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Natural abundance 13C spin diffusion enhanced by magic-angle spinning
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
12 August 1988
NATURAL ABUNDANCE 13CSPIN DIFFUSION ENHANCED BY MAGIC-ANGLE SPINNING W.E.J.R. MAAS and W.S. VEEMAN Department of Molecular Spectroscopy, Faculty of Science, Umversitysf Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands Received 15 April 1988; in final form 18 June 1988
We describe a technique to enhance 13Cspin diffusion by magic-angle spinning. The experiment is applied to camphor, where cross-peaks between two 13Cresonances are observed in a 2D exchange experiment when the spinner frequency is adjusted to match the difference in resonance frequencies of the two carbons involved.
1. Introduction For many heterogeneous materials, like for example polymer blends, macroscopic properties are determined by the miscibility of the various components on a molecular scale. Solid-state NMR has been proposed to be of value for determining the microscopic heterogeneity [ l-41, especially via measurement of ‘3C-‘3C spin diffusion rates between different molecular components. Because of the rs6 dependence of the spin diffusion rate a distinction can be made between an intimately mixed system and a system where the various different components are found in different domains with sizes appreciably larger than molecular dimensions. In particular, 13Cspin diffusion, compared to ‘H spin diffusion, is very suitable thanks to the much better spectral resolution under conditions of magicangle spinning ( MAS ) . Nevertheless, a particularly nice demonstration of the use of ‘H spin exchange in a 2D exchange experiment on polymer blends has been reported by Ernst et al. [ 1. In many polymer blends, however, one would like to exploit the higher resolution of a 13C spectrum. The disadvantage of 13Cspin diffusion in solids is the slow exchange rate due to the small mutual dipolar interaction relative to common differences in resonance frequency. In first approximation, in the absence of coupling to unlike spins, appreciable spin diffusion between different carbon chemical shift species can only occur when their dipolar interaction is of the same order
170
of magnitude or larger than the difference in resonance frequency. A factor which complicates this simple picture of 13Cspin diffusion in solids is the possible dipolar coupling with other nuclei, especially protons. When this interaction is strong, the static, anisotropic part tends to increase the carbon spectral differences, thereby slowing down exchange, while the fluctuating part makes it possible that for short time periods the resonance frequencies of two different spins match. Edzes and Bernards [ 5 ] applied partial proton decoupling during the mixing time of a two-dimensional exchange experiment to increase the rate of spin exchange in crystalline polyethylene, thereby increasing the probability that two exchanging nuclei have the same resonance frequency. Bronniman et al. [6] proposed spin locking of the 13C magnetization in the rotating frame during the mixing time. The 13Cchemical shift is then scaled by a factor of lo3 to lo4 while the carbons are decoupled from the protons. This technique was applied to static adamantane, producing cross-peaks for mixing times as short as 10 ms [6]. With magic-angle spinning, however, the spin exchange rate is appreciably reduced [ 61, and to observe the effects of spin diffusion in a 2D exchange experiment one needs excessively long mixing periods. This not only makes the experiments very time consuming but, more seriously, the diffusion rates may become smaller than 13Cspin-lattice relaxation rates, thereby making the experiment practically im-
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
Volume 149, number 2
CHEMICAL
PHYSICS LETTERS
possible. In this paper we propose to enhance the 13C13C spin diffusion, based on early experiments of Andrew et al. [ 71 and inspired by recent work of Griffin et al. [ 81. A different approach has been demonstrated by Meier and Ernst [ 9 ] by flipping during the mixing period the spinner axis to parallel to the magnetic field, so that the 13C-13Cdipolar interaction is not averaged out during the mixing.
2. 13Cspin diffusion in the presence of magic angle spinning In order to obtain high resolution 13Cspectra of amorphous or polycrystalline samples, magic-angle spinning (MAS) is frequently used [ 10, I 11. This technique, however, strongly reduces the ‘3C-‘3C dipolar coupling, which is the basic interaction responsible for 13Cspin diffusion, since MAS renders the dipolar Hamiltonian time dependent. As already pointed out by Andrew in 1963 [ 71 the time dependence of the flip-flop term of the dipolar Hamiltonian partly disappears when the spinner frequency equals the difference or half the difference in resonance frequencies of the two species involved. Recently, Griffin and co-workers [ 8 ] showed for doubly labelled glycine that the two 13Cresonance lines are split by mutual dipolar interactions when the spinner frequency is adjusted to match the difference in chemical shift frequencies. Suppose we have two isolated spins A and B, with resonance frequencies LL)~ and c+,, and coupled by a dipolar Hamiltonian
x [1;1,8-t(ZA,Z!! +z”ZB,)] .
(1)
Upon transformation to a doubly rotating frame, rotating with frequencies w+, and wg, defined by the transformation u(t) =exp( -io,Ztt_i%Z8t)
(2)
the non-secular dipolar flip-flop Hamiltonian (Z”,Z! +ZAZB,) becomes time dependent with frequency dr uA - LL),+Sample rotation at the magic angle introduces an additional time dependence (frequencies WRand 2WR) through modulation of the geometrical factor.
12 August I988
In general, both the periodicity of the spin part and of the geometrical part make the dipolar flip-flop term I”, Z!! + IA_Z”, ineffective for spin exchange. The total time dependence of this flip-flop term contains, among others, the following two terms: cos[ (d-wR)t]
and
cos[ (d-2w,)t]
,
(3)
therefore when the MAS frequency OR is chosen such that either oR =d or 2w, = A at least part of the flipflop term becomes time independent. As a consequence MAS no longer averages out the dipolar flipflop term and spin exchange between the spin species, coupled by the MAS frequency, can be almost as effective as in the non-spinning case. For a real system the above treatment is too simple, since not only spins A and B are coupled to other unlike spins but in addition have anisotropic chemical shifts which make the resonance frequencies o,, and ws dependent on the rotor position in the MAS experiment. In the case of dilute carbon spins especially the dipolar coupling with abundant proton spins has to be considered which itself may be effected by MAS. A description for such a real carbonproton system can be greatly simplified via the following assumptions: ( 1) The C-H dipolar couplings are for the main part eliminated by proton rf decoupling or by internal molecular motions so that the dipolar “C linewidth is smaller than the differences in isotropic chemical shifts of the various carbon species. (2) The MAS rate is much faster than the carbon chemical shift anisotropy, thereby averaging out the chemical shift anisotropy. With these approximations 13Cspin diffusion under magic angle spinning conditions can be described as above for the isolated pair if we take for the 13Clinewidth the remaining 13C-‘H dipolar linewidth. Due to the widths of the carbon resonances the conditions nw R = A for the MAS-enhanced spin diffusion become less sharply defined. In this paper the enhanced spin diffusion is demonstrated for natural-abundance 13Cin the camphor where due to internal molecular motions the proton-undecoupled 13C linewidth under MAS conditions is reduced to 4090 Hz. 171
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
3. Experimental
Data were recorded on a Brucker CXP 300, at a carbon frequency of 75.4 MHz, using a standard Bruker double bearing MAS probe. Camphor was supplied by Aldrich Co., and was used without further purification. We used a pulse scheme as proposed by Szeverenyi et al. [ 121, but in addition the mixing time is an integral number of the spinner revolution time. Although not really necessary for camphor in combination with the spinning speed used (oR is much larger than the 13Cchemical shift anisotropy), this is done to prevent any cross-peaks due to the chemical shift anisotropy [ 13 1. Note that during the mixing period no proton decoupling is applied. A phase cycling was used to suppress axial peaks and to select the anti-echo component in the r, domain [ 13,141. The spinner frequency was kept constant within + 10 Hz by a control system.
4. Results and discussion The technique proposed is demonstrated for camphor. Under MAS conditions the proton decoupled
12 August 1988
13Cspectrum shows ten resonances. The spectrum is shown in fig. 1 together with the structure of camphor (the carbonyl peak is not shown). Fig. 2A shows the 2D exchange spectrum of camphor, spun at 2760 f 5 Hz and with a mixing time of 4 s. Here the spinner frequency matches the frequency difference between Cl0 and C, (see fig. 1 ), which are separated by 2771 Hz, and at the same time matches Cs with C, and Cs with C,, separated by 2849 Hz and 2806 Hz, respectively. In fig. 2B we see a match with Cl0 and Cr, separated by 3569 Hz, and recorded with a spinner frequency of 3570? 10 Hz. Clearly, spin diffusion is enhanced only for those spins whose resonance frequency differences are matched by the MAS frequency. By varying the spinner speed in a region close to the perfect match (i.e. exactly matching the differences in chemical shift of the spins), we found that matching over a region which equals the width of the undecoupled resonances (40-90 Hz), as explained in section 3. In more rigid systems than camphor the undecoupled linewidths of course are much larger. This makes the MA8 matching less critical, but spin diffusion slow. Partial or complete ‘H decoupling during the (long) mixing time is necessary in that situation.
‘8\,.,‘9
98 10
Fig. I. Proton decoupled ’ 'Cspectrum of camphor, wR= 2800 Hz, together with the structure of camphor. The carbonyl peak C, is not shown.
172
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
12 August 1988
Fig. 2. Absolute mode 2D exchange spectra of camphor. Lorentzian line broadening was applied in both dimensions (3 Hz). 16 scans were accumulated. (A) w,=2768+ 5 Hz, mixing time 4 s. (B) 0,=3570+ 10 Hz, mixing time 2 s. The apparent doublet of diagonal peak C, is not real but due to spectral representation. 173
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
After submission of this paper we learned of similar one-dimensional work by Colombo, Meier and Ernst [ 151.
Acknowledgement
This work was supported by the Dutch Foundation for Pure Research (ZWO/SON). For technical assistence at the Dutch National NMR facility at Nijmegen we acknowledge Mr. J.W.M. van OS.
References [ 11P. Caravatti, P. Neuenschwander and R.R. Ernst, Macromolecules 18 (1985) 119; 19 (1986) 1889.
[ 2 ] P. Caravatti, J.A. Deli, G. Bodenhausen and R.R. Ernst, J. Am. Chem. Sot. 104 (1982) 5506. [3] P.M. Henrichs and M. Linder, J. Magn. Reson. 58 (1984) 458.
174
12 August 1988
[4] D.L. VanderHan, J. Magn. Reson. 72 (1987) 13. [ 5 ] H.T. Edzcs and J.P.C. Bernards, J. Am. Chem. Sot. 106 (1984) 1515. [6] C.E. Bronniman, N.M. Szeverenyi and G.E. Maciel, J. Chem. Phys. 79 ( 1983) 3694. [ 71 E.R. Andrew, A. Bradbury. R.G. Eades and V.T. Wynn, Phys. Letters 4 (1963) 99. [8] D.P. Raleigh, G.S. Harbison, T.G. Neiss, J.E. Roberts and R.G. Griffin, Chem. Phys. Letters 138 (1987) 285. [ 91 B.H. Meier and R.R. Ernst, The Fritz Haber Workshop on Modern Techniques in Magnetic Resonance, Tiberias, Israel (1987). [IO] M.M. Maricq and J.S. Waugh, J. Chem. Phys. 70 (1979) 3300. [ 111 J. Schaeffer and E.O. Stejskal, J. Am. Chem. Sot. 98 ( 1976) 1031. [ 121 N.M. Szeverenyi, M.J. Sullivan and G.E. Maciel, J. Magn. Reson. 47 (1982) 462. [ 131 A.F. de Jong, A.P.M. Kentgens and W.S. Veeman, Chem. Phys. Letters 109 (1984) 337. [ 141 A. Bax, Two dimensional nuclear magnetic resonance in liquids (Reidel, Dordrecht, 1982). [ I5 ] M.G. Colombo, B.H. Meier and R.R. Ernst, Chem. Phys. Letters 146 (1988) 189.
CHEMICAL PHYSICS LETTERS
12 August 1988
NATURAL ABUNDANCE 13CSPIN DIFFUSION ENHANCED BY MAGIC-ANGLE SPINNING W.E.J.R. MAAS and W.S. VEEMAN Department of Molecular Spectroscopy, Faculty of Science, Umversitysf Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands Received 15 April 1988; in final form 18 June 1988
We describe a technique to enhance 13Cspin diffusion by magic-angle spinning. The experiment is applied to camphor, where cross-peaks between two 13Cresonances are observed in a 2D exchange experiment when the spinner frequency is adjusted to match the difference in resonance frequencies of the two carbons involved.
1. Introduction For many heterogeneous materials, like for example polymer blends, macroscopic properties are determined by the miscibility of the various components on a molecular scale. Solid-state NMR has been proposed to be of value for determining the microscopic heterogeneity [ l-41, especially via measurement of ‘3C-‘3C spin diffusion rates between different molecular components. Because of the rs6 dependence of the spin diffusion rate a distinction can be made between an intimately mixed system and a system where the various different components are found in different domains with sizes appreciably larger than molecular dimensions. In particular, 13Cspin diffusion, compared to ‘H spin diffusion, is very suitable thanks to the much better spectral resolution under conditions of magicangle spinning ( MAS ) . Nevertheless, a particularly nice demonstration of the use of ‘H spin exchange in a 2D exchange experiment on polymer blends has been reported by Ernst et al. [ 1. In many polymer blends, however, one would like to exploit the higher resolution of a 13C spectrum. The disadvantage of 13Cspin diffusion in solids is the slow exchange rate due to the small mutual dipolar interaction relative to common differences in resonance frequency. In first approximation, in the absence of coupling to unlike spins, appreciable spin diffusion between different carbon chemical shift species can only occur when their dipolar interaction is of the same order
170
of magnitude or larger than the difference in resonance frequency. A factor which complicates this simple picture of 13Cspin diffusion in solids is the possible dipolar coupling with other nuclei, especially protons. When this interaction is strong, the static, anisotropic part tends to increase the carbon spectral differences, thereby slowing down exchange, while the fluctuating part makes it possible that for short time periods the resonance frequencies of two different spins match. Edzes and Bernards [ 5 ] applied partial proton decoupling during the mixing time of a two-dimensional exchange experiment to increase the rate of spin exchange in crystalline polyethylene, thereby increasing the probability that two exchanging nuclei have the same resonance frequency. Bronniman et al. [6] proposed spin locking of the 13C magnetization in the rotating frame during the mixing time. The 13Cchemical shift is then scaled by a factor of lo3 to lo4 while the carbons are decoupled from the protons. This technique was applied to static adamantane, producing cross-peaks for mixing times as short as 10 ms [6]. With magic-angle spinning, however, the spin exchange rate is appreciably reduced [ 61, and to observe the effects of spin diffusion in a 2D exchange experiment one needs excessively long mixing periods. This not only makes the experiments very time consuming but, more seriously, the diffusion rates may become smaller than 13Cspin-lattice relaxation rates, thereby making the experiment practically im-
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
Volume 149, number 2
CHEMICAL
PHYSICS LETTERS
possible. In this paper we propose to enhance the 13C13C spin diffusion, based on early experiments of Andrew et al. [ 71 and inspired by recent work of Griffin et al. [ 81. A different approach has been demonstrated by Meier and Ernst [ 9 ] by flipping during the mixing period the spinner axis to parallel to the magnetic field, so that the 13C-13Cdipolar interaction is not averaged out during the mixing.
2. 13Cspin diffusion in the presence of magic angle spinning In order to obtain high resolution 13Cspectra of amorphous or polycrystalline samples, magic-angle spinning (MAS) is frequently used [ 10, I 11. This technique, however, strongly reduces the ‘3C-‘3C dipolar coupling, which is the basic interaction responsible for 13Cspin diffusion, since MAS renders the dipolar Hamiltonian time dependent. As already pointed out by Andrew in 1963 [ 71 the time dependence of the flip-flop term of the dipolar Hamiltonian partly disappears when the spinner frequency equals the difference or half the difference in resonance frequencies of the two species involved. Recently, Griffin and co-workers [ 8 ] showed for doubly labelled glycine that the two 13Cresonance lines are split by mutual dipolar interactions when the spinner frequency is adjusted to match the difference in chemical shift frequencies. Suppose we have two isolated spins A and B, with resonance frequencies LL)~ and c+,, and coupled by a dipolar Hamiltonian
x [1;1,8-t(ZA,Z!! +z”ZB,)] .
(1)
Upon transformation to a doubly rotating frame, rotating with frequencies w+, and wg, defined by the transformation u(t) =exp( -io,Ztt_i%Z8t)
(2)
the non-secular dipolar flip-flop Hamiltonian (Z”,Z! +ZAZB,) becomes time dependent with frequency dr uA - LL),+Sample rotation at the magic angle introduces an additional time dependence (frequencies WRand 2WR) through modulation of the geometrical factor.
12 August I988
In general, both the periodicity of the spin part and of the geometrical part make the dipolar flip-flop term I”, Z!! + IA_Z”, ineffective for spin exchange. The total time dependence of this flip-flop term contains, among others, the following two terms: cos[ (d-wR)t]
and
cos[ (d-2w,)t]
,
(3)
therefore when the MAS frequency OR is chosen such that either oR =d or 2w, = A at least part of the flipflop term becomes time independent. As a consequence MAS no longer averages out the dipolar flipflop term and spin exchange between the spin species, coupled by the MAS frequency, can be almost as effective as in the non-spinning case. For a real system the above treatment is too simple, since not only spins A and B are coupled to other unlike spins but in addition have anisotropic chemical shifts which make the resonance frequencies o,, and ws dependent on the rotor position in the MAS experiment. In the case of dilute carbon spins especially the dipolar coupling with abundant proton spins has to be considered which itself may be effected by MAS. A description for such a real carbonproton system can be greatly simplified via the following assumptions: ( 1) The C-H dipolar couplings are for the main part eliminated by proton rf decoupling or by internal molecular motions so that the dipolar “C linewidth is smaller than the differences in isotropic chemical shifts of the various carbon species. (2) The MAS rate is much faster than the carbon chemical shift anisotropy, thereby averaging out the chemical shift anisotropy. With these approximations 13Cspin diffusion under magic angle spinning conditions can be described as above for the isolated pair if we take for the 13Clinewidth the remaining 13C-‘H dipolar linewidth. Due to the widths of the carbon resonances the conditions nw R = A for the MAS-enhanced spin diffusion become less sharply defined. In this paper the enhanced spin diffusion is demonstrated for natural-abundance 13Cin the camphor where due to internal molecular motions the proton-undecoupled 13C linewidth under MAS conditions is reduced to 4090 Hz. 171
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
3. Experimental
Data were recorded on a Brucker CXP 300, at a carbon frequency of 75.4 MHz, using a standard Bruker double bearing MAS probe. Camphor was supplied by Aldrich Co., and was used without further purification. We used a pulse scheme as proposed by Szeverenyi et al. [ 121, but in addition the mixing time is an integral number of the spinner revolution time. Although not really necessary for camphor in combination with the spinning speed used (oR is much larger than the 13Cchemical shift anisotropy), this is done to prevent any cross-peaks due to the chemical shift anisotropy [ 13 1. Note that during the mixing period no proton decoupling is applied. A phase cycling was used to suppress axial peaks and to select the anti-echo component in the r, domain [ 13,141. The spinner frequency was kept constant within + 10 Hz by a control system.
4. Results and discussion The technique proposed is demonstrated for camphor. Under MAS conditions the proton decoupled
12 August 1988
13Cspectrum shows ten resonances. The spectrum is shown in fig. 1 together with the structure of camphor (the carbonyl peak is not shown). Fig. 2A shows the 2D exchange spectrum of camphor, spun at 2760 f 5 Hz and with a mixing time of 4 s. Here the spinner frequency matches the frequency difference between Cl0 and C, (see fig. 1 ), which are separated by 2771 Hz, and at the same time matches Cs with C, and Cs with C,, separated by 2849 Hz and 2806 Hz, respectively. In fig. 2B we see a match with Cl0 and Cr, separated by 3569 Hz, and recorded with a spinner frequency of 3570? 10 Hz. Clearly, spin diffusion is enhanced only for those spins whose resonance frequency differences are matched by the MAS frequency. By varying the spinner speed in a region close to the perfect match (i.e. exactly matching the differences in chemical shift of the spins), we found that matching over a region which equals the width of the undecoupled resonances (40-90 Hz), as explained in section 3. In more rigid systems than camphor the undecoupled linewidths of course are much larger. This makes the MA8 matching less critical, but spin diffusion slow. Partial or complete ‘H decoupling during the (long) mixing time is necessary in that situation.
‘8\,.,‘9
98 10
Fig. I. Proton decoupled ’ 'Cspectrum of camphor, wR= 2800 Hz, together with the structure of camphor. The carbonyl peak C, is not shown.
172
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
12 August 1988
Fig. 2. Absolute mode 2D exchange spectra of camphor. Lorentzian line broadening was applied in both dimensions (3 Hz). 16 scans were accumulated. (A) w,=2768+ 5 Hz, mixing time 4 s. (B) 0,=3570+ 10 Hz, mixing time 2 s. The apparent doublet of diagonal peak C, is not real but due to spectral representation. 173
Volume 149, number 2
CHEMICAL PHYSICS LETTERS
After submission of this paper we learned of similar one-dimensional work by Colombo, Meier and Ernst [ 151.
Acknowledgement
This work was supported by the Dutch Foundation for Pure Research (ZWO/SON). For technical assistence at the Dutch National NMR facility at Nijmegen we acknowledge Mr. J.W.M. van OS.
References [ 11P. Caravatti, P. Neuenschwander and R.R. Ernst, Macromolecules 18 (1985) 119; 19 (1986) 1889.
[ 2 ] P. Caravatti, J.A. Deli, G. Bodenhausen and R.R. Ernst, J. Am. Chem. Sot. 104 (1982) 5506. [3] P.M. Henrichs and M. Linder, J. Magn. Reson. 58 (1984) 458.
174
12 August 1988
[4] D.L. VanderHan, J. Magn. Reson. 72 (1987) 13. [ 5 ] H.T. Edzcs and J.P.C. Bernards, J. Am. Chem. Sot. 106 (1984) 1515. [6] C.E. Bronniman, N.M. Szeverenyi and G.E. Maciel, J. Chem. Phys. 79 ( 1983) 3694. [ 71 E.R. Andrew, A. Bradbury. R.G. Eades and V.T. Wynn, Phys. Letters 4 (1963) 99. [8] D.P. Raleigh, G.S. Harbison, T.G. Neiss, J.E. Roberts and R.G. Griffin, Chem. Phys. Letters 138 (1987) 285. [ 91 B.H. Meier and R.R. Ernst, The Fritz Haber Workshop on Modern Techniques in Magnetic Resonance, Tiberias, Israel (1987). [IO] M.M. Maricq and J.S. Waugh, J. Chem. Phys. 70 (1979) 3300. [ 111 J. Schaeffer and E.O. Stejskal, J. Am. Chem. Sot. 98 ( 1976) 1031. [ 121 N.M. Szeverenyi, M.J. Sullivan and G.E. Maciel, J. Magn. Reson. 47 (1982) 462. [ 131 A.F. de Jong, A.P.M. Kentgens and W.S. Veeman, Chem. Phys. Letters 109 (1984) 337. [ 141 A. Bax, Two dimensional nuclear magnetic resonance in liquids (Reidel, Dordrecht, 1982). [ I5 ] M.G. Colombo, B.H. Meier and R.R. Ernst, Chem. Phys. Letters 146 (1988) 189.