Rotational Diffusion and Dielectric Relaxation in Nematic Liquid Crystals

Coffey, W. T.; Kalmykov, Yuri P.

doi:10.1002/9780470141724.ch10

Cited by 27 publications

(22 citation statements)

References 39 publications

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“…Here δ mn and τ mn denote the relaxation strength and the relaxation time of the (mn)th mode, respectively. Analytical solutions have been found by Coffey and Kalmykov [16]. The dielectric relaxation strength for a mode will be a part of its scaling factor.…”

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

Jang

Панов²,

Kocot³

et al. 2011

Phys. Rev. E

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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 as a function of both temperature and frequency, whereas C9 shows only negative 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 to much lower frequencies, such that C9 shows only negative over the entire temperature range. The molecular structure of a liquid-crystalline compound has been found to have a significant influence on its properties and the phase behavior. The typical structure of a calamitic mesogen consists of a rigid core having a couple of phenyl rings and one or two flexible terminal chains. The anisotropic properties of the core moiety plays a key role in the formation of the orientational order of liquid-crystalline (LC) phases, while the terminal chains stabilize positional order, reduce the melting points and extend the phase ranges. The bent-core or banana-shaped mesogens give rise to special kind of nematic phases, in addition to the well-known B1 to B8 phases [1,2], and during the past few years the isotropic-to-nematic (I-N) transition temperature has been consistently lowered and the range of the nematic phase extended [3]. These materials in their nematic phase display unusual physical properties. Some of these are giant flexoelectricity [4], unprecedented electroconvection [5], and splitting in small-angle scattering patterns [6]. The splitting in small x-ray scattering has been interpreted either in terms of a presence of smectic-C (SmC)-like nanostructures [7][8][9] in the nematic phase or in terms of the form factor of the banana system [10,11]. A strong debate about the appropriateness of such an interpretation is continuing [12]. In this Rapid Communication, dielectric and electro-optic spectroscopic studies of the two representatives of cyanoresorcinols, 4-cyanoresorcinols (C4 and C9), specifically are compared. The results of C7, whose behavior is in between the two, are also given [13]. Interestingly we find that C9 exhibits only negative dielectric anisotropy whereas C4 shows a reversal in from positive to negative both with temperature and frequency. We later examine in detail the various causes for the observed sign reversal in given in the recent literature. In contrast, however, we find that the Maier-Meier model, which includes the anisotropic Kirkwood correlation factors [14], explains the observed behavior extremely well. The unusual dielectric behavior of C9 is interpreted in terms of the short-range * jvij@tcd.ie molecular associations along and normal to the d...

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“…This explains the observed behavior of the crossover temperature in as frequency dependent. The calculation of relaxation times in terms of the nematic potential and S by Saupe is extended by Coffey and Kalmykov [16], who find the exact solutions for the various relaxation times. Each of these permittivities thus shows at least two relaxation modes.…”

mentioning

confidence: 99%

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

Jang

Панов²,

Kocot³

et al. 2011

Phys. Rev. E

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“…According to the linear response theory, Luckhurst and Zannoni derived the relation between the complex dielectric permittivity ε * k ( ω ) = ε ′ k ( ω ) − iε ″ k ( ω ) and the macroscopic relaxation function Φ k ( t ) ( k = ||, ⊥)

\frac{[{italicε}_{italick}^{*} (italicω) - {ε_{k}}_{\infty}] \{{italicε}_{italick}^{*} (italicω) - {italicR}_{italick} (italicω) [{italicε}_{italick}^{*} (italicω) - {italicε}_{k \infty}]\} {italicε}_{k 0}}{[{italicε}_{italick}^{*} (italicω) - {ε_{k}}_{\infty}] \{{italicε}_{k 0} - {italicR}_{k 0} [{italicε}_{k 0} - {italicε}_{k \infty}]\} {italicε}_{italick}^{*} (italicω)} = \int_{0}^{\infty} [- d {normalΦ}_{italick} (italict) / d t]

where R k is the reaction field factor, and subscripts 0 and ∞ denote, respectively, the frequencies much below and above the relaxation domain. Because the local field problem was not solved as yet, the permittivity is usually related to the microscopic correlation function γ k ( t ), and Eqn takes the form:

{italicε}_{italick}^{*} (italicω) - {ε_{k}}_{\infty} = {italicG}_{italick} {italicL}_{italiciω} [- \overset{true˙}{italicγ} (italict)]

Section: Remarks On the Ds Studies Of Nematicsmentioning

confidence: 99%

“…Because the local field problem was not solved as yet, the permittivity is usually related to the microscopic correlation function γ k ( t ), and Eqn takes the form:

{italicε}_{italick}^{*} (italicω) - {ε_{k}}_{\infty} = {italicG}_{italick} {italicL}_{italiciω} [- \overset{true˙}{italicγ} (italict)]

where G k is the total local field factor and is assumed frequency independent, γ k ( t ) is the dipole correlation function and L iω means the Laplace transform. The relation between the relaxation time τ DS [being integral of Φ( t )] and the correlation time τ μ [being integral of γ ( t )] is unknown as yet, so in practice, both times are treated as equivalent. According to Luckhurst and Zannoni, the relaxation times for nematics are dependent upon the order parameter S =

{\overset{P}{true}}_{2} (italiccosθ)

.…”

Section: Remarks On the Ds Studies Of Nematicsmentioning

confidence: 99%

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Comparison of the dielectric and NMR results for liquid crystals: dynamic aspects

Urban

Geppi

2014

Magnetic Reson in Chemistry

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Critical analysis of the results of studies of molecular rotational dynamics in liquid crystalline substances with the aid of the dielectric spectroscopy (DS) and nuclear magnetic resonance (NMR) is given. Both methods are known to be sensitive to different aspects of molecular rotations: the polarization vector and the relaxation time τ(DS) in the case of DS, a tensor describing a nuclear interaction and the correlation time τ(NMR) for NMR method. Furthermore, both methods provide correlation functions with different rank values. A common basis for the comparison between τ(DS) and τ(NMR) is postulated. Several examples of the temperature dependence of the correlation times coming from the two spectroscopic methods are presented. Qualitative agreements of the correlation times were achieved in most cases.

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Crossover formulas in the kramers theory of thermally activated escape rates—application to spin systems

Coffey

Garanin

McCarthy³

2001

Advances in Chemical Physics

135

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Rotational Diffusion and Dielectric Relaxation in Nematic Liquid Crystals

Cited by 27 publications

References 39 publications

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

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

Comparison of the dielectric and NMR results for liquid crystals: dynamic aspects

Crossover formulas in the kramers theory of thermally activated escape rates—application to spin systems

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