Acoustic investigations of relaxation processes in regions of polymorphic transformations of nematics

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Acoustic investigations of relaxation processes in regions of polymorphic transformations of nematics

V.A. Balandin, S.V. Pasechnik, O. Ya. Shmelyoff

To cite this version:

V.A. Balandin, S.V. Pasechnik, O. Ya. Shmelyoff. Acoustic investigations of relaxation processes in regions of polymorphic transformations of nematics. Journal de Physique, 1985, 46 (4), pp.583-588.

�10.1051/jphys:01985004604058300�. �jpa-00209998�

Acoustic investigations of relaxation _processes in regions

of polymorphic transformations of nematics

V. A. Balandin, ^{S. V.} Pasechnik and O. Ya. Shmelyoff

All Union Correspondence Machinery Institute, ^Problem Laboratory of Molecular Acoustics, Strominka 20, ^Moscow 107076, ^U.S.S.R.

(Reçu le 10 août 1984, accepté ^{le 10 décembre} 1984)

Résumé.

Nous analysons l’anisotropie de vitesse et d’absorption ultrasonore

fonction de la température ^{et de}

la fréquence. ^Nous déterminons les paramètres caractérisant la dépendance angulaire de la vitesse et de l’absorption

ultrasonore dans la phase nématique NPOB orientée

moyen du champ magnétique. L’analyse des résultats

été réalisée dans le cadre d’une théorie hydrodynamique généralisée ^tenant compte de deux processus relaxation- nels. La théorie relaxationnelle rend compte des données expérimentales

voisinage de la transition de phase nématique-smectique ^A.

Abstract.

The temperature-frequency dependences ^{of both} velocity and attenuation coefficient anisotropy,

as

well

their angular dependence coefficients in the nematic phase ^of nitrophenyl-octyl-oxybenzoate ^oriented by magnetic ^field

investigated. ^The analysis ^of experimental ^results

^{carried out} in the framework of gene- ralized hydrodynamic theory ^{with two} relaxation processes. It

shown that in the vicinity of the N-A phase

transition the experimental ^results

^described by the relaxation theory.

Classification

Physics ^Abstracts

61. 30C

1. Introduction.

The nematic-smectic A (N-A) phase transition, ^that in some cases is considered ^a second-order transition,

has been of growing interest both theoretically ^and experimentally ^{in the recent} years. At the same time,

a

number of theoretical predictions ^{for the} anisotropic

behaviour of ultrasound attenuation has not been

experimentally confirmated. In particular, ^there

different theoretical predictions about the critical behaviour of coefficients, ^which determine the angular dependences ^{of both} velocity and attenuation of the sound propagation ^{near the N-A} phase ^transition [1-3]. However, ^{most of} experimental ^works dealing

with the anisotropic ^sound propagation [4, 5] ^{do not}

contain the results of

combined analysis of both the attenuation and velocity anisotropy. ^The present results, exposing ^the pecularities of ultrasound _pro-

pagation ^{near N-A} phase transition in

liquid crystal

oriented by ^a magnetic field, ^{allow one to} experimen- tally ^{test some} theoretical predictions.

2. Experimental.

We investigated the effect of temperature ^{on the} anisotropic acoustical parameters of the nematic phase

of 4-nitrophenyl-4-octyloxybenzoate (NPOB), ^includ- ing ^the proximity ^of phase transitions N-A and N-I

(nematic-isotropic transition).

The sample ^{of NPOB was} synthesized ^{in Vilnus}

State University, Laboratory ^of Liquid Crystals. ^The angular dependences ⁰ (0 ^{is the} angle between the

wave

vector and magnetic ^field direction) ^{of the} absorption coefficient and sound velocity

^obtain-

ed. The measurements

made at 3.6, ^{8.8 and}

15 MHz, ^{and the} magnetic ^field strength ^{of 0.5 T. A} pulse-phase ^method [6]

^{realized in the} experimen-

tal setup [7]. The resolution of attenuation ACX/f2

1

10-14 S4 m-1, ^and of relative velocity ^variation Ac/cwas5

^{10-6. The} temperature. ^{was maintained}

to about 0.005 K by ^a double thermostabilization system [8], and measured by quartz thermometer. It

was found that the angular dependences ^{of sound}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004604058300

584

velocity and attenuation (as for other nematics

[4, 9]) could be described by ^the polynomial :

3. Results.

The temperature dependence ^of a,,,, b,,,, a,,, ba, ^obtained

at different frequences by application ^of equations (1)

and (2), ^{are shown in} figures ¹ and 2. Note the exis- tence of significant ^anomalies in the coefficients _a,

and bc ^{near the N-A} phase transition. The temperature dependence of the total velocity anisotropy Aclc

Ac(0)/c ^and attenuation anisotropy ACX(O)/f2 ^are

Fig. ^1.

^The temperature dependence ^{of the} parameters ae and be ^{at 3.6} (0) ; ^8.8 (0) ^{and 15} (A) ^MHz.

Fig. ^2.

^The temperature dependence ^{of the} parameters a.. and b. ^{at 3.6} (0); ^8.8 (0) ^{and 15} (A) ^MHz.

Fig. ^3.

^The temperature dependence ^{of the} complete anisotropy of velocity (0-3.6 MHz; D-8.8 MHz; ^{A- 15} MHz).

shown in figures ^{3 and 4.} Comparison of figures ^{3 and 1}

does not expose any pecularities ^{in the behaviour of}

the overall anisotropy of the sound velocity ^{near the}

N-A phase transition, contrary ^to a. and hc.

Fig. ^4.

^The temperature dependence ^{of the} complete

attenuation anisotropy (0-3.6 MHz; n-8.8 MHz; ^A- 15 MHz).

4. Discussion.

The frequency dependence of the total anisotropy

of the acoustical parameters in the nematic phase ^of

NPOB were analysed in the frame work of generalized hydrodynamic theory [10]. However, unlike the theory [10], ^we supposed ^that both relaxation processes contributed to each elasticity ^tensor component. ^In this case the expressions ^for frequency dependences

of the velocity ^{and the} attenuation anisotropies ^{can be} represented ^{as :}

where! 1 and! 2 ^are relaxation times, ^and åEi(j) = Elj)( (0) - E(j)(O) ^{is the} difference of extreme values of the respective elasticity ^tensor components, floo = as ⁺ CX6.

The values of Ac/c ^and åcx/f2, ^{measured at three}

frequencies, allow for the calculation of all unknown

quantities ^{in the} expressions (3) ^and (4). The values of

! l’ ! 2’ åEl) - åE11) and åE2) - M12) ^{are presented}

in table I. One can see a weak temperature dependence of! l’ while 2 increases about a decade when approach- ing T C. ^The temperature dependence! 2(T) ^{is satis-} factorily ^described by ^{the power law :} t2

1.5

10-9(åTc/Tc)-0.93(inseconds), where AT,

Tc - ^T.

The weak temperature dependence of L 1 ^{can be}

attributed to the

normal » relaxation process due ^to

Table I. - Relaxation parameters (Tr

^{338.8 K,} T,

^333.0 K).

conformational transition (rotational isomery) ⁱⁿ

the end chain of the molecule. A similar _process was

observed in MBBA [11, 12]. ^The temperature depen-

dence of the relaxation time of the

normal » contri- bution in MBBA [11] extrapolated ^{to the} temperature

Tc ^{for NPOB} gives ^{the value} of tl

^1.68

^{10 - 8 s,}

which is consistent with the data of table I. The agreement justifies the relaxation mechanism consi-

dered, ^and possibly tells about the independence ^of

the relaxation time of the

normal » contribution on

the length of end chain.

Analogous ^to references [11,12], ^the second relaxa- tion _process (with the relaxation time z2) significantly

increases when approaching Tc, ^{which can be attri-}

buted to the order parameter relaxation. It is confirmed

by ^the calculated divergence ^index (0.93 ± 0.1 ) ^{that it}

is close to the value 1.06 ± 0.11 ^{for MBBA} [11].

Anomalies in the acoustic parameters ^{near the} transition temperature Ts ^{can be} explained by ^both

fluctuation and relaxation _processes [1-3]. ^{As shown} above, the coefficients _ac, bc ^{and also} aa, ba ^{are of the}

same order of magnitude. ^{There is no term propor-}

tional to cos2 0 in the expression ^for angular depen-

dence of the sound velocity within the fluctuation

theory, ^so the behaviour of a, ^near Ts ^was supposed

to be considered in the frame work of relaxation

theory. ^{The critical} part ^{of the} velocity anisotropy

can be expressed ^{as :}

where q is the kinetic coefficient with the dimension

of inverse viscosity, #I, ^{and are} dimensionless

material coefficients describing ^the dynamic coupling

586

of the order parameter ^with hydrodynamic variables, Afl = #11

^fli, and T is the relaxation time. The

expression ^for ac, accounting equation (5), ^{can be}

written as :

where aeg ^{is the}

regular >> part of a,,, ^{not related to the}

critical phenomenon ^{near the N-A} phase transition.

The narrow nematic region ^of NPOB, resulting

from the joint effects of both the N-A and N-I transi-

tions, complicates the calculation of the

regular >>

part ^of (6). ^The procedure ^used

^the following.

Using the theoretical result [10], together ^{with the}

above mentioned proposal, ^and neglecting the effects of the N-A transition, the coefficients of angular dependence ^of Ac(0) /c ^{can be} expressed

Equations (7) ^and (8) ^were supposed ^{true in the}

whole nematic region. Consequently, using ^the expe- rimental results and the data of table I, the calculation of AE(i) - AE(’) ^was performed (Fig. 5). ^{It is known}

that the difference of the critical elastic constants, related the critical _process

T c’ ^has

^weak tempe-

rature dependence [13]. Figure ^{5 shows}

^flat region

in the temperature dependence ^of AE(’) - AE (2)

its value - 5

106 kg ^{m-1 s- 2. This} result, together

with the data of table I,

^{used to} calculate the

«

regular » contribution by equation (7). According

to reference [13], the difference of elastic constants

characterizing the normal _process, is

function of the order parameter. Thus, ^{it must} increase when the temperature decreases, which is in qualitative agree- ment with the results presented ⁱⁿ figure ⁵ (AE(’) - AE(l)). ^{So to} calculate the

regular » contribution,

the value for

weak temperature dependent region

far from Tc ^{was used. The}

regular » contributions to ac ^near TS

^{shown in} figure ^{6 for the} frequencies ^3.6

Fig. ^{5. - The} temperature dependence ^of E31 - E11)(.)

and AE§- E12) (0).

Fig. ^6.

Approximation of ac

^{the N-A} transition;

1-3.6 MHz; ^2-8.8 MHz; ^{1’ and} 2’-respective ^{values of}

«

regular » part.

and 8.8 MHz. Calculated in this _way,

regular >>

contributions

used to derive the critical part ^of

ac, according ^to equation (6). Using ^{this data} (for ^the

two frequencies), values Of T and A = {3.l ð/3/ rn

N-A transition

calculated and presented ⁱⁿ

table II. The increase of the parameters

and A I

when approaching Ts is observed. The temperature

dependence of the relaxation time can be described

Table II.

Parameters

and ^A

Ts.

by the well known expression [14] :

when devergence temperature Ts is less than Ts, ^so that AT*

^{T -} Ts - åT (Fig. 7a).

The fit of the data of table II by ^{the least} squares method allowed us to calculate the values of AT and To, which

equal ^{to 0.5 K and 2.2}

10-10 s, respec-

tively. The value of _To is an order of magnitude ^less

than previously obtained for CBOOA [5]. ^The depen-

dence of A on D Ts (on

logarithmic scale) ^{is shown}

in figure ^{7b. The} dependence is well described by ^the straight line, ^and consequently, by ^the analytical expression :

The values of A o ^{and X obtained} by ^{the least} squares method were about - 3.0

10-’ kg m-’ s-’ ^and

-

1.1 ± 0.1 respectively. ^{Thus, we} established the temperature dependence ^of P 1. Aj8/ Bn which had been

previously supposed ^{to be} temperature indepen-

dent [9].

Using equation (10), equation (6) ^can be rewritten

as :

The plot of the function (11), together ^{with the} experimental data, ^are presented ⁱⁿ figure ^{6. Note the} satisfactory agreement between the experimental ^and

calculated values of ac.

Unlike _ac, temperature-frequency dependence ^of bc ^{can be due to} both relaxation and fluctuation

.

contributions [9]. Analogous ^to (11) the relaxation contribution to bc ^{can be written as :}

Fig. ^7.

^The temperature dependence ^T, 31 API’1

the N-A transition.

Far from the N-A phase transition bc ^{does not} depend ^on temperature and its value is close to zero

(Fig. 1), ^{thus the}

regular >> part is omitted. The data

for bc ^at 3.6 and 8.8 MHz in the temperature region ATs

^{0 ...1.5 K were} approximated by expression (12) (Fig. 8). The contribution of fluctuations was not taken into account. The values of [(AP) 2 /17]0 ^{and Y}

are 3.8

10- 5 kg m-1 ^{s-’ and - 1.5 ± 0.1} respecti- vely. Equation (12) ^is

^{to be}

satisfactory approxi-

mation in the temperature region AT:

^0.5

^{3 K.}

Thus in this temperature ^and frequency range the fluctuations do not contribute significantly ^to bc.

The relaxation _process of the smectic order _para- meter also contributes to aa ^and ba, ^{but this} analysis

was not performed for aa because of the complicity ⁱⁿ separation ^{of the} regular part. According ^to [13], ^the

relaxation contribution to ba ^{is :}

Fig. ^8.

Approximation be

the N-A transition (0- 3.6 MHz ; D-8.8MHz).

Fig. ^9.

Approximation ba

the N-A transition (1-

3.6 MHz; ^2-8.8 MHz; 3-« regular

part).

588

The result of calculations based on equation (13)

and the experimental values of the critical part ^of

b« ^are presented ⁱⁿ figure ^{9. The} regular part of bIZ

was calculated according ^to [15] :

where _al is the Leslie coefficient.

Figure ^{9 shows the} qualitative agreement ^between the calculations according ^to (13), ^{and the} experimen-

tal values; moreover, there is a good quantitative agreement ^{at 3.6 MHz.}

5. Conclusion.

a) Angular dependences ^{of the} anisotropic ^acousti-

cal parameters ^{in the} vicinity ^{of N-A} phase ^transition

can be interpreted in the frame work of relaxation

theory.

b) ^{There is} quantitative agreement between the

theory ^{and the} experiment ^{for some} parameters.

c) ^Observed inconsistences in some parameters

may be due to not quite ^reliable separation ^{of critical}

and regular parts, ^{and also} by the existence of other contributions.

References

[1] Liu, M., Phys. ^{Rev. A 19} (1979) ^2090.

[2] SWIFT, J., MULVANEY B. J., Phys. ^{Rev. B 22} (1980)

4523.

[3] SWIFT, J., MULVANEY, ^B. J., ^J. Physique ⁴⁰ (1979) ^287.

[4] MIYANO, ^K. KETTERSON, ^J. B., Phys. ^{Rev. A 12} (1975)

615.

[5] KIRY, F., MARTINOTY, P., ^J. Physique ³⁹ (1978) ^1019.

[6] BALANDIN, ^V. A., NOZDREV, ^V. F., SHMELYOFF, ^O. Ya., Proceedings of the X-th All Union Acoustic

Conference, G, ^Moscow 1983, p. 52.

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[14] BROCHARD, F., ^J. Physique ³⁴ (1973) ^411.

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