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Nuclear relaxation of partially oriented pyridine determined by line width analysis of 1H NMR spectra
Volume 135, number 4,5
CHEMICAL PHYSICS LETTERS
lOApril 1987
NUCLEAR REL.AXATION OF PARTIALLY ORIENTED PYRIDINE DETERMINED BY LINE WIDTH ANALYSIS OF ‘H NMR SPECTRA D. IMBARDELLI,
G. CHID~CHXMO and M. LONGER1
Chemisf~ ~epa~fmenf, Universityo~Ca~abrla,87030 Arcavacatadi Rende (CS), Ztuiy Received 21 October 1986; in final form 28 January 1987
An NMR lineshape study of pyridine dissolved in nematic PCH mesophase has been carried out. Measurements of spectral frequencies and intensities enabled us to determine the order parameters defining the molecular orientation. Lineshape analysis indicates that the highly selective broadening of lines is mainly due to the coupling of protons with the rapidly relaxmg 14N quadrupolar nucleus. A further contribution to the line width comes from the dipolar intermolecular relaxation mechanism. The quadrupolar relaxation time of the 14Nnucleus and the correlation time of the intermolecular interaction were calculated.
1. Introduction
NMR analysis of molecules dissolved in a liquid crystalline mesophase is usually quite complex because of the large number of spectral transitions. On the other hand several relaxation mechanisms can selectively affect the line widths, in such a way that overlapping of neighbouring lines is favoured and spectral analysis is further hindered. This effect becomes highly evident in proton spectra of molecules containing quadrupolar nuclei. Line broadening occurring in the NMR spectra of spin-l/2 systems coupled to quadrupolar nuclei has been investigated in the case of molecules dissolved in isotropic media [ 1-6 1. Indirect scalar coupling mod~ation by quad~polar relaxation was found to be responsible for the broadening of the transitions. In the case of analogous spin systems dissolved in liquid crystalline media, the modulation of the direct dipolar couplings between strongly relaxed quadrupolar nuclei and spin- l/2 nuclei is expected to play a fundamental role in determining spectral features. This expectation is based on the evidence that direct coupling usually dominates over other local interactions. In this paper we present an NMR lineshape analysis of pyridine (fig. 1) in a nematic solvent, where a strong
Fig. 1. Nuclear notation and mofecuiar axes system for the pyridine molecule.
0 009-2614/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
319
Volume
135, number
CHEMICAL
4,5
PHYSICS
LETTERS
10 April 1987
selective broadening of spectral lines occurs. This study was carried out by extending to anisotropic media the theory already developed by Pyper [ 4-61 for isotropic solutions. It was assumed that the spin system, consisting only of protons, and the lattice, comprising the 14Nquadrupolar nuclei, are coupled by dipolar interactions [ 41. The equation of motion of the reduced density operator for the spin system is solved in the Liouville space, under the simplifying hypothesis that the i4N nucleus is very rapidly relaxing. The fit of the spectral line widths, while confirming that the main contribution to the broadening of partially oriented pyridine NMR transitions is due to the coupling of the protons to the 14N nucleus, also showed that smaller contributions due to magnetic field inhomogeneities and intermolecular dipolar interactions need to be included in order to achieve the best agreement between calculated and experimental line widths.
2. Experimental The sample was prepared by mixing the 15 moleoh of pyridine with the PCH nematic mesophase (Merck, Darmstadt). The NMR cell was a Wilmad Imperial test tube, sealed under an atmosphere of nitrogen, after degassing procedure, in order to avoid O2 paramagnetic relaxation. Before taking measurements the sample was left at rest for almost two days in the magnet, in order to achieve thermal equilibrium and a uniform orientation of the nematic director. The NMR spectrum was taken at room temperature from a Bruker WM-300 MHz spectrometer; only ten scans were needed to obtain a good signal-tonoise ratio. The digital precision of the spectrum is about 0.1 Hz/point (64 kbyte of computer memory have been used to cover a spectra1 width of 5 kHz).
3. Lineshape analysis theory As previously stated, in our experiment the quadrupolar nucleus is relaxing very fast, in such a way that the only effect that can be observed in the protonic subspectrum is line broadening. Then Pypers method [ 41, which assumes the quadrupolar nuclei to be a lattice in thermal equilibrium coupled to the spin-l/2 subsystem, is the most appropriate method for calculating the lineshape. In this way computational complications, due to the presence of a large set of strongly coupled dyn~i~al equations for the statistical operator, can be somewhat reduced. The total density operator can be approximated by PTOT(t)
=PL(t)/%(t),
(11
where pL( t) and ps( t) are the reduced statistical operators for the lattice and the spin system respectively. The two subsystems are coupled by the Hamiltonian .@I =
2n (Jnx+alx)
z,,z,,+t(J,,-D,)(z,+z~
+znzx+),
(2)
where Jm and &, are the scalar and direct couplings respectively, between the quad~polar nudeus x and the nth proton. In Liouville space [ 7-91 the temporal evolution of the combined spin system plus lattice is described by the Liouville superoperator Z.roT [ 4,s 1, ~~0~=5?0+5?,,
5?0=5?~+9L..
(3)
ZFr_and 2s are the Liouville superoperators describing the motion of the lattice and the spin system density operators respectively in the absence of X,, dp#=
320
-i~&.(Q
41,
(4)
CHEMICAL PHYSICS LETTERS
Volume 135, number 4,5
10 April 1987
dpsldt=-iYs[ps(t)-&.
(5)
9, is the Liouville superoperator for the coupling Hamiltonian Z,. Solving the equation of motion of the reduced density matrix for the spin system according to the method of Pyper [ 41, the following expression has been obtained for the transversal relaxation time of a non-degenerate spin- l/2 transition i-j (only the real part of the Redfield matrix element has been considered; the dynamical line shifts due to the imaginary part have been disregarded) W=
l/7-‘, =&,=
-2J,,(O)
+ C J&m,,)+ c
C JcrcAmcz). c
(6)
Spectral densities, under the hypothesis that the perturbation can be truncated to its pseudo-secular term: *I = C (Jo, + 2QJ n
(7)
IzJz,,
are obtained as exp (’IW~~~) exp( -iw,r)
exp( -r/TIN)
dr
where L is the number of eigenstates of the lattice, o se is the frequency connected with the transition between eigenstates 18) and (9) of the lattice and w, is the frequency of the transition between the spin system energy levels c and J. TIN is the eigenvalue of the superoperator .JZLand represents the quadrupolar relaxation time for the 14Nnucleus. The theoretical treatment of intermolecular dipolar interactions, which also contribute to the proton transition line width, has been given elsewhere [lo]. The intermolecular relaxation mechanism for the pyridine protons is expected to be of little importance with respect to that due to coupling with the rapidly relaxing 14N nucleus. Nevertheless it is possible to obtain, from the fit of the line width, the correlation time 7c of the intermolecular interactions.
4. Results and discussion The study of NMR spectrum of the pyridine molecule (see fig. 2) has been carried out as follows: (1) from
Fig. 2. Experimental proton spectrum of pyridine dissolved in Merck PCH mesophase.
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CHEMICAL PHYSICS LETTERS
Table 1
Jg [ 121, Ll,,couplings, internuclear distances R, [ 111 and order parameters of partially oriented pyridine
s~~=-0.109~0.004,
Atom pairs
J, (Ha) a)
D,l (Ha)
R, (A)
1;2 I;3 1;4 1;5 2;3 2;4 1;6 2;6 3;6
4.9o-to.05 1.90+0.05 1.00+0.05 -0.10+0.05 7.7050.05 1.302 0.05 7.17kO.05 1.12+0.05 -0.13+0.05
-287.48 -+0.05 ” - lQ8.36+0.05 b, - 149.36kO.05 ‘) -314.26kO.05 b, - 1091.51 kO.05 b, -275.18kO.05 ‘) - 179.88 + 0.02 =) -21.66+0.02 ‘) - 5.32 IO.02 =)
2.487F0.004 4.293 + 0.004 4.886 + 0.004 4.1121:0.004 2.509jrO.004 4.306 IO.004 2.060+ 0.004 3.903_+0.004 3.903 10.004
~~~-~~~~0.073~0.004.
‘) Scalar couplings calculated on the basis of the results reported in ref. [ 121. b1Directly measured parameters, ‘) Dn_laNcouplings evaluated using eq. (9). spectrum DH.+, dipolar couplings have been evaluated; (2) using these parameters and a geometry obtained from microwave spectra Ill ] the two ordering elements S,, and S,,-S,,,, defining the molecular orientation have been calculated according to [ 13,141
the lH NMR
D,,=(y,y,h/8x2r3)[S,,(3
cos%,-
1) -t (&X--S,,)
(cos2%X-cos2%J,
(9)
where r is the internuclear vector between nuclei i andj and t9,J (i=x, y, z) is the angle between this vector and the i axis; (3) from the orientationa parameters and a standard geometry [ II] DH_laNdipolar couplings, which cannot be directly obtained from the spectral analysis, have been calculated. J u _fdNcouplings have been derived by scaling the couplings measured by other authors [ 12 ] for i5N labelled pyridine, partially oriented in nematic solvents. The molecular frame and nuclear notation for pyridine are shown in fig. 1, while table 1 presents scalar and direct couplings as well as the orientational parameters. Linewidth calculations have been carried out following the method mentioned above, by means of a recently developed computer program, AZOREL, which uses scalar and direct couplings as constant input data. The linewidth fit has been obtained by varying the following parameters: (a) TIN, the quadrupolar relaxation time of the i4N nucleus; (b) T,, the correlation time of the
b
I Fig. 3. (a) Theoretical spectrum of partially oriented pyridine with a line width, common to all the transitions, of 3 Hz. (b) Calculated spectrum of partially oriented pyridine, obtained by using best-fit values of the motional parameters and field inhomogeneity: TiN=2.7~10-‘s, t,=l.47~10-‘~~,~,=2.3 Hz.
Volume 135,number 4,5
10 April 1987
CHEMICAL PHYSICS LETTERS
dipolar intermolecular interaction in the liquid crystalline solution [lo]; (c) Avo, the line broadening due to the magnetic field inhomogeneity. Fig. 3a shows a theoretical spectrum obtained disregarding the quadrupolar and intermolecular dipolar relaxation mechanisms, and taking into account only a field inhomogeneity of 3 Hz. It can be observed that this theoretical plot is quite far from reproducing the experimental line shapes of fig. 2. Fig. 3b is the plot resulting from the best fit to the line widths, obtained for the following values of the fitting parameters: TlN=2.7x 1O-4 s; 7,~ 1.47x lo-” s; Av,=2.3 Hz. The proton transitions are not degenerate, so they can be considered as pure Lorentzian lines, characterized by a single Tzrelaxation time. Contributions to the line widths due to the different relaxation mechanisms for the transitions labelled in fig. 2 are reported in table 2. As expected, the largely dominant selective relaxation comes from the coupling between the protons and the rapidly relaxing 14N quadrupolar nucleus. This mechanism generates line widths of between 0.4 and 108.2 Hz. The intermolecular relaxation mechanism is not very selective and moreover its contribution to the line broadening is quite small, even if it does need to be added, along with Av,, in order to improve the line width tit. It is not clear at the moment why the presence of 14N nuclei so strongly affects the proton spectra of pyridine in the PCH mesophase. Literature data on pyridine and its derivatives dissolved in other nematic solvents [ 12,15-l 71 do not show the presence of a strong selective line broadening. Since no simple correlation between the degree of order and the linewidth can be derived, it must be concluded that the different behaviour of the various systems must be mainly attributed to variations in T,,.
Table 2 Contributions to the line widths of the NMR spectral transitions of partially oriented pyridine having intensities greater than 1. AvTOT is the total line width. hv, is the broadening due to the coupling of protons to the 14Nnucleus, relaxing with a quadrupolar relaxation time T,,= 2.7x lo-“ s; Avy2is the broadening due to intermolecular dipolar interactions, which fluctuate with a correlation time 7,= 1.47~ lo- ” s; AvOis the broadening due to field inhomogeneities Line
Intensity
&TOT (Hz)
Av, (I+)
b2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
3.13 2.61 2.14 2.07 4.90 1.38 1.75 2.82 2.95 5.53 1.56 1.04 1.05 1.42 1.01 2.15 1.89 4.22 1.59 1.06 1.48 1.12 1.43 2.55 3.27
3.70 3.34 11.42 6.26 17.22 46.25 26.28 25.80 26.11 43.41 50.54 25.37 8.98 70.79 110.88 46.18 28.12 43.28 28.42 4.28 15.91 15.00 22.38 3.81 4.05
0.49 0.38 8.32 3.24 13.60 43.21 23.69 22.81 23.00 39.57 47.55 22.46 5.69 67.66 108.20 43.26 24.48 40.63 25.36 1.37 12.94 11.66 18.89 0.85 0.82
0.91 0.66 0.80 0.72 1.32 0.74 0.69 0.68 0.81 1.54 0.69 0.61 0.99 0.83 0.38 0.62 0.76 1.35 0.76 0.61 0.68 1.04 1.18 0.66 0.93
(Hz)
by0
(Hz)
2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3
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Further work should define the mechanism which determines TIN in the various nematic solvents. Perhaps the most obvious hypothesis is that TINis mainly influenced by anisotropic molecular rotational diffusion, but obviously the presence of specific solute-solvent interactions, modulating the electric field gradient tensor acting on the quadrupolar nuclei, cannot be excluded. Studies along these lines are in progress. A last comment which can be made is that the highly selective broadening occurring in ‘H NMR spectra of molecules containing quadrupolar nuclei can turn out to be an advantage, rather than a complication, in spectral analysis. The lines which are most broadened can be assigned to transitions of spins closest to the quadrupolar nucleus. This could give guidance in handling the spectral parameters during the trial-and-error procedure normally used in the spectral analysis of partially oriented solute molecules containing quadrupolar nuclei. Such a step could be somewhat simplified by the linkage of the AZOREL algorithm with existing standard computer programs which diagonalise the static Hamiltonians.
Acknowledgement
The authors acknowledge the Italian MPI and CNR for financial support.
References [ I] J.A. Pople, Mol. Phys. 1 (1958) 168. [2] J.P. Kintzingerand J.M. Lehn, Mol. Phys. 14 (1968) 133. [ 31 M. Suzuki and R. Kubo, Mol. Phys. 7 (1964) 201. [4] N.C. Pyper, Mol. Phys. 20 (1971) 449. [5] N.C. Pyper, Mol. Phys. 20 (1971) 470. [6] N.C. Pyper, Mol. Phys. 21 (1971) 1. [ 71 P.L. Corio, Structure of high resolution NMR spectra (Academic Press, New York, 1968). [ 81 P.D. Buckeley, K.W. Jolley and D.N. Pinder, Progr. NMR Spectry. 10 (1976) 1, [ 91 J. Jeener, Advan. Magn. Reson. Spectry. 10 (1982) 1. [ lo] G. Chidichimo, D. Imbardelli, M. Longeri and A. Saupe, to be published. [ 111 C.W.N. Cumper, J. Chem. Sot. Faraday Trans. II 54 (1958) 1266. [ 121 D. Catalano, C.A. Veracini, P.L. Barili and M. Longeri, J. Chem. Sot. Perkin Trans. II (1983) 171. [ 131 J.W. Emsley and J.C. Lindon, NMR spectroscopy using liquid crystal solvents (Pergamon Press, New York, 1975). [ 141 P. Diehl and C.L. Khetrapal, in: NMR basic principles and progress, Vol. 1 (Springer, Berlin, 1972). [IS] E.E. Bumell and C.A. de Lange, Mol. Phys. 16 (1969) 95. [ 161 P. Diehl, C.L. Khetrapal and H.P. Kellerhals, Mol. Phys. 15 (1968) 333. [ 171 J.W. Emsley, M. Longeri and A. Liguori, J. Chem. Sot. Perkin 2 (198 1) 1449.
324
CHEMICAL PHYSICS LETTERS
lOApril 1987
NUCLEAR REL.AXATION OF PARTIALLY ORIENTED PYRIDINE DETERMINED BY LINE WIDTH ANALYSIS OF ‘H NMR SPECTRA D. IMBARDELLI,
G. CHID~CHXMO and M. LONGER1
Chemisf~ ~epa~fmenf, Universityo~Ca~abrla,87030 Arcavacatadi Rende (CS), Ztuiy Received 21 October 1986; in final form 28 January 1987
An NMR lineshape study of pyridine dissolved in nematic PCH mesophase has been carried out. Measurements of spectral frequencies and intensities enabled us to determine the order parameters defining the molecular orientation. Lineshape analysis indicates that the highly selective broadening of lines is mainly due to the coupling of protons with the rapidly relaxmg 14N quadrupolar nucleus. A further contribution to the line width comes from the dipolar intermolecular relaxation mechanism. The quadrupolar relaxation time of the 14Nnucleus and the correlation time of the intermolecular interaction were calculated.
1. Introduction
NMR analysis of molecules dissolved in a liquid crystalline mesophase is usually quite complex because of the large number of spectral transitions. On the other hand several relaxation mechanisms can selectively affect the line widths, in such a way that overlapping of neighbouring lines is favoured and spectral analysis is further hindered. This effect becomes highly evident in proton spectra of molecules containing quadrupolar nuclei. Line broadening occurring in the NMR spectra of spin-l/2 systems coupled to quadrupolar nuclei has been investigated in the case of molecules dissolved in isotropic media [ 1-6 1. Indirect scalar coupling mod~ation by quad~polar relaxation was found to be responsible for the broadening of the transitions. In the case of analogous spin systems dissolved in liquid crystalline media, the modulation of the direct dipolar couplings between strongly relaxed quadrupolar nuclei and spin- l/2 nuclei is expected to play a fundamental role in determining spectral features. This expectation is based on the evidence that direct coupling usually dominates over other local interactions. In this paper we present an NMR lineshape analysis of pyridine (fig. 1) in a nematic solvent, where a strong
Fig. 1. Nuclear notation and mofecuiar axes system for the pyridine molecule.
0 009-2614/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
319
Volume
135, number
CHEMICAL
4,5
PHYSICS
LETTERS
10 April 1987
selective broadening of spectral lines occurs. This study was carried out by extending to anisotropic media the theory already developed by Pyper [ 4-61 for isotropic solutions. It was assumed that the spin system, consisting only of protons, and the lattice, comprising the 14Nquadrupolar nuclei, are coupled by dipolar interactions [ 41. The equation of motion of the reduced density operator for the spin system is solved in the Liouville space, under the simplifying hypothesis that the i4N nucleus is very rapidly relaxing. The fit of the spectral line widths, while confirming that the main contribution to the broadening of partially oriented pyridine NMR transitions is due to the coupling of the protons to the 14N nucleus, also showed that smaller contributions due to magnetic field inhomogeneities and intermolecular dipolar interactions need to be included in order to achieve the best agreement between calculated and experimental line widths.
2. Experimental The sample was prepared by mixing the 15 moleoh of pyridine with the PCH nematic mesophase (Merck, Darmstadt). The NMR cell was a Wilmad Imperial test tube, sealed under an atmosphere of nitrogen, after degassing procedure, in order to avoid O2 paramagnetic relaxation. Before taking measurements the sample was left at rest for almost two days in the magnet, in order to achieve thermal equilibrium and a uniform orientation of the nematic director. The NMR spectrum was taken at room temperature from a Bruker WM-300 MHz spectrometer; only ten scans were needed to obtain a good signal-tonoise ratio. The digital precision of the spectrum is about 0.1 Hz/point (64 kbyte of computer memory have been used to cover a spectra1 width of 5 kHz).
3. Lineshape analysis theory As previously stated, in our experiment the quadrupolar nucleus is relaxing very fast, in such a way that the only effect that can be observed in the protonic subspectrum is line broadening. Then Pypers method [ 41, which assumes the quadrupolar nuclei to be a lattice in thermal equilibrium coupled to the spin-l/2 subsystem, is the most appropriate method for calculating the lineshape. In this way computational complications, due to the presence of a large set of strongly coupled dyn~i~al equations for the statistical operator, can be somewhat reduced. The total density operator can be approximated by PTOT(t)
=PL(t)/%(t),
(11
where pL( t) and ps( t) are the reduced statistical operators for the lattice and the spin system respectively. The two subsystems are coupled by the Hamiltonian .@I =
2n (Jnx+alx)
z,,z,,+t(J,,-D,)(z,+z~
+znzx+),
(2)
where Jm and &, are the scalar and direct couplings respectively, between the quad~polar nudeus x and the nth proton. In Liouville space [ 7-91 the temporal evolution of the combined spin system plus lattice is described by the Liouville superoperator Z.roT [ 4,s 1, ~~0~=5?0+5?,,
5?0=5?~+9L..
(3)
ZFr_and 2s are the Liouville superoperators describing the motion of the lattice and the spin system density operators respectively in the absence of X,, dp#=
320
-i~&.(Q
41,
(4)
CHEMICAL PHYSICS LETTERS
Volume 135, number 4,5
10 April 1987
dpsldt=-iYs[ps(t)-&.
(5)
9, is the Liouville superoperator for the coupling Hamiltonian Z,. Solving the equation of motion of the reduced density matrix for the spin system according to the method of Pyper [ 41, the following expression has been obtained for the transversal relaxation time of a non-degenerate spin- l/2 transition i-j (only the real part of the Redfield matrix element has been considered; the dynamical line shifts due to the imaginary part have been disregarded) W=
l/7-‘, =&,=
-2J,,(O)
+ C J&m,,)+ c
C JcrcAmcz). c
(6)
Spectral densities, under the hypothesis that the perturbation can be truncated to its pseudo-secular term: *I = C (Jo, + 2QJ n
(7)
IzJz,,
are obtained as exp (’IW~~~) exp( -iw,r)
exp( -r/TIN)
dr
where L is the number of eigenstates of the lattice, o se is the frequency connected with the transition between eigenstates 18) and (9) of the lattice and w, is the frequency of the transition between the spin system energy levels c and J. TIN is the eigenvalue of the superoperator .JZLand represents the quadrupolar relaxation time for the 14Nnucleus. The theoretical treatment of intermolecular dipolar interactions, which also contribute to the proton transition line width, has been given elsewhere [lo]. The intermolecular relaxation mechanism for the pyridine protons is expected to be of little importance with respect to that due to coupling with the rapidly relaxing 14N nucleus. Nevertheless it is possible to obtain, from the fit of the line width, the correlation time 7c of the intermolecular interactions.
4. Results and discussion The study of NMR spectrum of the pyridine molecule (see fig. 2) has been carried out as follows: (1) from
Fig. 2. Experimental proton spectrum of pyridine dissolved in Merck PCH mesophase.
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lOApril 1987
CHEMICAL PHYSICS LETTERS
Table 1
Jg [ 121, Ll,,couplings, internuclear distances R, [ 111 and order parameters of partially oriented pyridine
s~~=-0.109~0.004,
Atom pairs
J, (Ha) a)
D,l (Ha)
R, (A)
1;2 I;3 1;4 1;5 2;3 2;4 1;6 2;6 3;6
4.9o-to.05 1.90+0.05 1.00+0.05 -0.10+0.05 7.7050.05 1.302 0.05 7.17kO.05 1.12+0.05 -0.13+0.05
-287.48 -+0.05 ” - lQ8.36+0.05 b, - 149.36kO.05 ‘) -314.26kO.05 b, - 1091.51 kO.05 b, -275.18kO.05 ‘) - 179.88 + 0.02 =) -21.66+0.02 ‘) - 5.32 IO.02 =)
2.487F0.004 4.293 + 0.004 4.886 + 0.004 4.1121:0.004 2.509jrO.004 4.306 IO.004 2.060+ 0.004 3.903_+0.004 3.903 10.004
~~~-~~~~0.073~0.004.
‘) Scalar couplings calculated on the basis of the results reported in ref. [ 121. b1Directly measured parameters, ‘) Dn_laNcouplings evaluated using eq. (9). spectrum DH.+, dipolar couplings have been evaluated; (2) using these parameters and a geometry obtained from microwave spectra Ill ] the two ordering elements S,, and S,,-S,,,, defining the molecular orientation have been calculated according to [ 13,141
the lH NMR
D,,=(y,y,h/8x2r3)[S,,(3
cos%,-
1) -t (&X--S,,)
(cos2%X-cos2%J,
(9)
where r is the internuclear vector between nuclei i andj and t9,J (i=x, y, z) is the angle between this vector and the i axis; (3) from the orientationa parameters and a standard geometry [ II] DH_laNdipolar couplings, which cannot be directly obtained from the spectral analysis, have been calculated. J u _fdNcouplings have been derived by scaling the couplings measured by other authors [ 12 ] for i5N labelled pyridine, partially oriented in nematic solvents. The molecular frame and nuclear notation for pyridine are shown in fig. 1, while table 1 presents scalar and direct couplings as well as the orientational parameters. Linewidth calculations have been carried out following the method mentioned above, by means of a recently developed computer program, AZOREL, which uses scalar and direct couplings as constant input data. The linewidth fit has been obtained by varying the following parameters: (a) TIN, the quadrupolar relaxation time of the i4N nucleus; (b) T,, the correlation time of the
b
I Fig. 3. (a) Theoretical spectrum of partially oriented pyridine with a line width, common to all the transitions, of 3 Hz. (b) Calculated spectrum of partially oriented pyridine, obtained by using best-fit values of the motional parameters and field inhomogeneity: TiN=2.7~10-‘s, t,=l.47~10-‘~~,~,=2.3 Hz.
Volume 135,number 4,5
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CHEMICAL PHYSICS LETTERS
dipolar intermolecular interaction in the liquid crystalline solution [lo]; (c) Avo, the line broadening due to the magnetic field inhomogeneity. Fig. 3a shows a theoretical spectrum obtained disregarding the quadrupolar and intermolecular dipolar relaxation mechanisms, and taking into account only a field inhomogeneity of 3 Hz. It can be observed that this theoretical plot is quite far from reproducing the experimental line shapes of fig. 2. Fig. 3b is the plot resulting from the best fit to the line widths, obtained for the following values of the fitting parameters: TlN=2.7x 1O-4 s; 7,~ 1.47x lo-” s; Av,=2.3 Hz. The proton transitions are not degenerate, so they can be considered as pure Lorentzian lines, characterized by a single Tzrelaxation time. Contributions to the line widths due to the different relaxation mechanisms for the transitions labelled in fig. 2 are reported in table 2. As expected, the largely dominant selective relaxation comes from the coupling between the protons and the rapidly relaxing 14N quadrupolar nucleus. This mechanism generates line widths of between 0.4 and 108.2 Hz. The intermolecular relaxation mechanism is not very selective and moreover its contribution to the line broadening is quite small, even if it does need to be added, along with Av,, in order to improve the line width tit. It is not clear at the moment why the presence of 14N nuclei so strongly affects the proton spectra of pyridine in the PCH mesophase. Literature data on pyridine and its derivatives dissolved in other nematic solvents [ 12,15-l 71 do not show the presence of a strong selective line broadening. Since no simple correlation between the degree of order and the linewidth can be derived, it must be concluded that the different behaviour of the various systems must be mainly attributed to variations in T,,.
Table 2 Contributions to the line widths of the NMR spectral transitions of partially oriented pyridine having intensities greater than 1. AvTOT is the total line width. hv, is the broadening due to the coupling of protons to the 14Nnucleus, relaxing with a quadrupolar relaxation time T,,= 2.7x lo-“ s; Avy2is the broadening due to intermolecular dipolar interactions, which fluctuate with a correlation time 7,= 1.47~ lo- ” s; AvOis the broadening due to field inhomogeneities Line
Intensity
&TOT (Hz)
Av, (I+)
b2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
3.13 2.61 2.14 2.07 4.90 1.38 1.75 2.82 2.95 5.53 1.56 1.04 1.05 1.42 1.01 2.15 1.89 4.22 1.59 1.06 1.48 1.12 1.43 2.55 3.27
3.70 3.34 11.42 6.26 17.22 46.25 26.28 25.80 26.11 43.41 50.54 25.37 8.98 70.79 110.88 46.18 28.12 43.28 28.42 4.28 15.91 15.00 22.38 3.81 4.05
0.49 0.38 8.32 3.24 13.60 43.21 23.69 22.81 23.00 39.57 47.55 22.46 5.69 67.66 108.20 43.26 24.48 40.63 25.36 1.37 12.94 11.66 18.89 0.85 0.82
0.91 0.66 0.80 0.72 1.32 0.74 0.69 0.68 0.81 1.54 0.69 0.61 0.99 0.83 0.38 0.62 0.76 1.35 0.76 0.61 0.68 1.04 1.18 0.66 0.93
(Hz)
by0
(Hz)
2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3
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CHEMICAL PHYSICS LETTERS
10 April 1987
Further work should define the mechanism which determines TIN in the various nematic solvents. Perhaps the most obvious hypothesis is that TINis mainly influenced by anisotropic molecular rotational diffusion, but obviously the presence of specific solute-solvent interactions, modulating the electric field gradient tensor acting on the quadrupolar nuclei, cannot be excluded. Studies along these lines are in progress. A last comment which can be made is that the highly selective broadening occurring in ‘H NMR spectra of molecules containing quadrupolar nuclei can turn out to be an advantage, rather than a complication, in spectral analysis. The lines which are most broadened can be assigned to transitions of spins closest to the quadrupolar nucleus. This could give guidance in handling the spectral parameters during the trial-and-error procedure normally used in the spectral analysis of partially oriented solute molecules containing quadrupolar nuclei. Such a step could be somewhat simplified by the linkage of the AZOREL algorithm with existing standard computer programs which diagonalise the static Hamiltonians.
Acknowledgement
The authors acknowledge the Italian MPI and CNR for financial support.
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