Molecular motions in thermotropic liquid crystals studied by NMR spin-lattice relaxation

Nuclear magnetic resonance relaxation experiments with field cycling techniques proved to be a valuable tool for studying molecular motions in liquid crystals, allowing a very broad Larmor frequency variation, sufficient to separate the cooperative motions from the liquidlike molecular diffusion. In new experiments combining NMR field cycling with the Jeener Broekaert order-transfer pulse sequence, it is possible to measure the dipolar order relaxation time (T1D), in addition to the conventional Zeeman relaxation time (T1Z) in a frequency range of several decades. When applying this technique to nematic thermotropic liquid crystals, T1D showed to depend almost exclusively on the order fluctuation of the director mechanism in the whole frequency range. This unique characteristic of T1D makes dipolar order relaxation experiments specially useful for studying the frequency and temperature dependence of the spectral properties of the collective motions.

Authorship

R.C. Zamar

Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, Córdoba, ArgentinaUniversidad Nacional de CórdobaArgentinaCórdoba, ArgentinaUniversidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, Córdoba, Argentina

C.E. González

O. Mensio

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (9)
Tables (1)

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Figure 1.
a) Typical modulation of the Zeeman field in a field cycling NMR experiment. b) Scheme of the Jeener-Broekaert pulse sequence combined with a field cycling. During the polarization period two phase shifted pulses are applied to create dipolar order. Subsequently the spin system evolves in a different magnetic field during the relaxation period. Finally, after switching back the Zeeman field to the detection value H_D, a read pulse is applied and the dipolar signal is acquired.

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Figure 2.
Proton relaxation dispersion T_1Z(n) for nematic and isotropic PAA. The nematic phase shows a square root frequency dependence, that is absent in the isotropic phase. The solid lines are model fits including OFD, self-diffusion, molecular rotation and a low frequency cut-off. Data from Ref.39.

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Figure 3.
Proton relaxation of the Zeeman and the dipolar order in nematic HpAB showing the three individual contributions for T_1Z(n) together with the rotation term for T_1D(n) (self-diffusion does not contribute to dipolar relaxation -see text). Rotations contributes appreciably to Zeeman order relaxation in the MHz regime, but are negligible for dipolar order relaxation in all measured range. Data from Ref.28.

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Figure 4.
Proton spin relaxation dispersion, T_1Z(n), for TBBA in smectic A and smectic C phases. The solid line is the fit according to Table I and Eq. (11) including again OFD, molecular rotations and self-diffusion. Data from Ref. 19.

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Figure 5.
Proton relaxation dispersion T_1Z(n) for the micellar, hexagonal, cubic and lamellar phase of a lyotropic potassium laurate-D₂O mixtures. The micellar and the hexagonal system show the n¹ dependence typical of smectics. The linear profile is absent in the isotropic phases. Data from Refs. 3,18.

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Figure 6.
Comparison of the frequency dependence of T_1Z in protons of 5CB (triangles), chain deuterons of 5CB-d₁₉ (open squares) and ring deuterons only (circles). Deuteron measurements allow to select a separate frequency window for different sites in the molecule. Data from Ref. 17.

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Figure 7.
The quotient T_1Z/T_1D as a function of the Larmor frequency in the nematic phase of HpAB and 8CB. This ratio exceeds the value of three in discrepancy with the semiclassical two-spins model. Data from Ref.28.

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Figure 8.
Frequency dependence of the dipolar order relaxation in the nematic phase of HpAB and 8CB. The full line corresponds to the prediction from the two-spin model and the dashed line is the best fit with the function T_1D^-1 = 3C_DJ¹(n)_intra + an^1/2 + b. Data from Ref.28.

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Figure 9:
Zeeman and dipolar relaxation rates, measured with the field cycling technique in nematic PAA and nematic PAA_d6 at the same temperature. The circles and squares are experimental T₁ and T_1D respectively. The upper full lines are the fitting to T_1Z with Table I and Eq.(11). The dashed lines are the semiclassical two-spin model for T_1D from Table I. The lower full lines are the best fits with the function T_1D^-1 = 3C_D J¹(n)_intra + an^1/2 + b (see the text). Data from Ref.29.

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, and Q is the nuclear quadrupole moment. Table I: Relaxation rates within the weak order theory of spin relaxation. In the three first cases the observable is the energy of interaction of isolated spins. For T1D-1 the observable is the secular dipole-dipole energy, and a model of isolated spin pairs is assumed. Here , and Q is the nuclear quadrupole moment.

Figure 1. a) Typical modulation of the Zeeman field in a field cycling NMR experiment. b) Scheme of the Jeener-Broekaert pulse sequence combined with a field cycling. During the polarization period two phase shifted pulses are applied to create dipolar order. Subsequently the spin system evolves in a different magnetic field during the relaxation period. Finally, after switching back the Zeeman field to the detection value H_D, a read pulse is applied and the dipolar signal is acquired.

Figure 2. Proton relaxation dispersion T_1Z(n) for nematic and isotropic PAA. The nematic phase shows a square root frequency dependence, that is absent in the isotropic phase. The solid lines are model fits including OFD, self-diffusion, molecular rotation and a low frequency cut-off. Data from Ref.39.

Figure 3. Proton relaxation of the Zeeman and the dipolar order in nematic HpAB showing the three individual contributions for T_1Z(n) together with the rotation term for T_1D(n) (self-diffusion does not contribute to dipolar relaxation -see text). Rotations contributes appreciably to Zeeman order relaxation in the MHz regime, but are negligible for dipolar order relaxation in all measured range. Data from Ref.28.

Figure 4. Proton spin relaxation dispersion, T_1Z(n), for TBBA in smectic A and smectic C phases. The solid line is the fit according to Table I and Eq. (11) including again OFD, molecular rotations and self-diffusion. Data from Ref. 19.

Figure 5. Proton relaxation dispersion T_1Z(n) for the micellar, hexagonal, cubic and lamellar phase of a lyotropic potassium laurate-D₂O mixtures. The micellar and the hexagonal system show the n¹ dependence typical of smectics. The linear profile is absent in the isotropic phases. Data from Refs. 3,18.

Figure 6. Comparison of the frequency dependence of T_1Z in protons of 5CB (triangles), chain deuterons of 5CB-d₁₉ (open squares) and ring deuterons only (circles). Deuteron measurements allow to select a separate frequency window for different sites in the molecule. Data from Ref. 17.

Figure 7. The quotient T_1Z/T_1D as a function of the Larmor frequency in the nematic phase of HpAB and 8CB. This ratio exceeds the value of three in discrepancy with the semiclassical two-spins model. Data from Ref.28.

Figure 8. Frequency dependence of the dipolar order relaxation in the nematic phase of HpAB and 8CB. The full line corresponds to the prediction from the two-spin model and the dashed line is the best fit with the function T_1D^-1 = 3C_DJ¹(n)_intra + an^1/2 + b. Data from Ref.28.

Figure 9: Zeeman and dipolar relaxation rates, measured with the field cycling technique in nematic PAA and nematic PAA_d6 at the same temperature. The circles and squares are experimental T₁ and T_1D respectively. The upper full lines are the fitting to T_1Z with Table I and Eq.(11). The dashed lines are the semiclassical two-spin model for T_1D from Table I. The lower full lines are the best fits with the function T_1D^-1 = 3C_D J¹(n)_intra + an^1/2 + b (see the text). Data from Ref.29.

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Molecular motions in thermotropic liquid crystals studied by NMR spin-lattice relaxation

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