Sound Propagation in Liquid Crystals

Miyano, Kenjiro; Ketterson, J. B.

doi:10.1016/b978-0-12-477914-3.50007-4

Cited by 20 publications

(10 citation statements)

References 79 publications

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“…15 The dependence of the anom-alies on direction of propagation is given by (14) where the upper (-) sign is for first sound and the lower (+) sign for second sound.…”

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confidence: 99%

Viscosities Diverge as1ωin Smectic-ALiquid Crystals

1982

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The nonlinear coupling between the velocity field and the layer-displacement field leads to a radical breakdown of the conventional hydrodynamical theory for smectic-A liquid crystals. Three of the five viscosities are found to diverge as l/co for small frequencies co with the result that the sound attenuation scales as a; (not co 2 as predicted by conventional hydrodynamics). It is also found that there is a simple relationship between the three diverging viscosities. Reanalysis of existing data appears to confirm the present prediction for the sound attenuation.PACS numbers: 61.30.-v, 62.80.+f Grinstein and Pelcovits 1 have recently shown that anharmonic effects lead to a qualitative change in the conventional elastic theory describing the equilibrium behavior of smectic-A liquid crystals. In particular they showed that the wave-number-dependent generalizations of the elastic moduli B and K 1 vanish and diverge respectively as \wq for small wave number q. We report in this Letter that the influence of anharmonicity on the dynamical behavior of smectics is far more dramatic. In particular, certain viscosities, measured at finite but small frequency a>, diverge as l/co. A consequence of these effects is that the attenuation of sound is linear rather than quadratic in frequency or wave number, a remarkable departure from conventional hydrodynamics.Surprising as these effects are, they may already have been observed in experiments on smectics A. For a number of materials (DDAMC, 2 DEAB, 3 and TBBA 4 ) there appears 5 to be an anomalous contribution to the damping of first sound that scales like co.We construct the nonlinear hydrodynamic equations governing smectic-A liquid crystals following standard procedures. 6 The hydrodynamic or slow variables are known 7 to be the density p, the velocity field v, and the layer-displacement fields. 8 Using arguments of rotational invariance, 1 and ignoring various "irrelevant" 1 ' 9 terms, one is lead to an effective free energy F=F'+^fd 3 xpv 2 ,where F' = |/ d 3 where the z axis has been taken to point in the ordering direction, dp is the deviation of p from its quiescent value p 0 , and A, B, C, and If x are the conventional elastic constants. The parameter!) (see Ref. 1) is chosen to ensure that the expectation value du/hz = 0. Integrating out the velocity and the density gives the free energy of Grinstein and Pelcovits, involving u alone, their elastic constant B' being related to B byIn the absence of anharmonic terms F reduces to the free energy of Martin, Parodi, and Pershan 7 (MPP). Given the governing free energy, the equations of motion can be written (summation over repeated indices is assumed here and below) 8,p+V«(pv) = 0,Equation (3) just expresses conservation of mass. The term pV { 6F'/6p -V { ubF/ §u in Eq. (4) represents the (reactive) pressure forces that drive sound in ordinary fluids, while the 6F/du terms are the elastic forces caused by distorting the smectic layers. Viscous effects are contained in the rj ijkl 51

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“…15 The dependence of the anom-alies on direction of propagation is given by (14) where the upper (-) sign is for first sound and the lower (+) sign for second sound.…”

mentioning

confidence: 99%

Viscosities Diverge as1ωin Smectic-ALiquid Crystals

1982

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“…Ketterson's expression for attenuation of sound in the "twisted nematic" approximation [27]. We find an anomalous increase in the attenuation given by CO where P is the angle between the direction of propagation of the sound wave and the pitch axis.…”

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confidence: 97%

Theory of acoustic properties near the cholesteric–twisted-grain-boundary-Aphase transition in liquid crystals

Williams

Swift

1992

Phys. Rev. A

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A theory of sound propagation and attenuation near the cholesteric -twisted-grain-boundary-A phase transition in liquid crystals is presented. A mode-coupling formalism is used to investigate the behavior of the viscosities at the transition. Pretransitional eff'ects are predicted in both the speed of sound and ultrasonic attenuation. The speed of sound is found to exhibit an isotropic dip, and the attenuation coefficient is anisotropic only in the prefactors, having isotropic critical exponents. These results are in qualitative agreement with experiment.PACS number(s): 64.70.Md, 64.60.Ht

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“…Ultrasonics is a versatile tool for studying the properties of solids [1,2], liquids [3][4][5], and liquid crystals [6][7][8][9]. In solids (in all type of solids) and liquids (pure and electrolytic solutions) the absorption and dispersion are well understood, and in most of the cases the absorption values are well explained.…”

Section: Introductionmentioning

confidence: 99%

Ultrasonic Studies of Ctab in Glycol

Kor

Yadav

Singh

2003

Molecular Crystals and Liquid Crystals

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Ultrasonic absorption and velocity measurements have been made in cetyl trimethyl ammonium bromide (CTAB) in nonaqueous solution of ethylene glycol as a function of concentration, temperature, and at a fixed frequency. The interferometer technique has been used to measure ultrasonic velocity at 2 MHz. A standard pulse transmission technique has been used for ultrasonic absorption measurement at 5 MHz. It is concluded that micelle formation takes place in the solution surfactant of CTAB in ethylene glycol.

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Sound Propagation in Liquid Crystals

Cited by 20 publications

References 79 publications

Viscosities Diverge as1ωin Smectic-ALiquid Crystals

Viscosities Diverge as1ωin Smectic-ALiquid Crystals

Theory of acoustic properties near the cholesteric–twisted-grain-boundary-Aphase transition in liquid crystals

Ultrasonic Studies of Ctab in Glycol

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