ABNORMAL SOUND ATTENUATION IN LAMELLAR SYSTEMS

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ABNORMAL SOUND ATTENUATION IN LAMELLAR SYSTEMS

D. Collin, J. Gallani, P. Martinoty

To cite this version:

D. Collin, J. Gallani, P. Martinoty. ABNORMAL SOUND ATTENUATION IN LAMELLAR SYS- TEMS. Journal de Physique Colloques, 1990, 51 (C2), pp.C2-33-C2-36. �10.1051/jphyscol:1990208�.

�jpa-00230377�

COLLOQUE DE PHYSIQUE

Colloque C2, supplement au n°2, Tome 51, Fevrier 1990 ler Congres Frangais d'Rcoustigue 1990

C2-33

ABNORMAL SOUND ATTENUATION I N LAMELLAR SYSTEMS

D. COLLIN, J.L. GALLANI and P. MARTINOTY

Laboratoire de Spectrométrie et d'Imagerie Vltrasonores, Unité de Recherche Associée au CNRS n°851. Université Louis Pasteur, 4, Rue Biaise Pascal, F-67070 Strasbourg Cedex, France

Résumé - Nous présentons des mesures de l'atténuation et de la vitesse ultrasonores, effectuées dans les phases smectique A et smectique C du terephthal-bis-p-p'- butylaniline (TBBA), montrant que l'hydrodynamique classique ne s'applique pas aux systèmes lamellaires.

Abstract - We present measurements of u l t r a s o n i c damping and v e l o c i t y , carried out in the Smectic A and Smectic C phases of t e r e p h t h a l - b i s - p - p ' - b u t y l a n i l i n e (TBBA), showing t h a t conventional hydrodynamics does not apply in the smectic-phases of l i q u i d - c r y s t a l s .

The Smectic A and Smectic C phases of l i q u i d c r y s t a l s consist of e q u i d i s t a n t fluid l a y e r s stacked one on top of the other (cf. f i g . 1 ) . These phases thus present a solid type s t r u c t u r e in the d i r e c t i o n which i s perpendicular t o the l a y e r s , and are considered to be the prototypes of one-dimensional s o l i d s .

Fig. 1 - Schematic representation of the Smectic A (1-a) and Smectic C (1-b) phases, and of the layer-undulation mode ( 1 - c ) , which i s the p r i n c i p a l deformation of the smectic phases. In the Smectic A phase, the molecules (the d i r e c t i o n of o r i e n t a t i o n of which i s represented by the vector n) are p a r a l l e l to the normal to the l a y e r s , whereas in the smectic C phase, they are inclined at an angle <f in r e l a t i o n to t h i s normal.

This notion of one-dimensional order i s not, however, completely rigorous, since the Landau- P e i e r l s c a l c u l a t i o n l\l p r e d i c t s t h a t p o s i t i o n - f l u c t u a t i o n s of the layers w i l l prevent a perfect long-range order from becoming e s t a b l i s h e d . This r e s u l t , suggesting t h a t these are large-amplitude f l u c t u a t i o n s , was long seen as nothing more than a mere s c i e n t i f i c c u r i o s i t y , and the t h e o r i e s applied used the w e l l - e s t a b l i s h e d concepts of conventional systems, even though the v a l i d i t y of such concepts for smectic phases has never been proven.

The influence of l a y e r - f l u c t u a t i o n s has been examined recently / 2 , 3 / . These new t h e o r i e s predict that such f l u c t u a t i o n s do in fact play an e s s e n t i a l r o l e , and notably t h a t they lead to v i s c o s i t i e s which, at low frequency f, diverge as 1/f, instead of remaining constant, as in conventional hydrodynamics. This behaviour, predicted by Hazenko, Ramaswamy and Toner

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990208

C2-34 COLLOQUE DE PHYSIQUE

(MRT), is the result of a non-linear (anharmonic) coupling between the velocity field and the thermally excited layer-undulation modes / 3 / .

A remarkable consequence of the l/f-type behaviour of the viscosities is the modification of the attenuation a of the ultrasound waves, which is thus written :

where a is the conventional attenuation term and b/f that associated with the anharmonic effects. Measuring the attenuation of the ultrasound waves as a function of frequency therefore constitutes a direct means of testing the theory. It should be pointed out that terms a and b are dependent on the angle 0 between the direction of sound-propagation and the normal to the smectic layers. To be more precise the term b is written

where K, is the constant associated with the undulation mode of the layers, and A, B, C, elastic constants of the compound, which can be determined from velocity measurements by the equation

A characteristic example of the results obtained in the Smectic A phase of Terephthal-bis-p- p'-Butylaniline (TBBA) is given in fig.2.

3.5

-

T B B A

2.5

-

\

2 1

1

Fig. 2

-

Representation of a/f2 as a function of l/f shows that, at low frequency, a/f2 diverges according to a l/f-type law, which-is in agreement with equation 1. This abnormal behaviour proves that conventional hydrodynamics do not a ~ v l v to the low-frequency range, which is precisely where they ouqht to.

Fig.3 shows that, as theoretically predicted, the anharmonic effects do not influence velocity, whereas they do affect attenuation.

T B B A T-TAN=- lS°C

Fig. 3 - Velocity measurements in the Smectic-A phase of TBBA.

F.ig.4 gives the angular variation of the abnormal part of the attenuation (i.e. of the b(0) term). This variation corresponds to that predicted by the MRT theory when 6n, < 0 (6n, is an effective-viscosity increment), and shows the existence of a "magic angle 0," given by cos2 0, = C/B (cf. equation 2), for which the anharmonic effects do not contribute to ultrasound attenuation. The solid line represents the theoretical curve calculated with

A = 1.26 10" dyn/cm2, B = 8.95 10' dyn/cm2, C = 3.65 10' dyn/cm2, and K, = 9.3 lo-' dyne. A, B, C, are deduced from the velocity measurements ; K, is the only adjustable parameter. These results also verify the theoretical equation (6n,)' = Sn, Sn,.

- -

k

U

f = 1.43 M H z

15 30 45 60 75 0 (deg)

Fig. 4 - Angular variation of the abnormal part of the ultrasound attenuation in the smectic

A phase of TBBA.

C2-36 COLLOQUE DE PHYSIQUE

The smectic C phase is also characterized by a llf-type attenuation, but the angular variation of the abnormal part of the attenuation (fig. 5) is quite different from that obtained for the Smectic A phase of the same compound.

Fig.5 - Angular variation of the abnormal part of the ultrasound attenuation in the smectic C phase of TBBA.

This change is due to the fact that the BIC ratio of the elastic constants, which is greater than 1 in the Smectic A phases, becomes smaller than 1 in the Smectic C phase. This unexpected inversion, which explains the disappearance of the "magic angle 8,", stems from the very anisotropic nature of the Smectic A - Smectic C transition 141.

Demonstrations of the anharmonic effects in the Smectic A and Smectic C phases, a detailed analysis of the results, and the extension of this study to compounds other than TBBA can be found in publications 5 and 6.

REFERENCES

111 Landau, L.D., in Collected Papers of L.D. Landau, edited by D. Ter Haar (Gordon and Breach, New York, 1985) ; Peierls, R.E., Helv. Phys. Acta Suppl.

1

I21 Grinstein, G. and Pelcovits, R., Phys. Rev. Lett.

47

131 Mazenko, G.F., Ramaswamy, S. and Toner, J., Phys. Rev. Lett. 49 (1982) 51 ; Phys. Rev. A 28 (1983) 1618.

141 Collin, D., Gallani, J.L. and Martinoty, P., Phys. Rev. Lett. 61 (1988) 102.

151 Collin, D., Gallani, J.L. and Martinoty, P., Phys. Rev. A 34 (1986) 2255.

161 Collin, D., Gallani, J.L. and Martinoty, P., Phys. Rev. Lett. 58 (1987) 254.