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Line-splitting and broadening effects from 19F in the 13CNMR of liquid crystals and solids
17 August 2001
Chemical Physics Letters 344 (2001) 68±74
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Line-splitting and broadening eects from 19F in the 13C NMR of liquid crystals and solids Giancarlo Antonioli, Deborah E. McMillan, Paul Hodgkinson * Department of Chemistry, University of Durham, Stockton Road, Durham DH1 3LE, UK Received 26 April 2001; in ®nal form 21 June 2001
Abstract The NMR resonances of 13 C spins in proximity to 19 F are often unusually broad, degrading resolution and limiting the ability to quantify the C±F interactions. We observe line-splittings and selective broadenings in a liquid crystal sample that strongly depend on the 1 H decoupling. We propose a simple rationalisation that successfully reproduces the experimental behaviour, and ®nd that suitably adapted decoupling sequences eectively eliminate the line-broadenings. Experiments on solid samples show similar variations with decoupling sequence, and the same eects may be general to H±X±Y systems. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction Previous f1 Hg13 C NMR studies of ¯uorinecontaining organic molecules have remarked on the marked line-broadening of resonances of carbons close to 19 F nuclei [1±4]. As well as degrading resolution, these line-broadenings obscure the splittings due to the C±F dipolar and J interactions. In liquid crystal systems in particular, these dipolar interactions provide valuable information on the (mean) conformation of molecules in the mesophase [4,5]. Simultaneous decoupling of 19 F removes this line-broadening [1±3], but requires specialised equipment and results in the loss of information about the C±F interactions. We recently observed these eects in the nematic phase of I35, and since we were interested in measuring the C±F couplings in this and related
systems, understanding (and eliminating) these line-broadenings was important. Rapid (but anisotropic) molecular motion means that the overall spectra appearance is determined by purely intramolecular eects, hence previous rationalisations in terms of C±F `dipolar dephasing' and short T2 s from F±F interactions were clearly inapplicable to I35. We propose a simple explanation in terms of o-resonance eects which convincingly reproduces the experimental behaviour, including the elimination of the line-broadenings by decoupling sequences that are robust with respect to 1 H chemical shift. We believe that related eects are also at work in solid systems, and we present some preliminary results in the ®nal section which con®rm this hypothesis. 2. In a liquid crystalline system
*
Corresponding author. Fax: +44-191-386-1127. E-mail address: [email protected] (P. Hodgkinson).
Experiments were performed on a Chemagnetics CMX spectrometer operating at a proton
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G. Antonioli et al. / Chemical Physics Letters 344 (2001) 68±74
Larmor frequency of 200.13 MHz. 13 C NMR spectra were obtained, using a variety of 1 H decoupling sequences, from a sample of I35 (Merck, UK) maintained at 40°C (10°C above the crystal±nematic phase transition). Fig. 1 shows the results for three decoupling methods: continuouswave irradiation, TPPM [6] and SPINAL64 [7]. It shows the striking dependence of 13 C resolution
69
on the decoupling sequence (these dier only in the pattern of their phase modulations). For CW decoupling in particular, it was not possible to ®nd a value of the 1 H transmitter frequency which gave good decoupling across the whole 13 C spectrum. The removal of intermolecular interactions by the rapid molecular motion means that each 13 C
Fig. 1. Comparison of 13 C NMR spectra of I35 using dierent 1 H decoupling methods: (a) continuous-wave, (b) TPPM, (c) SPINAL64. Experimental parameters: vRF 1 H 50 kHz, TPPM and SPINAL64 tip angle 165°, CP contact time 3 ms, recycle delay 5 s, T 40°C. Assignment of C±F doublets taken from Ref. [4].
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resonance should be split into a sharp doublet by the coupling (both dipolar and scalar) between the 13 C and the single 19 F nucleus, as can be seen in Fig. 1c. In spectra (a) and (b), however, this information has obscured a line-broadening which causes some doublets to broaden (C4), the collapse of single components of a doublet (C1), or even individual components to appear as doublets (C2 and C3). These observations are incompatible with
obvious causes of line-broadening in these systems; director variations due to RF heating of the sample, poor sample alignment, unusually small T2 's etc. In particular, the observation of additional splittings and the strong variation with the pattern of phase modulation strongly suggests a `coherent' origin in terms of the nuclear spin Hamiltonian. Fig. 2 shows the eect of the 1 H decoupler power, vrf , on the line-splittings of the CW spec-
Fig. 2. (Top) 13 C NMR spectra as a function of power of CW irradiation, expressed as the nutation frequency vrf . (Bottom) Comparison of selected slices of this data set with numerical simulations of the spectra for C2 using the experimental parameters plus the known dipolar couplings: dCH 1:5 kHz, dCF 1:7 kHz, dHF 5:2 kHz.
G. Antonioli et al. / Chemical Physics Letters 344 (2001) 68±74
trum. The behaviour is strongly reminiscent of the o-resonance eects familiar from both liquidstate [8] and, to a less extent, solid-state [9] NMR. The ®gure also shows a comparison of these spectra with simulations of the spin dynamics in a three spin 1 H±19 F±13 C model for carbon 2. The geometry of the biphenyl core in the nematic phase has been established by previous NMR studies [4], and this information was used to determine the dipolar couplings between C2, the 19 F and the 1 H nucleus of C3. The simulations, using a straightforward calculation of the density matrix evolution, reproduce perfectly the experimental dependence on vrf . The only variable was the 1 H oset, which was found to be dH 4 kHz. Consideration of the Hamiltonian for the system reveals the origin of these eects. Extending previous arguments developed for two nuclei systems [8,10] to the 1 H±19 F±13 C system, the Hamiltonian (in the rotating frame for all nuclei) is
71
C±H interactions, causing line-broadening or even splittings if single C±H interactions are resolved, cf. Fig. 3b. Indeed o-resonance decoupling has been used in the past as a simple way of obtaining scaled multiplet patterns to aid in the assignment of 13 C spectra. Corresponding eects from dipolar rather than J interactions have also been observed for single crystals [9]. Experimentally, o-resonance eects are minimised by optimising the position of the 1 H transmitter frequency to reduce the size of d. Combined with broad-band decoupling sequences which are designed to be robust with respect to the residual variations in d, v should then be small over the entire range of (proton) chemical shifts [10]. It is important to remember, however, that decoupling in solids and liquid-crystals is quite
H dH I1z dC I3z 2dHF I1z I2z 2dCH I1z I3z 2dCF I2z I3z HRF t;
1
where the eective couplings dij subsume any J couplings, dH and dC are the osets (shifts) of the 1 H and 13 C from their transmitter frequencies, and HRF is the time-dependent RF applied to the 1 H spins: HRF t vRF I1x cos / t I1y sin / t:
2
Since the decoupling RF is acting only on the 1 H spin space, and the other interactions are all secular with respect to the Zeeman interaction, the Hamiltonian can be blocked into sub-spaces labelled by the states of the 19 F and 13 C spins. The Hamiltonian in the 1 H subspace e.g., for 19 F in an a state and 13 C in a b state, is thus: Hba dH dHF
dCH I1z
dC =2 dCF =2 1 HRF t:
3
This has the same form as for the simple C±H case: the term proportional to the identity simply determining the eective shift of the 13 C resonance i.e., dC dCF , while the oset term now includes a contribution from dHF . As for the two spin system, an oset of the decoupling transmitter from exact resonance results in a non-zero scaling, v, of the
Fig. 3. Eect of various combinations of 1 H o-resonance shift H and H±F dipolar coupling dHF on a simulated C±F doublet under CW 1 H decoupling: (a) with no H±F coupling, on resonance, (b) o resonance or non-zero dipolar coupling, (c±e) dierent combinations of o-resonance shift and dipolar coupling.
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dierent from the decoupling of J in the solutionstate. The job of a decoupling sequence is to ensure that the net rotation of the 1 H spins is the same irrespective of the state of the rare spin [10]. J is generally small compared to the range of 1 H shifts and so the eective oset, dH J =2, is quite similar for the 13 C a and b states. In contrast, dipolar couplings are generally comparable to or exceed the shift range. As a result, sequences such as WALTZ-16 [11] that give good broad-band decoupling in the liquid-state are relatively ineective in both solid and, to a lesser extent, liquid crystal phases. The introduction of the H±F dipolar coupling into the eective oset of Eq. (3) may seem trivial, indeed its eect is equivalent to a non-zero oset, Fig. 3b. Unlike dH , however, it cannot be reduced by optimising the transmitter oset. Moreover, dHF can be large, much larger than the variations in dH due to the 1 H chemical shift range (500 Hz at a 1 H Larmor frequency of 200 MHz). For carbon 2 of I35, for example, the relevant H±F coupling is about 5.2 kHz (it is clearly resolved in the 19 F spectrum). This is now signi®cant compared to the decoupler B1 ®eld, vRF . The often asymmetrical nature of the broadening follows trivially; if dH is non-zero, the magnitude of the oset, jdH dHF j, will be dierent for the two components, leading to the asymmetrical splittings seen in Fig. 3c±e. It is clearly impossible to eliminate the broadening of both components of the C±F doublet simultaneously. The ¯ip-side is that the selective broadenings can provide information on the relative signs of couplings which is otherwise dicult to obtain. For instance, the H±F interaction is the same for C2 and C3 and by varying the oset in the CW-decoupled spectra, we can easily deduce their C±F couplings have opposite signs. In the case of C2 and C3, the coupling between the closest proton and the 19 F is strong. It is not immediately apparent that this rationalisation applies to other 13 C resonances where there is no clear three-spin C±H±F system. Simulations of the spin system of an entire phenyl fragment i.e., 13 C±19 F±1 H4 for C4, however, do successfully reproduce the experimental behaviour, with the inclusion or otherwise of the 1 H homonuclear couplings making no substantial dierence. If 1 H
homonuclear interactions can be ignored, then the spectrum from, say, a CFHA HB HC system is simply given by the convolution of the spectra from the individual CHF systems i.e., CFHA
CFHB CFHC . If one of these protons is particularly strongly in¯uenced by the 19 F (e.g., C2, C3) visible line-splittings will be seen, otherwise the convolution of a number of small splittings will result in a non-speci®c and increasingly Gaussian line-broadening (e.g., C4). The elimination of these line-broadenings, vital to quantitative use of the C±F splittings, is relatively straightforward. It reduces to ®nding a 1 H decoupling method which is suciently robust with respect to the eective 1 H oset, dH d. Increasing the decoupling power improves matters, cf. Fig. 2, but this is a notoriously inecient use of decoupler power and unsuited to liquid crystal samples. As discussed above, broad-band decoupling sequences from liquid-state NMR are not very eective, and it is necessary to use techniques developed speci®cally for the solid-state and/or liquid crystals. Of the many sequences tested, the SPINAL sequences [7] have given consistently good results with a minimum of optimisation. Novel sequences based on computer-optimisation of the phase modulation [12] have also shown promise. It is worth noting the sensitivity of the lineshapes to the quality of the decoupling to make it a good test sample; mis-setting of the parameters of the decoupling sequence will result in visible degradation of the spectral resolution. If, however, the sequence is correctly adjusted ± for SPINAL, this involves setting the tip angles of the sequence elements to 160 10° ± the 13 C linewidths become independent of the proximity to 19 F, not only improving resolution, but allowing the accurate quanti®cation of the C±F couplings. 3. In a solid system It has been possible to explain the broad linewidths of peaks close to 19 F in I35 in terms of a simple coherent eect, rather than invoking arguments involving 13 C±19 F dipolar dephasing and 19 F relaxation [1]. This particular problem may appear somewhat specialised, but we believe that the same
G. Antonioli et al. / Chemical Physics Letters 344 (2001) 68±74
eect occurs much more widely, although its coherent nature is obscured in samples of powdered solids by the orientational variation of the dipolar couplings. Since the size of the scaled splitting resulting from o-resonance decoupling is proportional to the C±H dipolar coupling, the 13 C peaks from isolated static C±H±F systems will be scaled dipolar Pake patterns. In practice, however, the width of the powder patterns is small and will be obscured by additional homonuclear and heteronuclear couplings, resulting in an overall unspeci®c line-broadening. Line-broadenings due to o-resonance CW decoupling in magic-angle-spinning (MAS) spectra have been extensively documented [13,14]. Phasemodulated decoupling sequences, such as TPPM, strongly reduce these eects. Their likely cause is the interference between the decoupling, C±H dipolar interactions and 1 H chemical shift anisotropy (CSA) [15], and although eects from a constant 1 H oset are eliminated by MAS, the time-dependent oset caused by a heteronuclear dipolar interaction, such as the H±F coupling, is of exactly the same form as the time-dependent shift due to the
73
CSA. Hence we would expect a similar linebroadening to apply in the 13 C MAS spectra of ¯uorinated molecules (as indeed is observed [1±3]). Experiments to con®rm this rigorously are currently underway, but some preliminary results con®rming this hypothesis are shown in Fig. 4. The system is an inclusion compound formed between urea and a ¯uorinated alkane, the urea forming a hexagonal framework of tunnels in which the linear guest molecules reside. Earlier studies of an analogous compound had remarked the strong broadening of the 13 C resonances of nuclei close to the 19 F [2]. This can be seen clearly in spectra (a) and (d). Changing the decoupling sequence greatly reduces these eects, especially using the SPINAL sequence. The signal from the CH3 is especially striking; the CH3 's next to another CH3 in the tunnel (head-to-head) have a slightly dierent shift from those next to a CH2 F [2]. In the CW spectra, the peak associated with the latter conformation is strongly broadened, while the two linewidths of the two peaks are indistinguishable (within the limits of the experiment) in the TPPM and SPINAL spectra.
Fig. 4. Spectra of the 1-¯uorononane/urea inclusion compound at ambient temperature for three decoupling methods: (a,d) continuous-wave, (b,e) TPPM and (c,f) SPINAL64. Spectra (a±c) are from a sample prepared with per-deuterated urea, (d±f) are from an analogous sample prepared with `normal' urea. Spectral parameters: vRF 1 H 45 kHz, contact time 3 ms, spinning speed 3 kHz. The linewidths in spectra (c) and (f) are 9 and 5 Hz, respectively (no line-broadening has been applied).
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Since the molecules rotate rapidly at ambient temperature about the axis of tunnels formed by the urea host, this system is very similar to liquid crystal, particularly in the sample with the deuterated framework. As it is a powder, however, we do not observe the distinct additional splittings seen in the (aligned) liquid crystal system, but rather a relatively unspeci®c broadening. The resolution of all spectra is degraded when the host molecules are protonated, but the trends are clearly the same, with the SPINAL sequence developed for liquid crystal samples giving superior resolution in this solid (albeit quite mobile) sample ± particularly noticeable for the carbon resonance at 26 ppm. 4. Conclusions It is clear that previous rationalisations of broad 13 C resonances in 1 H-decoupled spectra of lightly ¯uorinated molecules do not satisfactorily explain many experimental observations. A simple explanation in terms of o-resonance eects caused by H±F interactions appears to be more satisfactory, and correctly predicts that improved 1 H decoupling techniques can eliminate these broadenings without resorting to 19 F decoupling. Although `double decoupling' will be necessary in systems that are abundant in both 19 F and 1 H, this means that most experiments in lightly ¯uorinated systems can be conducted on standard doubleresonance equipment. Although this explanation can only be rigorously demonstrated in static, oriented systems such as liquid crystals or single crystals, it is reasonable to suppose that the same eects operate in solids under magic-angle spinning. We expect to see a similar loss of resolution in other H±X±Y systems in which the H±Y interactions are strong.
Acknowledgements The authors would like to express their gratitude to Prof. J.W. Emsley for drawing their attention to this problem and for the gift of the initial I35 sample, and to Prof. K.D.M. Harris and his group for assistance with the ¯uoroalkane/urea inclusion systems. Thanks are also due to the Alliance programme of the British Council for enabling stimulating discussions on decoupling problems with Prof. Lyndon Emsley and his group. References [1] E.W. Hagaman, J. Magn. Reson. Ser. A 104 (1993) 125. [2] A. Nordon, R.K. Harris, L. Yeo, K.D.M. Harris, Chem. Commun. 21 (1997) 2045. [3] K.D.M. Harris, Chem. Soc. Rev. 26 (1997) 279. [4] E. Ciampi, M.I.C. Furby, L. Brennan, J.W. Emsley, A. Lesage, L. Emsley, Liq. Cryst. 26 (1999) 109. [5] M.L. Magnuson, L.F. Tanner, B.M. Fung, Liq. Cryst. 16 (1994) 857. [6] A.E. Bennett, C.M. Rienstra, M. Auger, K.V. Lakshmi, R.G. Grin, J. Chem. Phys. 103 (1995) 6951. [7] B.M. Fung, A.K. Khitrin, K. Ermolaev, J. Magn. Reson. 142 (2000) 97. [8] A. Abragam, in: Principles of nuclear magnetism, 1961, Oxford University Press, Oxford, pp. 530±533. [9] K. Takegoshi, C.A. McDowell, J. Magn. Reson. 66 (1986) 14±31. [10] J.S. Waugh, J. Magn. Reson. 50 (1982) 30. [11] A.J. Shaka, J. Keeler, R. Freeman, J. Magn. Reson. 52 (1983) 335. [12] D. Sakellariou, A. Lesage, P. Hodgkinson, L. Emsley, Chem. Phys. Lett. 319 (2000) 253. [13] D.L. VanderHart, W.L. Earl, A.N. Garroway, J. Magn. Reson. 44 (1981) 361. [14] D.L. VanderHart, G.C. Campbell, J. Magn. Reson. 134 (1998) 88. [15] M. Ernst, S. Bush, A.C. Kolbert, A. Pines, J. Chem. Phys. 105 (1996) 3387.
Chemical Physics Letters 344 (2001) 68±74
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Line-splitting and broadening eects from 19F in the 13C NMR of liquid crystals and solids Giancarlo Antonioli, Deborah E. McMillan, Paul Hodgkinson * Department of Chemistry, University of Durham, Stockton Road, Durham DH1 3LE, UK Received 26 April 2001; in ®nal form 21 June 2001
Abstract The NMR resonances of 13 C spins in proximity to 19 F are often unusually broad, degrading resolution and limiting the ability to quantify the C±F interactions. We observe line-splittings and selective broadenings in a liquid crystal sample that strongly depend on the 1 H decoupling. We propose a simple rationalisation that successfully reproduces the experimental behaviour, and ®nd that suitably adapted decoupling sequences eectively eliminate the line-broadenings. Experiments on solid samples show similar variations with decoupling sequence, and the same eects may be general to H±X±Y systems. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction Previous f1 Hg13 C NMR studies of ¯uorinecontaining organic molecules have remarked on the marked line-broadening of resonances of carbons close to 19 F nuclei [1±4]. As well as degrading resolution, these line-broadenings obscure the splittings due to the C±F dipolar and J interactions. In liquid crystal systems in particular, these dipolar interactions provide valuable information on the (mean) conformation of molecules in the mesophase [4,5]. Simultaneous decoupling of 19 F removes this line-broadening [1±3], but requires specialised equipment and results in the loss of information about the C±F interactions. We recently observed these eects in the nematic phase of I35, and since we were interested in measuring the C±F couplings in this and related
systems, understanding (and eliminating) these line-broadenings was important. Rapid (but anisotropic) molecular motion means that the overall spectra appearance is determined by purely intramolecular eects, hence previous rationalisations in terms of C±F `dipolar dephasing' and short T2 s from F±F interactions were clearly inapplicable to I35. We propose a simple explanation in terms of o-resonance eects which convincingly reproduces the experimental behaviour, including the elimination of the line-broadenings by decoupling sequences that are robust with respect to 1 H chemical shift. We believe that related eects are also at work in solid systems, and we present some preliminary results in the ®nal section which con®rm this hypothesis. 2. In a liquid crystalline system
*
Corresponding author. Fax: +44-191-386-1127. E-mail address: [email protected] (P. Hodgkinson).
Experiments were performed on a Chemagnetics CMX spectrometer operating at a proton
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 7 7 4 - 6
G. Antonioli et al. / Chemical Physics Letters 344 (2001) 68±74
Larmor frequency of 200.13 MHz. 13 C NMR spectra were obtained, using a variety of 1 H decoupling sequences, from a sample of I35 (Merck, UK) maintained at 40°C (10°C above the crystal±nematic phase transition). Fig. 1 shows the results for three decoupling methods: continuouswave irradiation, TPPM [6] and SPINAL64 [7]. It shows the striking dependence of 13 C resolution
69
on the decoupling sequence (these dier only in the pattern of their phase modulations). For CW decoupling in particular, it was not possible to ®nd a value of the 1 H transmitter frequency which gave good decoupling across the whole 13 C spectrum. The removal of intermolecular interactions by the rapid molecular motion means that each 13 C
Fig. 1. Comparison of 13 C NMR spectra of I35 using dierent 1 H decoupling methods: (a) continuous-wave, (b) TPPM, (c) SPINAL64. Experimental parameters: vRF 1 H 50 kHz, TPPM and SPINAL64 tip angle 165°, CP contact time 3 ms, recycle delay 5 s, T 40°C. Assignment of C±F doublets taken from Ref. [4].
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resonance should be split into a sharp doublet by the coupling (both dipolar and scalar) between the 13 C and the single 19 F nucleus, as can be seen in Fig. 1c. In spectra (a) and (b), however, this information has obscured a line-broadening which causes some doublets to broaden (C4), the collapse of single components of a doublet (C1), or even individual components to appear as doublets (C2 and C3). These observations are incompatible with
obvious causes of line-broadening in these systems; director variations due to RF heating of the sample, poor sample alignment, unusually small T2 's etc. In particular, the observation of additional splittings and the strong variation with the pattern of phase modulation strongly suggests a `coherent' origin in terms of the nuclear spin Hamiltonian. Fig. 2 shows the eect of the 1 H decoupler power, vrf , on the line-splittings of the CW spec-
Fig. 2. (Top) 13 C NMR spectra as a function of power of CW irradiation, expressed as the nutation frequency vrf . (Bottom) Comparison of selected slices of this data set with numerical simulations of the spectra for C2 using the experimental parameters plus the known dipolar couplings: dCH 1:5 kHz, dCF 1:7 kHz, dHF 5:2 kHz.
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trum. The behaviour is strongly reminiscent of the o-resonance eects familiar from both liquidstate [8] and, to a less extent, solid-state [9] NMR. The ®gure also shows a comparison of these spectra with simulations of the spin dynamics in a three spin 1 H±19 F±13 C model for carbon 2. The geometry of the biphenyl core in the nematic phase has been established by previous NMR studies [4], and this information was used to determine the dipolar couplings between C2, the 19 F and the 1 H nucleus of C3. The simulations, using a straightforward calculation of the density matrix evolution, reproduce perfectly the experimental dependence on vrf . The only variable was the 1 H oset, which was found to be dH 4 kHz. Consideration of the Hamiltonian for the system reveals the origin of these eects. Extending previous arguments developed for two nuclei systems [8,10] to the 1 H±19 F±13 C system, the Hamiltonian (in the rotating frame for all nuclei) is
71
C±H interactions, causing line-broadening or even splittings if single C±H interactions are resolved, cf. Fig. 3b. Indeed o-resonance decoupling has been used in the past as a simple way of obtaining scaled multiplet patterns to aid in the assignment of 13 C spectra. Corresponding eects from dipolar rather than J interactions have also been observed for single crystals [9]. Experimentally, o-resonance eects are minimised by optimising the position of the 1 H transmitter frequency to reduce the size of d. Combined with broad-band decoupling sequences which are designed to be robust with respect to the residual variations in d, v should then be small over the entire range of (proton) chemical shifts [10]. It is important to remember, however, that decoupling in solids and liquid-crystals is quite
H dH I1z dC I3z 2dHF I1z I2z 2dCH I1z I3z 2dCF I2z I3z HRF t;
1
where the eective couplings dij subsume any J couplings, dH and dC are the osets (shifts) of the 1 H and 13 C from their transmitter frequencies, and HRF is the time-dependent RF applied to the 1 H spins: HRF t vRF I1x cos / t I1y sin / t:
2
Since the decoupling RF is acting only on the 1 H spin space, and the other interactions are all secular with respect to the Zeeman interaction, the Hamiltonian can be blocked into sub-spaces labelled by the states of the 19 F and 13 C spins. The Hamiltonian in the 1 H subspace e.g., for 19 F in an a state and 13 C in a b state, is thus: Hba dH dHF
dCH I1z
dC =2 dCF =2 1 HRF t:
3
This has the same form as for the simple C±H case: the term proportional to the identity simply determining the eective shift of the 13 C resonance i.e., dC dCF , while the oset term now includes a contribution from dHF . As for the two spin system, an oset of the decoupling transmitter from exact resonance results in a non-zero scaling, v, of the
Fig. 3. Eect of various combinations of 1 H o-resonance shift H and H±F dipolar coupling dHF on a simulated C±F doublet under CW 1 H decoupling: (a) with no H±F coupling, on resonance, (b) o resonance or non-zero dipolar coupling, (c±e) dierent combinations of o-resonance shift and dipolar coupling.
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dierent from the decoupling of J in the solutionstate. The job of a decoupling sequence is to ensure that the net rotation of the 1 H spins is the same irrespective of the state of the rare spin [10]. J is generally small compared to the range of 1 H shifts and so the eective oset, dH J =2, is quite similar for the 13 C a and b states. In contrast, dipolar couplings are generally comparable to or exceed the shift range. As a result, sequences such as WALTZ-16 [11] that give good broad-band decoupling in the liquid-state are relatively ineective in both solid and, to a lesser extent, liquid crystal phases. The introduction of the H±F dipolar coupling into the eective oset of Eq. (3) may seem trivial, indeed its eect is equivalent to a non-zero oset, Fig. 3b. Unlike dH , however, it cannot be reduced by optimising the transmitter oset. Moreover, dHF can be large, much larger than the variations in dH due to the 1 H chemical shift range (500 Hz at a 1 H Larmor frequency of 200 MHz). For carbon 2 of I35, for example, the relevant H±F coupling is about 5.2 kHz (it is clearly resolved in the 19 F spectrum). This is now signi®cant compared to the decoupler B1 ®eld, vRF . The often asymmetrical nature of the broadening follows trivially; if dH is non-zero, the magnitude of the oset, jdH dHF j, will be dierent for the two components, leading to the asymmetrical splittings seen in Fig. 3c±e. It is clearly impossible to eliminate the broadening of both components of the C±F doublet simultaneously. The ¯ip-side is that the selective broadenings can provide information on the relative signs of couplings which is otherwise dicult to obtain. For instance, the H±F interaction is the same for C2 and C3 and by varying the oset in the CW-decoupled spectra, we can easily deduce their C±F couplings have opposite signs. In the case of C2 and C3, the coupling between the closest proton and the 19 F is strong. It is not immediately apparent that this rationalisation applies to other 13 C resonances where there is no clear three-spin C±H±F system. Simulations of the spin system of an entire phenyl fragment i.e., 13 C±19 F±1 H4 for C4, however, do successfully reproduce the experimental behaviour, with the inclusion or otherwise of the 1 H homonuclear couplings making no substantial dierence. If 1 H
homonuclear interactions can be ignored, then the spectrum from, say, a CFHA HB HC system is simply given by the convolution of the spectra from the individual CHF systems i.e., CFHA
CFHB CFHC . If one of these protons is particularly strongly in¯uenced by the 19 F (e.g., C2, C3) visible line-splittings will be seen, otherwise the convolution of a number of small splittings will result in a non-speci®c and increasingly Gaussian line-broadening (e.g., C4). The elimination of these line-broadenings, vital to quantitative use of the C±F splittings, is relatively straightforward. It reduces to ®nding a 1 H decoupling method which is suciently robust with respect to the eective 1 H oset, dH d. Increasing the decoupling power improves matters, cf. Fig. 2, but this is a notoriously inecient use of decoupler power and unsuited to liquid crystal samples. As discussed above, broad-band decoupling sequences from liquid-state NMR are not very eective, and it is necessary to use techniques developed speci®cally for the solid-state and/or liquid crystals. Of the many sequences tested, the SPINAL sequences [7] have given consistently good results with a minimum of optimisation. Novel sequences based on computer-optimisation of the phase modulation [12] have also shown promise. It is worth noting the sensitivity of the lineshapes to the quality of the decoupling to make it a good test sample; mis-setting of the parameters of the decoupling sequence will result in visible degradation of the spectral resolution. If, however, the sequence is correctly adjusted ± for SPINAL, this involves setting the tip angles of the sequence elements to 160 10° ± the 13 C linewidths become independent of the proximity to 19 F, not only improving resolution, but allowing the accurate quanti®cation of the C±F couplings. 3. In a solid system It has been possible to explain the broad linewidths of peaks close to 19 F in I35 in terms of a simple coherent eect, rather than invoking arguments involving 13 C±19 F dipolar dephasing and 19 F relaxation [1]. This particular problem may appear somewhat specialised, but we believe that the same
G. Antonioli et al. / Chemical Physics Letters 344 (2001) 68±74
eect occurs much more widely, although its coherent nature is obscured in samples of powdered solids by the orientational variation of the dipolar couplings. Since the size of the scaled splitting resulting from o-resonance decoupling is proportional to the C±H dipolar coupling, the 13 C peaks from isolated static C±H±F systems will be scaled dipolar Pake patterns. In practice, however, the width of the powder patterns is small and will be obscured by additional homonuclear and heteronuclear couplings, resulting in an overall unspeci®c line-broadening. Line-broadenings due to o-resonance CW decoupling in magic-angle-spinning (MAS) spectra have been extensively documented [13,14]. Phasemodulated decoupling sequences, such as TPPM, strongly reduce these eects. Their likely cause is the interference between the decoupling, C±H dipolar interactions and 1 H chemical shift anisotropy (CSA) [15], and although eects from a constant 1 H oset are eliminated by MAS, the time-dependent oset caused by a heteronuclear dipolar interaction, such as the H±F coupling, is of exactly the same form as the time-dependent shift due to the
73
CSA. Hence we would expect a similar linebroadening to apply in the 13 C MAS spectra of ¯uorinated molecules (as indeed is observed [1±3]). Experiments to con®rm this rigorously are currently underway, but some preliminary results con®rming this hypothesis are shown in Fig. 4. The system is an inclusion compound formed between urea and a ¯uorinated alkane, the urea forming a hexagonal framework of tunnels in which the linear guest molecules reside. Earlier studies of an analogous compound had remarked the strong broadening of the 13 C resonances of nuclei close to the 19 F [2]. This can be seen clearly in spectra (a) and (d). Changing the decoupling sequence greatly reduces these eects, especially using the SPINAL sequence. The signal from the CH3 is especially striking; the CH3 's next to another CH3 in the tunnel (head-to-head) have a slightly dierent shift from those next to a CH2 F [2]. In the CW spectra, the peak associated with the latter conformation is strongly broadened, while the two linewidths of the two peaks are indistinguishable (within the limits of the experiment) in the TPPM and SPINAL spectra.
Fig. 4. Spectra of the 1-¯uorononane/urea inclusion compound at ambient temperature for three decoupling methods: (a,d) continuous-wave, (b,e) TPPM and (c,f) SPINAL64. Spectra (a±c) are from a sample prepared with per-deuterated urea, (d±f) are from an analogous sample prepared with `normal' urea. Spectral parameters: vRF 1 H 45 kHz, contact time 3 ms, spinning speed 3 kHz. The linewidths in spectra (c) and (f) are 9 and 5 Hz, respectively (no line-broadening has been applied).
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G. Antonioli et al. / Chemical Physics Letters 344 (2001) 68±74
Since the molecules rotate rapidly at ambient temperature about the axis of tunnels formed by the urea host, this system is very similar to liquid crystal, particularly in the sample with the deuterated framework. As it is a powder, however, we do not observe the distinct additional splittings seen in the (aligned) liquid crystal system, but rather a relatively unspeci®c broadening. The resolution of all spectra is degraded when the host molecules are protonated, but the trends are clearly the same, with the SPINAL sequence developed for liquid crystal samples giving superior resolution in this solid (albeit quite mobile) sample ± particularly noticeable for the carbon resonance at 26 ppm. 4. Conclusions It is clear that previous rationalisations of broad 13 C resonances in 1 H-decoupled spectra of lightly ¯uorinated molecules do not satisfactorily explain many experimental observations. A simple explanation in terms of o-resonance eects caused by H±F interactions appears to be more satisfactory, and correctly predicts that improved 1 H decoupling techniques can eliminate these broadenings without resorting to 19 F decoupling. Although `double decoupling' will be necessary in systems that are abundant in both 19 F and 1 H, this means that most experiments in lightly ¯uorinated systems can be conducted on standard doubleresonance equipment. Although this explanation can only be rigorously demonstrated in static, oriented systems such as liquid crystals or single crystals, it is reasonable to suppose that the same eects operate in solids under magic-angle spinning. We expect to see a similar loss of resolution in other H±X±Y systems in which the H±Y interactions are strong.
Acknowledgements The authors would like to express their gratitude to Prof. J.W. Emsley for drawing their attention to this problem and for the gift of the initial I35 sample, and to Prof. K.D.M. Harris and his group for assistance with the ¯uoroalkane/urea inclusion systems. Thanks are also due to the Alliance programme of the British Council for enabling stimulating discussions on decoupling problems with Prof. Lyndon Emsley and his group. References [1] E.W. Hagaman, J. Magn. Reson. Ser. A 104 (1993) 125. [2] A. Nordon, R.K. Harris, L. Yeo, K.D.M. Harris, Chem. Commun. 21 (1997) 2045. [3] K.D.M. Harris, Chem. Soc. Rev. 26 (1997) 279. [4] E. Ciampi, M.I.C. Furby, L. Brennan, J.W. Emsley, A. Lesage, L. Emsley, Liq. Cryst. 26 (1999) 109. [5] M.L. Magnuson, L.F. Tanner, B.M. Fung, Liq. Cryst. 16 (1994) 857. [6] A.E. Bennett, C.M. Rienstra, M. Auger, K.V. Lakshmi, R.G. Grin, J. Chem. Phys. 103 (1995) 6951. [7] B.M. Fung, A.K. Khitrin, K. Ermolaev, J. Magn. Reson. 142 (2000) 97. [8] A. Abragam, in: Principles of nuclear magnetism, 1961, Oxford University Press, Oxford, pp. 530±533. [9] K. Takegoshi, C.A. McDowell, J. Magn. Reson. 66 (1986) 14±31. [10] J.S. Waugh, J. Magn. Reson. 50 (1982) 30. [11] A.J. Shaka, J. Keeler, R. Freeman, J. Magn. Reson. 52 (1983) 335. [12] D. Sakellariou, A. Lesage, P. Hodgkinson, L. Emsley, Chem. Phys. Lett. 319 (2000) 253. [13] D.L. VanderHart, W.L. Earl, A.N. Garroway, J. Magn. Reson. 44 (1981) 361. [14] D.L. VanderHart, G.C. Campbell, J. Magn. Reson. 134 (1998) 88. [15] M. Ernst, S. Bush, A.C. Kolbert, A. Pines, J. Chem. Phys. 105 (1996) 3387.