ISSN:0301-5696    

DOI:10.1039/FS97813FX001

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Pulsed Nuclear Magnetic Resonance in Solids A Survey" BY ERWINL. HAHN Department of Physics University of California Berkeley California 94720 U.S.A. Receiued Jamary 27t11 1979 am grateful to the Faraday Division and Professors Toinpkins and Smith for the opportunity to speak on this occasion and to meet again with my European colleagues. A review of the progress of the whole of pulsed n.1n.r. techniques is a difficult task. The best I can do is treat certain highlights savour the essentials as one would at a gourmet smorgisbord and tell you mostly about things you already know. The flurry of papers I received in the mail to review indeed confirms the current high level of activity in this field. The conference research papers on the whole seem to have resulted from two kinds of pulse techniques (1) high resolution (homo-nuclear) and (2) double resonance (hetero-nuclear).Table I lists the kinds of measurements made by these techniques TABLE 1 .-FIVE CLASSIFICATIONS OF MEASUREMENTS BY PULSED N.M.R. IN SOLIDS TECHNIQUES high resolution (homo-nuclear) double resonance (hetero-nuclear) MEASLJREMENTS systematic T, T,przc self-diffusion motional rotational (classical) relaxation chemical shift tensor partial orientation structural studies n.q.r. spectroscopy tunneling (non-classical) spin polarization torsional spectroscopy (SPOTS) pulsed multi-photon spectroscopy in five separate classifications. The trends of pulsed n.m.r. research are guided by how kind or nasty Mother Nature can be.Nuclear magnetic interactions are suffi- ciently weak that magnetically coupled spin ensembles are often virtually isolated from outside perturbations because of motional narrowing effects caused by rapid fluctua- tions of local fields. Nuclear spin lattice relaxation time constants TI have been conveniently long in the jts to hour range such that primitive r.f. pulse methods could begin to make headway in the early stages of n.m.r. research. In quantum optics today * Since reference is made to work of researchers in the various papers of this symposium these references will not be given in this discussion. PULSED N.M.R. IN SOLIDS there is a corresponding pulse transient study approach analogous to that of n.m.r. However the time scale requirements of -s for laser pulses is much more stringent.If Mother Nature produces random pulses we can improve upon her by applying more pulses of our own or extra ones where Nature fails us to make a solid look like a liquid from a dipolar interaction point of view. Even in solids Nature causcs some narrowing of the n.m.r. spectrum as in the case of Ag in AgF (where the F-F interaction rate exceeds the local static Ag dipolar coupling inter- action) or during the onset of phase transition rotations in organic solids. Motional narrowing is signified by the relations z < (Amdd)-' or J> <Amdd) in exchange processes where T is the lattice fluctuation correlation time J is the spin exchange rate and (hcodd is the static dipole-dipole coupling parameter.Nature teaches us a lesson also in enabling us to realize double nuclear resonance coupling between two different nuclear ensembles that have finite magnetic heat capacities. The formalism in dealing with this problem is very much the same as in spin-lattice 7',theory where the phonon-heat bath is assigned an infinite heat capacity. Nuclear double resonance is distinguished by the need for tricks with various r.f. pulse schemes that bring the two spin-species into speaking terms with one another. A recent exciting development called Spin Polarization Torsional Spectroscopy (SPOTS) reported here by Pintar and his group is a novel cross-coupling effect in which the torsional degrees of freedom of the lattice exhibit a finite heat capacity and show a sharp resonance coupling to the proton spin system in the rotating frame of reference.HIGH RESOLUTION (HOMO-NUCLEAR) PULSE METHODS By intending to be comprehensive fig. 1 is perhaps more bewildering than informa- tive in showing how various techniques connect with the kinds of n.m.r. measurements pursued in solids. A certain procedure with pulses can measure or perform more than one thing at the same time very much like the circus acrobat shot out of a cannon who plays the violin at the same time. The blocks on the left and right arranged in columns show in historical sequence as well as in developing complexity the important pulse schemes for homo- and hetero-nuclear studies. The centre column and the connect- ing lines to then1 show roughly the measured effects as they relate to the various pulse schemes.First let us consider the homo-nuclear pulse techniques listed in the left column. The first block pertains to single and paired pulse sequences which create superposition states. However here the interest is in the diagonal population ele- ments which are suddenly and initially prepared at non-equilibrium with respect to the lattice. The signals which appear directly after such pulses therefore allow for Fourier transform spectroscopy and spin lattice relaxation measurements. The particular case of dipolar order preparation introduced by Jeener (lr/2-n/4 sequence) is included as well. The next block relates to the use of delayed echoes and their capability in measuring TI self-diffusion line shapes etc.In the following development of multiple pulse techniques for dipolar field averaging we see that the basic idea of Hamiltonian averaging first applied to external inhomogeneous static fields in liquids begins to emerge in a fashion which is repetitive or cyclic. The principle of precession phase reversal displayed by the simple Z/~-T-Z spin echo is extended by the Carr-Purcell sequence as seen from fig. 2. Meiboom and Gill added the subtle feature of the 71/2 r.f. field modulus phase shift to eliminate cumulative errors in the lr pulse sequence which follows the initial n/2 pulse. Com-binations of magnetization and r.f. field (phase) rotations have been introduced by Mansfield and by Waugh-Huber-Haeberlen (see the WAHUHA sequence for ex- ample) for dipolar averaging in solids.Such pulse sequences transform dipolar E. L. HAHN 9 PULSE METHOD INFLUENCED MEASURED DOUBLE RESONANCE (HOMONUCLEAR) EFFECTS METHOD(HETERONUCLEAR) OVERHAUSER kyklDS{ -DYNAM IC NUC. POLAR. K2 SPIN ECHO DOUB. RES. \ TORSIONAL TUNNELING MULTIPLE \ SPECTRA, QUANTUM RELAXAT ION (COHERENCE \ ABUNDANT B SPECT. TRANSFER) \r NQR SPECTRA 17~,14N,~ PURE D p%K-y\ SPINNING NQ R I POLARIZATION y: ENHANCEMENT -RARE B SPIN SPECT. DECOUPLING (A SPIN i SATURATION) INTRA-MOLEC. i DIPOLAR COUPLING I I A-A SY STE11s A-B I FIG.I .-Pulsed (homo-nuclear) and double resonance (hetero-nuclear) methods and the effects they measure. Rot,,,; Lab,, denote rotating and laboratory frame coordinate systems in which A or B spin ensembles are defined.Dip Rot and Dip Lab pertain respectively to dipolar ordered A spin system in the rotating frame (in high magnetic field) and to the dipolar order B system in zero mag- netic field. SLDR and ADRF denote Spin Locked Double Resonance and Adiabatic Demagnetiza- tion in the Rotating Frame. PULSED N.M.R. IN SOLIDS tensor terms from one to another of the x y z coordinates in such a way as to average the entire dipolar interaction to zero over a cycle of pulses. This holds providing one technically achieves the ideal limit of negligible pulse widths compared with the dipolar precession T2time constant. The path taken in precession phase may be in accord with a mirror sequence of pulses in which case the Loschmidt echo scheme is realized; FREE PRECESSION r-“Tl” MEASUREMENT T-TSPIN ECHO 2 7T I WAHUHA! x -xy -yx-xy-yx -xy yx -xy-yx-xy-yx -.....-...T-* ---_-_ 0 t 2t 3t 4tc 5’t FIG.2.-Schemes of pulsed n.m.r. in solids of increasing complexity. All designations &x 4-y imply the direction in which r.f. fields H are applied in the rotating frame. The sequences periodic in t below involve 7r/2 pulses. or the path may be cyclic which does not retrace the forward evolution of phase but nevertheless returns to the initial point by a different return route. In passing we should note that the magic angle mechanical spinning method of Andrew is becoming more popular and 1 have therefore included it as a category in fig.1 because it is often used in averaging techniques along with pulse schemes discussed in some of the symposium papers. One of the most novel and subtle recent approaches to high resolution n.m.r. is the method of multiple quantum n.m.r. transform spectroscopy introduced by Ernst E. L. HAHN and Pines independently. The principle of the method relies upon the transfer of coherence among superposition states which have been reached by multiple quantum transitions only. The " transfer of coherence " implies that an inspection pulse reveals the free precession signal at selection rule Am = -J=1 where the signal itself depends upon multiple quantum transitions involving selection rules Am > 1 created in the past.The levels are placed in coherent superposition states that remain but cannot radiate detectable high multipole fields. These states are excited with equal a priori MULTIPLE PULSE -MULTIPLE QUANTUM SPECTROSCOPY FDOUBLE (AM= 2) QUANTUM ,TRANSIT ION PROBEPULSE (1IM.I) INSPECTION -10) 1-1) FIG.3.-Multiple quantum pulse schemes. The upper scheme yields S(T)amplitude beat at chemical shift frequency 26 for the off-resonance condition 2~0-coI3= 26. The lower sequence is applied for general multiple photon transition n.m.r. spectroscopy. statistical probability upon application of all possible scans of z1 and z2 shown in the lower pulse sequence of fig. 3. The simpler sequence above serves as a means of deuterium chemical shift measurement in solids introduced by Pines and Vega.The extension of this procedure to finite N photon transitions by the n/2-z1-7r/2-z2 probe sequence below reveals the spectrum of proton coupling in intramolecular systems where an N photon transition corresponds to the number of protons which participate and are placed in coherent superposition. With the multi-level system placed into a PULSED N.M.R. IN SOLIDS particular phase superposition state and by exciting all such accessible ergodically allowed states the combined probe pulse Fourier transform analysis of all excitations reveals interactions corresponding to any chosen particular set of excited N protons. Thus for N = 5 in C6H6,a doublet appears. The result is equivalent to a deuterated benzene molecule with five deuterons and the doublet is caused by the remaining lone proton scaled in its splitting of course by a smaller dipole-dipole interaction factor.A characteristic triplet would occur for N = 4 and the deuteration would correspond to four deuterons etc. DOUBLE RESONANCE (HETERO-NUCLEAR ) PULSE METHODS If we look again at fig. 1 the right column deals with hetero-nuclear coupling among A-B spin ensembles often designated as I-S. The functions of double resonance spectroscopy enhancement and relaxation measurements are interconnected by the techniques listed. They are actually variants of one another all intended to measure spins B (or S) of low abundance or even ensembles of high abundance that are in- convenient to measure directly.Antecedent to the pulsed double resonance methods in current use are the con- tinuous wave (c.w.) methods of Overhauser ENDOR and dynamic nuclear polariza- tion. I will indicate that the latter often referred to as the “solide effect ” is actually an off-resonance variant of the usual double resonance scheme in which one system in the lab frame couples to another system in the rotating frame. It is of historical interest to note that the spin echo double resonance method applied in a paper in this Symposium for assessment of second moments of near neighbours in solids is the predecessor of the more sensitive double resonance methods which follow. The spin echo method has a sensitivity limited by T2for the abundant spins whereas the methods of greater sensitivity are limited by the much longer TItime constant.Therefore in the first instance off-diagonal disturbance of phase accounts for the perturbation by B spin neighbours and diagonal transfer of populations over a long TItime accounts for the success of the sensitive type of double resonance. Fig. 4 shows the comparison between the two kinds of double resonance. We are all generally familiar with the main principle. If we have NB rare spins and NA abundant spins the magnetization change of the A system in one dipole-dipole cross-relaxation contact is given roughly by We take Ns/NA as a crude measure of the ratio of magnetic heat capacities given nearly like magnetic moments for both systems. Since TiA/TABis the number of initial dipole-dipole flip contacts possible in a time TIA and if we desire the condition where n/s is the apparatus electronic signal-to-noise ratio then double resonance is successful if the condition --TIA >” 1 NB NA TAB applies.Fig. 5 and 6 show in succession the various pulse schemes for coupling of the abundant indicator A species to the second B species under investigation. Adiabatic E. L. HAHN SPIN ECHO DOUBLE RESONANCE (STATIC CASE) SPIN LOCKED DOUBLE RESONANCE demagnetization in the rotating frame (ADRF) transfers the dipolar order of the A species to Zeeman order in the rotating frame of the B species. Either the depletion in the A signal may be monitored by an inspection n/4 pulse in the first sequence of fig. 5 or the B signal growth itself may be recorded as shown in the second sequence.Strong irradiation of the A species usually protons decouples the B system (popu- larly 13C)from the A system. The free precession of the B spins its a virtually isolated system is recorded by the Fourier transform method. Population transfer from one rotating frame of the A system to that of the B system is shown in the last scheme of fig. 5. As noted the matching conditions for Larmor frequencies in the respective frames of reference determine the rate and efficiency of coupling. Off-resonance coupling to a B system with higher magnetic heat capacity allows for a larger signal but at a slower rate of population transfer from the A system. Fig. 6 shows in sim-plest schematic form a method for measuring Tlpof a B species and below is shown the basic sequence for field cycling double resonance.Field cycling double reso- nance has gained some popularity for the measurement of 170 D and I4N spectra in powders featured in the researches of Smith Brown and Edmonds. In zero field after adiabatic demagnetization of the proton system. the I7Oresonance creates an 170 6‘ high spin temperature ” reservoir of low heat capacity which couples to the cold proton dipolar order which is monitored as a signal change upon inspection of the proton magnetization in high field after adiabatic remagnetization. In abundant D and 14Nsystems simple schemes of level crossing following the n.q.r. saturation of these species show up as population changes in the proton system after level crossing has occurred.Edmonds has successfully analysed and exploited the n.q.r. of coupled PULSED N.M.R. IN SOLIDS ADRF -SLDR APPLICATIONS A-B DOUBLE RESONANCE 7r POLARIZATION ENHANCEMENT B SPECTRUM DECOUPLING ,,B SIGNAL B SPIN -Tip MEASUREMENT ALONG HIB Y HIA,x AB DECOUPLING FIG.5.-Adiabatic Demagnetization in the Rotating Frame (ADRF) and Spin Locked Double Resonance (SLDR) schemes. deuterium interactions with protons for the determination of structures in a number of organic systems. The spin polarization torsional spectroscopy (SPOTS) investigations of Pintar and his colleagues present a striking example of double resonance coupling of a proton system in its rotating frame with a sharp " lattice torsional resonance " transition in the lab frame.The constraints of spin-rotational coupling degrees of freedom give rise to a variety of possible level configurations depending upon the nature of rota- tional hindrance and molecular symmetries. Without being specific the manifold of I = 1 shown in fig. 7 reveals a Zeeman splitting in the rotating frame. If the rotating frame proton Larmor frequency col matches the condition where +I and -1 levels overlap (in the case shown) a dipole-dipole AM = &2 coupling interaction drives the torsional transition given by uT. Thus the double resonance condition = 42 is to be satisfied. The ordered cold proton reservoir therefore cools down the torsional system and a reduction in proton magnetization is noted in the first sequence for protons SLDR.In the next sequence after the torsional system is cooled by the protons ( after H is turned off) the torsional system relaxes in a time TIT. The torsional relaxation rate is monitored by the extent to which the proton system again couples to the torsional system when H is turned back on. E. L. HAHN TIEp >>TlA MEASUREMENT A SPIN SATURATION FIELD CYCLING DOUBLE RESONANCE AD I A BAT IC L REMAGNETIZATION ADI A 8ATlC 0EMAG NETIZ AT I0N -FIG.6.-A B-spin lattice relaxation time TIBmeasurement scheme (above) in which the A system first provides B spin polarization which subsequently recouples to the A system after it is depolarized by saturation pulses. The scheme compares to the SPOTS relaxation TITmeasurement method shown in fig.7. The bottom sketch indicates the basic procedure for field cycling double resonance. Now we follow up a previous reference to the " solide effect ". This effect is very useful for finding out the location of nearest dipolar coupled neighbours of the A and B species. We refer to fig. 8 and replace A by H which stands for hydrogen. The coupled system is represented here simply by spins I = 1/2 and IH = 1/2 with LC) > wA. The roles of the H and B species could as well be reversed. The viewpoint of product wavefunctions with perturbed wavefunction corrections because of the dipole-dipole coupling term c yields the forbidden transitions at (1iB -wH and wB + wtl frequencies. These transitions correspond to proton signal increase and decrease (possibly inverted) respectively.An alternative viewpoint is to consider the B system (in terms of pseudo-spin 1/2 two levels) as indicated for "0 ''N or D. The B and H systems are visualized as separate reservoirs coupled together by the dipolar coupling interaction and we now invoke the spin temperature hypothesis. The B system driven off-resonance by amount *Act) = uH,is viewed in the frame of reference corresponding to the z' axis of quantization. The effective field along this axis is given by [wh + (yBH,)2]1'2-(-OH PULSED N.M.R. IN SOLlDS "S POTS'I -S PIN P0 LA R I Z A T I 0 N TORSIONAL SPECTROSCOPY M 1 PROTON SLDR SIGNAL SHARP TORSIONAL ,'ORDINARY "TI I' SPECTRAL -2.DENSITY FUNCTION REDUCED SPECTRAL NOISE AT LOW TEMPS w FIG.7.-Spin polarization torsional resonance spectroscopy. The proton SLDR signal shows initial ''Strombotne-Walstedt " transients as a function of HI irradiation time for proton dipolar- Zeeman systems not initially at thermal equilibrium with one another. for wH>yBH,. The component of local dipolar field HLwhich is effective in causing transitions at the proton site at distance YHB away is given by where 0 -Y~H,/co~. With T2 taken as the overall inverse linewidth associated with the double resonance interaction (due mostly to inter-proton dipolar broadening) one obtains the same double resonance interaction rate WHB which is obtained by Fermi's golden rule in assessing the usual " solide effect ".For negative Aw (at CL)~-CO~)the B system is cold and therefore the proton population is enhanced (cooled). For positive Aw (at wB+wH) the proton population is heated or possibly inverted because the B system is at a negative temperature. I conclude by outlining a number of pitfalls and restrictions that arise in the course of carrying out double resonance experiments E. L. HAHN --dW = WH FIG.8.-Identity of " solide effect " quantum level and double resonance reservoir cross-coupling viewpoints. Positive and negative temperatures of the B system correspond to resonance conditions wB -wA and wA + we respectively and input positive and negative polarizations for the protons accordingly. (1) The abundant A system must not have TI relaxation times so long that data acquisition is agonizingly slow.On the other hand if T is too short insufficient sensitivity for detection of the B spin system is a common fate. Temperature cycling irradiation erc. are means by which long T,values can be shortened but it is extremely difficult or impossible to lengthen T, if so required. (2) The experimenter should beware of carrying out double resonance excitations in multilevel systems where a third level is displaced anywhere toward the halfway point between two upper and lower levels. This allows for double quantum transi- tions which can be misinterpreted as bonajde two-level spectra. Even if the third level is far away from the halfway point large intensities of r.f. excitation will never- theless provoke the two-quantum transition quite perceptibly.The phenomenon of harmonic coupling is also a possibility which may be misinterpreted. Here for ex- ample two B spins may flip at the same time providing " two quanta '' which exactly conserve energy for a one-quantum flip of an A spin dipolar coupled neighbour. PULSED N.M.R. IN SOLIDS (3) Nonlinearities in the electronic detection system can mix simultaneous double resonance input signals and therefore create sum and difference signals which may accidentally create resonances and lead to misinterpretations. The warning here is never to apply two signals simultaneously unless one is aware of nonlinearities that may result. (4) In systems with integer spin or in any system where the spin eigenenergy W varies with applied magnetic field H in such a way that dW/dH = 0 the property of “spin quenching ” holds at this inflection point.The spin system is then rather insensitive diagonally in its response to local field perturbations. Double resonance in the rotating frame is very weak or virtually impossible at such inflection points. (5)A current unsolved problem in double resonance is the question of how one should consider nearest neighbour protons for example in detecting 170 when these protons cause a splitting in the ‘’0 nuclear quadrupole resonance spectra. Should these protons be considered part of the entire proton bath which serves as the indicator species or should the localized complex of neighbouring protons coupled to 17Cbe redefined as a new “ B spin entity ”? The remaining more remote proton neighbours serve as the usual abundant reservoir.A difficulty arises in assigning the nearest neighbour protons a spin temperature in common with the rest of the proton bath. Therefore the new “ B spin entity ” seems to be the appropriate choice which poses the problem of defining its effective magnetic moment as it interacts as a unit with the proton bath.

ISSN:0301-5696    

DOI:10.1039/FS9781300007

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Theoretical and Experimental Investigation of Relaxation Processes in Multi-pulse Nuclear Magnetic Resonance Experiments BY L. N. EROFEEV G. B. MANELIS, E. B. FEL'DMAN B. N. PROVOTOROV AND B. A. SHUMM Branch of the Institute of Chemical Physics TT u .S.S.R.Academy of Sciences Moscow U.S.S.R. Received 3rd August 1978 In the last ten years multi-pulse n.m.r. have appeared to be very useful in the study of weak electron-spin interactions and different relaxation processes in solids. However at the present time the theory of multi-pulse experiments (the theory of the average hamiltonian)'.2 possesses a number of serious defects which limit understanding of the physical nature of line-narrowing and leads in some cases to fundamental divergencies with the experimental data.4*6 We note the following defects in the theory of the average hamiltonian.First of all the absence of any strict consideration of the dynamics of spin systems at small times t -T2(T2-IIZdjj-l) in the theory'*2 does not permit one to evaluate the spin density matrix in the quasi- stationary state at t -T2. Because of this additional assumptions on the form of the density matrix,'.2 which in some cases are not justified were inserted into the theory."6 Secondly the theory of the average hamiltonian averages the dipole-dipole interaction or its contribution for the time of cycle 2,.'s2 In this case the effect of local fields on spin motion was not fully accounted for at the times t -T2 3 z during which establishment of the above mentioned quasi-stationary regime usually occurs.A consistent account of the effect on spin dynamics both of the external pulses and also of the local fields leads to the conclusion that the time scale over which the averaging in this problem should proceed is T2 % 7,. Thirdly an important experimental finding is that the exponential character of magnetization damping in multi-pulse n.m.r. experiments was not explained in the theory of the average hamiltonian. Finally the experimental results 4p6 revealed an interesting analogy between the system behaviour in the fields created by the pulse train and in continuous external r.f. fields. This interesting circumstance alone suggests that during construction of a theory of line narrowing in multi-pulse experiments one might apply the main results of the well developed theory of continuous n.m.r.which could not be used in the framework of average hamiltonian theory. It should be emphasized that the system of nuclear spins in the multi-pulse experi- ments is an open system absorbing the energy of external r.f. fields. However the theory of the average hamiltonian describes such a system by a time-independent average hamiltonian as conservative. The magnetization damping of conservative systems may be caused only by spins de-phasing in the local fields determined by the non-averaged part of dipole-dipole interactions. That is why in the theory of the average hamiltonian the process of slow magnetization decay is connected with spin RELAXATION PROCESSES IN MULTI-PULSE N.M.R.de-phasing in averaged local fields. More correctly the process should be considered as that of slow heating-up of the spin system. Serious questions are raised as to whether spin systems in multi-pulse experiments are conservative ;this question alone deserves the closest consideration. In connection with the observed deficiencies in the average hamiltonian theory there have been attempts to describe the experimental results of multi-pulse line- narrowing in solids without recourse to hamiltonian a~eraging.~.’*~ Below we give the theory of line-narrowing of n.m.r. spectra in solids not using hamiltonian averag- ing but using the example of a pulse train 90; -2 -(qx -2~)~*~ (qx denotes the pulse which rotates spins through an angle q around the x-axis; 22 is the time interval between the pulses) evaluated at a field shifted from resonance by the value A (in frequency units) and corresponding experimental results.The theory treated in our report is mainly stimulated by experimental ~ork.~~~ The present account represents a generalization of the results of ref. (5)-(8),the main aim of which was to make plain the authors’ approach to a clear physical picture of line-narrowing in multiple-pulse n.m.r. spectra. DYNAMICS OF SPIN SYSTEM AT TIMES t-T2 The magnetization behaviour during the initial stages t -T2of the multiple-pulse experiment reflects the elementary spin processes which take place in the system. The experimentally obtained4e6 transfer process which is accompanied by a decrease in magnetization at times t -T, shows that in the system there is exchange of energy between Zeeman states and the dipole-dipole reservoir of interactions.The magnet- ization oscillations observed1P2p6 during the initial stages give witness to the precession of nuclear spins around some effective field at t 2,; the quasi-stationary regime which has been set in the system at the times t -T2determines the further magnetiza- tion damping. Thus it is necessary to begin the study of spin system dynamics from small times t 5 Tz. Let us first consider the spin system affected by the pulse train 90; -z -(qx -2~)~ where qx is the pulse which rotates spin through angle q around the x-axis and 22is the distance between the pulses (fig. 1). It is supposed that FIG.1.-Schematic of train90; -T -(pox-2~)~.x ,pointsof signal observation. the constant field directed in the laboratory frame along the z-axis is shifted from the resonance value w,/y (coo is the frequency of Larmor precession of nuclear spin y is the gyromagnetic ratio) by the resonance offset value A (in frequency units). In the frame rotating with the Larmor frequency around the z-axis the equation of the spin density matrix p(t)has the form (h= 1) wheref(t) is the pulse function determined by the formula E f(?)= q 2 6(T + 2Kt -?) K=O EROFEEV FEL’DMAN MANELIS PROVOTOROV AND SHUMM and*d is the secular (relatively to the z-axis) part of the dipole-dipole interaction. The density matrix p(t) in initial time t = 0 was given by the preparatory pulse of the sequence used p(0) = 1 -aoo~oSx, tr p(0) = 1 (3) where a.is the initial temperature of Zeeman reservoir. Consider the interaction representation and replace p(t) = L(t)y(t)L-’(t) (4) where L(t)= Texp{-i il [-f(t’)sx + Asz]dt’}. (5) The symbol T denotes the ordering in time product. If we now insert the effective exp(-2iroeS) = exp(-iAr??,)P- exp(-iAtS,) (6) pulse which characterises the external influence on the system in the interval 2r it will be easy to check’ that after fulfilling the canonical transformation (4) the equation for the density matrix will be8 . dp 1 -= (exp[-i g(t’) dt’s,,]$i exp[i g(t’)dt’,!?,,] p(t)}. (7) dt i i In formula (7) g(t) is determined by a formula analogous to (2) in which the angle p is replaced by the angle 0 = 2wez and the value of effective field o,as can be seen from formula (6) is determined by the following cos 2wez = cos p cos2 At -sin’ AT.(8) The direction of It of the effective field is obtained from sin 2Az -cos21 sin q -cos AT 2 n = sin 2wez ,n = 0 n = sin 2wez * (9) It is convenient to expand the operator 12; by the following $2 = A,gO + + A-12z1 + A2P; + A-22P;2 (10) where A? is a secular but 23 l; 2%’ are non-secular parts of the dipole-dipole interaction relative to the maxis 9:= 2 Bij[2SniSnj-+(s;&j+ &S;.)]; (1 1) r<j &==-a 2 2 Bj,(Sni9$ + SA&j); 2;l = -3 2 Bij(&& + s;Snj); i<j i<j cc A 9;= -2 2 Bij(SA$$); 9;’= -2 2 BijSzS;; Sf = s, 3 isnz.(12) i<j i<j The coefficients Ao,A fl A fz may be found from the formula8 3n,Z -1 A 7-2 ; A = A’ = n,d1 -n:e-’w; RELAXATION PROCESSES IN MULTI-PULSE N.M.R.Eqn (7) shows that for every time interval 22 spins rotate through the angle 0= 2~~2. We take into account spin rotation in the mean field by the usual method i.e. pass to the frame rotating at a frequency we. In this system of coordinates the density matrix p*(t) satisfies the equation ; where +(t)= exp{ -i [,/:g(t') dt' -wet11 and x(t) = exp {-2i [,/:g(t') dt' -wet1) are the periodic functions with the period of the pulse train 22. From eqn (14) it is seen that the fields affecting the spins may be divided into constant fields o, Aw=:and fields which fluctuate rapidly in time.The greatest influence on the motion of nuclear spins is provided by the field weand the constant local field; the contribution of the oscillating fields may be accounted by perturbation theory. To account for the fluctuating fields we expand the functions +(I) and x(t) in a Fourier series W . flR m . nn +(I)= 2 C,e-'T 'r; x(t) = 2 Bfle-'Ter n-a n= -W c = (-1)" sin wez ; B = (-1)" sin 2w,z nn + w,~ nn + 2we2 and eqn (14) is written in the form t1 -aJ n= -W where sin 2coe2 (A29$+ A-,9j2). (18) 2wez The primed sums in this paper denote omission of zero harmonics. Eqn (17) is similar to the equation for the density matrix in continuous spin- locking.' This similarity is not accidental and exhibits the experimentally observed anal~gy'*~.~ between the behaviour of magnetization in the multi-pulse experiment considered and continuous spin-locking.However the problem at the same time differs from continuous spin-locking by the presence of the time-dependent part of hamiltonian (1 7). Modulation by pulses and resonance offset dipole-dipole interaction in eqn (17) is a source of quanta which as will be shown below are absorbed by the spin system. Therefore absorption of these quanta by the spin system causes magnetization damping at times t i5,T2and leads to the above mentioned heating-up of the spin system. EROFEEV FEL'DMAN MANELIS PROVOTOROV AND SHUMM 23 The amplitude of the time-dependent hamiltonian part of eqn (1 7) may be decreased at n/t > colocafter carrying out the following canonical transformations.8 Consider first qOc 9 dtr(Xz)2/trSi-we.Then for each non-zero harmonic +(t) one eqn (17) canonically transformed can be For each non-zero harmonic x(t) we carry out the analogous transformations mn ;(t> = e-i 5z S ei P.'i 25 t S -p (t)e-r Sn e-i ei t Sn (21) m e where IT fi; ==.= mn + 0(A2Bm$i -A-2B;i@i2). (22) ~ Such transformations have been used in the theory of continuous spin-locking.' After performing the canonical transformations (19) and (21) eqn (17) may be written as follows:8 Here sin co,~ z2cofoc . P(t) -zco;oc - i.e. o,-coloc; co,,,z < 1. n 7t Thus as a result of performing the canonical transformations (19) and (23) the time-dependent part of the hamiltonian decreases by E = -times and may be (zco10c)2 7l accounted for easily by perturbation theory.Since the perturbative order p(t) is now sufficiently less than the order of interaction inserted in #o one may assume9 that at weT2-1 through to time -T2 the density matrix of the system with an accuracy of small non-diagonal terms has the form z Fst= 1 -clst#o tr pst= 1. (24) At times -T2 we may also neglect absorption of energy by the system from external r.f. fields and apply the law of energy conservation,8 i.e. the conservation of Z0 from which where M$ is the projection of the stationary value of magnetization on the observa- tion axis x and Mois the initial value of magnetization; time t is counted from the RELAXATION PROCESSES IN MULTI-PULSE N.M.R.middle of the interval between the pulses up to the point at which magnetization is observed (fig. 1). Formula (26) shows that decrease in magnetization in the quasi- stationary state of the system has two causes. First at time -T2 the magnet- ization which is initially parallel to the observation axis becomes parallel to the effective field direction and the magnetization component which was perpendicular to the effective field direction disappears.6 For this reason the observed magnetization decreases for time -T2 by n times. Secondly at times -7‘ an energy exchange between Zeeman and dipole-dipole reservoirs of intractions OCCU~S,~ which is not connected with the change in magnetization orientation; it also leads to an additional decrease in the observed signal.Fig. 2 represents the dependencies of Md/Mo 1.0 0.8 0.6 0.4 0.2 1 I 1 0 0.2 0.4 0.6 0.8 ATI rad FIG.2.-Dependence Md/Moon Ar. Lines correspond to formula (26) solid line at Hfoc= 0.86 Oe; dotted line at Hloc= 1.0 Oe. Experimental points 0,(p = 22.5”; x (p = 36”; A,VI = 60”; 0,(p = 90”. on the parameter A r at different angles q~,calculated from formula (26)at tl equal to zero. Solid lines correspond to HI. = wloc/y= 0.86 Oe(H; [l 111) in a CaF single crystal dotted ones to HI. = 1.0Oe (arranged to correspond with the experimental points but bearing in mind a non-exact crystal orientation). The divergence of the experimental points and the theoretical curve at q~= 90’ (fig. 2) may be explained by magnetization damping parallel to co due to the above heating of the spin system which causes the additional decrease in the observed value M&6 New treatments’~~ show that magnetization M is a periodic function with the period of the pulse train 22; this allows calculation of the magnetization in the intervals between pulses.In particular if A is equal to zero the signal form between pulses (with an accuracy in the terms -~~wt~~) is the following’ Experiments’ confirm both the period of the observed signal and the amplitude increase in the bell-shaped signal which is described by the second term in braces in eqn (27) by 0 and z increase (if A = 0 then 0 = q). At resonance offset the magnetization change in the intervals between pulses is determined not only by dipole-dipole interactions but primarily by resonance offset itself [M -cos A (t -22); z < t < 321.It has been experimentally checked’ EROFEEV FEL'DMAN MANELIS PROVOTOROV AND SHUMM that at any resonance offset M is changed with the period 22 and has a maximum value in the interval midway between pulses. At /A. zJ < 271 the observed signal in the intervals between pulses has a bell-shaped form; at larger A the magnetization change in the same intervals has a form close to sinusoidal,6 containing more than one period. In the case considered when wloc-LO the absorption of energy from external fields n/z> we,wlOcmust be accompanied by a change of reorientation of a large number of spins and therefore is connected with an energy change in the dipole-dipole interaction.At we> uloc the energy of the absorbed quanta is mainly consumed by spin flipping in the effective field; only a small portion of the absorbed energy enters the dipole-dipole reservoir. Besides at u,> wlOczero harmonics 4(t) and ~(t) whose amplitudes have previously been LO^^^ . z times more than other harmonics lose their distinguishing features. Therefore the canonical transformations (1 9) and (21) of eqn (17) must be supplemented with canonical transformation for zero harmonics +(t)and ~(t). Accordingly instead of eqn (23) for the density matrix F(t)we obtain i dP-= [-we,9, + + PI(?>, dt where PI(?)-zw:ocand may also be considered as a small perturbation. The spin system is characterized here by two motion integrals and at times -T2 its density matrix has the form pst = 1 + ctStwes,,-0.5P,,A09O, trp, = 1.(29) The condition of 2:conservation at times -T2 leads to pst= 0. The decrease in stationary magnetization compared with its initial value Mois almost fully determined by the establishment of magnetization along the direction of effective field at time -T2 ; Kt= n2 cos Atl. (30) MO SPIN SYSTEM DYNAMICS AT TIMES t> T2 At times t > T the spin system is determined not only by the effective field but by the time-dependent perturbation terms PI(?)in eqn (28) Each term in vl(t) represents some part of the dipole-dipole interaction modulated by pulses and resonance offset. Non-secular terms of perturbations Pl(t) are the source of quanta absorbed by nuclear spins which interact through 9:.At u wlOcthe main part of the absorbed energy falls on the Zeeman reservoir and only a small part of the energy is absorbed by the dipole-dipole reservoir.Energy absorption of qunta 7115 by the dipole-dipole reservoir at we > oIOc requires a change in the mutual orientations of too many spins and is thus a difficult process. If a certain term in Pl(t) causes the absorption process by n spins of quantum mn/z then the energy mn/z -nu is trans- ferred into the dipole-dipole reservoir. Such is the case in the theory of saturation.'O The most effective influence on the system should affect such terms in Pl(t) which provide energy absorption by the Zeeman reservoir only.8 Such a process is possible at RELAXATION PROCESSES IN MULTI-PULSE N.M.R.where n is the number of the absorbing spins and mn/z is the frequency of quanta absorbed by spins (m-integer). It can be showns that the only term in pl(t)-TCO~~ which can lead to energy absorption by the Zeeman reservoir is R3(t),determined as followsS I?,(?) = K3re' Fr[A,# #:I K3 = const. (32) Similarly' the only term -z2u:, responsible for absorption of the indicated type is R4(t):' R4(t) = K4z2ei!? ' {$; [$ 93,K4 = const. (33) The experiment had shown that6 one does not observe processes of energy absorption from external r.f. fields if they are caused by operators of higher order than -r3 . uu;loc. Processes with absorption of quanta of frequency 2n/zare not observed experimentally.Thus the main effects on spin system dynamics at times t > T2have such terms in pl(t) as k3(t),R4(t)etc. Therefore the equation for the density matrix of the spin system may be written as i 9= [-O,S + A0'2-; dt + I?,(t) + I?_,(?) + I?,(?) + I?-&) + a * * &)I (34) the notation . . . in eqn (34) shows that in PI(?)other terms which lead to full energy absorption by Zeeman reservoir of interactions must be taken into account. Satura-tion eqn (10)are obtained here by the standard method'' and have the form da -2nt2 [ (9K32F3 + 16z2K,2F4)a(t)+ dt dp dt where -*3 and the operators GT(; -3we) e:k -4we) are determined by the following expressions W co ~2 -3 [W+t6+3 (t ) dt 6:4 = Lei,t(?*4(t) dt (37) where 63(t> = [.A:(?) $s(t)l &A(?> ==eiAo*:t 2;e-iAo-&t G-3(t) = (G3(?)>+.(38) The symbol + means the transfer to the complex conjugated operator. EROFEEV FEL'DMAN MANELIS PROVOTOROV AND SHUMM 27 Similarly &(t) = {#i(t> J?;I~ 2i(t>= e i~odtr# e-iAo$:r. (39) &4(t) = {G4(t)}+. The analysis of eqn (35) shows that if the equation for the density matrix (34) has I time dependent terms such as ff,(t) g4(t)then magnetization damping kinetics is defined by the curve representing the sum of two exponents. In this case damping always occurs up to the complete Pisappearance of magnetization. The picture changes when only one term such as R3(t),A,(?)significantly contributes to magnetiza- tion damping. In this case as in the theory of saturation the change in Zeeman temperature occurs only until temperatures ~(t) and D(t) become equal and it is not necessary here for magnetization to disappear completely.Let for example the term ff,(t)make the main contribution to magnetization damping. Then the ratio of residual magnetization M& to the stationary one M," depends on the shift of the effective field 6w from its value we= n/37 to the following An experimental check of eqn (40) shows in the main satisfactory agreement with the theoretical predictions6 The corresponding comparison of theory with experi- ment is shown in fig. 3. The shift 60 from we= n/3z was inserted both with the angle change at the constant resonance offset A.z = 0.905 [at q = 72" and A.7 = 0.8 I -0.1 0 0.1 60 72 80 FIG.3.-Dependence M:,,/Ms",of quanta1 absorption process determined by operator &(I) (a) on AT at p = 72" (6)on v at At = 0.905.Solid line corresponds to formula (40) at Hloc= 0.86 Oe. 0.905 from eqn (8) it follows that LU,z n/3z]and with the resonance offset change at the constant angle q = 72". The divergence from theory may be explained by the influence on magnetization damping of ff4(t)and other terms. From eqn (35) it is easy to show that the term I?,(?) leads to a time of magnetiza-tion damping -zW2 where the term k4(t)leads to a time of magnetization damping -~7-~. Similarly the term &(t) -which is responsible for absorption of quanta by five spins gives the time of magnetization damping -T-~. Experimental dependences of time of magnetization damping T2,on z are given in fig.4.6 The values T2eand 7 are plotted logarithmically. For the process of magnetization damping determined by k,(t)it has been found that T, -T-'.~ whereas for the process of damping determined by ff,(t),T2,-z-j and for ff5;,(t),T2e-T-~. Eqn (35) describes the magnetization damping at arbitrary values of the para- meters (p A z and these give the whole picture of magnetization change in the experi- ments considered. However for practical comparison of theory with the experi- mental data it is necessary to calculate correlators F3 F4 etc. [see formula (36)]. RELAXATION PROCESSES IN MULTI-PULSE N.M.R. These correlators are very much like the function of free induction decay.The difference is in the multispin nature of the correlators. These correlators may be estimated as follows ' where Mi3)and Mi4)are the second moments corresponding to the multispin corre- lators considered. Assume for evaluation that the spins are independent. Then 1 on FIG.4.-Experimental dependences of T2:2.z f?r different quanta1 absorption processes A operator R3(t); 0,Rdf); * Rq(r). each spin absorbs a quantum n/37 while energy excess 1 -3: -co 1 transfers into the dipole-dipole reservoir. The probability of such a process of absorption is -exp { -(f-~0,)~/2,,) where M2is the second moment of the absorption line in the rigid lattice in which spins interact through A,$:. Thus the probability absorption of a quantum 71/7 here is -exp (42) Similarly (43) Dependences TZeon q at different 7 are given in fig.5. The comparisons of the experimental data with the theory have been carried out in the neighbourhood of p = 7c/2 and gave good agreement between theory and experiment.' Complete comparison of the observed dependences for magnetization damping times with the theory should be carried out on the basis of the numerical solution of eqn (35) which will be carried out in the near future. EROFEEV FEL'DMAN MANELIS PROVOTOROV AND SHUMM 1000 100 ; \ u b-2-10 1 45 60 90 $,'Ides FIG.5.-Experimental dependences of TZeon q from different values of T(A= 0). * 5 = 10 ps; A,T = 14.5 pus; e T = 20ps. CONDITIONS REQUIRED FOR APPLICATION OF AVERAGE HAMILTONIAN THEORY The discussion in the previous section of magnetization damping in the multi- pulse experiment considered shows that the main contribution to magnetization damping is made by the absorption by the spin system of quanta modulated by pulses and resonance offset dipole;dipole_ inter!ctions.The quanta absorbed are determined by multispin operators R3(t),R4(t),Rji2(t) etc. At the same time in the theory of the average hamiltonian the nuclear spin system is described by a time- independent hamiltonian. Thus such approach significantly differs from the average hamiltonian theory. Moreoever in the theory presented some conditions necessary for the application of average hamiltonian theory may be obtained. To our mind the average hamiltonian theory is qualitatively true if in some frame there is an oppor- tunity to consider the nuclear spin system as conservative.This is possible only when the main contribution to the quantal absorption by spins is made by one term of the type ff,(t),I?,(?) etc. and the effect of others may be neglected. In particu- lar such a situation occurs for the sequence 90; -z -(905 -2~)~ at A = 0. At p = n/2 and A = 0 the decisive contribution to magnetization damping is made by In a frame rotating with oscillation frequency ff4(t) at co 9 wlOC as is seen easily from eqn (34) the spin system is conservative at p = n/2 and A = 0. This frame coincides with the one in which average hamiltonian theory functions success- fully,' with an accuracy to small corrections similar to that in canonical trans-formations (19) and (21).At the same time it is experimentally shown4 that at p = n/4 and A = 0 the behaviour of the spin system differs significantly from the predictions of average hamiltonian theory. It is due to the change of quasi equilibrium type in the system at we -ulOc, which may be considered conservative at times t -T2 in the frame mentioned in ref. (4) [again with the accuracy to canonical transformations (19) and (2l)]. Thus the average hamiltonian theory is applied at we> colOCin the frame obtained by canonical transformations (4) at parameter values of the pulse train and resonance offset when quantal absorption is largely determined only by multi-spin processes while the effect of the others may be neglected.For co -wlocthe theory of the average hamiltonian is true only at small times t -T2in a frame where the RELAXATION PROCESSES IN MULTI-PULSE N.M.R. density matrix p*(t) satisfies eqn (14). The important role of canonical transfor- mations (19) and (21) should be emphasised both in setting up the quasi stationary regime and in studying the processes of slow magnetization damping at t 3 T2. These transformations permit one to isolate the contribution of each harmonic of modulation by pulses and resonance offset dipole-dipole interactions to the establish- ment of the quasi stationary state and to heating-up of the spin system. EXPERIMENTAL Measurements were made on a multi-pulse n.m.r. spectronieter- 1 I with a resonance frequency 57.0 MHz for the I9F nuclei.The magnetization component M was observed in the rotating frame under the effect of pulse train 90; -z -(p -2~)~. The polarizing field Ho was shifted from resonance to a value corresponding to the resonance offset A. A single crystal CaF served as a sample with cross-sectional dimensions about 6 nim. All the measurements were carried out at Hall [I I13 (to an accuracy of 5"P at room tempera- ture. Under such conditions the spin-lattice relaxation time was -5 s. The value of rotating magnetic field in the pulse is -35 Oe. lnhomogeneity of Ho in the sample volume corresponded to a line width of -50 Hz inhomogeneity in the field H is 2;;. The authors thank Yu. N. Ivanov for help with the work. U. Haeberlen and J. S.Waugh Phys. Rec. 1968 175 453. 'P. Mansfield and D. Ware Phys. Rev. 1968 168 318. W.-K. Rhim D. P. Burum and D. D. Ellernan J. Cherx Phys. 1978 68 692; 1978 68 1164. W.-K. Rhim D. P. Bururn and D. D. Elleman Phys. Rev. Letters 1976 37 1764. L. N. Erofeev and B. A. Shumm Zhur. eksp. teor. Fiz. Pis'riici 1978 27 161. L. N. Erofeev B. A. Shumm and G. B. Manelis Zhur. eksp. teor. Fiz. in press. 'Yu. N. Ivanov B. N. Provotorov and E. B. Fel'dman Zhur. eksp. teor. Fiz.Pis'rm. 1978 27 164. Yu. N. Ivanov B. N. Provotorov and E. B. Fel'dman Zhrrr. eksp. teor. Fiz. in press. M. Goldrnan Spiti Teiiiperritirre and Nirclerrr Mugtietic Resoriwice in Solids (Oxford Univ. Press London 1970). lo B. N. Provotorov Zhrtr. eksper. teor. Fiz.,1961 41 1582; 1962 42 882. L. N. Erofeev 0. D. Vetrov B. A. Shurnm M. Sh. lsaev and G. B. Manelis Prib. Tekhti. Eksp. 1977 2 145.

ISSN:0301-5696    

DOI:10.1039/FS9781300019

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Proton Magnetic Shielding in Single Crystals Evidence of Intermolecular Shielding Contributions BY ULRICHHAEBERLEN Department of Molecular Physics Max-Planck-Institute for Medical Research 6900 Heidelberg Jahnstr. 29 W. Germany Receioed 4th August 1978 Pyromellitic acid dianhydride (PMDA) Ca(HC00)2and Pb(HC00)2 were studied by multiple pulse techniques in single crystals. The shielding tensors cr of the respective protons are presented. The orientations of the proton shielding principal axes systems do not conform to molecular sym- metry and for the formate ion ACTis found to vary drastically from one crystal site to another. These findings are shown to be evidence of intermolecular shielding contributions. A simple method of accounting for these contributions is presented.About a decade ago multiple pulse techniques were introduced in pulsed nuclear magnetic resonance in solids.' The feasibility of suppressing strong homonuclear DD interactions in solids while retaining all information about the anisotropic features of the nuclear magnetic shielding was demonstrated. Strong homonuclear DD interactions prevail in solid state proton magnetic resonance and as a consequence multiple pulse techniques have proved most useful in this area. For a number of years it has been possible to measure reliably the full shielding tensors of protons in hydrogen bonds. The following features of the shielding CT of such protons soon emerged from the experimental results (i) the anisotropy ACTis " large "; typical num- bers are 20-30 p.p.m.This was very helpful in tracing out such tensors. (ii) c is close to axially symmetric and (iii) the most shielded direction which is the unique axis of CT,is always found near the hydrogen bond direction loosely defined as the direction of the vector joining the hydrogen bonded atoms. Hardly anyone wondered why the unique axis of CT is not found exactly along the hydrogen bond. Now we are able accurately to measure in molecular crystals the shielding of protons attached directly to carbon atoms. Because of the small anisotropies en- countered here 6 to 8 p.p.m. are typical numbers the experiments are much harder to do but they can be done on crystals of carefully chosen compounds. The surprise came when we investigated compounds where the symmetry of the molecules is such that thc orientation of the principal axis system (PAS) of the proton shielding tensor seemed to be fully determined by symmetry the experimentally determined orienta- tion of the PAS did not comply with the molecular symmetry elements.The reason could be either of the following. First the apparent discrepancy could point to ex- perimental inaccuracies much larger than we thought them to be; second it could reflect the influence of other molecules in the crystal on the shielding of the proton considered. After all the shielding of a nucleus in a crystal does not have to comply to ndecular symmetry but to the site symmetry of the nucleus in the crystal. In our examples the protons were occupying general sites in the crystal and our experimental results therefore do not contradict the rigorous crystal symmetry requirements.32 PROTON MAGNETIC SHIELDING IN SINGLE CRYSTALS In what follows 1 shall demonstrate that we are indeed observing substantial inter- molecular proton shielding contributions. Realizing this means we have to abandon the idea that with our multiple pulse techniques we can measure in crystals a molecular property the a-tensor of a proton in very much the same way as molecular isotropic shifts in dense fluids are measured (small corrections known as solvent effects apart). This appears to be a setback to our hopes that the proton a-tensors measured in single crystals characterize molecules and can be compared reasonably with good quantum chemical calculations calculations that naturally are done on isolated molecules.However the situation is not as bad as that. I shall show that the intermolecular contributions to the shielding of the protons can be treated with acceptable accuracy with simple methods and that by subtracting these intermolecular shielding contribu- tions from the measured a-tensors we can obtain numbers which characterize isolated molecules. The experimental work most relevant to the current topic is that on pyromellitic acid dianhydride (PMDA) and on the formate ion (HCO0)-. Both the PMDA molecule and the formate ion are planar and possess a twofold axis passing through the proton see fig. 1. This completely fixes the orientation of the shielding PAS in the isolated molecule.As mentioned above the proton sites possess no symmetry in the crystal. The fact that the formate ion can be studied in a variety of salts provides an opportunity to study the influence of a variety of intermolecular environments on proton shielding. The proton o-tensors of the formate ion in Ca-and in Pb-formate were determined completely and partially in Cd-formate. As each of these com- pounds contains two crystallographically inequivalent sites we had six sites to compare. EXPERIMENTAL The PMDA work was done on our old 90 MHz multiple pulse apparatus the formate work on a newly assembled 270 MHz machine. The phase- and flip-angle error compensat- ing version' of the MERV pulse ~equence,~.' which is hard-wired in our instrument was used to suppress the proton-proton DD interactions and to see the chemical shifts.The pulse spacing T was typically chosen as 3 ps although we can make it as small as 2 ps. The transmitter r.f.-power was adjusted on both spectrometers such as to obtain 90"-pulse widths of about 0.7 ,us. For PMDA and Ca-formate in which the protons are the only abundant spin species and in which the protons themselves are rather dilute the accuracy of adjusting the various pulse parameters is no longer a factor limiting the multiple pulse spectral resolution. The test is deliberately to misalign the pulses. Much more critical is the homogeneity of the applied field. Note that for practical reasons (in PMDA e.g. TI is of the order of 10 h) it is impossible to "shim " the field using the actual solid sample.Test samples are required for shimming. Extreme care is necessary to ensure that the test sample a spherical bulb containing doped water has exactly the same geometry as the actual samples. The actual samples must be shaped into spheres to avoid bulk susceptibility shape effects i.e. line broadening due to inhomogeneous bulk magnetization and above all n.m.r. line shifts reflecting merely the variation in the bulk magnetization accompanying any change of orientation of an odd-shaped sample in an applied field. Such unwanted n.m.r. line shifts can easily amount to several p.p.m. Grinding into spheres molecular crystals which are often soft and due to an often layered structure liable to fall apart during the grinding process is now one of the major obstacles in proton high resolution n.m.r.in single crystals. Our current record in resolution achieved on a single crystal sphere of Ca-formate is 34 Hz f.w.11 h. Due to the spin-+ Pb-207 isotopes (21:i natural abundance) and the spin- Cd-1 I 1 (1 3yA) and Cd-113 isotopes (12q:',) in Pb-and Cd-formate respectively the resolution was poorer in the multiple pulse spectra of these compounds. In principle these spins could be decoupled from the protons but the availability of the 270 MHz machine made this unnecessary. U. HAEBERLEN Another major difficulty in this area is assigning the measured shielding tensors to " their " sites. The very fact that the measurable a-tensors do not reflect molecular sym-metry is the basic reason for this difficulty.I defer the resolution of this delicate problem in the present cases and move directly to the results. RESULTS AND DISCUSSION The experimental results on PMDA and on Ca- and Pb-formate are shown pic- torially in fig. 1. Because one of the proton shielding principal axes designated X Y,2,is always approximately perpendicular to the planar molecules it is possible to display the essential results in planar figures. The principal components are given relative to a spherical sample of liquid water. The surprising feature of the PMDA results is that the in-plane principal directions deviate by as much as 26"from the two-fold axis passing through the protons. From the point of view of molecular symmetry the formate results look more pleasing at first sight in all four cases the a-principal axes systems are aligned quite well along the molecular symmetry elements (twofold axis normal to the plane).However the intermediate and the most shielded axes are interchanged for the two sites in Ca-formate and the anisotropies ACTare drastically different in Ca- and Pb-formate. PMDA O,,=-6.1 p.p.m X Y -S.B\I -8.4 L- -6.4 x -8.7 y A,4x 0,,=-12.2 p.p.m. oZ,=-12.6 p.p.m. site I Ca(HCOO) site I1 0,,=-16.8p.p.m. ozi-17.1 p.p.m. site I Pb(HCOO1 site 11 FIG.1.-Proton shielding in PMDA (top) and in the formate ion (bottom). The formate ion was measured in four sites two in Ca(HC00)2 and two in Pb(HC00)2. Principal directions are labelled by X Y and Z. All Z-directions are approximately perpendicular to the planar molecules.The numbers at the X and Y axes give the respective principal shielding components in p.p.m. relative to liquid water. 0 hydrogen carbon 0 oxygen. PROTON MAGNETIC SHIELDING IN SINGLE CRYSTALS Had we experimental results about the formate ion from only one site and had not the molecular symmetry argument for PMDA we would have claimed as would have others that we had determined " the " proton shielding tensor in PMDA and in " the " formate ion implying tacitly that these are the a-tensors in the isolated molecules. From the results shown above we must conclude that this approach is untenable. All we can safely say at this level is the shielding of that proton in this and that molecule in this and that crystal site is as we have measured it.Were this all our work would not be of much value. Fortunately there is a simple way to ap- proach the intermolecular shielding contributions. Consider a proton Pi in a mole- cule M and a molecule Mkwhich in the crystal is far away from Pi,so far away that all electric interactions between M and Mk can be neglected. Nevertheless M still affects the shielding of Pi. If we bring the crystal into a magnetic field B, this field will induce diamagnetic currents in Mk. These currents will produce a secondary field at the site of Pi which is felt by Pi as a shielding (or antishielding depending on the orientation of Rik,the vector joining Pi and Mk relative to BJ. As we have assumed Mk to be remote from Pi the secondary field can be represented as a dipole field.The induced dipole moment is pk= -1 Xk .Bo,where Lo is Avogadro's number LO and Xk the molar susceptibility tensor of M,. The contribution of M to the shielding of Pi is now simply given by where Rik= IRikl. Before summing eqn (1) over all k to get the total intermolecular shielding contribution we inspect what happens if Rikbecomes (i) very large and (ii) very small. (i) Ril,very large the model is valid but the calculation becomes cumbersome. However potential theory ensures that all contributions from some sufficiently large inner sphere with radius R around Pi to the outer surface of the crystal cancel provided the crystal has the shape of a sphere. We find R = 50 suffi-ciently large. (ii) Rik small the application of the point-dipole model becomes questionable since the extension of the induced current loops may become comparable with or even greater than Rik.In such cases we try to break down the molecules into functional groups to which group susceptibilities are assigned. 0 is then calculated as a sum of contributions from these functional groups. The critical point in calculating the intermolecular shielding contributions by summing up all 0 according to eqn (I) lies clearly in the molecular and still worse. the group susceptibilities. In our practical calculations we rely as far as possible on experimental suscepti- bilities. Where group susceptibilities are required we draw on the work of Schmalz et who suggest a set of local bond and atom susceptibilities which reproduce accurately total molecular susceptibilities.Before turning to the results of such calculations let us consider how sure we can be that such a calculation adequately covers intermolecular shielding contributions. There is no doubt that it does deal adequately with the direct magnetic intermolecular interactiow6 But there are also electric interactions resulting e.g. from an overlap of wavefunctions of neighbouring molecules which might affect the shielding of the nuclei. The proper question to ask is therefore whether or not the mechanism we are considering is the dominant one. The criterion is the difference aexptl-crCalc. If U. HAEBERLEN 35 the direct magnetic intermolecular interactions are dominant this difference should reflect e.g.the molecular symmetry in PMDA. For the formate ion the test is harder since we can calculate four such difference tensors two for Ca-formate and two for Pb-formate. They all should be equal and they all should reflect the sym- metry of the formate ion. Remember that the four experimental B tensor differ drastically! In our calculations on PMDA we considered the molecule to consist of the follow- ing functional groups an aromatic ring four carbonyi groups and two divalent oxygens. Omitting detail (which will be published elsewhere)' ccalc has an aniso-tropy of about 1.5 p.p.m. and is oriented such that the principal axes of B,,~~~ -B,,~~ are quite well aligned along the molecular symmetry axes. All remaining deviations are <8".We could hardly expect more. From this we obtain justification to propose that the difference tensor cexptl-ccalc be identified with the proton shielding tensor in the isolated PMDA molecule. This implies that the normal to the molecular plane is the least shielded direction a result that might have been predicted using the ring current model for aromatic systems. It would probably have been much harder to predict the remaining results :the C-H bond direction is the intermediate principal proton shielding direction whereas the in-plane-perpendicular-to-the-bond is the most shielded direction. With the formates there is a natural choice of entities to be represented as mag- netic point dipoles the metal cations Pb2+ and Ca2+ respectively and the formate anions.The problem lies again in the susceptibilities. The isotropic susceptibilities of Pb- and Ca-formate are known experimentally. By comparing the x values of a variety of organic and inorganic salts people have tried to extract x values per- taining to Ca2+ and Pb2+ ions.' The results are however not unique so that a choice had to be made within certain limits. The choice was guided by the desire to obtain as similar as possible difference tensors ~t,~~~ -cialoi running over the four formate ion sites available. These tensors should moreover reflect the symmetry of the formate ion. The values eventually chosen were X(Pb2+)=-47 x x(Ca2+)=-27 xloe6 xiso (formate ion) =-13 x and AX(formate ion) =-5 x c.g.s. units. With these input numbers the calculation yielded the following anisotropies Aoialc:6.4 and 4.4p.p.m.for the two sites in Pb-formate and 0.7 and 3.6 p.p.m. for the two sites in Ca-formate. These are suprisingly large numbers which immediately explain why the observable proton shielding tensors in the various formates differ so much. When the tensor were subtracted from the cLxptl tensor difference tensors were obtained which resemble each other in all their essential features and which do comply to the symmetry of the formate ion (i) the most shielded direction is close to the C-H bond; (ii) the least shielded direction is close to the normal of the plane of the ion; as a consequence the intermediate principal proton shielding direction is close to the 0-0 internuclear vector.The total shielding anisotropy is -5&1 p.p.m. the in-plane shielding anisotropy is 2.2 0.5 p.p.m. We believe that these features characterize the proton shielding of an isolated formate ion. Note that the measurable shielding displays these features at only one of the four sites see fig. 1; at the other three sites the intermolecular shielding contribu- tions exchange the most and the intermediate principal shielding directions. These examples thus support the conclusion that on the one hand intermolecular shielding contributions are important for protons in solids and on the other hand that they are covered reasonably well by the magnetic dipole model described above. For other nuclei such as 13C 31P etc. where the anisotropy of the local or intra- molecular shielding is usually much larger the intermolecular shielding contributions PROTON MAGNETIC SHIELDING IN SINGLE CRYSTALS will as a rule not be large enough to affect appreciably the measurable a-tensors but in precision work on these nuclei they should certainly also be taken into account.I thank Dr. S. Aravamudhan and Mr. H. Post for their assistance in this work. J. S.Waugh L. M. Huber and U. Haeberlen Phys. Rev. Letters 1968,20 180. * U. Haeberlen High Resolution NMR in Solids (Adv. Magnetic Resonance Suppl. 1 Academic Press N.Y. 1976). P. Mansfield J. Phys. C 1971 4 1444. 'W.-K. Rhim D. D. Elleman and R. W. Vaughan J. Chem. Phys. 1973 58 1772. T. G. Schmalz C. L. Norris and W. H. Flygare J. Amer. Chem. Soc. 1973 95 7961. McConnell has analysed the consequences of these interactions on the isotropic chemical shifts observable in fluids. H. M. McConnell J. Chem. Phys. 1957 27 226. 'S.Aravamudhan U. Haeberlen H. Irngartinger and C. Krieger Mol. Phys. 1979 in press. M. Prasad S. S. Dharmatti and D. D. Khanolkar Proc. Ind. Acad. Sci. 1947 26A,328.

ISSN:0301-5696    

DOI:10.1039/FS9781300031

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

19FMultipulse Nuclear Magnetic Resonance Study of Lithium Perfluoro-octanoate + Water Liquid Crystal Systems BY PETERG. MORRIS AND PETER MANSFIELD Department of Physics University of Nottingham Nottingham NG7 2RD AND GORDON J. T. TIDDY Unilever Research Port Sunlight Laboratory Port Sunlight Wirral Merseyside L62 4XN Received 3rd August 1978 Two modified MREV8 sub-cycles forming a partially permuted cycle (PP16) have been used in a multipulse study of the mesophases formed by the lithium perfluoro-octanoate (LiPFO) + water system. The lineshapes show characteristic axially symmetric chemical shift tensors which have been measured over a range of temperature (20-68 "C) and concentration (47.8-72 % LiPFO). The shift anisotropy in the hexagonal phase is halved in magnitude and opposite in sign to that observed in the lamellar phase indicating the presence of rapid rotational diffusion.A rotational study of an aligned hexagonal sample (47.8 % LiPFO 52.2 % H20)is used to demonstrate the effects of two dimensional averaging on a chemical shift tensor. The observed shift tensors are used to estimate values for the order parameter based on the known values of the 19Fchemical shift tensor elements for CF2 groups in Teflon at liquid nitrogen tempera- tures. When compared with chain dimensions estimated from X-ray data the values of S indicate the existence of rotational isomerisation for the surfactant chain. The molecular order generally increases with increasing concentration but a decrease is observed at the hexagonal/lamellar boundary.1. INTRODUCTION The development of multipulse techniques was originally directed towards the removal or the reduction of dipolar interactions in rigid solids so as to reveal the smaller and often more interesting chemical shift interactions which reflect the solid state electronic structure around resonant nuclei. Therefore much of the theoretical framework for multipulse experiments has been developed for an idealized rigid lattice although there has been some extension of the original theories to include spin-lattice relaxation time effects arising from molecular motions. However the basic premise that a certain reversibility of the spin system can be made to exhibit itself by application of appropriate r.f. pulse sequences has been assumed to be true in solids with rapid inter- and intra-molecular motions and such echo behaviour and multipulse line narrowing effects can readily be observed experimentally.It is therefore not too surprising that multipulse techniques can be applied in the study of liquid crystal systems; the potential for such experiments was realised by Losche and Grande.' More recently multipulse techniques in our laboratory have been used to investigate the dynamic properties of cesium perfluoro-octanoate (CsPFO) and ammonium perfluoro-octanoate (APFO) + D20 systems by observa- tion of the I9F resonance.2 The multipulse n.m.r. studies on liquid crystals are a small part of a wider series of studies by many groups using conventional n.m.r. techniques on both thermotropic and amphiphilic liquid Directly related to this work LIQUID CRYSTAL SYSTEMS are the 13Cproton double resonance experiments on a number of nematic liquid crystals6 and on lecithin bilayers.' The same technique has been used to study the 31P shift anisotropy also in lecithin bilayer~.~~~ In this paper we report results for lithium perfluoro-octanoate (LiPFO) + H20 liquid crystals obtained by 19F multipulse experiments.Three different liquid crystal phases occur in this system and were originally assigned complex hexagonal lamellar and reversed hexagonal structures." The complex hexagonal and reversed hexagonal structures are incorrect; these phases are now known to be a normal hexagonal phase and a second lamellar phase.'' From these results and using an extension of our previously developed theoretical model we have been able to obtain the order parameter S over the range 19.2-68.3 "C by recording and fitting the multipulse spectra.The values of S are consistent with a model for chain motion involving rapid rotation about the longitudinal chain axis and a wagging motion of the chain. The results demonstrate unequivocally that the order parameter changes sign at the hexagonal/lamellar phase boundary. 2. MULTIPULSE SEQUENCE The truncated spin interaction hamiltonian for a rigid solid of spins Zin a large static magnetic field Bois l3 where cc denotes the coordinate axis along which the static polarizing field is directed (usually the z axis). The first term is the dipolar interaction and Aij = -f(1 -3 cos2 0ij)/2r:j.The second term involves the chemical shift Siof the ith spin and a common offset from resonance Am. Normal 90" r.f. pulses applied along the x and y axis in the rotating reference frame alter the effective hamiltonian eqn (1) by simply changing a from its equilibrium value of z to either x or y. Over a properly chosen cycle (or subcycle) therefore the dipolar part of eqn (1) can be made to vanish identically (for ideal pulses) and a non-zero average hamitonian defined from the residues arising from the chemical shift and offset terms. The minimum number of orthogonal switched hamilton states of equal time weighting required to make the dipolar part vanish is three corresponding to a = x y and z. We shall call this the minimal subcycle.Fig. 1 shows various groupings of minimal subcycles to form a longer cycle. A reflection symmetry cycle is formed from two minimal subcycles placed back to back and has the property that second order terms in the expansion parameter T (pulse separation) of the effective spin hamiltonian vanish identically over the cycle. It has been shown14 that a larger cycle built up in such a way that all the permuta- tion states of the hamiltonian are cycled in three groups of reflection symmetry cycles removes correction terms up to third order in the average hamiltonian. This is true only for idealized 90" r.f. pulses. The effect of non-zero correction terms is to broaden the observed line width thus making the cycle less efficient.Non-idealized 90" pulses also broaden the line width by reintroducing lower order corrections which may not be removed by permu- tation symmetry. However in the case of the reflection symmetry cycle it is possible by using two similar cycles simultaneously to correct for finite r.f. pulse widths and r.f. inhomogeneity while maintaining second order interaction terms zero. Two such reflection symmetry cycles as shown in fig. 1 have been named the MREV8 P. G. MORRIS P. MANSFIELD AND G. J. T. TIDDY 39 I' I MREV8 c' I I I I I I I I I ,*-\ ,-. I I I I 8 '\ I q Yx XY z zTx XYZlZ xY YXJ ZZY YSTZl I +---121 I -12r ---_I 4 PP16 -1 * * I sub-cycle reflectiori symmetry cycle FIG.1 .-Multipulse timing sequence for the PP16 cycle used in liquid crystaI studies.P*a corre-sponds to 90" r.f. pulses applied along the a-axis in the rotating frame. S denotes the signal sampling pulse. The expected signal response at resonance is shown (solid lines). The broken lines corre- spond to a quadrature signal response. sequence.14-16 The chemical shift and offset terms remaining in the average hamil- tonian produce an effective scaling or reduction of the observed chemical shift of 3/dZ This cycle and its phase-corrected variant 16917 have been successfully employed for a number of years. We mentioned above the fully permuted cycle which removes all third order terms. A system which is intermediate to this is the partially permuted cycle (PP16). This comprises two MREVS cycles chosen so that two of the three possible permutation groups are covered in the cycle.It has been shownls that this cycle has a somewhat better line narrowing efficiency for small chemical shifts and offsets since the third order term is reduced to + of its value in the MREV8 cycle. The PP16 sequence is the cycle that we have used throughout this work and our previous work' in liquid crystals. We have found experimentally that this particular cycle is relatively easy to align and fairly stable in operation. We have therefore not found it necessary to use the phase compensated version of this cycle." The ideal chemical shift scaling factor for the PP16 cycle is 6The finite pulse width correc- tion to this factor is described elsewhere.18 3.CHEMICAL SHIFT THEORY As stated in Section 2 the truncated interaction hamiltonian for ''F nuclei com- prises two terms XDand Xcs.With the external magnetic field used here E 2.25 kG IXDI9 I%'csl and the single pulse spectra are characterized mainly by the dipolar interaction. However the multipulse sequence is designed to reduce the dipolar interaction to almost zero so that the dominant term in eqn (1) is in this case Xcs. For an external static field B the chemical shift interaction is Xcs = 2W:a(q')L43 (2) PA where p and q number groups of magnetically non-equivalent and equivalent nuclei respectively. All other symbols have their usual meaning. This can be expressed in terms of the irreducible spherical tensors Rik and T:; corresponding to the spatial and spin parts respectively.For a single spin eqn (2) becomes LIQUID CRYSTAL SYSTEMS ,water director d Fig. 2. Idealized representation of a LiPFO +water hexagonal phase. The first term in eqn (3) is simply the isotropic chemical shift Rft =3 trace (aaB)=cr and gives rise to a change in resonance frequency relative to the bare nucleus but does not lead to any line broadening. The 2nd rank tensor components occurring in eqn (3) are defined in the principal axes (PAX) system as RY$(PAX) = {cTZZ-CT) (44 RYZl(PAX) = 0 (4b) T:& =0 (4f1 where crxx oYyand oZzare the principal values of the chemical shift tensor y the magnetogyric ratio and I the spin displacement operators. In addition to the principal axes system defined w.r.t.the C-F bond it is useful in describing the motional and aggregate crystallite behaviour of liquid crystals in various phases to introduce a number of additional reference frames using simple tensor transformations operating on the spatial tensor components only. We define a molecular (MOL) frame in which the z axis coincides with the LiPFO molecular chain axis and in which there is rotation of the molecule about this axis. The two frames are related by the Euler angle QM = [0 w y(t)] through the trans- for mati on R;&(MOL) =29L,Mt (QM)RF&t(PAX). (5) M’ Fast rotation around one axis averages out the full chemical shift tensor making it axially symmetric.’’ In this case R::(MOL) =3 (011 -01) =3 ACT (64 P. G. MORRIS P.MANSFIELD AND G. J. T. TIDDY where 011 and oI are the principal components of the axially symmetric shift tensor. All other values of Rz2(MOL) for M + 0 vanish. From their measured values of ozz = -80 p.p.m. oyy= 10p.p.m. and oxx= 70 p.p.m. for rigid CF2groups in PTFE Garroway et al. have obtained the anisotropy da = 104.21 p.p.m. for a single rotating chain.20 This value is used below to obtain order parameters from the measured shift anisotropies. Depending on the liquid crystal phase we make further transformations similar to eqn (5) to go from the MOL frame to either the lamellar (LAM) frame or the hexagonal (HEX) frame. In the case of the LAM frame the Euler angle Q,(t) = [0,b(t),01 describes the director axis with respect to the MOL frame.For vibrational or wagging motion of the chain here regarded as rigid we consider later a model in which the angle p(t) undergoes a simple harmonic motion and derive an expression for the order parameter. In the case of the HEX frame the Euler angle Q,(t) = [~(t), 71/2 -/?(I) y(t)] describes the director axis (the surfactant cylinder axis) with respect to the MOL axis (see Fig. 2). The angles a(t) ~(t) describe the rotational diffusion of surfactant within the cylinder. Now the time average over the Wigner transformation coefficients for either LAM or HEX transformations defines the order parameter generally as == (9&[aL,H(f)l>av (7) which for the LAM frame gives s = (+[3 cos2P(t) -l]), = s (8) while for the HEX frame gives SH = -3(3[3 cos2P(t) -11) = -3s.(9) Note that S is the order parameter of the molecule relative to a direction normal to the surfactant/water interface. Finally to relate actual measurements we must transform the shift tensor to the laboratory (LAB) frame again using a transformation similar to eqn (5). The transformation from LAM to LAB employs the Euler angle a,, = (0 4 0) which describes the static distribution of crystallite directors with respect to the applied field. In this case the line position for the pth crystallite relative to a reference frequency cr) is p = -@) = tp + 3 S(a,P -ap;,(@). (10) u For an aligned sample the variation of line positions as a function of orientation is given by eqn (10). In the case of a non-aligned (poly-crystal) sample this must be spatially averaged over all 0 leading to the well-known lineshape expressionz1 where the sum is over all groups of non-equivalent nuclei and A is a normalization factor.The scaled values of shift tensor a and alsare given by GP -1 SI) -30 + 2s)q + +(I -s)ay (124 osl = +(I -s)oT + +(2 + S)of;.. (12b) This lineshape must be convoluted with 2 broadening function to account for relaxa- tion broadening and the residual dipolar interactions not fully removed by the multi- LIQUID CRYSTAL SYSTEMS pulse sequence. These effects which are in principle quite complicated are approxi- mated by a simple gaussian broadening'* so that the observed lineshape g(6) is given by +a g(6) =I- dS'f(6') exp { -(6 -6')2/2B2) where the characteristic broadening width B is to be determined experimentally.The transformation from HEX to LAB obeys a similar expression. However the hexagonal phase can be aligned such that the surfactant cylinders are distributed randomly in a plane normal to the alignment axis. For such a 2-D powder sample the transformation from HEX to LAB (Euler angle QLAB) can be effected by two con- FIG.3.-Euler angles for transformation from the HEX to LAB reference frame. secutive Euler rotations s1 =(0 n/2,n-d) ln2 =(0 0 0) where 0 is the angle between the normal to the director plane and Bo and 95 the azimuthal angle of the cylinder director axis; see fig. 3. For this case therefore the chemical shift line position rela- tive to the reference frequency w is given by 6 = a -1 S(q -al)[3 sin20 cos 2+ -(3 cos2 0 -I)].(14) 12 For the two special cases corresponding to 8 = 0" and 90" this reduces to +(all + a,) and +(q + 01) -+(a,,+ al) cos 295 respectively for S = 1. If the aligned sample is rotated about an axis perpendicular to the magnetic field then all the micelles will be parallel to each other with + = 0" and the lineshape func- tion g(0,d) will be given by g(0,d) = {[al sin28 + +(all+ al)cos201 -S}-t. (1 5) However if no such attempt is made there will be a random distribution over 4. Let the lineshape function for such a case be denoted by f(0,d) then the fraction of spins with line position in the range 6 to 6 + d6 will be given by m,6) = 44) d+ (16) P. G. MORRIS P. MANSFIELD AND G.J. T. TIDDY where n(4) will be a constant for a random distribution over 4. Thus From eqn (14) (S = 1) d6 = +(all+ aL)sin' 8 sin 24 d4 (18) so that f(8,6)oc I/[(all- aL)sin26 sin 241. (19) Substituting for 4in terms of 6 from eqn (14) this becomes The spectral function thus consists of a pair of delta functions at 6 = +(ali+ al) 6 = aI sin28 + +(all+ aL)cos28 which broaden into a doublet after convolution with the usual gaussian broadening function. For 8 = 90" the doublet peaks centre on aL and 3(all + aL)and as 8 is reduced to zero it collapses to give a singlet centred at 3bl + 01). 4. EXPERIMENTAL The samples of LiPFO + H20were prepared by mixing weighed constituents as reported previously.'0 All data were taken on the computer-controlled line narrowing spectrometer operating at 9.0 MHzwhich is described elsewhere." The multipulse spectra were recorded with the PP16 (partially-permuted) sequence operating with z = 6.4 ps.This achieved a true linewidth of 70 Hz for I9Fnuclei in a single crystal of CaF2 oriented with its [l 111 direction along the magnetic field at an offset of 500 Hz. Single pulse spectra were recorded by fourier-transforming the FID following one 90" r.f.pulse. Usually from 128 to 1024 spectra were accumulated to improve the signal-to- noise ratio. The sample temperature was regulated by blowing air of controlled temperature through the probe and was monitored by a copper/constantan thermocouple. Temperature stability during the experiments was estimated in most cases to be better than 0.5 "C.If no attempt is made to control temperature rapid sample heating occurs. This can be as much as 30 "C or so over the period of a typical multipulse experiment and is presumably the result of either unusually large dielectric absorption or ionic conduction. (Under similar conditions no noticeable temperature rise was apparent with water samples.) A two-dimensional powder sample of the hexagonal phase (47.8% LiPFO) was prepared by cooling from the isotropic phase in a field of wl T. At room temperature the sample preserved its alignment for a number of days without any noticeable change and could be rotated in the magnetic field without any trace of alignment relaxation. The accuracy of the angle setting when recording rotation spectra of the aligned samples was better than 0.5".5. RESULTS AND DISCUSSION HEXAGONAL MESOPHASE Typical multipulse spectra recorded at 20 "C for samples in the hexagonal meso- phase are presented in fig. 4. The different sign and reduced magnitude of the chemical shift anisotropy compared with lamellar phase spectra (see fig. 6) are clear. This indicates that the surfactant molecules are at right angles to the director and also undergo rapid rotational diffusion about this axis. The order parameter S was deter-mined by visual comparison of theoretical lineshapes generated by a computer and the LIQUID CRYSTAL SYSTEMS FIG.4.-19F multipulse spectra of LiPFO + water in the hexagonal phase referred to fluorine in CaFs at zero offset T = 20 "C.(a) 47.8% LiPFO SH = -0.21 ; (6)57.4% LiPFO SH= -0.25; (c)62.0%LiPFO SH= -0.29. experimental spectra. The solid curves in fig. 4 are the calculated lineshapes. Order parameters were determined also at higher temperatures and all the values are listed in table 1. The fact that only one spectral line is observed for the CF2 groups and that this can be fitted with a single negative order parameter provides good evidence in favour of TABLEOR ORDER PARAMETERS FOR LiPFO SAMPLES composition /"/o LiPFO temperature 1°C phase" order parameter isH,sL) 47.8 48.2 H -0.21 47.8 57.4 52.6 20.o isotropic H 0 -0.25 57.4 48.1 H -0.25 62.0 20.0 H -0.29 62.0 68.3 H -0.29 68.0 21.4 D 0.44 72.0 19.2 F 0.54 72.0 27.1 F 0.54 72.0 34.2 F 0.54 72.0 39.0 D 0.54 a H = hexagonal; F D = lamellar.P. G. MORRIS P. MANSFIELD AND G. J. T. TIDDY 45 the normal hexagonal structure for this phase.ll There is insufficient multipulse resolution to observe differences in the chemical shifts of the CF2 groups along the chain. Fig. 5 shows a series of multipulse spectra obtained from the two-dimensional powder sample (47.8% LiPFO). When 0 = 0" (magnetic field at right angles to the director) a singlet is observed fig. 5(a). This broadens into a doublet [fig. 5(b)]as the sample is rotated the maximum splitting occurring for 0 = 90" in agreement with the lineshape prediction of eqn (20). The doublet was barely resolved because of the small shielding anisotropy of this sample. Fig. 5(c) shows the spectrum of this kLnd o;o;o;oo4-j 0 oo 20 40 60 80 100 offset I p.p.rn FIC-5.-I9F multipulse spectra for a 47.8 % LiPFO sample measured for a range of temperatures.The reference compound is fluorine in C6F6 at zero offset. Curves (a)and (b)correspond to the two- dimensional powder averages in the hexagonal phase with the magnetic field normal to and in the plane of the cylinder directors respectively. Curve (c) shows the behaviour in the isotropic phase. (a) T = 19.5 oc e = 00; (6) T = 19.5 oc e = 900; (c) T = 52.6 oc. sample in the isotropic phase (at 52.6 "C) for comparison. Unfortunately we were unable to orient the more concentrated samples (which have higher shift anisotropies; see table 1). The anisotropic susceptibility of the amphiphiles means that the hexagonal meso- phase can be aligned in a magnetic field the minimum energy configuration being when the director (cylinder axis) is perpendicular to the field direction.This is the alignment direction expected from the shift anisotropy. If no attempt is made to spin the sample then the directors of separate crystallites will be distributed at random over the plane thus defined. Spinning the sample at right angles to the field direction however can lead to perfect alignment along the rotation axis.22 The single pulse spectra not shown here but obtained under the same experimental LIQUID CRYSTAL SYSTEMS conditions as for fig. 5 indicate a large angular variation of linewidth due to the un- averaged dipolar interaction ; this completely masks the effects of the two-dimensional averaging on the chemical shift tensor.Consequently no splitting of the CF2 line is observed in this case. LAMELLAR D AND F PHASES The multipulse spectra of both D and F phases (fig. 6) are very similar to those observed for the CsPFO and APFO + D20 lamellar systems.' 20 GO 60 80 100 offset 1p.p.m. FIG.6.-19F multipulse spectra for a 72% LiPFO sample referred to fluorine in CbF6at zero offset. Curve (a) corresponds to the lamellar F phase and (b) to the lamellar D phase. Note the reversed asymmetry of the CF2 peaks w.r.t. those of fig. 4. S = 0.54. (a) T = 19.2 "C,(6) T = 39 "C. Order parameters are listed in table 1. The 72.2 % LiPFO sample is particularly interesting since it is in the F phase at room temperature but undergoes a phase transition to the D phase at z 35 "C.Despite leaving the sample to equilibrate for over an hour there was no noticeable change in the spectrum on passing through the phase transition. The viscosity of the F phase is far higher than that of the D phase and it is remarkable that this is not reflected in a change of order parameter at the D/F transition. It suggests that an inter-layer cooperative effect is present which prevents the layers sliding over each other. It is worth emphasizing that all the spectra recorded were fitted with shift tensors scaled by a single order parameter S. This is strong evidence for the constancy of order parameters along the chain as has been observed for hydrocarbon surfac- and perhaps for the rigidity of the molecule.Certainly the order para- meters of the terminal CF2 groups (at C6 and C,) do not decrease by a factor of two or more as happens for hydrocarbon chain^.'^^^ The spectral width of the fluoro-methyl peak is identical to that found previously for CsPFO' and is relatively insensi- tive to variations of the order parameter. Unfortunately the results presented here do not contribute in great measure to the P. G. MORRIS P. MANSFIELD AND G. J. T. TIDDY detailed understanding of the nature of the chain disorder. However on the assump- tion of a rigid molecule executing a wagging motion (which would appear to be a reasonable model) it is possible to estimate the size of the angular fluctuations. Assuming a model in which p(t) [eqn (8) and (9)] varies harmonically over a range &Po then P(t) = Po cos wt (21) which when averaged over the motion gives an order parameter where J0(2p0)is a zero'th order Bessel function of the first kind.,' Note that this reduces to unity when Po is zero.A similar model has been employed by Seiter and Chan32 to describe motional averaging of dipolar splitting in hydrocarbon surfactant bilayers. Evaluation of this expression indicates that the amplitude of the motion varies from about 45"(S = 0.6) to 62"(S = 0.35). These results refer to the extrema. Calculations based on S = +(3 cos2PL-I) give for OL 31" (S = 0.6) and 41" (S =0.35). From the previously reported X-ray data" the surfactant layer dimensions are estimated to be 16.6 and 17.0 A for D and F phase samples in table 1.For an all- trans chain with S = 1 a value of 22.5 A can be calculated from known bond lengths. The X-ray data are consistent with an all-trans chain tilted at an angle BL = 41" (S = 0.35). This is clearly inconsistent with measured values of 0.44 and 0.54 (table 1) and shows that the chains cannot be in the all-trans conformation. On the basis of a rotational isomer model Shindler and Seelig25 have given an expression to calculate the effective chain length (L) from order parameters of CD2 groups (ScD) for hydrocarbon surfactants where n is the number of chain segments and i refers to the position of the group along the chain. The values of S in table 1 are a factor of two larger than values of ScD because they relate to the molecular axis rather than the CF bond.Chain lengths of 16.6 and 17.5 A are calculated from values in table 1 for the D and F phase samples at 20"' including an addition of 2 A for the head group and terminal CF group. These are in excellent agreement with the X-ray results. The magnitudes of the order parameters for the fluorocarbon chain are generally similar to values reported for hydrocarbon chains.2s30 Mely et ~1.~~9~~ observed little change in chain order parameters at the hexagonal/lamellar boundary for hydro- carbon soaps (apart from the factor of two due to change in alignment of chains w.r.t. the director). Our results indicate that the molecular order is higher in the hexagonal phase than in the lamellar phase. This suggests that the molecule is longer in the hexagonal phase (at the low-water boundary) a fact that is consistent with the increase in surfactant dimension estimated from X-ray results." 6.CONCLUSION Our results show that by fitting the spectra obtained using multipulse techniques to remove the dipolar broadening it is possible to measure the order parameter S over a range of concentrations and temperatures. This in turn has enabled us to confirm the hexagonal phase structure and the rapid translational diffusion of the amphiphiles 48 LIQUID CRYSTAL SYSTEMS around the cylinder surfaces corresponding to localized cylindrical rotation. Com-parison between chain dimensions estimated from X-ray results and values calculated for particular models using the S values indicates the presence of rotational iso- merisation for the fluorocarbon chain.We would like to thank Dr. N. Boden and his colleagues for communication of results prior to publication. A. Losche and S. Grande Proc. 18th Congress Ampere (Nottingham) 1974 1 201. A. Jasinski P. G. Morris and P. Mansfield Mol. Cryst. Liq. Cryst. 1978 45 183; Proc. 19th Congress Ampere (Heidelberg) 1976 185. A. Johansson and B. Lindman in Liquid Crystals and Plastic Crystals ed. G. W. Gray and P. A. Winsor (John Wiley and Sons New York 1974) vol. 2 p. 192. G. R. Luckhurst Liquid Crystals and Plastic Crystals ed. G. W. Gray and P. A. Winsor (John Wiley and Sons New York 1974) vol. 2 p. 144. G. J. T. Tiddy Nuclear Magnetic Resonance (Spec. Period. Rep.Chemical Society London) 1975 vol. 4 p. 233 and 1977 vol. 6 p. 207. A. Pines and J. J. Chang Phys. Rev. A 1974 10,946; A Pines D. J. Ruben and S. Addison Phys. Rev. Letters 1974 33 1002. J. Urbina and J. S. Waugh Proc. Nat. Acad. Sci. U.S.A. 1974 71 5062. R. G. Griffin J. Amer. Chem. Sac. 1976 98 851. S. J. KohIer and M. P. Klein Biochem. 1976 15 967. lo E. Everiss G. J. T. Tiddy and B. A. Wheeler J.C.S. Faraday I 1976 72 1747. l1 N. Boden M. Holmes P. Jackson and K. McMullen personal communication July 1978. G. J. T. Tiddy J.C.S. Faraday I 1977 73 1731. l3 A. Abragam The Principles of Nuclear Magnetism (Clarendon Press Oxford 1974). l4 P. Mansfield J. Phys. C 1971 4 1444. l5 W.-K. Rhim D. D. Elleman and R. W. Vaughan J. Cheni. Phys. 1973,58,1772.l6 (a) U. Haeberlen in High Resolution NMR in Solids Selective Averaging in Advances in Magnetic Resonance ed. J. S. Waugh (Academic Press N.Y. 1977); (b) M. Mehring in N.M.R. Basic Principles and Progress ed. P. Diehl E. Fluck and R. Kosfeld (Springer- Verlag Berlin 1976). l7 P. Mansfield and U. Haeberlen Z. Naturforsch 1973 28a 1081. l8 A. N. Garroway P. Mansfield and D. C. Stalker Phys. Reu. 1975 11 121. l9 M. Mehring R. G. Griffin and J. S. Waugh J. Chew. Phys. 1971,55,746. ’O A. N. Garroway D. C. Stalker and P. Mansfield Polymer 1975 16 161. 21 N. Bloembergen and T. J. Rowland Phys. Rev. 1955 97 1679. 22 C. L. Khetrapal A. C. Kunwar A. S. Tracey and P. Diehl in N.M.R. Basic Principles and Pro- gress Lyotropic Liquid Crystals ed. P. Diehl E. Fluck and R.Kosfeld (Springer-Verlag Berlin 1975) vol. 9. 23 B. Mely J. Charvolin and P. Keller Chem. Phys. Lipids 1975 15 161. 24 W. Niederberger and J. Sedlig Ber. Bunsenges. phys. Chem. 1974 78 947. 25 H. Schindler and J. Seelig Biochem. 1975 14 2283. 26 G. W. Stockton and 1. C. P. Smith Chem. Phys. Lipids 1976 17 251. ’’G. W. Stockton C. F. Polnaszek A. P. Tulloch F. Huson and I. C. P. Smith Biochem. 1976 15 954. 28 K. Abdolall E. E. Burnell and M. I. Valic Chem. Phys. Lipids 1977 20 115. 29 J. H. Davies and K. R. Jeffrey Chem. Phys. Lipids 1977,20 87. 30 L. W. Reeves and A. S. Tracey J. Amer. Chem. SOC.,1975 97 5729. 31 I. S. Gradshteyn and I. M. Ryzhik Tables of Integrals Series and Products (Academic Press New York 1965) p. 403. 32 C. H. A. Seiter and S. I. Chan J. Amer. Chem. Sac. 1973 95 7541. 33 B. Mely and J. Charvolin Chem. Phys. Lipids 1977 19 43.

ISSN:0301-5696    

DOI:10.1039/FS9781300037

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Fourier Transform Multiple Quantum Nuclear Magnetic Resonance BY GARY DROBNY PINES STEVEN ALEXANDER SINTON P. WEITEKAMP DANIEL AND DAVIDWEMMER Department of Chemistry University of California Berkeley California U.S.A. Received 18th December 1978 The excitation and detection of multiple quantum transitions in systems of coupled spins offers among other advantages an increase in resolution over single quantum n.m.r. since the number of lines decreases as the order of the transition increases. This paper reviews the motivation for de- tecting multiple quantum transitions by a Fourier transform experiment and describes an experi- mental approach to high resolution multiple quantum spectra in dipolar systems along with results on some protonated liquid crystal systems.A simple operator formalism for the essential features of the time development is presented and some applications in progress are discussed. The energy level diagram of a system of coupled spins 1/2 in high field is shown schematically in fig. 1. The eigenstates are grouped according to Zeeman quantum number mi with smaller differences in energy within a Zeeman manifold due to the couplings between spins and the chemical shifts. For any eigenstate li) of the spin Hamiltonian H (in frequency units) H I i> = mi I i> I I i) = mi I i). The single quantum selection rule' of the low power C.W. experiment and the one dimensional Fourier transform experiment arises because (i I I 1 j) vanishes unless Simple combinatorial considerations show that the number of eigenstates decreases as \mil increases and the number of transitions decreases as lqijl increases.The highest order transition possible is the single transition with 141 = 21 where I is the total spin. For a system of N spins 1/2 transitions up to order N are possible. Detection of multiple quantum transitions in C.W. experiments is well kn~wn.~-~ Extension to high order transitions is not promising since the transitions observed are a sensitive function of r.f. field strength. This leads to difficult spectral simulations and experimental problems of saturation and sample heating. The alternative time domain experiment is the determination of multiple quantum transition frequencies by following the time development of multiple quantum coherences point by This work treats a class of such multidimensional I III I 1 -x+22 I I I I I I I I.I I I -X+-' I I4 2 FIG. 1.-Schematic representation of the high field energy level diagram of coupled spins 1 /2. Broken arrows indicate the forbidden types of transition observed in Fourier transform multiple quantum experiments. p1 p2 q=o frequency (Aw= 5.967 kHz ) FIG. 2.-Multiple quantum spectrum of benzene (1 5 mol %) in p-ethoxybenzylidene-n-butylaniline(EBBA) at 20 "C. The three pulse sequence was PI = 71/2~,P2 = ~/2~,P3 = n/2,. The magnitude spectra obtained for 11 values of r spaced at 0.1 ms intervals from 9.6 to 10.7 ms were added. The value of fl ranged from 0 to 13.824ms in 13.5 ps increments for each r.A single sample point was taken at f2 = r after P3. One half of a symmetrical spectrum is shown. DROBNY PINES SINTON WEITEKAMP AND WEMMER experiments in which the irradiation consists of pulses at the Larmor frequency. Time proportional incrementation of the r.f. phase (TPPI) allows separate determination of the spectra of all orders free from effects of magnet inhomogeneity. EXPERIMENTAL The spectrometer is of pulsed Fourier transform design with super-conducting magnet (Bruker) operating in persistent mode at a proton frequency of 185 MHz. Phase shifting was performed at 185 MHz by a digitally controlled device (DAICO 100D0898)under con- trol of the pulse programmer. Samples were approximately 400 mg sealed in 6 mm glass tubing after degassing by repeated freezing and evacuation.All observations are in the nematic phase. Synthesis of 4-cyan0-4'-[~H]~,pentyl-biphenyl was by the procedure of Gray and Mosley.8 RESULTS The spectrum of benzene dissolved in a liquid crystal served as a prototype in the development of the single quantum n.m.r. of complex spin systems in ordered phase^.^ The multiple quantum spectrum of ordered benzene is shown in fig. 2. The resolution is limited by magnetic homogeneity and the inhomogeneous linewidth is proportional to 141. P P n P s q=o 9=1 q=2 9=3 q=4 9=5 q=6 FIG.3.-MuItipIe quantum spectrum of benzene at 22 "C and TPPI pulse sequence. The sample is the same as in fig. 2. The pulses are PI = ~c/2~ = ~/24 P2 and P3 = x/2, where 9 = AWtl.The increment in 9 was 29.5 degrees and the increment in t1was 10 /is for each of 1024 points. The magnitude spectra for eight values of T between 9 and 12.5 ps were added. The magnetization was sampled at t = z. FOURIER TRANSFORM MULTIPLE QUANTUM N.M.R. The spectrum of fig. 3 demonstrates the use of the spin echo to remove inhomogene- ous line broadening and the use of time proportional phase increments (TPPI) to restore the offset. Resolution is limited by truncation of the multiple quantum free induction decay and scale of reproduction. The actual linewidth is less than 2 Hz for all orders and suffices to resolve all allowed transitions of all orders. An application of the TPPI method to the eight proton system of an alkyl-deuter- ated cyano biphenyl liquid crystal is shown in fig.4. All eight orders are observed. Resolution is limited by truncation. Actual linewidths are tlOO Hz in a spectral width of ~40 kHz for each order. 9=0 q=1 g=2 q=3 g=4 FIG.4.-Proton multiple quantum spectrum of 4-cyano-4'-['H1 I]pentyl-biphenyl at 23.3 "C by TPPI. The increments are 22.5 degrees in p and 1.5 ps in tl for each of 1024 points. The time r took five values between 0.5 and 1.0 ms and the magnetization was sampled at 64 intervals of 5 ps starting at t2 = (r +0.1) ms. DISCUSSION THREE PULSE EXPERIMENT The time development of the spin system during the pulse sequences of fig. 2 and 3 is conveniently discussed in terms of a spherical tensor operator expansion of the density matrix.For any time where Tt is the qth component of a spherical tensor operator of rank k." The label a completes the specification of a complete basis of tensor operators. The initial equilibrium density matrix is p(0) = c;l(o)Iz= c;l(o)T;l and immediately after a 71/2, pulse (q>H cultpl =n/2) DROBNY PINES SINTON WEITEKAMP AND WEMMER The Zeeman quantum number q is conserved during evolution under a high field Hamiltonian. Thus neglecting relaxation p(t) = k,% 1* 1 CkqT(t)TkyrL (6) at any time c after the initial 71/2 pulse and no multiple quantum coherence has been created. After a period of time on the order of the inverse of the coupling frequencies terms with k < 21 will be present. A second strong pulse may then rotate T:? into Tp with -k < q < k.Thus at time t,after the second pulse all orders with -21 < q < 21 have in general been created and evolve during the time t at the eigen- frequencies cuij= cui -cuj. If the only observable measured is the transverse magnetization corresponding in the rotating frame to the 141 = 1 operators I and I,, it is not possible to follow the evolution of orders with 141 # 1 directly. Rather a third pulse at time t after the second pulse is needed to rotate the various tensor components back to Tyl. These may then evolve into the signal observed at time t2 after this detection pulse. The signal may be written then as S(Z ti t2) == CA1(O)Tr[1+p(~ + + t2)]. (7) Viewed as a function of tl this is the multiple quantum free induction decay.It is collected pointwise by variation oft on successive shots and is an example of a multi- dimensional n. m.r. experiment. SEPARATION OF ORDERS BY FREQUENCY OFFSET In order to obtain an increase in resolution over the single quantum experiments it is necessary to separate the spectra of different order. Consider the decomposition of the density matrix at time 7(tl = 0) into Zeeman components 21 By construction p,(t) = 2 C:a(t)T:x and it follows from the definition of the ku spherical tensor operators that p,(' 9)= exp (i912)p4(') exp (-i9'2) = exp(iq9)p4(z)' (9) If we let 9 = Acut, then eqn (9) corresponds to a calculation of the effect of a frequency offset term -Awl in the rotating frame Hamiltonian.Thus a modulation by exp (iqdwt,) is caused by the offset shifting the spectrum to qAw as seen in fig. 2. The difficulty with this approach to separation of orders is that the effect of magnet inhomogeneity is proportional to (41. The sample volume at position r with offset Am@) contributes a term p,(z tl,r) = exp (iqAu(r)t,)p,(t + t,) and integration over Y leads to damping of the coherence with a time inversely proportional to 141. HIGH RESOLUTION SPECTRA BY TIME PROPORTIONAL PHASE INCREMENTS (TPPI) The Hahn spin echo technique may be used to remove the inhomogeneous broad- ening. A 71 pulse at t1/2 changes q to -q allowing a refocusing of the coherence at tl for all orders. However this 71 pulse also removes the separation of the orders which was a result of the frequency offset.54 FOURIER TRANSFORM MULTIPLE QUANTUM N.M.R. A solution to this dilemma is to view eqn (9) not as the effect of a frequency offset but as a shift of the r.f. phase. In particular consider the effect of preparing the system with pulses of phase p and @ = 9 + n at time zero and z respectively with I9 = I cos 9 -I, sin 9. Then p(t p) = exp (iOI,) exp (-iHz) exp (-iO’Iv) x p(0)exp (iO‘Z,) exp (iHr) exp (-iOZ9) = exp (iq1,) exp (iOZ,) exp (-iHz) exp (-iO’Zx) x p(0) exp (iO’I,) exp (iHz) exp (-iOZx) exp (-ipIz) = exp (iV4)P(4 exp (-Wz) = cexp (iqdpf3W. 4 The result is that again P,(L 9)= exp (iW)P&) but this modulation is now an artifact of the r.f. phase of the first two pulses and does not depend on the evolution of the system during t,.However since each point t of the signal is collected separately we may set p = Amt1 for some parameter Am thereby recovering an apparent offset. The actual evolution during tl may include an echo pulse to remove the effect of field inhomogeneity as in fig. 3 or a train of 71 pulses to remove the effect of small chemical shifts and heteronuclear couplings from the dipolar spectra. This TPPI technique may be compared to the method of phase Fourier transforma- tion (PFT) discussed The PFT method generates a signal array S(z t, t2,p) by repeating the experiment for each t and p where again p describes the phase of the preparation pulses as in eqn (10). Fourier transformation with respect to phase with q as the conjugate variable separates the orders.A second Fourier transformation with respect to t gives the spectra. In the TPPI experiment the phase and time dimensions are collapsed into one by the relation p = Awt,. A single time Fourier transformation gives the spectrum of each order with apparent offset qAcu as in fig. 3 and fig. 4. MULTIPLE QUA NTU M SPECTROSCOPY 0F LIQUID CRYSTALS Although the spectroscopy discussed is of general applicability it is worthwhile to note the particular suitability of the m.f.t.n.m.r. method to the study of liquid crystals. The diffusion present in such systems sharply reduces the intermolecular dipolar couplings. This allows one to obtain resolved spectra reflecting only the intramolecular couplings without dilution of the spin system.Combinatorial arguments suggest that it suffices in general to analyse only the 191 = N -2 and N -1 spectra to determine all couplings in a system of N spins 1/2. Since these transitions N N N involve only the relatively small Iml = --1 and -2 -2 Zeeman manifolds of 22 the basis of kets the diagonalizations are simpler than those needed for single quantum spectroscopy. Should the study of mixtures be of interest partial deuteration of the background species will reduce its contribution to the high order spectra more rapidly than to the single quantum spectrum and thus the requirement for isotopically pure synthesis is reduced. Applications in progress include the configurational analysis of both ring and chain regions of liquid crystals the study of relaxation effects in multiple quantum spectra DROBNY PINES SINTON WEITEKAMP AND WEMMER and improvement of signal to noise by removal of the dipolar Hamiltonian during detection and sampling of magnetization at many times t2.We would like to acknowledge the help of Mr. Sidney Wolfe in synthesis of the liquid crystals and of Terry Judson in preparation of the manuscript. Support for this work was by the Division of Materials Sciences Office of Basic Energy Sciences U.S. Department of Energy. D.P.W. held a Predoctoral National Science Foundation Fellowship. I. J. Lowe and R. E. Norberg Phys. Rev. 1957 107 46. W. A. Anderson Phys. Rev. 1956 104 850. J. I. Kaplan and S. Meiboom Phys. Rev. 1957 106 499.K. M. Worvill J. Mag. Res. 1975 18 217. (a)H. Hatanaka and T. Hashi J. Phys. SOC. Japan 1975,39 1139. (6) H. Hatanaka T. Terao and T. Hashi J. Phys. Soc. Japan 1975,39 835. W. P. Aue E. Bartholdi and R. R. Ernst; J. Chem. Phys. 1976,64,2229. (a)S. Vega T. W. Shattuck and A. Pines Phys. Rev. Letters 1976,37,43. (6) S. Vega and A. Pines J. Chem. Phys. 1977,66 5624. * G. W. Gray and A. Mosley Mol. Cryst. Liq. Cryst. 1976 35 7 1. A. Saupe Z. Narurforsch 1965 20a 572. lo A. R. Edmonds Angular Momentum in Quantum Mechanics (Princeton University Press Prince- ton N.J.; 2nd Edn. 1960) Chap. V p. 68. A. Wokaun and R. F. Ernst Chem. Phys. Letters 1977,52,407. l2 A. Pines D. Wemmer J. Tang and S. Sinton Bull. Amer. Phys. SOC. 1978,23,21.

ISSN:0301-5696    

DOI:10.1039/FS9781300049

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

High-Resolution I3CNuclear Magnetic Resonance in Solids BY EDWARD0. STEJSKAL AND THEODORE JACOB SCHAEFER R. STEGER Monsanto Company 800 N. Lindbergh Blvd. St. Louis Missouri 63166 U.S.A. Received 1st August 1978 A procedure is demonstrated for determining the relative contributions of spin-lattice and spin- spin interactions to TIp(C), the relaxation time characterizing the loss of spin-locked carbon polariza- tion. This involves the characterization of relaxation processes associated with several cross-polariza- tion experiments. Three glassy polymer Tlp(C)values are shown to be dominated by spin-lattice effects while a crystalline polymer relaxes through a spin-spin mechanism. The combination of cross-polarization,' high-powered heteronuclear decoupling2 and magic-angle spinning3p4 has made it possible to obtain high-resolution natural- abundance 13Cn.m.r.spectra in solid^.^*^ These spectra are sufficiently detailed to permit the relaxation behaviour of individual carbon lines to be studied. In particular there are several relaxation processes which can occur in cross-polarization n.m.r. experiments with the potential to yield information about molecular motions and interactions. In order to make use of these relaxation phenomena it is necessary to establish first whether they are the result of spin-spin or spin-lattice interaction^.^ To answer this question we have made 'H-l3C (1-S) cross-polarization (CP) measurements on both glassy and partially crystalline polymers and have charac- terized the following relaxation times T,,(SL) the time for polarization transfer in a matched CP experiment; T,,(ADRF) the time for polarization transfer when the protons have been adiabatically aligned in the dipolar field; Tlp(H) the time for loss of spin-locked proton polarization; Tlp(C),the time for loss of spin-locked carbon polarization; and TI, the time for loss of proton polarization aligned in the dipolar field.(Although it is conventional to refer to these relaxation processes by the relaxation times indicated we seldom find that they are all simple first-order processes.) We have devised a straightforward phenomenological analysis of these strongly related phenomena which has the ability to separate the fundamental pro- cesses which are occurring and identify the contributions of molecular motion.The results of this analysis agree well with an assessment of the relaxation phenomena based on a variety of qualitative physical arguments.' EXPERIMENTAL The "C n.m.r. experiments were performed at 22.6 MHz on a home-built 13C-'H double resonance spectrometer with an external 19F field-frequency lock. We employ quadrature detection * and spin temperature alternation for increased sensitivity and to obtain distortion- free spectra. The sample probe has a single r.f. coil which is double-tuned'O~l' for both I3C and 'H. This provides greater uniformity and conformity of the two r.f. fields. Spin-ning experiments are based on the Lowe ge~metry.~ E. 0. STEJSKAL J. SCHAEFER AND T. R. STEGER The relaxation phenomenon that interests us most is Tlp(C),both with and without sample ~pinning.~ However since spinning complicates the T,,(ADRF) process by interact- ing strongly with the proton dipolar order we have chosen to study the five relaxation pro- cesses on stationary samples.The further effects due to spinning may then be assessed with little trouble.12 Fig. 1 depicts the three CP pulse sequences that,were used. The SL se-.ao? I-S decoupling 'H 9Q ; SL 13C 0, .-1 .e G i 1 H l3 c IH I hold I l3C P time (schematic 1 FIG.1.-Schematic representations of the three cross-polarization (CP) pulse sequences used to study CP relaxation processes. In the first sequence (SL) polarization is transferred between carbons and protons each spin-locked in its own r.f.field. The r.f. fields have been adjusted to satisfy the Hartmann-Hahn condition. In the second sequence (ADRF) polarization is transferred after an adiabatic demagnetization in the rotating frame has aligned the protons in the dipolar field. The final sequence (TIP)depicts the sequence used to measure Tlp(C)after carbon polarization has been generated through a spin-locked contact. quence was used to obtain T,,(SL) and TIP(H). The TIPsequence was used to obtain Tlp(C). The ADRF sequence was used both to obtain TID(by varying the time beween the ADRF step and the start of the contact) and to obtain data from which T,,(ADRF) was ultimately derived. Table 1 summarizes the experimental data and the several parameters derived from them.It also identifies the four polymer systems that were studied. As may be seen in fig. 2 the methyl-carbon resonance in poly(2,6-dimethylphenyleneoxide) is clearly distinguishable in the spectrum. Similarly the a-methyl carbon in poly(methy1 methacrylate) and the aliphatic carbons in polystyrene can be isolated even without spinning. The crystalline component of polyoxymethylene is considerably broader than the rubbery component and may be identified on that basis. We chose one crystalline polymer and three glassy polymers to provide a variety of degrees of molecular motion for contrast. HIGH-RZSOLUTION l3cN.M.R. IN SOLIDS TABLE 1 .-lH AND I3CRELAXATION PARAMETERS AT 30°CFOR FOUR SOLID STATIONARY MOULDED POLYMER PLUGS OF DIMENSIONS COMPARABLE WITH THOSE OF R.F.COIL polyoxymethylene polystyrene poly(methy1 POlY(2,6-(crystalline (aliphatic methacrylate) dimethylphenyl-component) carbons) (a-methyl ene oxide) carbon) (methyl carbons) 36 36 36 36 10 7.2 5.9 3 .O 1000 1000 1000 1000 167 52 14 4.8 50 2.8 7.7 30 50 1.2 8.O 20 20(85%) 30(85%) 1 20(85%) 500(85%) 2( 15%) 3( 15%) W5%) 50(15%) 8.5 12.8 51 213 12 15 56 210 5.5(90%) 12(90%) 1OO(UO%) 0.4( 10%) 2.4(10%) 5(10%) -2.4 8.6 34 9.0 3.0 10 32 0 81 83 85 . 0.01 10 20 30 tlms FIG.2.-Typical Tlp(C)relaxation data. The insert spectrum of poly(2,6-dimethylphenyleneoxide) is typical for the solid in the absence of magic-angle spinning; the broad aromatic region is dearly distinguishable from the narrower methyl region.The data points represent the peak amplitude S of the methyl region in arbitrary units as a function of hold time. The average scatter is <l%. For these measurements the contact time was I ms and H1 was 28 kHz. Each point represents 800 replications accumulated in 1600 s. The sample was in the form of a moulded plug with a volume of 0.9 cm3. E. 0. STEJSKAL J. SCHAEFER AND T. R. STEGER DATA ANALYSIS The ADRF experiment contains all of the elements of relaxation to be c~rnpared.'~ The equation governing the evolution of the carbon signal S during the contact time is dS -S0e-'/'1D -S S dt-TP TPL' (1) where we have used T:s for TIs(ADRF) TpLto represent the (spin-lattice) relaxa-tion process that dissipates S through contact with the lattice and Soto represent the total carbon polarization available in the absence of dissipative relaxation processes.If S =Si,when t =0 then Sirepresents carbon polarization developed during the rise of the carbon r.f. field presumably during the short time when that field and the proton local field nearly match. As we shall see below we may make the substitution l/TlP(C)=VTPL +1/T& (3) with the result that eqn (2) becomes We note that The Tlpexperiment is analysed in similar terms.' If no net proton polarization winds up in the dipolar field we can set So to zero. Si now represents the carbon polarization developed during the initial CP process. Thus as anticipated by eqn (3) Note that Tis still governs the spin-spin coupling between the spin-locked carbons and the protons in the dipolar field even though the latter have no net polarization.In the event that all proton dipolar order is not suppressed that is if Sodoes not vanish exactly the magnitude of Socan be estimated in a T, experiment from which the spin- locked carbon-proton contact has been omitted. Eqn (4) then justifies removing the contribution of a non-vanishing So from normal Tlp data by subtraction. This correction was made on the Tlpdata reported in this paper although it was scarcely necessary except for polyoxymethylene. One further caution should be mentioned. Following the removal of the proton r.f. field for a period of several proton T2values the carbon polarization is perturbed; after that it settles down into a smooth Tlpdecay.This can be seen in the first point in fig. 2 taken after 10 ,us hold. We do not normally begin collecting data in this time domain but wait 20-50 ,us. The SL experiment is similar to the ADRF experiment except that several of the parameters are of different 01-igin.I~ The appropriate differential equation is 7' where we have used HIGH-RESOLUTION l3C N.M.R. IN SOLIDS for T,,(SL) and replaced So and T, by S and T,,(H) respectively. TIPLreplaces TpLsince the protons are spin-locked by the r.f. field. Since S = 0 when t = 0 The relationship between S and Sois given by5 sM(YS Hl/yl HL)E (9) where ys and y1 represent the carbon and proton gyromagnetic ratios Hl the r.f. field applied to the carbons and HLthe local field of the protons coupled to the carbon of interest.The local field HL can be estimated from either the proton second moment (Hi z 3M2)or T2(by assuming a reasonable line ~hape).'~ The factor E represents the efficiency of the ADRF transfer. In the development just given it has been assumed that T,,(SL) T,,(ADRF) Tl,(C) and TpL(C)are simple first-order time constants. For polymers this is generally not the case a fact we ascribe to dynamic structural and orientational heterogeneity in the solid. [TIDand Tl,(H) have spin diffusion to help eliminate this heterogeneity; carbon relaxation processes do not.] The easiest way to deal with this complication is by a multiple relaxation-time model. (Since we are dealing with polycrystalline or amorphous systems we do not see transient oscillation^^^ in the various CP processes.) For example TlPmight be represented by a two-phase model TlPSa(fraction fa) and Tlp,b (fraction fb) where fa +f = 1 and (Tip) = dfa/Tlp,a +fb/Tlp,b)-l* The average value (Tl,) also corresponds to the relaxation time derived from the initial slope of the relaxation curve.We prefer this quantity when a single number is to be used to describe the relaxation process since it is the most completely representa- tive of all the processes going on and can be defined by a relatively few data points. (It does however require high-quality data to measure accurately.) Our relaxation data clearly required that both TpL(C)and T,,(ADRF) be treated as non-exponential processes. We chose to use a two-phase model for each giving rise to a system of four different phases as the most comprehensible way to introduce heterogeneity.In this case eqn (5) must be modified to Note that although after a few milliseconds the T,,(C) decay seems to become mono- disperse this does not mean that the effects of the T,,(C) and T,,(ADRF) dispersions disappear early in the ADRF experiment. As the polarization builds up through the influence of T,,(ADRF) it is simultaneously pulled down by the T,,(C) process. This competition goes on throughout the entire ADRF experiment. RESULTS Fig. 3 portrays the results of our T,,(ADRF) measurements. For each system we also measured the following quantities H1 SM,Si,Tl,(H) TID,(Tlp(C))and the rest of the Tl,(C) decay.We estimated HL from proton n.m.r. data and chose E = 0.75 which gave an estimate of So. These quantities (except for SMand with So normalized to 1000) are given in table 1. Also given is (T,s(ADRF))t = 0 derived from eqn (10) and the slope of the data near t = 0. Note that we do not take the slopes directly from fig. 3 which is a logarithmic plot but from a linear plot. To obtain the curves plotted in fig. 3 we adjusted the parameters of the T,,(ADRF) and E. 0. STEJSKAL J. SCHAEFER AND T. R. STEGER TpLrelaxation processes until a reasonable fit was obtained. It became apparent early that TpLwould not contribute significantly to the polyoxymethylene relaxation data. This simplified the analysis of that particular curve. From the polyoxy- methylene fit we obtained the particular two-phase TI,(ADRF) pattern (1 5% re-laxing ten times as fast as the rest) and the value of E both of which were used in -----0 5 10 15 tlrns FIG.3.-Evolution of carbon polarization S in the TIs(ADRF) experiment for four solid stationary polymers polyoxymethylene poly(methy1 methacrylate) poly(2,6-dimethylphenylene oxide) and polystyrene.Further details are given in table 1 including the parameters determining the curves fit to the data. all four fits. The breakdown of the TpLtwo-phase pattern into 10-90% is charac- teristic of most of our T,,(C) data-as the fitting procedure progressed it also seemed appropriate for TpL. The final parameters arrived at are given in table 1. We also calculated (TIs(ADRF)) and (TpL) for comparison with (T,,(ADRF) jt= 0 and (Tlp(C)).Finally a comparison between (TI,(ADRF)/ and <TPL)gave rise to the estimate for the spin-lattice part of (T1,(C)} the last entry in table 1. For all three glassy polymers the spin-lattice contribution to (T1,(C)) is far more important than the spin-spin contribution. DISCUSSION We have presented a procedure for analysing the origins of the Tl,(C) relaxation process. The weakest part of this analysis from a quantitative standpoint is the estimation of So relative to Si. However changing So by 20% does not change the fact easily seen in fig. 3 that in those systems in which spin-lattice processes dominate S never rises to anywhere near So during the ADRF experiment even if the T, decay is allowed for.Clearly the dissipative effects of spin-lattice interactions dominate the constructive effects of spin-spin interactions in these systems. In general this behaviour is diagnostic of significant amounts of spin-lattice processes contributing to Tl,(C). No doubt a more elaborate fitting procedure could have produced better fits to the data. That was not the point of this exercise. The point was to show that a HIGH-RESOLUTION l3cN.M.R. IN SOLIDS phenomenological examination of the relaxation data could show that in some systems Tl,(C) must be dominated by a spin-lattice process even though in others a spin-spin process may be dominant. No appeal to detailed physical estimates of the relative importance of these two modes of relaxation is needed.A finer adjustment of the fitting parameters would not change these conclusions. There are other methods for reaching similar conclusions that make use of specific physical models (such as H1 dependence of relaxation) but they are less reIiable because of the oversimplifications implicit in the models. Naturally we do not expect to apply our full procedure often only often enough to identify classes of systems and ranges of experimental conditions where the origin of T,,(C) is clear enough to make it a useful parameter for characterizing molecular motion or structure. For ~ instance so long as HI > HL,a system with motion for which T~ -kHz will prob- ably be dominated by spin-lattice processes. This will include most glassy polymers and biopolymers at room temperatureI5 and probably plastic crystals near the melting point.On the other hand crystalline polymers and small organic molecules well below the melting point will show little effect of spin-lattice processes on T,,(C). It is possible that heavily cross-linked polymers will form an intermediate case to be decided individually. Although we have applied this analysis to non-spinning samples the general conclusion as to the importance of spin-lattice interactions does not change if the samples are spun at high speed (-kHz). Spinning perturbs the T,,(C) experiment by collapsing the dispersion of relaxation rates due to orientation relative to H, by plac- ing the sample under dilational stress which can alter molecular motions by modulat- ing the spin-spin interaction and by adding additional (usually negligible) mechanical motion to the spin-lattice interaction.l29 l5 We conclude by recommending that T,,(C) be used in much the same way that other n.m.r. relaxation times are. Seldom is it true that TI,for instance is determined solely by a single motion of a single internuclear interaction; nevertheless if the dominant source of relaxation is known Tl can provide useful information. Similarly Tlp(C)can be used to understand those classes of systems in which its dominant source is clear even if a full theoretical analysis does not yet exist. The procedure given in this paper need only be used to identify the behaviour of classes of systems or to facilitate an in-depth study of a particularly difficult system.S. R. Hartmann and E. L. Hahn Phys. Rev. 1962,128,2042. F. Bloch Phys. Rev. 1958 111 841. E. R. Andrew A. Bradbury and R. G. Eades Nature 1958 182 1659. 1. J. Lowe Phys. Rev. Letters 1959 2 285. A. Pines M. G. Gibby and J. S. Waugh J. Chem. Phys. 1973 59 569. J. Schaefer and E. 0.Stejskal J. Amer. Chem. Soc. 1976 98 1031. ’J. Schaefer E. 0. Stejskal and R. Buchdahl Mncromolecules 1977 10 384. E. 0. Stejskal and J. Schaefer J. Magnetic Resonance 1974 14 160. E. 0.Stejskal and J. Schaefer J. Magnetic Resonance 1975 18 560 lo V. R.Cross R.K. Hester and J. S. Waugh Rev. Sci. Instr. 1976 47 1486. M. E. Stoll A. J. Vega and R. W. Vaughan Rev. Sci. Instr. 1977 48 800. l2 J. Schaefer E. 0. Stejskal T. R. Steger and R. A. McKay manuscript in preparation. l3 D. E. Demco J. Tegenfeldt and J. S. Waugh Phys. Rev. B 1975 11,4133. l4 M. Goldman Spin Teniperature and Nuclear Magnetic Resonance in Solids (Oxford Univ. Press London 1970) p. 29. l5 J. Schaefer and E. 0. Stejskal in Topics in Carbon-13 NMR Spectroscopy ed. G. C. Levy (Wiley-Interscience N.Y. 1979) vol. 3 chap. 4.

ISSN:0301-5696    

DOI:10.1039/FS9781300056

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

High Resolution I3C Nuclear Magnetic Resonance in Cured Epoxy Polymers Rotating Frame Relaxation BY A. N. GARROWAY, W. B. MONIZAND H. A. RESING Chemistry Division Naval Research Laboratory Washington D.C. 20375 U.S.A. Received 27th July 1978 The combination of cross-polarization dipolar decoupling and magic angle spinning produces high resolution l3C n.m.r. spectra in organic solids. Carbon rotating frame relaxation is complicated by the presence of the strongly interacting proton spin system spin-spin and spin-lattice processes will both promote relaxation. Dipolar order is created when the proton system is spin locked and is rapidly destroyed by magic angle spinning. Some implications of these spin-spin mechanisms on determination of I3C TIPare examined and illustrated by an experimental study on a model cured epoxy polymer diglycidyl ether of bisphenol A (DGEBA) cured with piperidine.For this specimen at room temperature we find that for r.f. fields above z 40 kHz the decay of the carbon spin lock magnetization after the first 100ps or so is not dominated by spin-spin relaxation and can reflect molecular motion. Over the temperature range 242-324 K the TIPfor the methyl carbon is described by an activation energy of 11 kJ mol-'. From the truncation of the dipolar hamiltonian by Van Vleck' to magic angle spinning2 to the rather complex multiple pulse sequence^,^,^ it is well established that coherently driving nuclear spin-spin interactions can selectively average them away. It has almost become an article of faith that a suitable combination of rather robust averaging schemes can convert a solid into a liquid insofar as coherent averaging in spin or real space can substitute for rapid and random isotropic motion.High reso-lution I3C n.m.r. in organic solids is a case in point; here the solid state methods of cross-p~larization,~~~ dipolar decoupling 'and magic angle spinning have generated reasonably narrow spectra&" (in amorphous polymers linewidths of a few p.p.m. and substantially less in crystalline solids). Such encouraging results should not blind us to the presence of the strongly interacting proton spin system. It is appealing' to examine I3C rotating frame relaxation rates. In the absence of strong proton-proton coupling these reflect molecular motional fluctuations in a rather interesting frequency regime (say 25-100 kHz) and further as the carbon- carbon coupling can generally be ignored the carbon nuclei will monitor local motions rather than performing the sort of averaging implicit in a proton relaxation rate.Here we shall examine some aspects of the complications of tight proton coup- ling in the determination of I3C rotating frame relaxation and specifically how spin- spin relaxation is to be distinguished from spin-lattice relaxation. While these are rather general concerns we shall concentrate on organic solids under conditions of magic angle spinning and apply some of these notions to the results of a preliminary study on a model cured epoxy. Different considerations apply when the sample is not spun and will be examined elsewhere.12 l3cN.M.R.IN POLYMERS EXPERIMENTAL A Bruker SXP spectrometer modified for cross-polarization and magic angle spinning at a carbon frequency of 15 MHz was employed. Both proton and carbon resonances can be independently observed and variable r.f. fields up to 70 kHz can be applied to each species. Unless otherwise noted a magic angle spinning speed of 2 kHz was used. The model epoxy was prepared from commercial diglycidyl ether of bisphenol A (DOW DER 332) and 5 % by weight of piperidine and cured for 16 h at 393 K. The specimen was cast in a mould into the form of a Lowe-Kes~emeier-Norberg~~-~~ type spinner. THEORETICAL In this section we look for manifestations of spin-spin coupling on 13C rotating frame relaxation.The plan is to decide how TIPshould be measured and also to estimate the spin-spin contribution to the relaxation rate. (Here Tip is defined as the observed rotating frame relaxation time constant.) We shall consider spin-spin processes under rigid lattice conditions and use the results as an upper bound on spin-spin rates at higher temperature; we adopt the naive view that higher tempera- ture introduces spin-lattice processes and reduces purely spin-spin couplings. In the following we assemble a number of results for spin-spin coupling and specialize them to organic solids. The hamiltonian governing the spin system is comprised of proton-proton (11) and proton-carbon (IS) dipolar coupling as well as interactions with the static and r.f.irradiation. Carbon-carbon coupling is ignored. If each species is irradiated on resonance with r.f. fields wll,coIS(=yIBII,ysB,,) then in the doubly rotating frame5*15 where HII(O'is the usual (high field) homonuclear dipolar hamiltonian' and HII(ns) is a nonsecular term which when viewed in this frame will involve frequencies at ~2~0,~. Similarly the nonsecular heteronuclear term HIS("')involves & wlI & qS; in the event that wlI = wls (Hartmann-Hahn ~ondition),~ part of the IS interaction is restored to secularity. All nonsecular terms corresponding to oscillations at the static field Larmor frequency cool coosare dropped. We wish to examine the entire time evolution of the S spin lock magnetization (S,) under the influence of the spin-spin hamiltonian of eqn (1).It is most con- venient to divide the behaviour into short and long time domains although one can pass smoothly16 through both regimes but at the expense of computational com-plexity which is unwarranted here. In the short time period the subject of transient oscillations has been treated in detail for the case of sudden application of static and r.f. fields to dipolar ordered spin locking by r.f. pulses in which the magnetization is obtained by a 71/2 preparatory pulse 21 p22 and for heteronuclear cros~-polarization.~~~~ These effects can be estimated by a simple argument. A large static or r.f. field splits the hamil- tonian into secular and nonsecular terms. A sudden change in the hamiltonian introduces coherences in the nonsecular terms but as a taste of this non-equilibrium state is transferred to more and more spins via strong dipolar coupling the oscilla- tions die out in prelude to the establishment of a spin temperature determined solely by the secular part of the hamiltonian.If the (appropriate) initial inverse spin temperature is pi,then the energy associated with such a coherence is" A. N. GARROWAY W. B. MONIZ AND H. A. RESING By conservation of (total) energy the influence of this decay can be calculated. This energy is associated with the “ step ” in the “ step plus oscillation ” description” of transient oscillations. First consider spin locking the proton (I) system. A 42 preparatory pulse is followed at t = 0 by the spin lock pulse.At t = 0 the initial magnetization is (Iz)i and the inverse temperature of the spin lock state is Pli= ~ooor/co,r where Podescribes the lattice temperature. The energy associated with the oscillation of the nonsecular hamiltonian is then for on resonance irradiation E = PIi(tr [H(yi)]Iz + tr [H(yl)l2}/tr I (34 where M(;J and M(f2 are the second moments of the I1 and IS interactions and N, Ns are the number of spins. This energy is supplied by the proton spin lock reservoir and so both the spin lock signal and spin temperature are diminished according to in agreement with explicit calculations.22 The IS contribution may be ignored in this expression and in the following. As these oscillations dephase the energy ~(~owoI/wl,)A4(~~ is transferred into the (secular) dipolar reservoir.As the local field under irradiation is +coL = 3[3M($]+ this implies an effective dipolar inverse spin temperature during irradiation of P; = 3Pooor/coo,l = 3p1i. When the r.f. field is removed the full (high field) dipolar hamil- tonian becomes secular and the effective dipolar spin temperature is then Thus the dipolar system is described by a temperature not very different from the initial spin lock temperature (DIi)or the spin lock temperature after the transient oscil- lation eqn (4). These circumstances are indicated schematically in fig. 1. We have implicitly assumed wII is sufficiently large to preclude any further cross-relaxation between the I dipolar and I spin lock systems during this interval.We also inquire into the transient arising when the S spins are spin locked following a 7t/2 pulse. Here only the IS term becomes nonsecular and after these oscillations die out in something like the T2of the I1 coupling the S spin lock magnetization is fractionally reduced as 22 In the experiments to be presented the S magnetization was prepared not by a n/2 pulse but rather by a single contact cross-polarization between carbon and proton spin lock states matching the Hartmann-Hahn condition; we shall refer to this as a matched SL cross-polarization. The pulse sequence is also shown in fig. 1. The cross-polarization contact times (1 ms) are sufficiently long to allow any transient oscillation during cross-polarization to die out. As the heat capacity of the S spin lock system is negligible in comparison to that of I the final inverse spin temperature of all the reservoirs is approximately PI given by eqn (4).Removing the I r.f. field at the start of the S TIPmeasurement makes the IS interaction nonsecular. Two types of oscillations ensue. The first produces a decrease in the S spin lock magnetization identical to eqn (6). The second arises from the IS dipolar order established during l3C N.M.R. IN POLYMERS cross-polarization and is analogous to the transient expected when S spins are cross- polarized from a dipolar ordered ~tate.~.'~ We find that the second mechanism fractionally increases the spin lock magnetization by x+[Mfi)/co&]and so partly com- pensates the decrease of eqn (6).We therefore expect a transient when the carbon magnetization is prepared either by a n/2pulse or by cross-polarization. lHRF~ 13C RF -------c 1 'Hi pc -W Wl" 1H FIG. 1.-R.f. pulse sequence and spin temperatures appropriate to a TIPmeasurement. The carbon magnetization is prepared by cross-polarization against a proton spin lock state. The inverse spin temperatures of the dipolar proton and carbon spin lock systems are indicated as &-, BH and BC,respectively; PHiis the initial inverse temperature. If the sample were mechanically rotated the dipolar order would die out rapidly (see text and fig. 2). The implications of these step reductions are (i) the initial rapid drop in the carbon magnetization during a spin lock pulse is related only to the strength of the proton- carbon dipolar coupling and (ii) in the case the carbon magnetization is prepared by SL cross-polarization the protons will be in a state of dipolar order at the start of the carbon spin lock pulse.This last observation will be later modified if the sample is spun. In the long time regime a simple thermodynamic can be applied. The rate (Ts-D)-l at which the S spin lock state decays through its coupling to the I dipolar state (D) has been discussed at length3*16*23*24 and under the assumption that the correlation function for the spin fluctuations responsible for the coupling is lorentzian then where the fluctuation time is24 A. N. GARROWAY W. B. MONIZ AND H. A. RESING and where are defined conventionally.(This relaxation time is also called9*16 TAyFF,though the dipolar state need not be prepared by adiabatic demagnetization in the rotatingframe.) The cross-relaxation rate (TI-s)-l when both I and S are irradiated has also been examined :3-5~16there a gaussian correlation function seems more appropriate. In this case =+n*MMfg)zI-s {+exp [-$(co, -~o,~)~.r~-,] + 3 exp [-$(% +~ls)2~21-s1L(8) where the correlation time zI-s is given el~ewhere~*~*'~ and is of the same order of magnitude as zS-,. Interestingly the time constant Ti-s with wls =0 is appropriate for the T2,of the free induction decay of the S spins under I deco~pling.~~ The stronger r.f. field dependence in eqn (8) ensures that for fields beyond some size the T2effects governing the carbon linewidth will diminish more rapidly than those cross-relaxing the S spin lock state :narrow lines do not provide a bound on the spin-spin contribu- tion to TIP.(However if spin-lattice effects do indeed predominate then T2s= TIPs when the relevant r.f. fields are The actual effect of the S spin lock to I dipolar state cross-relaxation depends on the relative spin temperatures of the two reservoirs. What is the appropriate dipolar temperature? If the sample is not spun then as we have just seen the carbon and dipolar temperatures are not too different during the time that only the carbons are spin locked. However spinning the sample about any axis not parallel to the static magnetic field will contribute to the dipolar spin lattice relaxation rate (T',,) -1.27-29 For perpendicular spinning the contribution is,27-29for a powder of spin 4 where SZ -Lf,,,/27ris the spinning speed and the factor [3n]arises29 by the assumption of a lorentzian correlation function.The appropriate dipolar fluctuation time is based on ref. (30) I1 G2=3lW2'* (9b) The theory is not yet presented for spinning at the magic angle but for slow spinning one expects the same qualitative features. We remark that magic angle spinning an organic solid at 2 kHz will reduce the effective T, down to 100 pus or less. So magic angle spinning ensures that any proton dipolar order (created by the transient oscillation during the proton spin lock) is dissipated over the order of 100 ,us and for times much longer than this the carbon spin lock state sees a completely dis- ordered proton system which is tied strongly to the lattice.Hence this pathway a carbon-proton spin flip costing the carbons wlSin energy followed by rapid dissipa- tion of the proton dipolar order will compete on an equal footing with the (motional) spin-lattice contribution to TIP. (If the sample were not spun then T, might become rate limiting.)12 We have ignored sample spinning except for its influence in T,,. Provided the spinning is slow compared to the various fluctuation frequencies of the order of the proton-proton local field coL,the effect of sample spinning on other spin-spin processes can be regarded as introducing side-bands via the amplitude modulation of HIS:the narrowing of the proton-proton fluctuation spectrum is not ~ignificant.~' Hence the l3C N.M.R.IN POLYMERS frequencies cols should be replaced by cols & 52 this does not qualitatively alter any conclusions for the regime at hand in which cols col > coL 9 52. With this qualitative theoretical framework we turn now to some experimental results on a model epoxy diglycidyl ether of bisphenol A (DGEBA) cured with piperi- dine. RESULTS AND DISCUSSION We wish to establish experimentally the fate of dipolar order under mechanical spinning. Fig. 2 shows the contribution to the dipolar spin-lattice relaxation rate due , 0.l0.1 0.2 0.5 1.0 2.0 5.0 to mechanical rotation perpendicular to the static field for the cured epoxy at room temperature. The dipolar state was prepared by the two pulse Jeener-Broekaert sequence32 and the remaining magnetization monitored by a 71/4 proton inspection pulse.For reference the " static " TI,is 1.1 ms while the extrapolated spinning con- tribution at 2 kHz is ~665ps; though at that speed one should really examine how dipolar order is created under spinning conditions. In the figure the straight line depicts a square law dependence on rotation speed and reasonably represents the data. The correlation time extracted from the data by means of eqn (9a)gives a value for the dipolar fluctuation time of Z = 19 ps. From the initial slope of the proton free induction decay also at room temperature we find a proton second moment of 8.4 & 0.4 GL. From this value and the relation between the moment and dipolar fluctuation time eqn (9b),we estimated zD = 22 ps in qualitative agreement with the above sample spinning result.(For this epoxy we find that at room temperature the A. N. GARROWAY W. B. MONIZ AND H. A. RESING proton second moment is not except for the methyl contribution significantly motionally averaged; such averaging is seen at 325 K and above.) The foregoing establishes a dilemma. We would like to compare the observed Tlpwith the spin-spin relaxation time TS-, measured by preparing a state of dipolar order and using it to cross-polarize the S spin lock state. However the sample spin- ning required for high resolution spectra also rapidly destroys dipolar order. Now high speed spinning is not mandated; we have performed some experiments at spin- ning speeds of 400 Hz for which the effective T, is only 700 ps.As we shall find the observed carbon Tlpvalues range from about 2.5 to 60 ms hence T's-D B TIDand under these conditions it is quite difficult to measure Ts-Ddirectly. Instead we shall appeal to the r.f. field dependence of the observed Tlp,noting the exponential depend- ence embodied in Ts-D,eqn (7a) compared to the weaker dependence expected for motional effects.33 To compare the field dependence of the various I3C Tlpvalues in the epoxy we should like to normalize by dividing out the interaction strength Mi;) which appears in Ts-Dor indeed in the equivalent expression for the relaxation induced by isotropic motion. Accordingly we normalize by TI-s(0) the matched SL cross-polarization time given in eqn ($a)with wI1-wls = 0.Hence -~ The correlation times z,-~ z ~ are comparable and are determined largely by I1 rather than IS couplings. [We do not take eqn (8) too seriously especially when M\i) N -MI:) e.g. for protonated carbons for then the initial transient' will play a large role in the cross-polarization.] There is however an effect of sample spinning on T,-,(O) which should be examined. For reference the 13Cspectrum of the piperidine cured DGEBA epoxy is shown in fig. 3. For each of the seven resolved peaks the dependence on spinning of the matched SL cross-polarization times Tl-s(0)[TCH= T,-,(O)] is shown in fig. 4 and has been discussed elsewherez6 in a different light. Here the r.f. fields were 38 kHz DGEBA + PIP I 2 00 100 0 p.p.rn.FIG.3.-I3C spectrum of the piperidine (PIP) cured DGEBA epoxy polymer at room temperature. The assignments have been discussed" and the structure indicates a possible polymerization me~hanism.~~ l3cN.M.R. IN POLYMERS and the proton T,,found to be 2.6ms. The relaxation behaviour of the non-protonated carbons shows some averaging from the magic angle spinning. The protonated carbons relax so rapidly due to their larger interaction M,',2),that the cross-polariza- tion process is largely completed in the time the specimen rotates say one-half revo- lution. We shall not attempt to fit these data to any model of narrowing but note rather that the reported time constants reflect an averaging for the non-protonated but not for the protonated carbons.To normalize in a more consistent fashion we shall estimate the non-spinning relaxation times by using the values for the 1 kHz rotation. I I I 500 DGEBA + PIP X AA x 4 oc 0 0 non -protonated v) 300 I \ 4 I h-200 T + + + I 4 100 P Q protonated U 0 0 1 2 3 froti k ti z FIG.4.-Magic angle spinning alters the cross-polarization rates. Here TCH[!T,-40)] is the time constant for spin lock cross-polarization under the Hartmann-Hahn condition at r.f. fields of 38 kHz. We then display in fig. 5 the r.f. field dependence of the 'jC TIPtimes (at 2 kHz spinning) normalized by the TCHvalue (at 1 kHz) of the previous figure. The TIP relaxation times were measured mindful of the concern over the initial transient no data within the first 500 ps were used to determine TIP.The decay of the magnetiza- tion of the protonated aromatic carbon is certainly non-exponential and the reported time constants are a fair description of the behaviour over the first 80 yo of the decay. In the absence of a concrete theory for the decay a single parameter must suffice. From fig. 5 we see that the values T,,/T,- [or equivalently the ratios of the spec- tral densities J(0)/J(culs)],cluster within about a factor of three at each field and depend rather weakly on r.f. field. We can make a crude estimate of the expected A. N. GARROWAY W. B. MONIZ AND H. A. RESING r.f. field variation of the spin-spin contribution Ts-D to the observed spin-lattice relaxation.The correlation time governing the dipolar fluctuations which relax the carbons is given in eqn (7b). To overestimate the spin-spin effects we produce an underestimate of the correlation time zest,by assuming that in this epoxy the correla- tion time is independent of the details of the local IS coupling; that is We have both the experimental proton second moment and the fluctuation time z, = 19 ps from the TI sample spinning experiment; we use the latter value to infer from eqn (96) z~~~= 3+2D = 33 ps. This fluctuation rime will determine the r.f. field dependence of the pure spin-spin processes. In fig. 5 the broken line represents the ~ spin-spin contribution predicted by eqn (lo) with T~ =-rest= 33 ps and assuming that T1-s = 7S-D.This curve presumes that TCHis correctly given by eqn (8) which is certainly not the case for protonated carbons. As a second and more restrictive 1000 500 200 x 100 I LU . 0. L- P g 50 I DGEBA+ PIP I 20 10 I 1 I 30 50 70 f (=YB,/2n) /kHz FIG.5.-R.f. field dependence of the 13C TIPtimes. The Tlp values have been normalized by TCH (at 1 kHz spinning). The broken line estimates the field variation expected if the observed rotating frame relaxation were exclusively determined by spin-spin coupling TS-,; see eqn (10) in the text. The dashed line represents the same field dependence and has been drawn through the 32 kHz data as an even more restrictive estimate; there is no evidence whether or not the low field data are deter- mined exclusively by spin-spin effects.As the relaxation times at 43 and 66 kHz are shorter than those predicted for purely spin-spin effects the high field results (and perhaps even at 32 kHz) indicate molecular motion. l3cN.M.R. IN POLYMERS estimate suppose that the relaxation at low field were due solely to spin-spin events the dashed curve in fig. 5 represents that hypothesis with the same exponential field ~ dependence as before (T =~ 33~ ps). Clearly the T, values at higher field (43 and 66 kHz) cannot be due to spin-spin effects; they are too short. We have no experi- mental indication either way about the 32 kHz data. Hence the conclusion of this rather lengthy argument is that above around 40 kHz for this epoxy at room tempera- ture the I3C TIPvalues are not determined exclusively by spin-spin events but reflect spin-lattice effects.This is not an idle exercise; in oriented polyethylene at room temperature the apparent 13C TIPis dominated by spin-spin effects even at an r.f. field of 80 kHz." We now examine the temperature dependence of the I3C TIPmeasured with an r.f. field of 55 kHz for which the relaxation times should indicate molecular motions. In fig. 6 the T, data are presented directly without normalization by TCH. Over 242-324 K the only significant temperature dependence arises from the methyl group. The activation energy inferred from the data (dashed line) is 11 kJ mol-' (2.6 kcal mol-') in quite fortuitous agreement with the value (2.6 kcal mol-') ob-tained from rather complete proton relaxation studies3' in long alkanes.The other spectral line (0) showing a rather weak temperature variation is unfortunately an un- resolved peak comprising methylene and methine resonances and it is unclear how to 100 0 0 0 0 50 X x x 800 0 0 8 X < X x x L4 \ 20 ul \ \ E 3. \+ Q 0 B k- 10 P 4 4 a DGEBA + PIP 5 ~~ 2 3.0 3.5 4.0 4.5 103/ T FIG.6.-Variation in I3C TIPvalues with temperature. Only the methyl resonance shows a well- represent defined dependence with an apparent activation energy of 11 kJ mol-'. The squares (0) an unresolved methylene-methine resonance and little can be inferred from its behaviour. A.N. GARROWAY W. B. MONIZ AND H. A. RESING 73 interpret the resulting composite relaxation rate. It may be that this dependence reflects the rather labile nature of the epoxy molecule at the polymerization reaction site. In conclusion the determination of 13CTIPis complicated in solids by the presence of strongly coupled proton system. Transient oscillations will fractionally diminish the carbon spin lock magnetization over the time scale of approximately the proton- proton T2and create dipolar order in the case where carbon magnetization was created by cross-polarization. Spin-spin fluctuations can transfer order from the carbon spin lock to the dipolar reservoir ; sample spinning rapidly destroys dipolar order preventing the dipolar system from becoming a bottleneck.Hence under sample spinning spin-spin fluctuations which reduce the carbon spin lock magnetization will compete on an equal footing with the carbon (motional) spin-lattice coupling. A direct comparison of this spin-spin relaxation time Ts-Dis preferable but quite diffi- cult when Ts-D TID. Instead for a cured DGEBA epoxy we observe the r.f. field dependence of the I3CTIPvalues to be much weaker than that crudely estimated for a purely spin-spin relaxation mechanism. Hence the observed 13CTIPvalues are not dominated by spin-spin effects at least for spin lock fields above z 40 kHz. Over the range of temperature 242-324 K the methyl carbon TIPshows an activation energy of 11 kJ mol”. Conversations with D. L. VanderHart have helped delineate the role of dipolar order in these experiments.This work is sponsored in part by the Naval Air Systems Command. J. H. Van Vleck Phys. Rev. 1948 70 1 168. E. R. Andrew Progr. N.M. R. Spectroscopy 1971 8 1. M. Mehring High Resolution N.M.R. Spectroscopy in Solids N.M.R. Basic Principles and Progress 1976 11 1. U. Haeberlen High Resolution NMR in Solids Selective Averaging Adv. Mag. Resonance 1976 Supplement 1. S. R. Hartmann and E. L. Hahn Phys. Rev. 1962 128,2042. A. Pines M. G. Gibby and J. S. Waugh J. Chem. Phys. 1973,59 569. (a) F. Bloch Phys. Rev. 1958 111 841; (b) L. R. Sarles and R. M. Cotts Phys. Rev. 1958 111 853. a J. Schaefer and E. 0.Stejskal J. Amer. Chem. SOC. 1976,98,1031. J. Schaefer E. 0.Stejskal and R. Buchdahl Macromolecules 1977 10 384.lo E. Lippmaa M. Alla and T. Tuherm XIX Congress Ampere Proc. (Heidelberg 1976) voi. 113. A. N. Garroway W. B. Moniz and H. A. Resing Preprints of the Div. of Organic Coatings and Plastics Chem. 1976,36,133. l2 D. L. VanderHart and A. N. Garroway J. Chem. Phys. submitted. l3 I. J. Lowe Phys. Rev. Letters 1959 2 285. l4 H. Kessemeier and R. E. Norberg Phys. Rev. 1967 155 321. A. G. Redfield Phys. Rev. 1955 98 1787. l6 D. E. Demco J. Tegenfeldt and J. S. Waugh Phys. Rev. B 1975,11,4133. l7 R. L. Strombotne and E. L. Hahn Phys. Rev. 1964,133 A1616. la J. Jeener H. Eisendrath and R. Van Steenwinkel Phys. Rev. 1964 133 A478. l9 J. Jeener R. DuBois and P. Broekaert Phys. Rev. 1965 139 A1959. loJ. Jeener Adv. Magnetic Resonance 1968 3 206.21 P. Mansfield and D. Ware Phys. Rev. 1968 168 318. 22 P. Mansfield K. H. B. Richards and D. Ware Phys. Rev. B 1970,1,2048. ”D. A. McArthur E. L. Hahn and R. Walstedt Phys. Rev. 1969 188 609. 24 H. T. Stokes and D. C. Ailion Phys. Rev. B 1977 15 1271. 25 M. Mehring ref. (3) chap. 4. 26 A. N. Garroway W. B. Moniz and H. A. Resing A.C.S. Symposium Series in press. 27 J. F. J. M. Pourquie and R. A. Wind Phys. Letters 1976 55A,347. J. Jeener VI Int. Symp. Magnetic Resonance (Banff Canada 1977) unpublished. l3cN.M.R. IN POLYMERS 29 A. N. Garroway J. Magnetic Resonance in press. 30 J. Jeener Waterloo N.M.R. Summer School Waterloo Canada 1977) unpublished. 31 E. 0.Stejskal J. Schaefer and J. S. Waugh J. Magnetic Resonance 1977,28. 105.32 J. Jeener and P. Broekaert Phys. Rev. 1967 157,232. 33 N. Bloembergen E. M. Purcell and R. V. Pound Phys. Rev. 1948,73 679. 34 S. A. Sojka and W. B. Moniz J. Appl. Polymer Sci. 1976 20 1977. 35 D. C. Douglas and G. P. Jones J. Chem. Phys. 1966 45 956.

ISSN:0301-5696    

DOI:10.1039/FS9781300063

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Oxygen-17 Nuclear Quadrupole Double Resonance Spectroscopy BY THEODORE L. BROWNAND C. P. CHENG School of Chemical Sciences University of Illinois-Urbana Urbana Illinois 61801 U.S.A. Received 4th August 1978 The Slusher-Hahn technique for detection of nuclear quadrupole transitions of low abundance spins at zero magnetic field is briefly described. Factors affecting the observed line shapes are dis- cussed. The "0n.q.r. spectra for a variety of substances studied at 77 K are presented. The results for several compounds are discussed in terms of the Townes-Dailey model which leads to an assign- ment of oxygen 2p orbital populations. The development of nuclear quadrupole resonance (n.q.r.) spectroscopy has been limited by difficulties in detection of the quadrupole transitions particularly for the light elements.The double resonance experiments pioneered by Redfield' and Hahn and co-worker~~-~ offer the possibility of very high sensitivity in observing the n.q.r. spectra at zero magnetic field of low abundance spin systems of half-integer spin 12 3/2. Despite their potentially broad application these techniques have not thus far been widely employed. Oxygen-17 (I = 5/2) is present in low abundance (0.037 yo),and is thus a good candidate. Because oxygen is an important constituent of so many substances particularly those of biological interest a spectroscopic probe of the electronic and structural environment about this element could have consider- able value. Hsieh Hahn and Koo called attention to the possibilities inherent in 170 n.q.r.double resonance spectroscopy by reporting results for eight organic s01ids.~ More recently two other organic compounds were studied by Kado and co-workers using a slightly different technique.' These remain the only published n.q.r. studies of natural abundance level 170. We have begun an extended series of studies of natural abundance level I7On.q.r. spectra. In this paper we describe briefly some experimental aspects particularly as relates to observed line shapes. A potpourri of results for several types of compounds is shown and consideration is given to the interpretation of the n.q.r. data in terms of a simple bonding model. DESCRIPTION OF THE DOUBLE RESONANCE EXPERIMENT The 170spectra were obtained on solid polycrystalline samples at 77 K using the Slusher-Hahn double resonance techniq~e.~ In this method in addition to the " rare " spin system (S) for which the quadrupole resonances are sought there must be present an abundant spin system (I) with appropriately long spin-lattice relaxation time.In all our experiments the abundant spin system is 'H. The procedure involves four steps as outlined in fig. 1 (1) the sample is placed in a high magnetic field (-1 T) for a period of the order of the proton high field TI. A magnetic moment corresponding to ordering of the proton spins develops. The sample is adiabatically demagnetized by rapid physical removal to a region of zero magnetic field. This process isentropic because it occurs on a time scale short in relation to spin-lattice energy exchange,6 results in a drop in 'H spin temperature OH to (0.1 K.(2) The sample is irradiated with a strong r.f. field (the S channel) for a period r0. Phase shifts of 180" are applied periodically (e.g. every 500 ps) to accomplish multiple excitation of the 170 spin system and to bring about energy exchange between I7O and the 'H spin systems (vide infra). The irradiation period 2 3 4 I I ' I I ! ( 180. phase shifts) FIG.1.-Schematic description of the Slusher-Hahn double resonance method for observation of zero field nuclear quadrupole transitions of low abundance nuclei such as "0. 70varies from 1 to 20 s. It is chosen to be on the same time scale as TID,the zero field spin-lattice relaxation time for 'H.T, is typically from 0.1 to loA5times the high field TI. It is the major limiting factor in determining whether the experiment is feasible on any given sample. (3) Following irradiation in zero field the sample is returned to high field with recovery (in part) of the 'H spin system magnetization. If the strong r.f. irradiation in zero field has corresponded to a pure quadrupole transition of ''0 the recovered magnetization of the proton system will be smaller than when the irradiation is off-resonance. (4) The 'H magnetization that remains is measured by application of a 90" pulse and quantitative measurement of the free induction signal that follows. Finally a series of 90" pulses is applied to the sample to saturate the proton magnetization to provide a reproducible starting point for the next cycle.The experiment as described is repeated after incrementing the S channel frequency by a predetermined amount e.g. 5 kHz. To understand what occurs it is useful to view the process occurring in zero field T. L. BROWN AND C. P. CHENG in terms of the rotating frame coordinate system and to employ Redfield's concepts of spin temDerature in the rotating frame.6 The 170 nuclear spins precess about the major axis of the field gradient tensor. One can imagine that interaction of the field gradient tensor with the nuclear quadrupole moment produces two oppositely oriented nuclear magnetizations corresponding to & values of m.7 Each of these sets of oppositely directed nuclear spins interacts with the appropriate circularly polarized component of r.f.At resonance in the rotating coordinate frame the effective field operating on the 170 spins is OH,,. Initially there is no sample magnetization along Hls; the 170 spin system may be said to be completely disordered with respect to ordering along HIS. To put it another way the spin temperature in this reference frame is infinite. The two oppositely directed components of the 170 magnetization precess about H, with frequency aysHls. (The constant a with magnitude about 2 results from the transformation of the r.f. interaction hamiltonian into the rotating coordinate frame;8,9 it is a complex function of the asymmetry parameter 7 and the particular pair of spin levels involved in the transition.) Energy exchange of the 170spin system with the lattice is expected to be slow.However the possibility exists for mutual spin flip-flops involving the protons surrounding each 170. Energy exchange between the two spin systems induced by the secular part of the dipolar interaction between 170 and protons in the rotating coordinate system is most effective when Hahn's double resonance condition aysHls = yHHL,is met. Typically with HL of the order of 3 x H, is optimally on the order of 9 x T. The experimentally applied Hl should be 2-4 times this large. When the double resonance condition is approximately satisfied spin energy can be exchanged between 170and 'H spin systems. 170magnetization thus develops along H, at a rate determined by the cross-relaxation rate between the 170 and 'H spin systems.In the course of this process the 170spin temperature decreases; the 'H spin temperature is correspondingly increased. Application of 180" phase shifts at appropriate intervals results in reheating of the 170spin system so that multiple exchanges between the two spin systems occur.8 The multiple exchanges can be con- tinued for times of the order of the proton T, or less. CROS S-RE LAX AT ION DY N AMI CS The effectiveness of the double resonance method and the lineshapes of the detected signals depend on the details of the cross-relaxation between the quadrupolar and abundant I = 3spin systems. Let t be the period of irradiation between 180" phase shifts; the total irradiation time zo (fig. 1) is then Nt.The magnetization remaining in the I spin system following irradiation and remagnetization M,(N) as compared with initial magnetization M,(O) is approximately3 lo M,(N)/M,(O)= exp {(-Nt/T,,) -2N41 -exp (-t/TIs)]sin2v,). (I) In this expression E represents the ratio of heat capacities of the two spin systems NsCs(aH,s)2/NICI HL2 < 1. Here N and NI are the numbers of S and I spins per unit volume and the C terms are the appropriate Curie constants for the spin systems in the rotating frame. ?'kl represents the cross-relaxation rate during irradiation. We assume Tkl 4 T2'. The angle vs is a measure of the angle between the effective field about which the S magnetization precesses and the axis of the field gradient tensor tan vs = ysaHls/(cug-us).Here COO represent the pure quadrupole resonance fre- quency and usis the frequency of the applied r.f. Hlsis the effective r.f. field strength. Because the sample is polycrystalline Hls varies with the orientation of the individual field gradient tensors with respect to the applied r.f. The amplitude of the detected signal is given by Ml(zo)-MI(N),where MI(zo)is the I spin magnetization recovered after time z0 = Nt at zero field with no S spin irradiation M,(N)= MI(zo)exp (-2N41 -exp (-t/TIs)]sin2 v,). (2) The cross-relaxation rate during irradiation is clearly of importance in determining the line shape. In one limit TI < t the I and S spin systems attain a common spin temperature during each time interval t. If this condition applies at resonance then the amplitude of the detected signal is M,(zo)exp(-2N~).The signal in effect " satur-ates " for ~NE 2 3. The cross relaxation rate can be expressed as l/T,s = (1/2) sin2 v,MlSJ(Aw,). (3) Here MiSis the second moment of the heteronuclear dipolar coupling due to the parti- cular set of S spins giving rise to the transition being observed assuming 100% abundance. The cross-polarization spectral density function J(Awe)has as its argu- ment J(Aw,) is of the form J(Aw,) = cos [(Aw,)z]c,(z)dz im where C(z) represents the correlation function for relaxation of the appropriate com- ponent of I spin magnetization. Expressed in its simplest approximate form as a gaussian,'? lo C(T) = exp (-z2/Til). (4) This leads to 1/ =~(474) ~sin2V,M~~T,, ~ exp (-ACO:Tf1/4).(7) When saturation does not occur variations in intensity and half-height widths of the resonance lines are due mainly to variations in MiS. To arrive at a more precise statement of the line shape it is necessary to take into account an averaging of the angle between HL and Hls. EXPERIMENTAL All n.q.r. data were obtained on solid polycrystalline samples in liquid nitrogen 77 K. The apparatus employed is similar to that described by Slusher and Hahn. Provision has been made for automatic control of the experiment cycle with continuous tuning of the S channel final stage as frequency is changed. The instrument is capable of scanning from about 180 kHz to 4 MHz without operator intervention. More details are provided else- where.'' RESULTS AND DISCUSSION Fig. 2 shows the ''0 spectrum of nitrobenzene; a pair of transitions is expected for an Z = 5/2 system as observed. This example represents a quite common situation; with proton TI of several seconds a very good signal to noise ratio is easily attained. Table 1 provides a sampling of n.q.r. data obtained on several different types of com- T. L. BROWN AND C. P. CHENG FIG.2.-"'O n.q.r. spectrum of nitrobenzene 77 K (frequency in kHz). TABLE 1 .-OXYGEN-I 7 NUCLEAR QUADRUPOLE RESONANCE DATA 77 K ' ~~ ~ compound vq -;/kHz v; -&/kHz (e2Qq,,/h)/MHz rl y-picoline-N-oxide 4594(4) 263 l(2) 15.630(4) 0.328( 3) p-chlorobenzaldeh yde benzoyl cyanide phenolnitrobenzene phthalimide 3086(2) 3 1 52( 2) 2320(3) 37 14( 2) 2642( 1) 28 18( 1) 1900(1) 1902( 1) 1945(3) 2573( 1) 1321(1) 1468(1) 10.648(2) 10.838(2) 8.476(5) 13.089(2) 8.807(3) 9.455(2) 0.437(2) 0.4 1 2(2) 0.792( 3) 0.576(1) O.OOO( 1) 0.18l(2) formic acid 2060(2) 2343(1) 1032(2) 1190(1) 6.867(2) 7.829( 1) O.OO(3) 0.111(2) diphenyl sulphoxidediphenyl sulphone triphenylphosphine oxide potassium bicarbonate 2804(2) 2003(1) 1403(2) 2232(2) 201 2(2) 1822(2) 1498(2) 1057(2) 708(1) 1358(2) 1705(2) 1635(5) 9.494(2) 6.734(3) 4.683(2) 7.686(3) 7.3 99(4) 6.765(5) 0.221(2) 0.208(5) 0.085(15) 0.422(3) 0.720(2) 0.936(3) a Last place uncertainties in parentheses.pounds. These results illustrate most of the characteristic features of ''0 spectra. Note that the range of e2Qqz,/hand q values is quite large. Triphenylphosphine oxide and y-picoline-N-oxide represent two cases of singly connected oxygen in which the field gradient parameters are dramatically different reflecting substantial differ- ences in the relative degrees of 0 and n bonding.In those cases in which the compound embodies two or more structurally different oxygens these are seen as separate sets of signals. There may be uncertainty in the assignments when the signals for two different oxygens are rather close. In these cases it is helpful to be able to observe the Am = 2 transitions. This is usually possible when q is of the order of 0.4 or larger. In addition the intensity or width of the signals (depending on the conditions of the experiment) may vary considerably for structurally different oxygens and the corresponding pairs are easily seen to belong together.FIG.3 .-Pairing of molecules in phthalimide via hydrogen bonding. Phthalimide provides an interesting example which illustrates the sensitivity of the ''0 n.q.r. parameters of the carbonyl group to intermolecular interactions. The X-ray structure determination of phthalimide I2 at room temperature reveals a pairing of the molecules via hydrogen bonding as shown in fig. 3. Assuming that this structure is maintained at 77 K the 170 n.q.r. spectrum should reveal the presence of two non-equivalent oxygen atoms. The n.q.r. spectrum of phthalimide at 77 K is shown in fig. 4. Four transitions associated with 170 and two associated with 14Nat 1960 and 2280 kHz are seen. The 14N transitions are readily distinguished since they are observed in a level-crossing experiment.13 The pairing of the I7O transitions 1321 with 2642 kHz and 1468 with FIG.4.-"0 and I4N n.q.r.spectrum of phthalimide. The transitions at 1960 and 2280 kHz are assigned to 14Nonthe basis of their observation in a simple level-crossing double resonance experiment. Survey spectra such as this are supplemented by detailed study of individual lines. T. L. BROWN AND C. P. CHENG 81 2818 kHz is unambiguous solely in terms of frequencies; v+-$ cannot be more than twice vz -1. The 1321 and 2642 kHz pair are more intense than their counterparts in 22 the other pair. This suggests that the cross-relaxation rate is greater for the 170atom that gives rise to the 1321 and 2642 kHz transitions.We have noted in other cases that the close approach of protons to oxygen in hydrogen bonding leads to more intense or broader signals as expected from eqn (2) and (7). We therefore can assign the 1321 and 2642 kHz pair of transitions to the carbonyl group involved in hydrogen bonding. It is interesting to note (table 1) that the intermolecular hydrogen bonding inter- action results in substantial changes in the I7O field gradient parameters in phthali- mide. The pairing of molecules via hydrogen bonding in this substance is quite similar to base pairing of complementary nucleotide bases. The observation of I4N 'D and 170 n.q.r. spectra in solid samples of paired bases could provide a detailed and sensitive description of charge distribution and strength of hydrogen bonding interaction.Such a multi-nuclear n.q.r. study is now entirely feasible. The I7O n.q.r. data can be interpreted in terms of the charges resident in the 2p orbitals of the oxygen by application of the classic Townes-Dailey m0de1.l~ In the case of singly connected oxygen the analysis is closely similar to the familiar procedure for treating halogen n.q.r. data.15 Because n bonding is always present to some ex- tent in singly connected oxygen analysis of the n.q.r. results provides insights into differences in the occupations of the oxygen 2p orbitals of 0 and n symmetry. The details of the assumptions made in applying the Townes-Dailey model to oxygen in various bonding situations are recounted elsewhere." Table 2 shows the results of TABLE 2.-POPULATIONS OF OXYGEN 2p ORBITALS BASED ON TOWNES-DIALEY ANALYSIS OF "0 N.Q.R.DATA. compound %s PO P P y-picoline-N-oxide 20 0.96 1.70 2.00 nitrobenzene 20 1.07 1.49 2.00 p-chlorobenzaldehyde 25 1.39 1.41 2.00 diphenyl sulphoxide 25 1.27 ' 1.95 1.87 diphenyl sulphone 25 1.27' 1.79 1.75 triphenylphosphine oxide 25 1.39 ' 1.75 I .74 'The oxygen sigma bond population is assumed from an interpolation of the values obtained for C-0 and N-0 bonds assuming a linear relationship with orbital electr~negativities.'~ the analysis for several of the compounds listed in table 1. The n.q.r. data provide a rather well-defined measure of the extent of n bonding in most of the systems studied; y-picoline-N-oxide is a particularly interesting example.Using the axis system shown in fig. 5 the major axis (Le. 2)of the field gradient tensor lies along the z axis of the molecular coordinate system shown in fig. 5. The 2p orbital has an occupation of 2 inasmuch as there is no possibility of significant delocalization of the charge in this orbital. If it were not for some n bond interaction between the 2p orbital and the ring q would be essentially zero. The non-zero value for q and the observed value for e'Qq,,/A coupled with a value of 20.9 mHz for the partial quadrupole coupling constant contribution due to a single 2p electron on oxygen,16 provide enough informa- tion to calculate the occupations of all three 2p orbitals of the oxygen atom as listed in table 2. Detailed analysis of the 170 n.q.r.data for extended series of related compounds X 1 1 FIG.5.-Molecular axis system x y z and major axis of the "0field gradient tensor (2) in pyridine- N-oxide. will in time permit interesting and useful insights into the structural and bonding environments of oxygen in a variety of compounds. In addition to a dependence upon obvious changes in chemical environment the field gradients at 170 appear to be quite sensitive to hydrogen bonding interactions. The results we have described here and many others we have obtained demonstrate that the technique pioneered by Hahn and co-workers provides a powerful broadly applicable means of obtaining n.q.r. spectra of 170 in natural abundance and furthermore that t ie n.q.r.data hold promise as a useful probe of structure and bonding. This research was supported by the National Institutes of Hea th. A. G. Redfield Phys. Rev. 1963 130 589. R. E. Slusher and E. L. Hahn Phys. Rev. Letters 1964 12 C508. R. E. Slusher and E. L. Hahn Phys. Rev. 1968 166 332. Y. Hsieh J. C. Koo and E. L. Hahn Chem. Phys. Letters 1972 13 563. R. Kado Y. Takarada and H. Hatanaka Phys. Letters 1974,47A 49. A. G. Redfield Science 1969 154 1015. M. Bloom E. L. Hahn and B. Herzog Phys. Rev. 1955,97 1699. * S. R. Hartmann and E. L. Hahn Phys. Rev. 1962,128,2042. Y. N. Hsieh Ph.D. Thesis (University of California Berkeley 1973). lo M. Mehring High Resolution NMR Spectroscopy in Solids (Springer-Verlag Berlin 1976) chap. 4. C.P. Cheng and T. L. Brown J. Amer. Chem. Soc. submitted. Von E. Matzat Acta Cryst. 1972 B28 415. l3 D. T. Edmonds Phys. Reports 1977 29 233. l4 C. H. Townes and B. P. Dailey J. Chem. Phys. 1949 17 782. l5 E. A. C. Lucken Nuclear Quadrupole Coupling Constants (Academic Press New York 1969) chap. 7. l6 J. S. M. Harvey Proc. Roy. Soc. A. 1965,285 581. The b2term measured -10.438 f0.030 = MHz equals 2e2Q/5<r3>;since eqZlo= -4e/5<r3> eZQq~lo/h 20.9 MHz. l7 (a)J. Hinze and H. H. Jaffe J. Amer. Chem. Soc. 1962 84 540; (b) J. Phys. Chem. 1963,67 1501 ; (c) J. Hinze M. A. Whitehead and H. H. Jaffe J. Amer. Chem. Soc. 1963,85 148.

ISSN:0301-5696    

DOI:10.1039/FS9781300075

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Double Quadrupole Resonance Study of the Pyridine -tWater Complex M. DAVIDSON T. EDMONDS A. L. WHITE BY MARGHERITA DONALD AND ANTHONY The Clarendon Laboratory Parks Road Oxford OX1 3PU Received 24th July 1978 A water + pyridine complex is formed at temperatures below 190 K. Using double nuclear resonance techniques the 2D,14Nand ''0 nuclear quadrupole resonance spectra of isotopically en- riched examples of this complex have been measured at 77 K. From these data it may be deduced that the complex consists of 4 water molecules and 1 pyridine molecule and that one proton of the first water molecule is hydrogen bonded to the lone pair of the pyridine nitrogen atom with an N * * H hydrogen bond of 1.8 30.2 A. The second proton of this water molecule is hydrogen bonded to the oxygen of the second molecule in a configuration like that of water in ice.The second water molecule is almost exactly ice-like and each of its protons is hydrogen bonded to the oxygen atoms of the third and fourth water molecules which are equivalent. These two water molecules are only very weak hydrogen bond donors with 0-H bond lengths around 0.97 A. We believe that nuclear quadrupole resonance (n.q.r.) could soon become a very important tool for the investigation of the electronic structure of solids. Its great advantage over nuclear magnetic resonance (n.m.r.) is that the energy level splitting measured is caused by the electric field built into the molecule and not by the mag- netic field imposed from outside. This means that n.q.r is a truly microscopic tech- nique that does not require the presence of long range order and so produces high resolution spectra from powdered solids or frozen solutions.The major disadvantage at present of n.q.r. over n.m.r. is the relatively small amount of theoretical work that has been devoted to the interpretation of the spectra. The electric field gradient is a single electron function involving only ground state molecular wave functions and so should be more easily calculated than the chemical and contact shifts in n.m.r. The experimental techniques of double quadrupole resonance have advanced very rapidly in recent years and it is partly to illustrate this advance and partly because we are particularly interested in the problem of water bonded to organic and particularly biological molecules that we embarked upon this study.EXPERIMENTAL The techniques of double quadrupole resonance have recently been reviewed by ourselves and others2 so that we will not describe the methods here. The apparatus used for the experi- ments reported here has previously been described in detail.' A particularly important feature is the variable temperature cryostat3 which enabled us to form the specimen within the quad- rupole resonance spectrometer itself. The pyridine (AnalaR grade) and the D20 (99.8%) were obtained from B.D.H. and the H20 was deionized tap water. The specimens were prepared by weighing and were then enclosed in PTFE Teflon sample tubes (which hold E 1.5 cm3) for insertion into the spectrometer.The presence of the complex was first detected by the changes in the proton TIrelaxation D.Q.R. OF THE PYRIDINE + WATER COMPLEX times and in the change in the 14Nspectrum observed when a mixture of pyridine and H20 was slowly cooled within the apparatus from room temperature to 77 K. A low tempera- ture differential thermal analyser was then constructed. The two cups of the analyser were filled respectively with water and the water + pyridine mixture. The temperature of the cups was then lowered from 300 to 77 K at a rate of M 10 K min-'. On warming the temperatures of the two cups followed each other closely until at z170 K the tem- perature of the cup holding the mixture rose abruptly indicating the release of heat whilst the cup containing ice continued to rise at the previous controlled rate of M 1 K min-'.If this experiment was repeated except that the initial cooling was interrupted and both samples were caused to dwell at M 190 K for several hours before cooling further to 77 K the anomaly at 170 K was absent. These results are consistent with a disorder to order transition occurring at about 170 K in the first experiment while the dwell time at 190 K allows the transition to occur on cooling in the second experiment with the ordered phase being present at all lower temperatures. The presence of pyridine + water complexes has been inferred before from infrared spectra when the constituents were present in low concen- tration in organic solvents at room temperature. For example Johnson et ~1.~ obtained evidence for 1:1 2 1 and possibly 3 1 water to pyridine complexes in this manner.As far as we know the low temperature bulk complex has not previously been observed. RESULTS To form a complex the two constituents are mixed at room temperature and the result is introduced into a sample tube which is immediately plunged into liquid nitrogen. When it has reached 77 K it is introduced into the cryostat of the quad- rupole resonance spectrometer held at 77 K. In this condition the high field proton relaxation time T,(H)is only a few seconds and the zero field relaxation time T,(O)is a small fraction of a second. The cryostat temperature is then allowed to rise while the spectrometer is set repetitively to display on a chart recorder the height of the proton free induction decay one minute (say) after a saturation combe of 1000 n/2pulses has been applied.The signal initially falls slowly as the temperature rises then as the transition approaches rises only to fall abruptly at the transition due to a sharp increase in T,(H) that occurs. This fall is accompanied by an abrupt change in the duration of the free induction decay from say 20 ps to several hundred microseconds. The sample is maintained just above the transition temperature (z 190 K) for 3 h or so before being returned to 77 K for measurement. The T,(H)has now increased to z3 min and T,(O)has become z 2 s. QUADRUPOLE RESONANCE OF I4N No I4Nquadrupole resonance spectrum was obtained in samples formed by plung- ing the sample tube directly into liquid nitrogen.This is to be expected if the solid so formed was largely disordered. When the sample has been held at 190 K for 3 h or so to form the complex and then returned to 77 K a previously unmeasured I4Nspectrum was observed with v = 3439 & 1 kHz vo = 690 i.2 kHz corresponding to quad- rupole coupling constants of e2qQ/h= 4125 & 3 kHz r = 0.335 *0.003. This is to be compared to the nitrogen quadrupole coupling constants of frozen pyridine which are e2qQ/h= 4610 kHz and = 0.388 at 77 K. The same new spectrum was observed over a wide range of pyridine + water mixtures provided the sample was properly prepared as above. We have in fact recently completed (in press) a 14Nand 'D quadrupole resonance study of lanthanum nicotinate dihydrate and related compounds including nicotinic acid and nicotinamide.As revealed by X-ray and neutron diffraction the structure of the pyridine ring near the nitrogen site is in each case very close to that of pyridine M. M. DAVIDSON D. T. EDMONDS AND A. A. L. WHITE 85 in each case the nitrogen accepts a hydrogen bond. The hydrogen bond donors are water molecules for the three inequivalent nitrogen sites in the nicotinate and an amide and a hydroxyl group for nicotinamide and nicotinic acid respectively. The results obtained for the 14Nquadrupole coupling constants are similar to those we obtained from the spectra we attribute to the pyridine + water hydrogen bonded complex. In fact in the study we refer to above there is found to be a good linear correlation between the value for e*qQ/hmeasured from the I4Nspectrum and I /R3where R is the N H hydrogen bond length.If we apply this to the pyridine + water complex we find with conservative errors a value of N H hydrogen bond distance of 1.8 & 0.2 A. In fact in the nicotinate there are two sites with quadrupole coupling constants at 77 K very similar to those we measure in the pyridine + water complex namely e2qQ/h= 4220 & 2 kHz q = 0.327 and e2qQ/h= 4222 & 2 kHz 7 = 0.335 which have measured N H hydrogen bond lengths of 1.8 5 0.05 and 1.9 & 0.05 A to the neighbouring water molecule.6 QUADRUPOLE RESONANCE OF 2D To observe the deuteron spectra of the water molecules participating in the complex we use mixtures of normal protonated pyridine and water isotopically enriched in varying degrees with D,O.In the rapidly cooled sample we observe no deuterium spectrum no matter what isotopic enrichment is used. The fact that we do not even .. .. ** . 5 I.. .. .*.'.' ** * a. ....... . 41' .. 130 140 150 160 170 180 kHz FIG.I.-Typical deuterium n.q.r. spectra for the complex. Trace (a) was obtained from a mixture with molecular ratio 4 water (10% D20)to 1 pyridine while trace (6) was obtained from a 1 D20to 10 pyridine mix. (a) Cycle time = 5 min irradiation time = 2 s linear peak-to-peak irradiation field = 16.3 x T; (6) these parameters = 1 min 2 s and 18.2 x T respectively. observe the known' deuterium spectrum for ice tells us that the constituents have not separated on freezing (zone-refined) but that we have a disordered solid.With samples prepared as described above with a dwell time of several hours at 190 K we observe spectra such as those displayed in fig. 1. Despite wide differences both in water-to- pyridine ratio and in isotopic enrichment of the water the spectra are all broadly simi- lar. They consist of a single line around 137 kHz (line A) an easily separable high D.Q.R. OF THE PYRIDINE + WATER COMPLEX frequency multiplet centred around 178 kHz (multiplet C) and a complex central multiplet stretching from about 145 kHz to about 173 kHz (multiplet B). In an attempt to determine the water-to-pyridine ratio of the complex we measured using a planimeter the areas under line A multiplet B and multiplet C for 10 spectra obtained with specimens having widely different water-to-pyridine ratios and isotopic enrichment.There is a slight arbitrariness in deciding upon the separation of multi- plets B and C but it is not too serious if advantage is taken of the obvious symmetry of multiplet C. Two facts emerge from such an analysis. The first is that the ratio of the areas of multiplet C to line A is consistent for all the 10 specimens and is 4.2 with a mean error of 0.5. A second useful ratio is that of the area of multiplet B to the sum of the areas of multiplet C and line A. This ratio is plotted for the 10 specimens in fig. 2. The ratio is seen to remain approximately constant at z 2.2 for molecular percentages of water from 10 to w 70 % and then between 70 and 80 ”/ it rises steeply.The form of fig. 2 and the ratio quoted earlier are both consistent with a 4 water to 1 pyridine complex. If we assume line A to be a single line and use the ratio determined above we deduce that multiplet C consists of 4 lines. The baseline ratio of 2.2 deduced from fig. 2 would then lead to the conclusion that multiplet B contains 5 x 2.2 = 11 lines (the exact agreement is of course fortuitous). Thus we deduce a total of 16 lines which is what we expect for 4 water molecules with 8 deuteron sites. This conclusion is further supported by the rise in the ratio displayed in fig. 2 at around 70 to 80 molecular per cent water. As the water content increases we would expect this ratio to remain constant so long as all the water can take part in complex formation.However eventually there is excess water which forms ice which will coexist with the complex. As the ice spectrum consists ’of v-lines around 154 kHz and v lines around 167 kHz both of which lie within the span of multiplet B we expect excess ice to contribute to the area of multiplet B but not to contribute to that of either line A or multiplet C causing the ratio plotted in fig. 2 to rise. The solid line in fig. 2 is the theoretical form expected for a 4 water to 1 pyridine multiplet. Bearing in mind that with a finite dwell time at 190 K we are unlikely to convert 100 % of the specimen to the complex so that the experimental ratio will tend to be too large the agreement is quite good.0 50 %molecular water 100 FIG.2.-Ratio of area under the central multiplet in the deuterium spectrum of the complex to sum of the areas for the upper multiplet and lower line plotted against the molecular percentage of water in the mix. The solid line is the theoretical prediction of this ratio for a 4water to 1 pyridine complex. Percentage of D,O in water is 0 99.8 A 50 and 010 %. M. M. DAVIDSON D. T. EDMONDS AND A. A. L. WHITE Before leaving fig. 2 we would mention the dangers of using intensity information in a double resonance experiment because of the possibility' of frequency dependent sensitivity. However because the overall frequency width of the spectrum is only 50 kHz and in view of the consistent ratio of high frequency multiplet area to low frequency line area we believe there is no large frequency dependent element in the sensitivity in this case.Without further experimental data it would be a hopelessly arbitrary task to fit a 16 line spectrum to data such as displayed in fig. 1. Fortunately we are not in that position because we can measure the double transition quadrupole resonance (d.t.q.r.) spectrum of the complex. We have recently described in detailsv9 the detection of I I I I I i i f !I I. ........ .... .-..",.:-. ...... .. -. .*:.. ........ ... I. .-. ...... .... .*. .' '. .. . . 2. . *. . . . i" ..* I 300 320 kHz 340 FIG.3.-Double transition quadrupole resonance (d.t.q.r.) spectrum of deuterium for the complex obtained from a 4 DzO to 1 pyridine molecular ratio mix.Cycle time 5 min irradiation time 20 s and linear peak-to-peak irradiation field 5.2 x T. The predicted line positions based upon the assignment of the single transition spectra are indicated as heavy arrows for intense lines light arrows for weaker lines and dashed arrows for the weakest lines. d.t.q.r. and have also developed the theoryl0 which explains the intensities and posi-tions of the spectral lines observed so that we will not repeat it here. Suffice it to say that d.t.q.r. is observed when two neighbouring deuterons make simultaneous transitions and together absorb a single input photon. By observing this spectrum it is possible to deduce which of the various single transition spectra lines must belong to near-neighbour deuterons or in this case to deuterons resident on the same water molecule.The d.t.q.r. spectrum of the pyridine + D,O complex is displayed in fig. 3. Space does not here allow a description of how by iteration between the single transition spectrum and the d.t.q.r. spectrum one can arrive at a detailed 16 line fit of the single transition spectrum so that we will confine ourselves to two remarks. We have previously Shown'O that each water molecule gives rise to one dominant line in the d.t.q.r. spectrum so that the fact that there are three indicated in fig. 3 by heavy arrows points to three inequivalent water molecules in the complex. The strong spectral line at about 323 kHz is close to that found in ice but the other two strong lines are markedly different.In fig. 4 and 5 are displayed two measured single transition spectra of the pyridine D.Q.R. OF THE PYRIDINE + WATER COMPLEX FIG.4.-Measured deuterium spectrum of the complex obtained from a 1 D,O to 1 pyridine mixture compared with the theoretical prediction of the spectrum. Cycle time 1 min irradiation time 2 s and linear peak-to-peak irradiation field 13 x T. kHz FIG.5.-Measured deuterium spectrum of the complex obtained from a 3 water (50 % DzO) to 1 pyridine mixture compared with the theoretical prediction of the spectrum. Cycle time 5 min irradiation time 2 s and linear peak-to-peak irradiation field 10.4 x T. + water complex together with a 16 line computer prediction of the spectrum.For simplicity we assumed the individual line shape to be lorentzian and that each of the 16 lines had the same height and width. The height and width are determined by fit-ting the isolated line at 137.5 kHz so that the only remaining freedom is in the line positions. The line centre positions for the predicted spectra are identical for fig. 4 and 5 but for fig. 4 a full width at half height of 2 kHz was determined whilst the same parameter for the fit in fig. 5 is 3 kHz. Partially deuterated specimens are expected to have wider linewidths than fully deuterated ones because of the broadening effect of the magnetic moment of the protons. The intensity fit of fig. 5 is good which is addi- M. M. DAVIDSON D. T. EDMONDS AND A.A. L. WHITE tional evidence for a 16 line spectrum and hence a 4 water to 1 pyridine complex. The intensity fit of fig. 4 is less good but is much improved if one corrects for the fact that in a fully deuterated water specimen we expect v+ lines to be slightly more intense than v-lines due to the coupling between deuteron and proton being predominantly by level crossing rather than by continuous coupling." We have previously shown l2that two deuterons in the same water molecule interact magnetically so that for example the v+ lines become a six line multiplet rather than a doublet. This effect is only important if the two deuterons are in nearly identical sites. We have in fact allowed for this in the theoretical line fits but the effect is small. The TABLE1 .-DEDUCED DEUTERIUM QUADRUPOLE RESONANCE SPECTRAL LINE POSITIONS AND CORRESPONDING QUADRUPOLE COUPLING CONSTANTS FOR THE FOUR WATER MOLECULES OF THE COMPLEX water ~~ deuteron u-/kHz v+/kHz e2qQlr-'/kHz 3 D1 137.6 149.5 191.4 0.124 1 D2 155.0 167.6 215.1 0.117 D3 153.4 167.2 213.7 0.129 2 D4 155.0 169.0 216.0 0.130 D5 162.4 179.4 227.9 0.149 3 D6 165.8 177.0 228.5 0.098 ~~~~ D7 162.4 179.4 227.9 0.149 4 DB 165.8 177.0 228.5 0.098 spectral line frequencies and quadrupole coupling constants assigned to the 8 deuterons are included in table 1.This assignment predicts line positions in the d.t.q.r. spec- trum indicated by arrows in fig. 3. Before leaving deuterium spectra we show in fig. 6 the deuterium spectrum of the complex formed between fully deuterated pyridine and protonated water.Also in fig. 6 is displayed the spectrum of a frozen mixture of fully deuterated pyridine and normal protonated pyridine. The pyridine water complex spectrum is remarkable for its simplicity and its narrow lines. We have not yet attempted a detailed analysis of these spectra but their structural information content is clearly high. QUADRUPOLE RESONANCE OF 170 The complex was formed using normal pyridine and D,O enriched to 10 % in 170and the 170quadrupole resonance spectrum measured is displayed in fig. 7. There are three chief low frequency lines at 1765 & 10 1840 & 10 and 1980 rt 10 kHz and three high frequency lines at 3520 -& 10 3655 10 and 3970 &-10 kHz. The line at 3440 kHz is the v line of the I4N spectrum.There should of course be two lower frequency lines for each inequivalent oxygen the two frequencies adding to give the frequency of the high frequency line belonging to the same oxygen atom. However the low frequency lines are nearly degenerate and previous measurements 90 D.Q.R. OF THE PYRIDINE -/- WATER COMPLEX .... ....*......(a).. . .. ,0.... .. .. ..* :. -* c f..". -a. * ........ ... -.-..... *...*:-4.. .. . .I. * ... . .......*.* 5 ... .... "2. -* ..... ... ..-... ... .......... .. ... ... .... ..... .......... . ......... I .... ..... ... .... U. ... ... *I ....: ..-...L.. " ,.. I 3600 3400 -*.I . 3800 4000 . :;.*; .. .... .. 2100 2300 1700 "0° kHz Fic. 7.-"0 quadrupole resonance spectrum for the complex obtained from a mixture with molecular ratio 2 D20(10 % enhanced in 170) to 1 pyridine. The line at 3440 kHz belongs to the 14Nspectrum. Cycle time 5 min irradiation time 10 s and linear peak-to-peak irradiation field 1.04 x lo-* T. .. ,.. ' *,,* M. M. DAVIDSON D. T. EDMONDS AND A. A. L. WHITE of the I7Ospectrum in water molecules using the level crossing technique show that one of the two lower frequency lines dominates in intensity. The frequencies of the two corresponding lines in normal ice are13 1750 and 3390 kHz. The quadrupole coupling constants of the three inequivalent sites in the complex are e2qQ/h= 6.66 & 0.04 MHz; q = 0.99 -J= 0.02 e2qQ/h= 6.94 & 0.04 MHz; q = 0.98 & 0.02 e2qQ/h= 7.51 -+ 0.05 MHz; q = 0.99 & 0.02.The fact that is so nearly unity points to oxygen sites with almost perfect tetrahedral environments. The conclusion drawn.from the 170results is very like that drawn from the d.t.q.r. results namely that there are three inequivalent water molecules one similar to water in ice and two distinctly different. CONCLUSIONS We conclude that the complex consists of 4 water molecules and one pyridine molecule that two of the water molecules are nearly equivalent and that one water molecule is hydrogen bonded to the lone pair of the nitrogen atom of the pyridine molecule with an N H hydrogen bond distance of 1.8 & 0.2 A.The hydrogen bonding model we are led to is shown below. \ \ 8 Analysis of the spectrum of deuterated pyridine with protonated water should add to the structural information particularly how the units shown above pack in the solid. Taking the water molecules in turn the molecule (D,D,) has the best defined deu- terium quadrupole coupling constants which are determined by the two resolved lowest frequency lines in the single transition spectrum and the lowest frequency lines of the d.t.q.r. spectrurri. The v and v-frequencies for this molecule are probably accurate to 50.1 kHz. The coupling constants for D are typical for that water site hydrogen bonded to a pyridine ring as we found in the study of lanthanum nicotinate and related compounds mentioned above.The consants for D are very close indeed to those in ice as one might expect for a site hydrogen bonded to another water molecule tetrahedrally (170 result). Perhaps the most interesting result of this whole study is the shape of molecule (DID2). The remarkable flexibility of the water mole- cule is displayed in that although the OD bond is very different from that in ice the ODzbond is almost identical to ice which may indicate that the layer of water required to match a biological organic molecule to its aqueous environment may be only one molecule thick. Molecule (D3D4)is again very " ice-like " as would once more be expected con- D.Q.R. OF THE PYRIDINE + WATER COMPLEX sidering its shape and hydrogen bonding neighbours.Molecules (D5D6)and (D,D,) are identical and are very weak hydrogen bond donors as may be deduced from their high deuterium quadrupole coupling constants and corresponding l4 short 0-D bond lengths (E 0.97 A). With further experimental and theoretical work the structural information that could be extracted from spectra such as those displayed here is enormous. For example on the experimental side it may well prove possible to identify the neighbours of a given quadrupole nucleus by the fine structure displayed in the solid-state satellite lines' that accompany it in this case to identify which deuteron is bonded to which oxygen and we have embarked upon an attempt at this. On the theoretical side a good treatment of the quadrupole coupling constants for the deuteron in water as a function of 0-D bond length is needed.The potential is great as the empirical correlation shows13 that a change of only A in 0-D bond length produces an easily measured change of 0.5 kHz in e2qQ/hwhich could make deuterium n.q.r. by far the most precise structural tool for this purpose. Also the value of which measures the departure of the electrical field gradient from axial symmetry should correlate with the degree of bentness of the hydrogen bond to some extent. M. M. D. and A. A. L. W. are grateful to the S.R.C. for support grants. The apparatus was built with the help of a grant from the Chemistry Committee of the S.R.C. D. T. Edmonds Phys. Reports 1977 29C 234. 'R. Blinc Adv.Nuclear Quadrupole Resonunce 1975,2,71; J. L. Ragle and G. L. Minott Adv. Nuclear Quadrupole Resonance 1978 3 205. D. T. Edmonds and J. P. G. Mailer J. Phys. E 1977 10 868. J. R. Johnson P. J. Kilpatrick S. D. Christian and H. E. Affsprung,J. Phys. Chem. 1968 72 3223. L. Guibe Ann. Phys. 1962 7 177. J. W. Moore M. D. Glick and W. A. Baker J. Amer. Cheni. Soc. 1972 94 1858. D. T. Edmonds and A. L. Mackay J. Magnetic Resonance 1975,20 515. D. T. Edmonds S. D. Goren A. L. Mackay and A. A. L. White J. Magnetic Resonance 1976 23 505. D. T. Edmonds and J. P. G. Mailer J. Magnetic Resonance 1978 29 213. lo D. T. Edmonds and A. A. L. White J. Magnetic Resonance 1978 31 149. l1 D. T. Edmonds and J. P. G. Mailer J. Magnetic Resonance 1977,26,93. l2 D. T. Edmonds M. J. Hunt and A. L. Mackay J. Magnetic Resonance 1975,20,505. l3 D. T. Edmonds and A. Zuseman Phys. Letters 1972 41A 167. l4 M. Shporer and A. M. Achlama J. Chem. Phys. 1976 65 3657. l5 D. T. Edmonds S. D. Goren A. A. L. White and W. F. Sherman J. Magnetic Resonance 1977 27 35.

ISSN:0301-5696    

DOI:10.1039/FS9781300083

出版商:RSC    

年代:1978

数据来源: RSC