12849
J. Phys. Chem. 1994, 98, 12849-12855
Multiple-Pulse COSY NMR Spectroscopy of Oriented Molecules in Thermotropic Cholesterics P. Lesot, F. Nielsen, J. M. Ouvrard, and J. Courtieu* Laboratorie de Chimie Structurale Organique, ICMO, URA CNRS no. 1384, Universitg de Paris-Sud, 91405 Orsay, France Received: June 4, 1994; In Final Form: September 22, 1994@
The coherent reduction of anisotropic NMR interactions in molecules oriented in a thermotropic cholesteric phase, using a multiple-pulse COSY experiment, is described. The technique, which directly modifies the spin part of the nuclear spin Hamiltonian, allows the transformation of second-order spectra into first-order spectra. An experimental study of the evolution of the chemical shift and dipolar reduction factors is presented. The effects of the finite pulse duration in the multiple-pulse sequence are discussed, and explicit equations for the anisotropic interactions which take into account the pulse widths are obtained. The technique in cholesteric solvents is illustrated by using two specific examples for AB and ABC type of spectra: 2,6dichloro-3-nitropyridine and 2-cyanofuran.
a
Introduction Cholesteric solvents are optically active liquid crystals which allow for the NMR visualization of enantiomer^.'-^ The observation of each enantiomer is obtained through a doubling of the spectra, from which detailed structural information can be extracted. Unfortunately, the observed 'H-NMR spectra are generally second-order spectra and very complicated to decipher even at high magnetic Therefore, it is interesting to find an effective method for simplifying the proton spectra of molecules dissolved in such media, in order to fully exploit their analytical potential. The f i s t approach to simplify the analysis of the anisotropic 'H-NMR spectra was achieved by averaging the anisotropic interactions, by rotation of the sample around an axis perpendicular to Later this approach evolved to the variable angle sample spinning (VASS) technique, introduced by Homreich,s in which the sample is rotated quickly around an axis tilted at an angle 0 to the magnetic field. This technique showed great potential with uniaxial fluid liquid crystal such as nematics?-" Nevertheless, this technique fails in cholesteric or chiral smectic liquid crystal solvents due to the particular behavior of the director field in the magnetic field BO.l2J3 Indeed, cholesterics are known to be twisted nematics, which under the influence of chiral centers give rise to a director field of helical ~tructure.'~J~ When the samples are spun about an axis tilted from Bo, the helicity axis h tends to align either parallel (Axm < 0) or perpendicular (Axm > 0) to the rotation axis. Consequently, the directors n are distributed in planes which are perpendicular or parallel to the spinning axis and are not homogeneously oriented relatively to BO,as shown in Figure 1. In both cases, the spectra for the dissolved molecules have the appearance of a powder pattem.16-18 Only few experiments, where the anisotropic interactions were averaged to zero by using a fast magic angle spinning (MAS) technique, have been reported.lg Another way to reduce the anisotropic spin interactions consists of using a multiple-pulse sequence which results in a coherent reduction of the spin Hamiltonian through spin reorientation.20,21Recently, this laboratory has reported the coherent reduction of dipolar splittings through a 16-pulse @
Abstract published in Advance ACS Abstracts, November 1, 1994.
0022-365419412098-12849$04.50/0
h A
Bo
R
z +
,y X
b
h
X
J
Figure 1. Orientational behavior of director n of a Ax,,, 0 cholesteric phase in the magnetic field upon rotation around an axis R parallel to Bo (a) and tilted by an angle B from Bo (b). h is the cholesteric helical axis.
sequence, named flip-flop-16 (FF-16).22 Furthermore, it was demonstrated that the technical difficulties generally encountered in multiple-pulse experiments synchronized with the sampling of the magnetization can be avoided if the pulse train is applied during the tl period of a simple COSY experiment, as diagrammed in Figure 2. Under these conditions a normal onedimensional spectrum is expected in Y Z and a reduced spectrum along V I , following a t l evolution under the theoretical zeroorder FF-16 average Hamiltonian expressed in eq 1:
% . & represents the chemical shift Hamiltonian, the scalar coupling Hamiltonian, and 6the dipolar coupling Hamiltonian. KCSand KD are the chemical shift and dipolar reduction factors, respectively. In the ideal case of 6 pulses, these reduction factors can be expressed as 0 1994 American Chemical Society
Lesot et al.
12850 J. Phys. Chem., Vol. 98, No. 49, I994 a
FF-16 SEQUENCE
*
Y 4 ...........
4 ...............................
'2
tl
l/SWl= n . t P l 6 w i t h n = 1.2.3 ...NE
4 ...............
.................................... i......K ........... >..~
b
C
4 ....................................
r,=25'h
+t;+
2t,
(CHC13) and an A2 (CH2C12) proton spin system, respectively, dissolved in a mixture containing cholesteryl esters and bicyclohexyl nematic. Such a cholesteric mixture is oriented homogeneously with the helical axis parallel to Bo and consequently allows for obtaining high-resolution ~ p e c t r a . ~ , ~ ~ All spectra presented in the following parts have been obtained with a Ax negative mixture of 45/55 by weight ratio of cholesteryl butyrate and Merck ZLI 2806 nematic liquid crystal. The molecules under study were dissolved in the mixture at about 10% by weight. NMR experiments were performed on a Bruker AM250 high-resolution spectrometer operating at a frequency of 250.16 MHz for protons. Samples were introduced in 4 mm 0.d. tubes which were inserted in a 5 mm tube with D20 in order to provide a deuterium lock signal. The samples were spun at 50 Hz along Bo, and the temperature was regulated under air flow. Rf pulses were achieved through the decoupling channel in the reverse mode (tw9O0FY 13.5 ps). The 2D spectra were obtained in magnitude mode with 128(tl)*1024(tz)digitization and unshifted sinebell digital filtering in the v1 and v2 dimensions.22
Results and Discussion The action of the FF-16 sequence on the anisotropic interactions is studied as a function of pulse angles (a)and of the timing ratio Z!&i!Z!, dv).The experimental and expected values of the chemical shift and dipolar reduction factors are plotted in Figure 3. The analysis of the experimental results shows a divergence between experimental values of the reduction factors and theoretical values calculated according to eqs 2 and 3. This effect, caused by the finite pulse length, tw,of radio frequency pulses, has already been reported in studies performed on an A2 spin system oriented in a nematic phase.21q22By using the average Hamiltonian theory, reviewed by Meh~ing?~ it is possible to calculate the zeroth-order spin Hamiltonian of the FF-16 sequence taking into account the finite pulse widths (see the Appendix). The new expressions of the corrected chemical shifts and dipolar couplings reduction factors, labeled K& and KD", are given respectively by
+
Figure 2. (a) Representation of the flip-flop-16 COSY sequence. No
phase cycling is done on the multiple-pulse sequence. (b) Schematic diagram of the FF-8 sequence as 6 pulses. txis the total duration of a symmetric two-pulse subcycle. P: indicates the a pulse angle rotation about the v = x or y axis of the rotating frame. The second half of the FF-16 sequence is symmetric to the first according to the definition given by Wang and Ramshaw. (c) Zoom on a two-pulse subcycle of the FF-16 sequence in which the finite pulse width tW is apparent. The times 6~and 6, are the real spacing between pulses. (d) Schematic description of the interaction Hamiltonian tensors associated with the different periods in the subcycle shown in part c. 22,
Kcs =
+ z, cos(a) 2,
and
+
where 'tK= 22, ztl is the total duration of a basic two-pulse cycle. To illustrate these principles, simple spin systems dissolved in nematic solvents have been studied, and the potential of the method was demonstrated.22 Taking into account the usefulness of the applications in cholesteric media, where the VASS method is not useful, the logical step is to check the feasibility of the multiple-pulse technique for molecules dissolved in these chiral phases. This paper presents an experimental study of the reduction of the anisotropic interactions of molecules oriented in cholesteric media. To illustrate these principles, it will be shown how the technique allows the transformation of an AB spectrum into an AX spectrum and an ABC spectrum into Ah4X spectrum. The influence of finite pulse width in the multiple-pulse sequence will be presented.
Experimental Part The experimental study of the evolution of the chemical shift and the dipolar reduction factors is performed, using an A
and
+ +
where z, = tJ8 = 2 z ' ~ z',, 2t, is the total duration of a symmetric two-pulse cycle, including the pulse duration. The times r', and z', are the real spacing between pulses, as diagrammed in Figure 2, and tw is the a pulse duration. Introducing tw = 0 in the expressions for Kcsf- and KD'Wgives, as expected, the reduction coefficients in the 6 pulse case, KCS and KD, eqs 2 and 3. The experimental values, KcseXPand K D ~ ~asP ,a function of a,correlate with the expected values according to eqs 4 and 5. As already stated in the previous paper, the minimum attainable scale factor can be strongly decreased by increasing r', and r',,22 which will change the spectral width in v1. Thus, decreasing the v1 spectral width and keeping a equal to 90°,it is possible to average to zero the dipolar splitting or to change the dipolar
Oriented Molecules in Thermotropic Cholesterics
J. Phys. Chem., Vol. 98, No. 49, 1994 12851
a
Oo
20"
0
6V 8 4 1W lu)' 140. 160. 180'
4V
0.2
a
0.4
7'
0.6
0.8
1
0.8
I
/(27Ir + 7;)
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--
-0,3
' 0
1v 20"
34 4 4
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Figure 3. Comparison between the experimental chemical shift and dipolar coupling reduction factors, KcsCXPand and calculated reduction factors, KCS,KD, KCS'W, and KD'w,calculated according to eqs 2, 3,4, and 5 , respectively. (a) KC^, KCS,and K& as a function of a (tww"= 12.5 ps, fJ(2f1 4- fJ = 3/4, SW2 = 2000 Hz,and SWI is about 2000 Hz). (b) KcseXP,KCS, and KCS'~ as a function of the timing ratio f , J ( 2 f ~ f,,) (a= 180", tw'80'= 25.5 ps, and SW2 = 2000 Hz).The values of the timing ratio are 1/23, 1/17, 1/11, 115, 113, 1/2,2/3, 3/4, 5/6, 9/10, and 23/25. KD, and KD" as a function of a (tww' = 12.5 ps, SWZ= 2500 Hz,and SW1 is about 2500 Hz). (d) K p , KD,and K+ as a function of (c) KD~~P, the timing ratio fV/(2z'n z',,) (a= go", tww"= 14.7 ps, and SW2 = 2000 Hz). The values of the timing ratio are 1/17, 1/11, 1/5, 113, 112, 2/3, 314, 9/11, 5/6, 9/10, and 15/16. In all experiments, the times and z',, are taken to fit the desired values of timing ratios and the spectral width z',, 2tw). In the experiments corresponding to Figure 3a.b and 3c,d the chemical shifts in the vz in the VI dimension is equal to 1/8(2fn idimension are 900 and 0 Hz,respectively. The dipolar splitting constant for the AZ spin system in the vz dimension is 1900 Hz.
+
+
+
coupling sign. When the spectral width is decreased, the duty cycle, i.e. the ratio 2tw/z,, tends to zero, and the experimental reduction factors approach the theoretical value when tw = 0. The evolution of the experimental values, KcseXPand K D ~ ~ P , as a function of the timing ratio z',/(2z'1 t',),is also in agreement with the pulse width dependent coefficients in eqs 4 and 5 . Notice further in Figures 3b,d that the values of KcseXP and K D ~ are ~ P smaller for dV/(2t'1 f,) -= 1/2 and larger for z'J(2t'~ z'q)' > 1/2 than those stated by theory using 6 pulses. This shows a remarkable property of the pulse width, since for t',/(2z'~ T',) < 1/2 it causes further reduction relative to the ideal case of the 6 pulse.
TABLE 1: Experimental Data and Corresponding NMR Parameters of the Exwriments Reported in Figure 4 ina vi- V? vi- V/ Dij' Dd dex" (deg) twb > (A-1 1)
G
P,(d = Ll-'(t)T,Ll(t)
+
+ %(a> +
+ r', cos(a) + 2tw (22!2
+ 6, + 2tw)
(4)
Inserting eq A-10 into eq A-11, the dipolar interaction can be expressed as = K,'"%
=K , " W i5j
with
20?ti20
(A-14)
Oriented Molecules in Thermotropic Cholesterics
References and Notes (1) Sackmann, E.; Meiboom, S.;Snyder, L. C. J. Am. Chem. SOC.1968, 90, 2183. (2) Lafontaine, E.; Bayle, J. P.; Courtieu, J. J. Am. Chem. SOC. 1989, 111, 8294. (3) Lafontaine, E.; Pechiney, J. M.; Mayne, C. L.; Courtieu, J. Liq. Cryst. 1989, 2 , 189. (4) Saupe, A.; Englert, G. Phys. Rev. Lett. 1963, 11, 462. (5) Emsley, J. W.; Lindon, J. C. In NMR Spectroscopy Using Liquid Crystal Solvents; Ed.; Pergamon Press: New York, 1975; Chapters 1, 2. (6) Tsvetkov, V. Zh. Eksp. Theor. Fiz. 1935, 9, 603. (7) Lippmann, H. Ann. Phys. 1958, I , 157. (8) Hornreich, R. M. Phys. Rev. A 1977, 15, 1967. (9) Courtieu, J.; Alderman, D. W.; Grant, D. M. J. Am. Chem. SOC. 1981, 103, 6783. (10) Courtieu, J.; Alderman, D. W.; Grant, D. M.; Bayle, J. P. J. Chem. Phys. 1982, 77, 723. (11) Courtieu, J.; Bayle, J. P.; Fung, B. Prog. NMR Spectrosc. 1994, 26 (2), 141. (12) Bayle, J. P.; Khandar-Shahabad, A,; Courtieu, J. Liq. Cryst. 1986, I, 189.
J. Phys. Chem., VoE. 98, No. 49, 1994 12855 (13) Bayle, J. P.; Khandar-Shahabad, A.; Gonord, P.; Courtieu, J. J. Chem. Phys. 1986,83, 177. (14) Friedel, G. Ann. Phys. (Paris) 1922, 8, 273. (15) Buckingham, A. D.; Ceasars, G. P.; Dum, M. B. Chim. Phys. Let?. 1969, 3, 540. (16) Luz, 2.;Poupko, R.; Samulski, E. T. J. Chem. Phys. 1981, 74, 5825. (17) Sackmann,E.; Meiboom, S.; Snyder, L. C. J. Am. Chem. SOC.1967, 89, 5981. (18) Sackmann, E.; Meiboom, S.; Snyder, L. C.; Meixner, A. E.; Dietz, R. E. J. Am. Chem. SOC.1967, 90, 3567. (19) Bayle, J. P.; Lafontaine, E.; Courtieu, J. J. Chem. Phys. 1988,85, 985. (20) Ouvrard, J. M. Ph.D. Thesis, University of Paris-Sud, CNRS No. 1167, 1990. (21) Ouvrard, J. M.; Ouvrard, B. M.; Courtieu, J.; Maine, C. L.; Grant, D. M. J. Magn. Reson. 1991, 93, 225. (22) Lesot, P.; Ouvrard, J. M.; Ouvrard, B. N.; Courtieu, J. J. Mugn. Reson. 1994, I07A, 141. (23) Canet, I.; Wvshall, J.; Courtieu, J. Liq. Cryst. 1994, 16, 405. (24) Mehring, M. In Principles of High Resolution NMR in Solids; 2nd ed.; Springler-Verlag: New York, 1983; Chapter 3. (25) Haeberlen, U.; Waugh, J. S. Phys. Rev. 1968,175, 453. (26) Meluing, M.; Waugh, J. S. Phys. Rev. B 1972, 5, 3459. (27) Wang, C. H.; Ramshaw, D. Phys. Rev. B 1972, 6, 3253.
