values of T 2 for water given by the Hahn method in a two pulse multiple exposure sequence (Method I) with the , \\ . . . . series (Method II). Method I gave a value of 0.2 seconds compared with the Carr and Purcell measurement of 2.0 seconds. Carr and Purcell(9) have described a method for measuring T^, the spin-lattice relaxation time. The effect of an initial TT pulse is to o invert the magnetization vector 180 into the - z direction. T^ relaxation processes begin to return the z - component to its original value. 8 TT ~ pulses applied at various times f nutates the total magnetic moment vector into the equatorial plane. A free induction decay signal appears after the 9 0 ° pulse. The signal amplitudes increase algebraically in an apparatus provided with r . f . phase detection and provide a measure of T i . For one value of X i . e . ^ null there is no t a i l . T]_ at this point is calculated approximately from; ^ NULL = T l l n 2 <12) The null method of measuring T-j can only be used if the pulse duration is very accurately set. Douglas and M c C a l l (10) have used' the spin echo method to measure self diffusion coefficients of a series of paraffin hydrocarbons and obtained linear plots of ln D vs 1/T. Diffusion coefficients of C H 4 , C F 4 and mixtures of the two in argon have been measured by Rugheimer and Hubbard (11) from T^ pulse data. Woessner (12) has calculated the effects of diffusion for a three and four pulse sequence. He has measured diffusion coefficients (13) from the proton T^ values of n -paraffins in C C I 4 solutions and considered (14) the movement of molecules undergoing restricted diffusion. A publication by Stejskal and Tanner (15) investigated the effect of a controlled magnetic field gradient on the spin echo experiment. By keeping the field gradient small during the application of the pulse and during the time of the echo, they were able to observe the effects of smaller diffusion constants from the change in amplitude of the broadened echo and to overcome the requirement that 9 "if H i ^  (AU) Jjyg * n v e r Y inhomogeneous fields needed for certain diffusion studies. C) Chemical Exchange Theory in Nuclear Magnetic Resonance: A nucleus with spin I \ O which exchanges; between two or more chemically distinct environments precesses at a different Larmor frequency in each of the sites. The exchange mechanism represents a time dependent process which wil l influence the shapes and widths of the resonance signals (3). Neglecting the effects of spin-spin coupling and considering the sites to be equally populatedj the N . M . R . spectrum shows two signals of equal amplitude and line width when k<^w. In the region of rapid exchange—k) w and UJ = PaU)a+ Pj-y^ o ~~ t l i e t w o s i 9 n a ^ s collapse to a single peak, (k = rate constant, co = chemical s h i f t . ) The theory of nuclear transfer effects in magnetic resonance was originally developed by Gutowsky, M c C a l l and Slichter (16) who modified the Bloch (1) equations for chemical exchange between two equally populated sites. Subsequent investigations considered exchange between unequally populated sites (17) and the effects of chemical ex-change with nuclear spin-spin coupling (18). Hahn and Maxwell (19) and-McConnell (20) generalized the modified (16) Bloch (1) equations' and McConnell (20) considered a nucleus being transferred between two sites having different relaxation properties. Alexander (21, 22, 23) has further developed the exchange theory of nuclear spins in magnetic resonance using spin dtensity matrices. H i s work represented a quantum mechanical 1 0 extension of the c lass ica l theory developed by Piette and Anderson ( 2 4 ) . An interesting review article discussing the use of steady state N . M . R . techniques to the study of chemical exchange rates has been written by Loewenstein and Conner ( 2 5 ) . The investigation into the use of pulse methods to study chemical exchange began in 1 9 6 1 . At that time Woessner ( 2 6 ) considered the mechanism of nuclear transfer in magnetic resonance as being somewhat analagous to the diffusion process. In this regard, chemical exchange effects are a function of the T f pulse repetition frequency in the Carr-Purcell ( 9 ) experiment (equation ( 1 1 ) ) „ Luz and Meiboom ( 2 7 ) have calculated the spin echo decay rate in the presence of chemical exchange. They have derived the following theoretical equation for the dependence of T 2 upon the pulse repetition frequency in the region of rapid exchange: ^ = T ^ + Pa Pb< S u > ) 2 £ [ l - ( 2 V t C o R ) t a n h ( t a p / 2 ^ ( 1 3 ) where: T° is the natural relaxation time. P a , P b a r e t n e n u c l e a r populations in sites A and B. & id is the chemical shift, t _ D is the pulse repetition frequency. 2 X is the mean exchange lifetime. The contents of the results reported in this thesis are based upon a theoretical study of spin echoes and chemical exchange developed 11 b y B l o o m , R e e v e s a n d W e l l s ( 2 8 ) . T h e t h e o r y t o d a t e h a s b e e n c o n f i n e d t o t h e c a s e o f e x c h a n g e b e t w e e n t w o s i t e s i n t h e a b s e n c e o f s p i n - s p i n c o u p l i n g . I n o r d e r t o d e v e l o p e q u a t i o n s d e s c r i b i n g t h e n u c l e a r m a g n e t i z a t i o n , p r o b a b i l i t y t h e o r y i s u s e d t o c o m p u t e t h e p h a s e a n g l e d i s t r i b u t i o n f u n c t i o n ?(0 , t ) o f t h e n u c l e a r s p i n s i n t h e x ' - y ' p l a n e a l l o w i n g a n y n u m b e r o f s i t e t r a n s f e r s a n d r . f . p u l s e s i n a t i m e t . C o n s i d e r i n d i v i d u a l n u c l e i w i t h s p i n I ^ O w h i c h c a n e x c h a n g e b e t w e e n t w o s i t e s A a n d B i n a m o l e c u l a r s y s t e m . I n t h e a b s e n c e o f t r a n s f e r b e t w e e n t h e t w o s i t e s , n u c l e i l o c a t e d i n A a n d B w i l l p r e c e s s i n t h e i r r e s p e c t i v e s i t e s w i t h a n a n g u l a r f r e q u e n c y o f U) a n d u ) ' ^ . T h e e x p r e s s i o n f o r t h e n u c l e a r m a g n e t i z a t i o n i s g i v e n b y : M ( t ) = ^ ( p a c o s u J a t + p b c o s u ) b t U + ( p a s i n u ) a t + p b s i n u 0 5 t ) _ l | G ( t ) (14) w h e r e : P a / P b a r e t h e f r a c t i o n a l p o p u l a t i o n s i n s i t e s A a n d B . G ( t ) i s a r e l a x a t i o n f u n c t i o n d e s c r i b i n g t h e d e c a y o f M x ( t ) a n d M (t) a n d i n t h i s t r e a t m e n t G ( t ) = 1. T h e a c c u m u l a t e d p h a s e c a n b e w r i t t e n a s : t 0 (t) = ^ U ) ( f ) d f (15) o T h e a p p l i c a t i o n o f a TT p u l s e a t a t i m e f a f t e r t h e f i r s t Im-p u l s e t r a n s f o r m s t h e p h a s e 0 (Z) i n t o 2 ^ Q -0{T) w h e r e 0 Q i s t h e p h a s e o f t h e f i e l d i n t h e r o t a t i n g c o - o r d i n a t e s y s t e m . F o r s i m p l i c i t y , 0O= 0 . T h e p h a s e c o l l e c t e d b y a n u c l e u s a s i t e x c h a n g e s b e t w e e n A a n d B d u r i n g a t w o p u l s e - e c h o s e q u e n c e i s i l l u s t r a t e d i n f i g u r e I I I . 12 U sing recursion formulae in order to follow the accumulated phase of a nucleus performing " n " jumps in a time "t", the BRW theory-derived the following expressions for the nuclear spin magnetization M a(t) and M (t): M b ( t , - ^ ( . ^ ) v b * V l " - < . 1 ' , W > a b d . b . where: fa,f-^ are the a priori lengths of the magnetization vectors in A and B. 0a, 0^  are the intial phases. ,0 , the phase of the r . f . field in the rotating co-ordinate system is assumed to be zero. For each 1 8 0 ° pulse M (t) and Mj3(t) must be , , , ~2i'fi o multiplied by e ' . Equations (16a) and (16b) are solutions to the equations for M a(t) and M b(t) derived by Hahn and Maxwell (19) and McConnel l (20). A matrix operator _E having as a matrix element E i j = 2<e > < e ) > ? = 2 <17> k ik x / k j has been used to evaluate the amplitude of the spin echo at a time 2 ^ . The magnetization M ( 2 X ) is expressed in matrix form as: E a a E a b \ | M * ( 0 ) \ E b a E b b ' M b <°V (18) 13 In the Carr-Purcell (9) experiment, ?f pulses are applied at (2n+l)rf / n = 0 , l , 2 . . . and the theory has developed the relationship of the magnetization at the 2n echo to the initial magnetization M (0) as: M{4n*£) = (EE*) nM(0) n even (19) For the case of chemical exchange between sites, they (28) have shown that the echo envelope is in fact a superposition of two exponentials and as such: , r v , - r i 4 n t - r o , 4n r t , 4 M (Ant) = A^e + A 2 e * (20) where: r i » r 2 a r e t n e t i m e constants which are independent of the initial conditions. Aj , A 2 are the amplitudes which depend upon the initial conditions, The eigenvalue equation involving the matrix operator is given as: (MVi = ^ i e ~ 4 k ^ i Mi = (2D ib where: yM. . are the eigenfunctions. j\ are the eigenvalues. Substituting in equation (12) the generalized expression for the time constants i s : r. = k - • ( l n / l ^ t ) (22) 14 Spin echo results reported in this thesis were obtained using diode detection where the signal is proportional to the magnitude of the nuclear magnetization in the x-y plane and is independent o f u J Q . This is a more convenient method experimentally as the resonance condition does not have to be so precisely defined as it would be using phase sensitive detection. Theoretically however, using diode detection, the echo envelope is more complicated because of cross terms introduced between the eigenfunctions^/^ ^ a n c ^ • However for a two site exchange both methods of detection will give an exponential envelope decay which corresponds to the larger of the two time constants r ^ and r ^ . Results reported here measure r^. Although theoretically predicted, r 2 has not as yet been experimentally observed. For the case of equal populations, the eigenvalues are always real. The time constant for the decay of the echo amplitudes in a Carr-Purcell sequence is given by: r, = k - _ i _ sin h" 1 F (23) 1 i t F has been computed for the exchange regions as: UJ>k: F = - ^ sin 2 f ( l 0 2 - k 2 ) 1 / / 2 (24) (U)2 - k2) 1 / 2 U0< k: F = — ^ sin h 2t(k 2-\iJ 2) 1 / / 2 (k 2 - J ) (25) U) = k: F = 2k t (26) ri = — - -7- incorporates the effect of exchange 1 T2 T2 and the natural relaxation time. 15 1/T„ is the observed time constant. 2 c . p . o T 0 is the natural relaxation time which is obtained in nonviscous liquids from a measure of T . 1 k is the mean fate constant for the exchange = 2 LL) is half the chemical shift = X is the I£,Tf pulse interval. Some limiting cases for r computed in BRW theory and amenable to experimental verification are: In this thesis an attempt has been made to v e r i f y experimen-t a l l y the BRW theory using two molecules each of which involves nuclear transfer between two equally populated sites. Allerhand and Gutowsky (29) have used Woessner's equations (26) to derive an expression similar to the Meiboom equation (27). However the equation leads to inaccuracies in the slow exchange region for systems with two sites separated by a large chemical shift. As a result Allerhand and Gutowsky (30) derived closed form expressions for the decay of the echo amplitudes in the Carr-Purcell sequence. Their expression is the same as equation (23) derived in the Bloom, Reeves and Wel ls theory (28). EQUATION CONDITIONS SHORT X LIMIT L O N G X LIMIT 16 Pow.les and Strange (31) have theoretically considered the modulation of the echo amplitude for a two site exchange system with nuclear spin-spin coupling. They have investigated the effect of amplitude modulation for the hydroxyl proton exchange in methyl alcohol . Gutowsky, Void and Wells (32) have formulated a general theory of chemical exchange effects in N . M . . R . Assuming equal relaxation in the sites, in the Carr-Purcell sequence they have used density matrices to indicate that both exchange and J coupling effects could be removed in the limit of rapid pulsing. Further, in the region of very fast exchange, the modulation of spin echoes due to spin-spin coupling is removed. Allerhand (33) has' derived general equations which describe the effect of homonuclear coupling on the Carr-Purcell experiment. Since chemical exchange may be incorporated as a relaxation mechanism into basic relaxation-theories (4),. it is amenable to study by pulse double resonance experiments. This technique for the study of relaxation processes in liquids has been developed by Baldeschwieler (52). Though the technique has not as yet been used to derive kinetic data for chemical exchange the obvious application exists . D) Hindered Internal , Rotation and Molecular Conformation: Experiments in nuclear magnetic resonance have contributed significantly to the study of structural isomerism. Many amides and nitrites have potential energy barriers which are due to the partial 17 d o u b l e b o n d c h a r a c t e r o f t h e C - N , O - N a n d N - N b o n d s (25) „ T h e s e b o n d s a s s u m e t h e i r p a r t i a l d o u b l e b o n d c h a r a c t e r f r o m r e s o n a n c e f o r m s o f t h e t y p e : ° \ + / R 2 ° : + * ° : C== N \ N = 0 ^ \ N = N / \ \ R l , R3 R 2 If t h e b a r r i e r t o c o n v e r s i o n f r o m o n e i s o m e r t o a n o t h e r i s . r e l a t i v e l y h i g h , t h e n t h e e x c h a n g e w i l l b e s u f f i c i e n t l y s l o w t o r e s o l v e t w o s e p a r a t e s i g n a l s i n t h e N 0 M 0 R 0 s p e c t r u m . T h i s o c c u r s i n t h e r e g i o n w h e r e t h e r a t e c o n s t a n t i s l e s s t h a n t h e c h e m i c a l s h i f t . M a n y p u b l i c a t i o n s h a v e c o n s i d e r e d t h e a p p l i c a t i o n o f N . M . R . t o t h e s t u d y o f h i n d e r e d i n t e r n a l r o t a t i o n ( 2 5 ) , V a r i a t i o n s i n t h e m e t h o d o f e x p e r i m e n t a t i o n a n d e v a l u a t i o n of d a t a h a v e l e d t o d i s c r e p a n c i e s a m o n g i n d e p e n d e n t w o r k e r s w h o r e p o r t d i f f e r e n t a c t i v a t i o n p a r a m e t e r s f o r t h e s a m e c h e m i c a l s y s t e m . P e r t i n e n t t o o u r i n v e s t i g a t i o n s i n t h i s l a b o r a t o r y , R o g e r s a n d W o o d b r e y (34) h a v e s t u d i e d h i n d e r e d i n t e r n a l r o t a t i o n i n a s e r i e s o f s u b s t i t u t e d N , N - d i m e t h y l a m i d e s „ T h e y h a v e m e a s u r e d t h e m e a n l i f e t i m e o f a n u c l e u s e x c h a n g i n g b e t w e e n . t w o s i t e s a s a f u n c t i o n o f t e m p e r a t u r e b y c a l c u l a t i n g t h e r a t i o o f t h e m a x i m u m t o m i n i m u m s i g n a l i n t e n s i t i e s (35) I n N , N - d i m e t h y l t r i c h l o r o a c e t a m i d e a n d N , N - d i m e t h y l c a r b a m y l c h l o r i d e t h e a c t i v a t i o n p a r a m e t e r s w e r e n o t i n a g r e e m e n t w i t h t h e s p i n e c h o m e a s u r e -m e n t s o f G u t o w s k y (29) o C a r r - P u r c e l l m e a s u r e m e n t s m a d e i n t h i s l a b o r a t o r y (36) h a v e r e p o r t e d a h i g h e r v a l u e c o m p a r e d w i t h R o g e r s a n d 18 W o o d b r e y (34) f o r t h e a c t i v a t i o n e n e r g y o f N , N - d i m e t h y l t r i f l u o r o a c e t a m i d e . S i n c e t h i s c o m p o u n d h a s a s m a l l c h e m i c a l s h i f t , i t w a s p r o p o s e d t h a t t h e s p i n e c h o m e t h o d p r o v i d e d a b e t t e r e s t i m a t i o n o f t h e t r u e r a t e c o n s t a n t s . T h e s p i n e c h o m e t h o d h a s t h e a d v a n t a g e o f m o r e e a s i l y t a k i n g i n t o a c c o u n t v a r i a t i o n s w i t h t e m p e r a t u r e o f T ° a n d t h e c h e m i c a l s h i f t . P h i l l i p s (37) h a s c o n d u c t e d a v a r i a b l e t e m p e r a t u r e s t u d y o f N , N - d i m e t h y l n i t r o s a m i n e . T h e r o o m t e m p e r a t u r e N . M . R . s p e c t r u m c o n - , s i s t e d o f t w o p e a k s c h e m i c a l l y s h i f t e d b y 26 c s . H e h a s r e p o r t e d a b a r r i e r h e i g h t f o r t h e e x c h a n g e o f t h e m e t h y l g r o u p s o f 23 K c a l . / m o l e . B r o w n a n d H o l l i s (38) h a v e q u e s t i o n e d t h e p r e v i o u s a s s i g n m e n t s o f t h e N . M . R . s p e c t r a o f a l k y l n i t r i t e s a n d n i t r o s a m i n e s . T h e y f e l t t h a t o t h e r m e c h a n i s m s a p a r t f r o m h i n d e r e d i n t e r n a l r o t a t i o n s h o u l d b e c o n s i d e r e d f o r t h e i n t e r c o n v e r s i o n . B l e a r s (39) h a s s t u d i e d t h e N . M . R . s p e c t r u m o f d i m e t h y l n i t r o s a m i n e u p t o 1 9 0 ° C . H i s r e p o r t e d a c t i v a t i o n e n e r g y , o b t a i n e d f r o m t h e r a t i o o f I m i n / I m a x > O I 25 K c a l / m o l e i s i n g o o d a g r e e m e n t w i t h t h e v a l u e o b t a i n e d b y P h i l l i p s ( 3 7 ) . S o l v e n t e f f e c t s o n t h e e n e r g y b a r r i e r h a v e b e e n r e p o r t e d f o r t h e h i n d e r e d i n t e r n a l r o t a t i o n i n s o m e m o l e c u l e s . W o o d b r e y a n d R o g e r s (40) h a v e f o u n d a s t r o n g d e p e n d e n c e o f t h e b a r r i e r h e i g h t u p o n t h e n a t u r e a n d c o n c e n t r a t i o n o f t h e s o l v e n t . T h e y r e s o l v e d t h e i r r e s u l t s b y c o n s i d e r i n g t h e m o r e p o l a r o f t h e t w o p o s s i b l e r e s o n a n c e f o r m s i n s o m e d i - s u b s t i t u t e d a m i d e s i s s t a b i l i z e d t o a h i g h e r d e g r e e i n m o r e p o l a r s o l v e n t s . L a r g e s o l v e n t e f f e c t s i n t e r p r e t e d i n t e r m s o f d i p o l a r 19 association have been found between dimethylformamide and solvent (41). Blears (39 ,42) has considered the effect of solvents in dimethylnitrosamine, and in the complexing of boron halides with dimethylformamide, variations in the activation energy are attributed to changes in theTf character of the C-N bond when one of the resonance forms is stabilized by the formation of the complex. Nuclear magnetic resonance rate studies of the ring inversion in saturated six-membered ring systems have been investigated in cyclohexane, substituted cyclohexanes, piperazine and dioxane. Since cyclohexane is an AgBg system, the rate of inversion has been studied using cyclohexane-d-Q. Bovey et al (43) studied con-o o formational isomerism in CgD^H from -75 to -47 Any line broadening arising from H-D coupling was eliminated by double resonance. Anet, Ahmad and Hall (44) obtained an activation energy of 11.3 Kcals/mole for CgDjjH studied from -94° to -32°C. However in a second publication (45) discussing ring inversion in cyclohexane, Anet indicated that his earlier work contained an arithmetical error in the rate constant calcula-tion. His corrected value of Efl is 10.9 Kcal/mole. Allerhand, Chen and Gutowsky (46) have used the spin echo method to study conformational isomerism of CgH-^ a n ^ GgD-^ -^ H. In the limits of slow and fast ex-change regions, the exchange contribution is comparable to instrumental capabilities of measuring the total linewidth. Rapid pulsing in the Carr-Purcell experiment eliminates instrumental line broadening effects. In 20 cyclohexane-d^, T° , the natural relaxation time, increased from 10 to 85 seconds over a 100° temperature range. Using the spin echo method Gutowsky measured the exchange rate over five orders of magnitude. The activation energy and frequency factor for cyclohexane and cyclohexane-d^ were given as 9.5 Kcal/mole and 4.5 x 10^ sec. * Spin echo studies of intramolecular exchange in the coupled AB system 1,1-difluorocyclohexane (47) and the chair to chair isomerization of perfluorocyclohexane (48) have also been reported. 21 EXPERIMENTAL CHAPTER II A) Preparation of Compounds (i) N,N-Dimethylnitrosamine : Secondary amines upon treatment with nitrous acid yield nitrosamines which are stable yellow liquids or low melting point solids. N,N-dimethylnitrosamine was prepared by the reaction of dimethylamine hydrochloride and sodium nitrite in acid solution. The mixture was distilled rapidly to dryness and the distillate was treated with an excess of potassium carbonate. The nitrosamine appeared as a yellow oil which was further treated with more solid potassium carbonate in order to remove the water. The dimethylnitrosamine was transferred to a small distilling flask and the liquid was dried over fresh anhydrous potassium carbonate. The pure compound, boiling point 150-151°C, was collected after two successive distillations under a nitrogen atmosphere. The overall reaction is given as: (CH 3) 2NH + HN0 2 —> (CH 3) 2NNO + H 20 (ii) N,N-Dimethylcarbamyl Chloride: The sample of N,N-dimethylcarbamyl chloride was obtained from K & K Laboratories Co. Ltd. with an indicated boiling point of 165-167°C. It was further purified by double distillation under a nitrogen atmosphere. 22 The samples used in this investigation were prepared for analysis in five millimeter outer diameter tubes which had been rounded off at one end. The tube containing the sample was mounted on a high vacuum system and the sample was thoroughly degassed by freezing with liquid nitrogen and allowing it to warm to room temperature under vacuum. This freeze-pump-thaw procedure was repeated several times and the tube was then sealed off. The compounds were checked for purity spectroscopically using a Varian A-60 N.M.R. spectrometer. B) The Spin Echo Spectrometer: The spin echo spectrometer described below was constructed in our own laboratories.* The apparatus is a further development of one constructed several years ago and is designed for nuclear magnetic resonance work in liquids. The major features of the apparatus include: (a) a radio frequency generator (Figure IV) consisting of a highly stable 10 Mc./s. crystal oscillator, a pulse modulator stage, two frequency doublers, a 40 Mc./s. driver stage and a push-pull final amplifier stage; (b) a Tektronix 545A oscilloscope, a Tektronix 162 waveform generator and three type 163 pulse generators in order to synthesize the modulating pulse train; (c) a Varian crossed-coil probe modified by appropriate changes of capacitors in the transmitter coil circuit to facilitate * Acknowledgements are accorded to Mr. K. H. Abramson and to Mr. E. Fisher for their work on the pulse machine. 1/ + 3 2 0 V 8 0 m A quiescent O 7 0 mA pulsing RF GENERATOR pulsed RFoutput (155 V P-Pacross 100 fl. carbon resistor) 0 . 0 0 5 / j f 3 K V - I 8 0 V O -4 7 K J 2 W I 2 W 23 impedance matching. The probe was used for both high resolution and spin echo experiments; (d) a L.E.L.-I.F. amplifier which was used as a broadband receiver. (Figures V, VI). The generation of the Carr-Purcell pulse sequence is illustrated in figure VII. The 10 Mc./s. crystal was thermostatically maintained at 85°C in a crystal oven. Phase coherent 40 Mc./s. R.F. pulses were obtained by allowing the 10 Mc./s. oscillator to run continuously while pulse modulating the first doubler stage. Leakage of 40 Mc./s. during the "pulse-off" period was eliminated by careful interstage shielding. The Meiboom-Gill method (49) of phase shifting the ff pulse by 90° with respect to the ff pulse was accomplished in the second doubler grid If circuit. To achieve this, a pulse, identical to the — pulse, switches a back-biased semi-conductor diode into its conductive state so that effectively a phase-changing capacitor is placed across the tuned circuit if o for the duration of the ^ pulse. This 90 phase change minimizes the effect of accumulative error which might occur in the width of the pulses during a ^ , T | , i f . ••• (Carr-Purcell (9)) pulse series. The R.F. output power of the transmitter was approximately 250 watts corresponding to a rotation of the magnetization vectors in 15-20 microseconds. 2 In order to Initiate a pulse train, a positive gate voltage was fed from the "+ GATE A" terminal of the oscilloscope to the trigger inputs of two type 163 pulse generators one of which produced the single ff pulse and the other the 90° phase shifting pulse (49). In this manner 1 from receiver' coi SO Mc/sec reference R.F * phase from transmitter LE.L. amplifier to y axis oscilloscope' 4 0 Mc/sec reference frequency quadrupler S cp shifter RECEIVER CIRCUITS 2 0 Mc/sec 4 0 Mc/sec 10 Mc/sec crystal osc. frequency doubler frequency doubler power amplifiers 1 reference 10 Mc/sec + 4 i phase shift 545A Tektronix scope O + g a t e A I scope n _ n D.C. pulses STL zr t gate U -•v*— I wave type type type form 1 6 3 1 6 3 1 6 3 generator pulse unit pulse unit pulse unit type 7T/2 7T 7r/2 pulse 162 pulse pulses shift crossed coil probe transmitter coil 4 0 Mc/sec pulses P R O D U C T I O N O F P U L S E D a P H A S E S H I F T E D R.F the initiation of the ^ pulse and phase shifting pulses coincided with the commencement of the oscilloscope trace. The production of pulses at timesH , , 57? . . . . was achieved by employing the same "+ GATE A" from the oscilloscope to gate a type 162 waveform generator which produced a saw-tooth train of variable frequency. The negative-going saw-tooth was then used to trigger another type 163 pulse generator resulting in a train of IT pulses. The series of TT pulses were delayed from theXf pulse by adjustment of the "OUTPUT PULSE DELAY" control on the pulse generator. In the same manner the time between TT pulses-the pulse repetition period- was adjusted by the "PULSE INTERVAL" control on the waveform generator and measured with a Hewlett-Packard 522B electronic counter. Receiver coil orthogonality and the leakage paddles on the Varian crossed-coil probe were adjusted in order to obtain excellent isolation between the transmitting and receiving coils, This adjustment was made such that the central portion of the R.F, pulse was negligible and only the high frequency components- the leading and trailing edge of the pulse- were detected as two small spikes. Optimizing these adjustments in this manner resulted in quick receiver recovery times and avoided inducing into the receiver coil large "ringing currents" which could distort the overall H^  from the transmitter coils. The modified L.E.L.-I.F, amplifier used as a receiver, maximum receiver gain of 2 x 10^ with a bandwidth of 3 Mc./s., provided 25 both diode and phase sensitive signal detection. Originally, in the phase sensitive detection mode, the receiver was supplied with a 10 Mc./s., 3 volt signal from the crystal oscillator of the transmitter. The signal was fed to a frequency quadrupler which produced the phase reference signal. The incoming N.M.R. signal from the probe was then mixed with the phase reference signal in the input transformer of the receiver to produce a phase detected signal. However it was found that the power available from the transmitter did not drive the quadrupler to 40 Mc./s. and as a result the zero-beat of the free induction decay against the phase reference signal, a condition necessary to define resonance, was being accomplished against the 10 Mc./s. leakage only. The action of frequency quad rupling in one stage produced a signal with changing amplitude between cycles-a condition not suitable for the intended operation. As a result an amplifying stage was used in order to raise the power available from the transmitter to that required for frequency modulation. (Figure VIII). Further, in order to achieve more efficient frequency multiplication with a reasonably uniform output amplitude, two stages of frequency doubling were used. (Figure IX). C) Magnet Systems: The results reported in this thesis were obtained on a Varian 12" magnet shimmed for high resolution. The magnet was the first to be marketed by Varian Associates and was obtained in 1963 from the 10MHz i 75,1/t Input (•)—3r from Tx ^ Receive General Radio Delay Line .30I-SI4O4 j Oj-25nsec j (all resistors 1/2 W unless otherwise indicated) REFERENCE SIGNAL A M P L I F I E R , MULTIPLIER, PHASER AND A T T E N U A T O R (a) Fundamental Frequency (b) Frequency Quadrupling In One Stage ( 0 Frequency Doubling (d) Frequency Quadrupling By Two Successive Shell Development Oil Company. The magnetic field was stabilized by means of a Varian V-K3506 Super-Stabilizer. In order to obtain maximum field homogeneity, the Varian field homogeneity attachment coils were modified to allow sufficient room for the proble assembly to fit in the center of the magnet gap. The outer shape of the coil system was cut leaving a coil area comparable to the area of the magnetic pole faces. Contact cement was placed around the rim of the pole faces and the homogeneity coil plates were glued to the polefaces and aligned during the short period necessary for the glue to set. The temperature of the magnet cooling water was held at a constant 19°C by means of a contact Jumo thermometer. Whenever the temperature rose above 19°C a relay switch initiated the flow of raw water through the circulating coils in the fiber-glass-lined drum. As an added preventive measure the high voltage power supply was automatically cut off if the magnet temperature ever exceeded 35°C. Careful control of the surrounding temperature of the magnet system was achieved by insulating the magnet housing with styrofoam. Furthermore, a box, inner-lined with styrofoam, was constructed around the magnet. Plug-in panels and a sliding door assembly enabled complete accessibility to the probe as well as complete insulation from outside temperature fluctuations during an experiment. 27 Variable high temperature e x p e r i m e n t s — 3 0 - 2 0 0 ° C — were carried out by directing an air flow through a 650 watt heater. The heated air then passed through a stainless steel and teflon tube, both connected in series, and in this manner was directed into the probe assembly and passed around the sample tube. Stabilization of the air . flow was accomplished by connecting a large ballast tank into the circuit before the heater. The flow rate was controlled by a needle valve and the air pressure was monitored before and after the needle valve . Low t e m p e r a t u r e ' — 2 0 - - 1 0 0 ° C ~ experiments were carried out by directing a. flow of dry nitrogen gas through a set of circulating coils immersed in a dewar of liquid nitrogen and then directed into the probe „ Temperatures were measured with a copper-constantin thermo-couple the sensing end of which was placed in an N . M . R . sample tube in order to simulate accurately the sample temperature. Temperature control during an experiment was monitored on a Speedomax recorder by the use of a second thermocouple located just above the sample in the variable temperature insert. In this manner temperatures are reliably o quoted to an accuracy of +0.5 C . Nuclear magnetic resonance signals were observed on a Tektronix model number 545A osci l loscope. This unit was used in conjunction with both the high resolution and spin echo spectrometers. 28 D) Measurement and Reliability: The Carr-Purcell traces were photographed with a Polaroid oscilloscope camera using type #47, 3000 A. S.A. film and photographs were subsequently measured for echo amplitudes. Carr-Purcell (9) measurements of T£ are reliable only to within the stability limitations of the spectrometer. Earlier publications concerned- with the measurement of relaxation times using the Carr-Purcell method quoted values of T£ to within 15-25%. The present work was directed toward the attainment of more accurate and reproducable values of T 2» Effects of diffusion were further minimized by working in * a very homogenious Hg field. The non-spinning samples had a T^ , IT* measured from the free induction tail , of 50 milliseconds and in a ^ ft *TT ° • •» pulse sequence, overlap of the detected pulses and echoes occurred. In many cases, at each pulse repetition frequency an average of at least two traces was used in quoting the value of ^2{Q p )° E) Computer Programs: ic A computer program, "BESFIT", was written in order to provide statistically the best fit of the experimental data in the deter-mination of the rate constant k and the chemical shift u) . This iterative FORTRAN program was designed for use on the I. B . M , 7040 computer. The values of ^2(C P )' ^ e °kserved time constant of the 29 exponential decay in the Carr-Purcell experiment, T i 5 , the natural relaxation time and f , the TT' pulse repetition frequency, are read in as data for a given set of temperatures. In order to initiate execution of the program, reasonable guesses of k andU) are also read in as data. The best fit of the data to the equation r, =. —1 L = k --L. s i n h _ 1 F (23) 1 T 2 ( C . P ) n 2 / t is computed and the sum of the squares of the errors is printed out. The trial values of the rate constant and the chemical shift are now changed by computed increments obtained by differentiating equation (23) with :. respect to k and uO . The entire process is repeated with new trial values of k and UJ . The best fit determination of the data is printed out on the basis of the minimum of the sum of the squares of the errors. Generally twenty iterations.are allowed in order to converge on a value within +0 .5 sec - * of the rate constant and chemical shift. Three sub-routines to the program have been added in order to compute k and UL) according as: k is less than, equal to or greater than lO . The program' is designed to change automatically from one subroutine to another in order to establish the best fit of the data on the basis of the trial values of k and of u) . * Thanks are accorded to M r . R. Wolfe and to Dr. J. F . Herring for teaching me some of the complexities of computer programing. 30 The program retains the computed values of k for a given temperature and enters this data into a fourth subroutine designed to compute the energy of activation, E a, and the frequency factor, A, according to the Arrenhius equation, k = Ae"Ea/RT (29) Once again reasonable guesses of E a and A are read into the program. A least squares program is used for the calculation of k from the "short U limit" plot of l A 2 ( c p ) v s (U)^ b) , and the subsequent evaluation of the energy of activation and the frequency factor in the Arrenhius plot of log k vs 1/T. 31 EXPERIMENTAL RESULTS CHAPTER III Carr-Purcell spin echo experiments have been carried out on the protons in N, N-dimethylnitrosamine (DMNA) and N, N-dimethylcarbamyl chloride (DMCC). DMNA DMCC CH.. O CH~ ^  . O 3 ^ N - N ^ 3^N-C* C H 3 CH 3 y ^ c i Using the steady-state method it is possible to study hindered internal rotation in a molecule without any contributions to the spectrum from non-exchanging nuclei providing signals do not overlap. The relatively small proton chemical shifts and large H^ fields used in the pulse method impose a non-selective condition upon the experiment. In this regard the molecules under investigation were chosen because all of their protons participate in the exchange. A) N, N- Dimethylnitro samine: DMNA was selected as a suitable molecule for testing the BRW (28) theory since the chemical shift between the two methyl groups is large and there are no interfering protons in the system. The compound is a liquid over a large temperature range. It is very stable and relative-ly nonhygroscopic. Unfortunately the full temperature range covering the three exchange regions could not be studied as the coalescence temperature of 190°C is well above the boiling point of the sample. In this regard more homogeneous magnetic fields were required for DMNA in order to investigate the exchange rates at higher temperatures where diffusion processes are rapid. (i) Free Induction Tail Experiments: In figure X the diode—detected free induction decay for-. N, N-dimethylnitrosamine is illustrated for a series of temperatures up o to 195 C. At room temperature the steady state spectrum of DMNA shows two signals of equal intensity chemically shifted by 30.3 c s . at 40 Mc./s. When nuclei are restricted to a certain site, the free induction decay signal is the sum of the free precessions from all signals (26). A resolved chemical shift appears in the free induction decay as an ampli-tude modulation. This modulation appears because the transverse components of magnetization rotate at different angular velocities with respect to the rotating frame in A and B and in the stationary co-ordinate system the magnetization M is given by: M x = M 0 s i n © 1 j ^ a s i n ( i ) a t e " t / / T 2 a + P bsin(x) bte t / / T 2 ^ J where : © 1 = ^ j t w P a,P b are the populations in sites A and B. (30) FREE INDUCTION TAIL EXPERIMENTS IT, N-DIMBTHYXNITROSAMINE V V m . l n l i ' l i l r vs,...;. i . . „ _ . . . — ^ 20.S °C li|0 °C 11*8 °c 164 °c l8o °c 191 °C 19* • • • • i J O i • • • • ^ oo Free i n d u c t i o n t a i l s i g n a l s f o r pure N,N-Dimethylnitrosamine at v a r i o u s temperatures. At 20«f>°C the measured modulation p e r i o d i s 33o2 msec., correspoding t o a chemical s h i f t d i f f e r e n c e of 3002 c.s. Room temp-erature steady-state measurements at liO Mc.s. produce a chemical s h i f t of 30o3 c.s. Time s c a l e i n a l l of the above i s 20 msec/cm© 33 At room temperature, using diode detection, the free induction signal shows the modulations expected for small exchange rates. The measured modulation period is 33.2 milliseconds corresponding to a chemical shift of 30.2 c s . This is in excellent agreement with the steady state value. The sample was not spinning as this is likely to cause additional modulations to the free induction tail. As the temperature is increased, the signal- is altered corresponding to the larger exchange rates, At 195°C the modulations have virtually been removed from the free induction decay. It is interesting to compare the changes with temperature in the free induction decay of DMNA with those obtained by Reeves and Wells (50) for the unequally populated case of methyl nitrite. The behaviour of the free induction decay signals of DMNA corresponds qualitatively to the predictions made by Woessner (26). (ii) Carr-Purcell Trains: Spin echo Carr-Purcell trains of the protons in DMNA are illustrated in figure XI. The traces were recorded at a sample 'tempera-ture of 135°C and the Meiboom-Gill phase shift (49) was used in all cases. The spin echo trains in figure XI correspond to the TT pulse spacing indicated in the left column. The calculated values shown in column 3 vary from 10.1 seconds in the limit of rapid pulsing to 0.2 seconds when the pulse interval, 2 r£, is 40.75 milliseconds. In order to obtain a full scale display of the decay, the corresponding settings of the time base are changed and recorded in column 4. 2 C A R R - P U R C E L L TRAINS ; N.N-DIMETHYLNITROSAMINE T 2 ( C P . ) (sec) Time Base (sec/div) IO.I 2.0 9.21 2 .0 6.30 2 . 0 2.68 1.0 2 . 0 3 1.0 1.44 0 .5 0 . 7 2 0 .2 0 . 2 0 0.1 Pulse Interval (2 T ) , (msec) 1.30 2 . 0 5 2 .58 8.11 10.24 13.02 20.48 4 0 . 7 2 34 When pulsing rapidly, and with, the sample placed.in a homogeneous H Q f i e l d , no individual echoes are resolved. At 40.75 milliseconds, the decay is still exponential but with such a large /ff pulse spacing indiyudual echoes are now resolved. The amplitudes of the echoes are not modulated in the Carr-Purcell train as the transverse components of magnetization are a l l rephased when the echo maxima occurs. The measurement of T. 2 from Carr-Purcell trains is very sensitive to the proper adjustment of the baseline. Any deviations in the baseline after . a trace has been photographed is indicative of magnetic field drift from the resonance condition. In this connection, prior to observing a decay, the zero beat of the free.induction t a i l , using Lphase sensitive detection, was checked for the resonance condition. A series o f f f - pulses was inserted and revert-ing, to diode detection, the baseline was adjusted on the: longest time scale . In the actual decay the XT'pulses were removed shortly before the trace had swept full scale and the drop-to the original baseline indicated no field drift. Careful attention to spectrometer conditions during an experiment, the inclusion of the 9 0 ° phase shift (49) and working, in a homogeneous H Q . f ield has.increased the reproducibility of the spin.echo trains. In this regard the T 2 values are estimated to have a random error 5%. Previous claims (46). estimate T 2 to within 10-20% and at higher temperatures their error in some cases was 40%. (iii) Limiting.Cases—Off and On Resonance: For the case of N jN-dimethylnitrosamineanother feature of the spin echo experiment was introduced to provide an independent check of the rate constant data. Wayne, Zamir and Strange (51) have suggested that accumulated error in the 180° pulses can be corrected by working at certain off resonance conditions without • using the Meiboom-Gill 90° phase shift. The condition that must be observed in the ff - TT pulse separation is: 2^ = (2n + 1 + Y ) T (3 1) 2 Tf where: T = (AuJ) 0 n is an integer (AtO ) Q is the frequency difference from the resonance condition. Rate constant determinations for DMNA are measured at approximate-ly 4.5 Kc.s. off resonance. At this point variations in 1^ were recorded for IT -pulse intervals ranging from 1.0 to 10.0 milliseconds. The off resonance experiments were limited by the narrow pulse interval range over which T 2 could be measured reliably. The resonance position was periodically checked by the number of modulations of the phase sensitive detected free induction decay signal. The proton T 2 values measured for DMNA are given in figures XII and XIII for the off and on resonance conditions. The data are presented as plots 2 of 1/ T 2(Q p ) as a function of (u)^) . This follows from the shortH limit expression r" = | k (U)^) 2 (27) off resonance 0 4 8 12 16 20 24 (cur)2x I0"2 on resonance 36 presented in the Bloom, Reeves and Wel ls theory (28). Within the validity of equation (27) the slopes (x3/2) of the lines in figures XII and XIII give an estimation of the rate constants for the exchange at each temperature. The values of UJ were obtained from steady state measurements. Extrapolation of the lines to (U) 1^) = O provides a value of T 2 , the natural relaxation time. A least squares computer program was designed to evaluate the . rate constants and values of T ^ . Generally the correlation between 1 / T 2 and 9 (U)^) was better than 0.95. A comparison of figures XII and XIII shows good agreement between the off and on resonance data. A large temperature dependence of T 2 is observed in D M N A . However it is rather unusual that the natural relaxation time decreases with increasing temperature. Since the exchange region for this compound requires a high sample temperature the production of small b'tit increasing amounts of paramagnetic nitric oxide as the temperature is raised, l e a d s to this T 2 temperature dependence.. This behaviour is associated with the equilibrium: ( C H 3 ) 2 N N O ( C H 3 ) 2 N - N ( C H 3 ) 2 + 2NO Values of the rate constants computed from the s h o r t ^ l i m i t plot for the on and off resonance condition are listed in table I. 37 TABLE I N, N-DIMETHYLNITROSAMINE 9 9 RATE CONSTANTS FROM r& k + k + 7 k ( ) Off U00 On U00 T(°C) k(sec 1) T(°C) k(sec - 1) 131 2.52 131 2.20 135 3.27 136 .1 . 9 2 140 4.57 140 ,1.97 146 5.75 152 6.44 151 7.56 162 8.73 159 11.8 169 14.6 166 21.8 177 25.5 17 2 33.0 1 8 3 ' 27.4 183 48.7 190 61.5 192 129 The most"important parameter derived from these experiments.is the rate constant k. It is seen from table I that agreement between the rate constants from the on resonance measurements using the 90° phase shift with the off resonance values is satisfactory. Further it is reasonable to expect, in this case, that there is a better agreement in the lower temperatures where diffusion effects are not as rapid. 38 (iv) Calculation of 'r^': The time constant T 2 for the decay of the echo amplitudes in the Carr-Purcell experiment is a function of T° , the natural relaxation time, of the populations in the sites A and B,, (for DMNA, p a = p^ = 0.5) of the chemi-cal shift ,0^-10^ and of the pulse repetition frequency 2^. It is interesting then to plot ln l / T 2 as a function of In 1/2^ and derive the rate constants from the best fit determination to equation (23): r l = k " (4^)sinh_1F (23) A comparison of the data off and on resonance is illustrated for DMNA in figure XIV. The general shapes of the curves for the complete dependence of T 2 ( Q p ) upon the pulse repetition frequency is not seen in figure XIV. This is especially the case for the off resonance results because of the limited pulse interval range over which T 2 could be measured. Only the region below the coalescence temperature could be studied for DMNA. The on resonance measurements extend over a greater range of pulse intervals. The data was computerized to obtain the value of k using equation (23). Trial values of k and T° for the program were obtained from the slope and intercept in the short ^  limit approximation. The value of u)was obtained from high resolution studies. Values of the rate constant k obtained from the best fit to the data are listed in table II. 39 TABLE II  N, N-DIMETHYLNITROSAMINE RATE CONSTANTS FROM r. = k-(~4b) sinh" 1 F Off CO Q On iO o o „ T( C) k(sec T(°C) k(sec 1) 131 2. 20 131 3. 20 135 2.80 136 3.20 140 3.70 140 3.40 146 5.10 152 6.30 151 5.80 162 8.00 159 10.1 169 31.9 166 25.4 177 41.9 17 2 55.4 183 47.5 183 74.9 190 61.8 192 102 Agreement of the rate constants between the two methods is satisfactory. Further discussions of the ln 1/T 2(c p ) versus ln 1/2^ graphs are postponed since the general shape of the lines for the complete dependence of T 2 upon TT -pulse spacing is best seen in N,N-dimethylcarbamyl chloride. A comparison of the rate constant data for selected tempera-tures of dimethylnitrosamine are presented in table III. Included are unpublished A-60 steady state measurements made in this laboratory by 40 D r s . L . W . R e e v e s a n d E . J . W e l l s . T A B L E III  C O M P A R I S O N O F R A T E C O N S T A N T S T k<A> k<A> k<B> k< C > k ( C ) ° C o f f U j 0 o n W 0 A - 6 0 o f f l 0 o o n u) 0 140 4 . 5 7 1 . 9 7 2 . 5 5 3 . 7 0 3 . 4 0 151 7 . 5 6 6 . 4 4 4 . 9 0 5 . 8 0 6 . 3 0 160 11.8 8 . 7 3 1 0 . 3 1 0 . 1 8 . 0 0 183 4 8 . 7 2 7 . 4 4 4 . 0 7 4 . 9 4 7 . 5 192 129 6 1 . 5 - 102 6 1 . 8 2 2 (A) — L e a s t S q u a r e A n a l y s i s o f r ^ ^ k + k ± j k(u)%) (B) - - S t e a d y S t a t e A - 6 0 (C) — C o m p u t e r C a l c u l a t e d — t i m e c o n s t a n t ' r ^ ' . (v) A c t i v a t i o n P a r a m e t e r s : T h e t e m p e r a t u r e d e p e n d e n c e o f t h e r a t e c o n s t a n t f o r d i m e t h y l -n i t r o s a m i n e i s i l l u s t r a t e d i n f i g u r e XV f o r t h e o f f a n d o n r e s o n a n c e e x p e r i m e n t s . T h e a c t i v a t i o n e n e r g y E a a n d f r e q u e n c y f a c t o r A a r e d e t e r m i n e d f r o m t h e A r r h e n i u s e q u a t i o n k = A e x p ( - E a / R T ) (29) b y t h e s l o p e a n d i n t e r c e p t o f t h e l i n e s . A c t i v a t i o n e n e r g i e s a r e d e t e r -m i n e d a s l e a s t s q u a r e l i n e s t o a l l r a t e c o n s t a n t d e t e r m i n a t i o n s . T h e o f f 2 . 5 r 2.0 1.5 .0 0.5 o = spin echo 2.5 E =22.9±l 7 kcal/mole • = computer calculated sin h"'F fit 2.0 off resonance i.o 0.5 o = spin echo E =21.9+1.6 kcal/mole 0 = computer calculated sin rf' F fit 1 = A - 6 0 on resonance 0 I i i i i i i i i ' ' Ql i i i i i — i — i — i — J — i — i — i — i — i — i — i — i 1 — i 2.1 2.2 2.3 2.4 2.1 22 2.3 2.4 l / T xlO"3(°K") $1 41 resonance graph includes the rate constant .data determined from the short ^ l i m i t approximation and the sinh~*F f i t . In addition the on resonance line includes.the steady state rate constant data of Reeves and W e l l s . The re-ported errors in the activation energy are quoted for a 90% con-fidence-l imit . Agreement between the two methods is very satisfactory. , In table IV,the activation parameters are listed for the off and on resonance experiments. Values of the activation parameters obtained by other workers are also tabulated. is determined from A H * = E a - RT C (32). where T c is the coalescence temperature which for D M N A is 1 9 0 ° C . The probable statistical errors in ^ are similar to those quoted for the activation energy. The frequency factor, A , , is used in the determination of the e n t r o p y , A S , ' according.to the equation A = >^e(^)e ^R- (33) •"16 >o where K is the Boltzmann constant = 1.381 x 10~ e r g / ^ C T c is ,the coalescence temperature = 4 6 3 ° K -27 h is the Planck's constant = 6.624 x 10 e rg . sec . R is the gas constant = 1.98 c a l / ° G / m o l e . and V , t h e transmission coefficient = 1. 42 TABLE IV N, N- DI METH YINITRO S AMINE COMPARISON OF ACTIVATION PARAMETERS AH*' A S * REF 21.9 -3,92 21.0 -2.93 18.8 -10.9 24.6 1.04 (37) (39) The calculation o f r , off resonance was limited by the narrow 1 pulse interval range over which T 2 could be measured. B) N, N-Dimethylcarbamyl Chloride: The equations derived in the Bloom, Reeves and Wells theory |2&! are tested experimentally by conducting Carr-Purcell spin echo measurements on the protons in dimethylcarbamyl chloride. In this study an attempt has been made to minimize the effects of errors by carrying out the measurements over as large a temperature range as possible. DMCC has a boiling point of 165°C. The results reported here were obtained over a range of 129°(-27°C to 102°C) for temperatures above and below coalescence, METHOD U ) Q Short % off Short X on Sinh * off Sinh * on S.S. 40Mc S.S. 60Mc A 6.04 x 10 1.00 x10 1.13 x 10 1.20 x 10] 0.7 x 10 1,6 x 10 . E a 22.9 ±1,7 21.9 ±1.6 19.7 -± 3.4 25,5 ± 2.5 23.0 25 ± 5 43 All measurements for this compound were carried out at 40 Mc./s. At each of the temperatures, 1/T2 was measured as a function of?f -pulse spacing. At least 16 pulse separations were used ranging from 1.0 milliseconds in the limit of rapid pulsing to 0.4 seconds. The chemical shift between the two methyl groups has been measured in our laboratory as 11.0 c s . at 100 M c / s . at -20°C where the effect of exchange on the chemical shift is negligible. This chemical * shift corresponds to a modulation period of 227 milliseconds. Since T 2 is approximately 50 milliseconds no modulations appear on the free induction tail for DMCC. Carr-Purcell trains were recorded using the same method as reported for DMNA. (i) The Calculation of 'r^: The rate constant k and chemical shift UJ between the methyl groups may be obtained from the observed dependence of T 2 upon the TT-pulse spacing according to equation (23). In figure XVI, ln 1 / T ^ Q p y is plotted as a function of ln 1/2^ from -27°C to + 102°C. The coalescence temperature for DMCC is approximately 50°C at 40 Mc./s. The curves follow the general shape predicted by Gutowsky (30). At -27°C chemical exchange effects are virtually absent and the value of T 2 is independent of the pulse repetition frequency. As the temperature increases, chemical exchange effects occur. If a nucleus I / o 4 4 jumps from site A to site B, i t s precessional frequency changes from tO to LL) k and the dephasing rate of the nuclear moments changes. In the limit of rapid pulsing, the value of l / I ^ approaches 1/T° in the absence of exchange since the dephasing as a result of the exchange i s n e g l i g i -ble. When the T) -pulse spacing i s large, a l l of the nuclei involved in the exchange w i l l have transferred between A and B many times between pulses. As a result i n this l i m i t , the curve approaches the linewidth in the exchange broadened steady state spectrum for the fast exchange li m i t . The computer program, BESFIT, was used to derive the values of k and UO on the basis of t r i a l values of the rate constant and chemical shift. Trial values were normally selected from measurements in the limit of slow and rapid pulsing. The proton spin echo determina-tions for these parameters are l i s t e d i n table V. In the slow exchange region the values of k and U) were ea s i l y determined. At higher temperatures however the convergence limit was altered in order to fit the experimental data. 45 TABLE V N , N-DIMETHYLCARBAMYL CH'LORIDE 1 • 2K' "BESFIT" TO r1 = M-^W) s i n h _ 1 F TEMPERATURE k \jj ° C sec--'- r a d . / s e c , -27.0 0.99 13.7 -24.0 1.08 17.6 -17.0 0.65 13.8 -0.50 0.86 13.8 6.50 1.42 13.8 22.5 3. 54 13.7 27.8 6.41 13.7 38.3 9.59 13.7 43.0 17.4 16.6 48.2 27.2 16.3 53.5 40.0 16.2 57.9 58.5 17.5 62.8 73.3 16.3 65.5 83.2 16.4 76.0 113 14.1 95.8 349 10.3 4 6 (ii) Limiting Cases: There are certain aspects of equation ( 2 3 ) in the limits of slow and rapid exchange which are of interest in this investigation. It follows from equation ( 2 7 ) that a plot of 1 / T 2 ( Q p ) a s a I u n c t i o n of (U)^) gives a straight line whose slope is an approximate measure of the rate constant for the transfer process. The results for DMCC are illustrated in figure XVII. In order to avoid crowding of the points in the limit of rapid pulsing, the values of 1 / T 2 ( Q p ) are plotted without scale and the temperatures are vertically displaced on the diagram. For each of the lines, the correlation in the least squares analysis between 1 / T 2 ( Q p ) and (U)rt)2 up to 7 2 . 4 ° C is better than 0 . 9 6 . These results used in figure XVII fall within the limits of k^^O, U ^ ^ l . Equation ( 2 7 ) is applicable in the slow and fast exchange region. The rate constants derived from the least squares fit to the straight lines are presented in table VI. For very rapid exchange (k^ lO ) and a large TT -pulse spacing, equation ( 2 8 ) . may be used as the limiting expression to derive the rate constant. The chemical shift, was obtained from steady state measure-ments. The calculated rate constants are presented in table VI. For comparison purposes' results obtained for this molecule by Allerhand and Gutowsky ( 2 9 ) are also presented. His results have been calculated from Carr-Purcell proton spin echo measurements made at 2 6 . 9 Mc./s. for the pure liquid. TABLE VI 47 N,N-DIMETHYLCARBAMYL CHLORIDE  RATE CONSTANTS TEMPERATURE SHORT V REF. (29) LONG ~°C r^lkOOft r{ =UJ2/2k -27.0 2.25 -24.0 1.35 -17.0 5.64 -0.50 1.80 6.50 2.40 22.5 5.28 26.5 5.3 33.0 10.3 5.1 38.3 15.3 10.0 43.0 21.8 11.8 47.0 13.0 48.2 32.9 19.1 53.5 39.0 27.5 28.7 57.9 57.5 34.7 60.0 40.0 62.8 76.1 47.3 65.5 112 53.4 72.4 152 92.0 83.7 76.0 200 108 79.0 138 82.8 152 131 90.4 258 95.8 348 102 476 In table VI values of the rate constants in the l o n g ^ limit could only be obtained above 48°C since q is derived from the linear part of the curves in figure XVI. Gutowsky (29) has investigated chemical exchange in DMCC over a 52° temperature range. His rate constant 48 values are in good agreement with the results presented here in the limit of slow pulsing. o (iii) T 2 and Tj Data: The contributions to the steady state apparent linewidth for a molecular system in which nuclear transfer occurs are given by the following parameters: 1 1 . 1 , 1 r n ^ m O r p 1 m L2 2 i • 2EX (34) T° is the nuclear transverse relaxation time in the absence of exchange. Instrumental contributions to the linewidth are given by l / T ; , , and 1/T 2EX includes the exchange effects. 1/T2° i s r e l a t i v e l y small for protons in liquids compared to l/T^' s o that the measurement of the natural relaxation time using steady state methods is quite restructive. Removal of 1 / T 2 is made possible by observing the dependence of the measured T 2 as a function of pulse separation. In this regard an accurate measurement of T 2 ° should be possible using the spin echo method. In liquids molecular rotation and diffusion take place rapidly. Following the assumptions of Brownian motion, Bloembergen, Purcell and Pound (4) have calculated that T ^ and T 2 ° are approximately equal when 2Tt~^ J T ^ .^O where ^  is the correlation time and is a measure of the time of local field fluctuations. 49 The temperature dependence of l / I ^ 0 for the protons in DMCC is illustrated in figure XVIII. Values of T 2° were obtained from the short ^ limit approximation at (u)^) = 0 and from the extrapolation of the curves in figure XVI to the limit of fast pulsing. At several temperatures Tj was measured from the amplitude decay of the free induction tail in a o 180-90 two pulse experiment. From the slope of the line in figure XVIII, the activation energy, A.E v^ g, for motion in the pure liquid may be obtained from the equation * l = Aexp(AE v i £/RT) (35) where T£ is the viscosity coefficient and ^  cJ- ^  C°^T~ ' From a least squares fit to the line in figure XVIII, the energy of activation is 1.70 Kcal./mole. For comparison purposes A E v. g for CHC1 3 is 1.76 Kcal./mole. In table VII a comparison of T 2° with the values reported by Allerhand and Gutowsky (29) is presented. Unlike dimethylnitrosamine which exhibited an unusual T° temperature dependence, T2° for DMCC increases from 2.7 seconds at -27.0°C to 10.3 seconds at 102°C. 50 TABLE VII T E M P E R A T U R E D E P E N D E N C E OF To TEMPERATURE T° T°(Ref 29) °C SEC. SEC. 26.5 6.2 4.5 33.0 6.8 5.7 38.0 6.8 6.2 42.5 7.4 5.6 47.0 7.6 8.0 54.0 7.6 8.6 60.0 8.9 9.0 71.0 9.8 9.3 79.0 10.3 8.8 (iv) Activation Parameters: The temperature dependence of the rate constant for dimethylcarbamyl chloride is illustrated in figure XIX. For comparison purposes the rate constants are plotted as a function of temperature for the two limiting cases in the regions of slow and rapid pulsing. Rate constants obtained from the best fit to equation (23) are also included in the diagram. 51 I n t a b l e V I I I t h e a c t i v a t i o n p a r a m e t e r s a r e l i s t e d . A l l v a l u e s o f E_, a n d A w e r e c a l c u l a t e d f r o m t h e l e a s t s q u a r e s l i n e . T h e a • - l r -k e n t h a l p y , A H ' , ' a n d e n t r o p y , S , w e r e c a l c u l a t e d i n t h e s a m e m a n n e r a s d e s c r i b e d f o r d i m e t h y l n i t r o s a m i n e „ T a b l e V I I I c o n t a i n s v a l u e s o f t h e a c t i v a t i o n p a r a m e t e r s r e p o r t e d f o r D M C C b y R o g e r s a n d W o o d b r e y (34) u s i n g h i g h r e s o l u t i o n m e t h o d s . I n c l u d e d a s w e l l a r e t h e s p i n e c h o r e s u l t s o f A l l e r h a n d a n d G u t o w s k y ( 2 9 ) , T A B L E V I I I N , N - D I M E T H Y L C A R B A M Y L C H L O R I D E A C T I V A T I O N P A R A M E T E R S M E T H O D A A S * R E F S P I N E C H O 1.03X1011 1 4 . 0 ± 0 . 7 1 3 . 3 - 1 0 . 3 -S P I N E C H O 11 1 .16x10 1 4 . 4 + 0 . 9 1 3 . 7 - 1 0 . 0 -S P I N E C H O 4 . 2 8 x l 0 1 0 1 3 . 6 ± 1 .1 1 2 . 9 -11 .9 -S P I N E C H O 7 . 9 0 x l 0 1 0 1 4 . 0 ± 0 . 9 1 3 . 3 - 1 0 . 5 (29) S . S 7 2 . 5 0 x 1 0 9.7+0.5 - - (29) S . S 1 . 3 0 x l 0 6 7 . 3 + 0 . 5 (34) I n t a b l e V I I I A H * a n d h S*are e v a l u a t e d a t 3 - 2 6 ° K . S t e a d y s t a t e c o m p a r i s o n m e a s u r e m e n t s w e r e o b t a i n e d f r o m t h e i n t e n s i t y r a t i o s o f t h e s i g n a l s . A n H A - 1 0 0 t e m p e r a t u r e s t u d y u s i n g t h e c o m p l e t e t h e o r e -t i c a l l i n e - s h a p e f i t f o r D I ! C C i s p r e s e n t l y i n p r o g r e s s i n o u r l a b o r a t o r y . 52 In the spin echo study of DMNA and DMCC the rate constant is the important parameter. Errors in the exchange rate, k, are considered to be + 15%. Chemical shift values are reported to within •+ 5%. An attempt was made to accurately measure T 2 in the Carr-Purcell experiment. The accuracy of T 2 measurements was poorer for DMNA at higher tempera-tures. Since the determination of T° involves an extrapolation in the limit of fast pulsing an error of + 10% is claimed. The ^"PaLs 6 repeti-tion period was measured throughout the experiment with a Hewlett-Packard counter. Values of 2 ^ are accurate to better than 1%. 53 D I S C U S S I O N CHAPTER IV The hindered internal rotation about the N-C and N-N bonds in DMCC and DMNA is an exchange process which has previously been studied by high resolution N.M.R. (34,37 ,39). For DMCC, determinations have been made by independent workers for the activation energy, E^, a which range from 7 to 14 Kcal/mole. In each case the error is approxi-mately ±1 Kcal/mole and the analyses only account for random errors. Previous studies measured the exchange rate over a narrow temperature range in which case systematic errors could not be detected or were not considered. The effect of systematic errors may be very serious and could result from false assumptions in the treatment of the experimental data. In this investigation the spin echo method has been used to study exchange processes in two molecules. It is felt that this method could serve as an independent check on steady state measurements of rate constants. Only when both methods agree could a satisfactory set of data be established for the rate process. A) Experimental Consideration: The proton T^  values for DMNA were obtained from two experiments differing only in their method of eliminating accumulated error in the width of the 180 pulses. Both methods have the advantage of simplicity in operation and a slight improvement in the apparent signal to noise ratio was noted using the off resonance method of Wayne, Zamir and Strange (51). However, by working on resonance and using the 90° phase shift (49) the range of pulse intervals over which could be measured was extended. The Meiboom-Gill modification has generally been accepted as adequate in preventing errors and instabilities in the r.f. pulse widths from not becoming cumulative in their effects upon the echo amplitudes, but does introduce problems of radiation damping (53) in common with adiabatic fast passage (3). All spin echo measurements were made at 40 Mc./s. In the investigation of the two molecules it is possible that systematic errors resulted from inhomogeneities in the H^ field. The H^ field homogeneity could be improved by placing the sample in a tube specially designed so that all of the sample rests in a spherical bulb at the end of the tube. The sample tube is then lowered slowly into the probe while observing the signal following the 180° pulse. The elimination of the decay signal insures that the sample is located in a homogeneous Hj field. Random errors result from the measurement of 1^ i n ^ e Carr-Purcell experiment. The exponential decays are measured directly from the photographs by plotting the logarithm of the echo amplitude as a function of time. In attempting to investigate the accuracy of T measurements, baseline adjustments are important. A deviation of 1% in the baseline could introduce an error of 5% in the value of T2« The use of a high speed recorder and a logarithmic amplifier would be advantageous to the measurement of T^. Digital averaging.techniques could be used to eliminate random but not systematic errors. In these experiments the resonance condition was fairly difficult to maintain in the homogeneous H Q field. Small magnetic field drifts even over five minutes necessitated readjustments. The choice of diode or phase sensitive detection does not affect the magnitudes of the echoes in the Carr-Purcell train. Using diode detection, the echo envelope is predicted to be slightly more complicated (28). Ideally then reproducible Carr-Purcell trains could be obtained by stabilizing the magnetic field with a field frequency lock system. As such there would be strict adherence to the resonance condition and the echo decay could be phase sensitive detected. Experimentally at the present time this is a difficult procedure. When the barrier hindering a simple internal rotation in a 4-molecule is ^ 15 Kcals, then assuming AS = 0, the rotational isomers usually have distinguishable high resolution N.M.R. spectra at room temperature. In the spin echo method however, nuclei within 7J of. the exchanging nuclei w i l l interfere with the observation of the exchange effects. In this regard selective site pulsing would be possible by decreasing the power of the H, field. However the necessary compensating^ feature is the resultant increase in the pulse width required o to maintain the 90-180 Carr-Purcell condition (58). In this case ca lcula -tions have been made which show that calculated curves for a rate of 5 -1 10 sec. indicate that errors of as much as 10% would result from the assumption that t w = 0, where t w is the pulse width. B) Sensitivity of the Rate Constant and Activation Parameters to Systematic  Errors: The importance of systematic errors in the spin echo method is indicated by the comparison of the rate constant data and the activation parameters presented .for D M N A and D M C C . In table IV the activation energies for the barrier to internal rotation in D M N A are . in good agreement within the quoted errors. The values of the entropy of activation range from -3.92 e . u . to +1.04 e . u . The reported value of A s = -10.9 e . u . for the off resonance dependence of T^ upon pulse spacing is not considered to be significant in light of the limited range of pulse intervals available. For the hindered internal rotation in these systems the entropy of activation is expected to be approximately zero, since there is little change in the degree of randomness of the activated complex. Assuming that A- S is zero and 1 13 hence calculating the frequency factor from K T / h to be approximately 10 sec, \ the activation energy E a can be calculated from the Arrenhius equation. At the coalescence temperature which for D M N A is 463 °K 57 the rate constant k i s calculated from k = (36) where A^ i s the chemical shift between the methyl groups i n c./s. For DMNA k T = 67.1 sec. and substituting into the Arrenhius equation c the activation energy i s 23.6 Kcal./mole. . For DMCC at i t s coalescence o -1 temperature of 326 K k =9.79 sec. and E a = 18.1 Kcal./mole.. How-c ever consistently low values of the entropy averaging -10 e.u. are report-ed for DMCC. It i s apparent that these low entropies result from systematic errors. The steady state measurements of Gutowsky (29) and 6 7 —1 Rogers (34) report frequency factors i n the region of 10 to 10 sec. It i s clear that these abnormal frequency factors must be regarded with suspicion. In the spin echo method the value of k i s determined from the complete dependence of T 2 upon pulse repetition period. Normally the steady state measurement of the chemical shift in the absence of exchange-effeqts i s used. As such k can be determined over the entire exchange region. The intercept of the line at infinite temperature L = 0. i n the 7 T Arrenhius plot can be used directly to calculate the entropy of activation at T from the equation (37) i t r- KT -A.S^= 4.5:7'Qog10A - 0;.4335 - loq{--~ For high-resolution studie's the calculation of AS i s s l i g h t l y more complicated and caution i s required i n the evaluation of the frequency 58 factor "A. In the slow exchange region, the intercept to log k of the Arrenhius line is the frequency factor. In the fast exchange region the frequency factor no longer corresponds to the intercept but is modified by the chemical shift term. The transverse relaxation time is given by: W H E R E : J - =TTA9 1 / 2 p , p, are the fractional populations in the exchange sites, a D For equal populations, i i ^ A - ^ B ) 2 T T ^ A - ^ B ) 2 T 2 T^ 8 k 2 k (39) so that the frequency factor in the fast exchange region is given by: ir2[-i>A-)>B)2 m 2 x (intercept) from which the calculation of A s is straightforward. The plot of log k as a function of 1/T is usually linear. From the slope of the line the activation energy is calculated. However, Gutowsky has stated (46) that this value of E g represents the apparent activation energy which is a composite quantity including not only the true activation energy but an additional term o{ which might impart a slight temperature dependence of the activation energy itself. This then is a systematic error which w i l l also change the frequency factor from A to A1. The Arrenhius equation takes the form: 58 k 1 = A'expl^-(E a+0O/RTJ (41) and k 1 i s the apparent rate constant. From the T 2 spin echo measurements, the most difficu l t regions to accurately f i t the experimental data are i n the very slow and very fast exchange regions. Assume then at the coalescence temperature T , the apparent and true rate constants are approximately equal. On this basis it i s seen—that a - systematic error w i l l add the term (&(/T c) to A S. In the two compounds studied the coalescence temperature of DMNA i s 190°C compared with 50°C for DMCC, It i s conceivable that such a systematic error as described could account for the consistently low values of A S7^ reported for DMCC. For both compounds the spin echo results appear to be converg-ing on the "correct" value of KT/h for the frequency factor. However, the consistently low frequency factors obtained from the steady state method i s indicative' of systematic .instrumental errors i n addition to 1. • " -random errors i n the measurement. By observing the dependence of the measured T 2 as a function of pulse repetition frequency it i s possible to eliminate the instrumental contributions to the linewidth given by l/T^-The p o s s i b i l i t y of saturation broadening (3) of the resonance line intro-duces a Systematic error i n the steady state method, but this can and usually i s avoided. For high resolution studies H p and T° are small enough so that saturation effects to the line shape w i l l be negligible. For 0 o a fixed H, f i e l d saturation broadening depends upon T. and To which are 59 of course temperature dependent. As a result saturation w i l l vary-throughout the temperature range of the investigation. In the spin echo method molecular diffusion processes w i l l reduce the apparent value of T^ . The extent to which the decays are attenuated depends upon the temperature and the pulse repetition frequency. In the Carr-Purcell experiment diffusion effects are minimized when the pulse spacing is small. In table III the rate constants for DMNA are listed for the on and off resonance experiments and compared to the steady state values of Reeves and Wells. At lower temperatures, where exchange effects are virtually absent, agreement in the values of k for a l l methods is satisfactory. At approximately 160°C, the values of k measured off resonance are slightly greater, until at 192°C k = 2k ,. The oil %> on vu0 off resonance dependence of T 2 was measured only over a narrow range of pulse intervals extending from 1.0 to 10.0 milliseconds. DMNA was studied only, in the slow exchange region up to approximately 190°C. In this region the fact that the values of k are rather high compared to the on resonance and steady state values indicates that the observed T 2 is too short. Since the rate constants are consistently high both in the limit of rapid pulsing and for the complete fit to the experimental data, the off resonance method of measuring T 2 suggested by Wayne, Zamir and Strange (51) appears to be affected by a systematic error which attenuates the Carr-Purcell decay. Molecular diffusion processes w i l l introduce a systematic error in the 60 measurement of T 2 . However, diffusion effects w i l l be more pronounced at higher temperatures i n the fast exchange region. In table III there i s good agreement i n the rate constant data between the A-60 results ob-tained by Reeves and W e l l s and the complete fit to the on-resonance spin echo measurements. Further, the activation energy and the entropy value of +1.04 e.u. obtained by the spin echo method i s i n good agreement with the energy of acti v a t i o n for DMNA corresponding to A S = 0, D M C C was investigated by the spin echo method from the slow exchange region where at -27°C exchange effects are v i r t u a l l y absent up to 102°C where k>\(jO- The rate constant data i s presented in tables V and VI. In the limit of slow pulsing (r^ = {JJ /2k), the values of k were c a l c u l a t e d from r^ which was measured dir e c t l y from the linear portion of the ln 1/T 2 versus ln 1/2^ curves i n figure XVI. In table VI it i s noticed immediately that the values of the rate constant for large pulse spacing are approximately one half of k derived from the short ^ limit e x p r e ssion. If H i s large compared with k a l l of the n u c l e i w i l l have exchanged many times between pulses and steady state conditions are 'approximated. In this region it i s apparent that there i s the p o s s i -b i l i t y of a systematic error introduced because of d i f f u s i o n e f f e c t s . As a result , T 9 i s decreased and since -=^o( 7- the value of k i s l e s s than L T2 k the "true" rate constant for the exchange. Rate constants measured i n the short ^  l i m i t ' agree favourably with the values of k obtained from the complete dependence of 1/T 9 upon the pulse i n t e r v a l . It i s interesting 61 to note that the rate constant data of Allerhand and Gutowsky (29) agree only with our spin echo results reported for the long H l imit . In their paper (29), results are reported in detail for N , N-dimethyl trichloroacetam-ide and in each section only the final results and no dependence diagrams are illustrated for D M C C . In light of the agreement with our spin echo results added to the fact that Allerhand and Gutowsky have i worked in relatively inhomogeneous H Q 5 msec.) fields, it i s suggested that diffusion effects have contributed to reducing their values of k for the exchange process. - 4r F o r'AS - = 0 , the activation energy for D M C C is 18.1 Kcal/mole from equation (36) and the Arrenhius equation. The reported values of E Q all agree within experimental error. However the low frequency factors of / " ^ l O ^ lead to values of A S which average at r*> -10 e . u . Previous high resolution studies of the hindered rotation in D M C C (29,3-4) 7 6 reported frequency factors of 10 and 10 . The spin echo results reported by Allerhand and Gutowsky (29) extended over a temperature range of 5 2 ° which makes it slightly more difficult to detect systematic errors. An HA-100 temperature study of D M C C is in progress in our laboratory. It is hoped that a full theoretical line shape fit to the experimental data wi l l converge on the true rate constants for the exchange process. The spin echo method represents an interesting technique for the study of hindered rotation in D M C C . There has been considerable discussion of the experimentally determined entropies of activation and at this time this should s t i l l be considered as an unsolved experimental problem. DMCC and DMNA were suitably chosen for this spin echo study as they differ in chemical shift between the methyl groups and they can be studied over non-overlapping temperature regions. The results derived from the two compounds have indicated the importance of considering systematic errors in the evaluation of the activation para-meters. The limiting expressions in the BRW (28) theory provide a simple experimental verification of the theory and provide an estimation of the rate constants and activation parameters. However, the informa-tion content of the 1/T2(C.P.) v e r s u s l / 2 l > curves is more exact providing a large range of pulse intervals are used. In attempting to obtain the best fit of the experimental data to the equation r x = k - sinh" 1 F (23) no problems were encountered in fitting the data in the region where u J ) k . This was the case for both DMNA and DMCC. DMNA could not be studied above coalescence. For DMCC it was difficult to fit the data properly in the fast exchange region. This was due in part to the choice of initial trial values of k and u) . For k^ L O , the convergence limit to the best fit of the experimental data had to be changed in order to compute a value of k andU) . In general for DMCC, the computed rate constants have converged on values which are lower in the fast exchange region, than the experimentally determined values of k from equation (28). The chemical shift for a two site system undergoing exchange can be determined from the l/Tg versus 1/2^ curves as the chemical shift term (jj appears in equation (23). From table V it is seen that the values of uJ correspond to the chemical shift value reported for DMCC by the steady state method. Above the coalescence temperature the values ofu) become appreciably larger. If systematic errors in the spin echo method tend to make l/Tg too long, then in the fast exchange limit, substituting trial values into equation (23), the chemical shift is too large. Since the computer program varies k as well as u) in order to obtain the best fit to the experimental data, the high values of may result from a systematic error in the temperature dependence of the rate constant. The chemical shift itself is probably temperature insensitive, and in any case it would seem fortuitous if any temperature dependence of UJ occurred only above T c which has no special significance from the point of view of chemical structure. As a result the value of u) from the low temperature high resolution spectrum is considered as acceptable. Allerhand and Gutowsky (46) have encountered similar problems in attempting to fit experimental spin echo data in the fast exchange region. In their study of cyclohexane and cyclohexane-d^, at lower temperatures k, lO and l/T^ could be determined. As the temperature was increased the natural relaxation time could no longer be determined and in the region where k ^ u ) • an assumed value of u) was used. As 64 yet unpublished results by Reeves has investigated the chair-chair isomerization of cyclohexane. A careful HA-100 high resolution study investigated the exchange over approximately 100° in small temperature increments. The reported activation energy is 12.1 Kcal/mole from line-width studies. This is higher than the previous values reported by Gutowsky (46) and Anet (44,45). Most important, the frequency factor 14 -1 is 1.15 x 10 sec. corresponding to an entropy of activation of +4.4 e.u. Once again attempts to fit the spin, echo data in the fast exchange were not conclusive. However, these results are indicative of the fact that systematic errors limiting previous high resolution studies are further minimized at higher frequencies. o The temperature dependence of , the natural relaxation time is illustrated in figure XVIII for DMCC. The extrapolation of the line to (CO^ty)2 = 0 in the short "7^  limit plot (figure XVII) gives values of T^ which are in good agreement with the results obtained from the complete o T 2 dependence upon pulse repetition frequency. Incorrect values of T 2 w i l l introduce an error factor in the determination of the rate constant. It is conceivable that such an error will affect the values of k and U_) in the fastest exchange region. In regions below this, the exchange o contribution to l/T 2 is much larger than 1/T2. The range of rate constant measurements using the spin echo method is limited by the upper tempera-ture limit of 1/T^ according to the equation It is noteworthy to mention at this point that one of the most careful studies involving the measurement of the spin lattice relaxation time has been done by N. J. Trappeniers (54, 55,56), His experiments involved the use of the pulse method to measure in polymers and to establish a "spin relaxation phase diagram" in methane and deuterated methanes. Mehlkopf and Smidt (57) have described their spin echo attach-ment to a steady state 60 Mc./s. spectrometer. They indicate the o possible errors which are introduced for incorrect adjustment of the 180 pulse and they describe a method for eliminating field drift effects. C) Comments on the Spin Echo Method: The spin echo method represents a fairly well-established tech-nique for measuring rate constants. Most important it introduces an independent means of verifying high resolution experiments. The spin echo rate determinations not only include the regions available to the high resolution method but extend the measurement to faster rates. All measurements in this investigation were carried out using an r.f. frequency of 40 Mc./s. In the fast exchange region the rate is directly propor-tional to the square of the chemical shift so that with an increase in the r.f. frequency above 40 Mc./s. the spin echo measurements w i l l extend the rates to several fold faster compared to the present maximum. The main disadvantage of the spin echo method to date is its lack of selectivity. In particular for exchange studies non-exchanging nuclei within a range of have to be selectively deuterated. The rate constant data is obtained from the complete dependence of T 2 upon pulse interval. Approximate expressions in the limit of slow and fast pulsing represent an internal check on the rate constant data. High resolution rate constant measurements are limited by the effects of inhomogeneous fields which broaden the signal. The spin echo method has the advantage of extending beyond this region by rapid pulsing in the Carr-Purcell experiment. Further, effective heteronuclear decoupling occurs in the spin echo method where the exchange signals are modulated equally in the transfer sites. Nevertheless it is important to recognize that systematic limitations do exist in the spin echo method. This study is an attempt to minimize systematic errors. Many papers in the literature discussing N.M.R. rate measurements must be read with caution if abnormal frequency factors are reported. The "true" values of rate constants in magnetic resonance should be the result of a spin echo investigation extending over as wide a temperature range as possible in addition to a high re-solution study which includes a complete theoretical line shape fit to the experimental data. We should look forward to the time when a single hindered barrier has been studied by: (a) Carr-Purcell measurements of T 2 in comparison to full line shape calculations of high resolution spectra preferably in a f i e l d frequency locked mode, and (b) the double resonance method (59) compared to studies by the rotary echo method In the very slow exchange region (60). 6 8 B I B L I O G R A P H Y 1. F . Bloch. Phys. Rev., 70., 460 (1946) 2. I. I. Rabi, N . F . Ramsey and J. Schwinger. Rev. of M o d . Phys. 26, 167 (1954) 3. "High Resolution Nuclear Magnetic Resonance Spectroscopy". J. A. Pople, W . G . Schneider, H . J . Bernstein. M c G r a w - H i l l , (1959). 4. N . Bloembergen, E. M . Purcell and R. V. 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