Rotational Diffusion and Dielectric Relaxation in Nematic Liquid Crystals. In: Prigogine I, Rice SA, Vij JK, editors. Advances in Chemical Physics. Hoboken: John Wiley & Sons, Inc.; 2000. pp. 487-551. [DOI: 10.1002/9780470141724.ch10]

Distortions in structures of the twist bend nematic phase of a bent-core liquid crystal by the electric field

The dielectric spectra of the twist bend nematic phase (N_{TB}) of an achiral asymmetric bent-core liquid crystalline compound are studied for determining the various relaxation modes. Dielectric measurements are also carried out under the bias field E up to 8 V/µm. Two molecular and two collective relaxation processes are observed. The orientational order parameters with respect to the local and the main directors determined using molecular modes are used to find the heliconical angle. The results also show that the order parameter with reference to the main director reverses its trend from increasing to decreasing at temperatures of a few degrees above the N_{TB} to N transition. The collective relaxation modes are assigned to (a) distortions of the local director by the electric field at a frequency of ∼100kHz while the periodic helical structure remains unaltered (mode attributed to flexoelectricity); (b) changes in the periodic structure arising from a coupling of the dielectric anisotropy with the electric field at the lowest frequency in the range of 100 Hz-10 kHz. Frequency of the higher frequency collective mode (∼100kHz) depends primarily on the heliconical angle and has anomalous softeninglike behavior at the N-N_{TB} transition. The lowest frequency mode is studied under the bias field E; the modulus of the wave vector gradually vanishes on increasing E (except for an initial behavior, E^{2}<0.1V^{2}/μm^{2}, which is just the opposite). The transition from the twist bend to splay bend structure is observed by a sudden drop in the frequency of this mode, followed by a linear decrease in frequency by increasing E. The results agree with the predictions made from the currently proposed models for a periodically distorted N_{TB} phase.

External dc bias-field effects in the nonlinear ac stationary response of dipolar particles in a mean-field potential

External dc bias-field effects on the nonlinear dielectric relaxation and dynamic Kerr effect of a system of permanent dipoles in a uniaxial mean-field potential are studied via the rotational Brownian motion model postulated in terms of the infinite hierarchy of differential-recurrence equations for the statistical moments f_{n}(t)=〈P_{n}〉(t) (the expectation value of the Legendre polynomials P_{n}). By solving these equations, the nonlinear dielectric and Kerr-effect ac stationary responses are evaluated for arbitrary dc field strength via perturbation theory in the ac field. Simple analytic equations based on the large separation of the time scales of the fast intrawell and slow overbarrier (interwell) relaxation processes are also derived.

Short-range correlations seen in the nematic phase of bent-core liquid crystals by dielectric and electro-optic studies

Three bent-core nematic liquid crystals having the same core but with different terminal groups, short (C4) and long (C7,C9) tails, are investigated by dielectric and electro-optic contrast spectroscopic techniques. C4 shows sign reversal in the dielectric anisotropy Δε' as a function of both temperature and frequency, whereas C9 shows only negative Δε' in the entire mesophasic region. The behavior of C7 is intermediate of the two. Results of a dielectric study show that both C7 and C9 exhibit strong short-range polar correlations normal to the director. The correlation lengths of these interactions are found to be similar to those from the x-ray scattering. An increased hindered rotation for C9 compared to C4 moves the dielectric dispersion for ε(|') to much lower frequencies, such that C9 shows only negative Δε' over the entire temperature range.

Dielectric properties of mixtures of a bent-core and a calamitic liquid crystal

Dielectric spectroscopy measurements have been performed on a bent-core nematic liquid crystal and on its binary mixtures with a calamitic nematic. We have detected more dispersions in the bent-core compound than in the calamitic one, including one at an unusually low frequency of a few kilohertz. The dispersions detected in the mixtures have been identified and the spectra have been split into contributions of the constituents. In order to connect the dielectric increment with the molecular dipole moment we have applied a sophisticated conformational calculation not performed before for a large, flexible mesogen molecule with numerous polar groups.

Anisotropic rotational diffusion and dielectric relaxation of rigid dipolar particles in a strong external dc field

Dielectric response functions of polar particles (macromolecules) diluted in a nonpolar solvent subjected to a strong external dc electric field are evaluated using the anisotropic noninertial rotational diffusion model. Simple analytic formulas for the longitudinal and transverse components of the dielectric susceptibility and relaxation times are given using the effective relaxation time method. These formulas are tested against numerical solutions of the underlying infinite hierarchy of differential-recurrence equations for statistical moments (ensemble averages of the Wigner D functions) which are obtained by averaging the governing Langevin equation for noninertial rotational Brownian motion over its realizations. The calculations, involving matrix continued fractions, ultimately yield the exact solution of the infinite hierarchy of differential-recurrence relations for the dielectric response functions. In the isotropic rotational diffusion limit, the solution reduces to the known results.

Anisotropic rotational diffusion and transient nonlinear responses of rigid macromolecules in a strong external electric field

Nonlinear transient responses of polar polarizable particles (macromolecules) diluted in a nonpolar solvent to a sudden change in magnitude of a strong external dc field are evaluated using the anisotropic noninertial rotational diffusion model. The relaxation functions and relaxation times appropriate to the transient dynamic Kerr effect and nonlinear dielectric relaxation are calculated by solving the infinite hierarchy of differential-recurrence equations for statistical moments (ensemble averages of the Wigner D functions). The calculations involve matrix continued fractions, which ultimately yield the exact solution of the infinite hierarchy of differential-recurrence relations for the first- and second-order transient responses.

Orientational order and dynamics of the dendritic liquid crystal organo-siloxane tetrapodes determined using dielectric spectroscopy

The dielectric measurements have been carried out on the two zeroth generation dendrimers with four branched arms (called tetrapodes) based on the siloxane cores. The results are analyzed in the framework of the molecular theory of dielectric permittivity by Maier and Meier for nematogens. At least four molecular processes are resolved in the dielectric relaxation spectra in the nematic phase for each of the two tetrapodes. Three of them are assigned to the reorientation of the monomeric unit whereas the fourth is assigned to the rotation of the molecular segments in the individual arms of the monomeric unit around the long molecular axis. The dielectric relaxation strength of the low frequency process has been used to calculate the orientational order parameter. The dynamics of the resolved processes has been quantitatively analyzed using the results of the microscopic model of the rotational diffusion, given by Coffey and Kalmykov [W. T. Coffey and Yu. P. Kalmykov, Adv. Chem. Phys. 113, 487 (2000)] using the calculated order parameter. All molecular processes: the rotation around the short molecular axis (end-over-end rotation), precession around the director and the rotation around the long molecular axis (also called the spinning motion) are shown to have successfully been reproduced by the model. The anisotropy of the rotational diffusion coefficients gradually increases with a reduction in temperature, to a factor of 3 in the nematic phase relative to its isotropic phase.

Stochastic molecular motions in the nematic, smectic-A, and solid phases of p,p'-di-n-heptyl-azoxybenzene as seen by quasielastic neutron scattering and 13C cross-polarization magic-angle-spinning NMR

Molecular rotational dynamics in p,p'-di-n-heptyl-azoxybenzene was studied by means of quasielastic neutron scattering (QENS) and 13C cross-polarization magic-angle-spinning (CPMAS) NMR. Fast reorientation of the hydrogen nuclei was observed by QENS in the two liquid crystalline (LC) phases nematic and smectic A, as well as in the crystalline phase. The latter could not be restricted to the -CH3 rotations alone, and a clear indication was found of some other reorientation motions persisting in the crystal. Two Lorentz-type components convoluted with the resolution function gave an excellent fit to the QENS spectra in both LC phases. The narrow (slow) component was attributed to the reorientation of the whole molecule around the long axis. The corresponding characteristic time of approximately 130 ps agreed well with the values obtained in recent dielectric relaxation and 2H NMR studies. The full width at half maximum of the broader (fast) component shows a quadratic Q dependence (Q is the momentum transfer). Hence the corresponding motions could be described by a stretched exponential correlation function and were interpreted as various "crankshaft-type" motions within the alkyl tails. The 13C CPMAS experiments fully corroborated the QENS results, sometimes considered ambiguous in complex systems.