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ELECTROHYDRODYNAMIC INSTABILITIES ABOVE A NEMATIC TO SMECTIC A (OR C)
TRANSITION
M. Goscianski, L. Léger
To cite this version:
M. Goscianski, L. Léger. ELECTROHYDRODYNAMIC INSTABILITIES ABOVE A NEMATIC TO SMECTIC A (OR C) TRANSITION. Journal de Physique Colloques, 1975, 36 (C1), pp.C1-231-C1- 235. �10.1051/jphyscol:1975141�. �jpa-00216220�
JOURNAL DE PHYSIQUE Colloque C1, supplkment au no 3, Tome 36, Mars 1975, page C1-231
Classification Physics Abstracts
7.130
ELECTROHYDRODYNAMIC INSTABILITLES
ABOVE A NEMATIC TO SMECTIC A (OR C) TRANSITION (*)
M. GOSCIANSKI and L. LEGER (**) Laboratoires d'Electronique et de Physique Appliqute
3, avenue Descartes, 94450 Limeil-Brevannes, France
R6sumB. - Des observations d'instabilites 6lectrohydrodynamiques dans des materiaux pour lesquels le paramktre de Helfrich 5 2 depend trks fortement de la temperature sont prksentees et discutees.
Quand 5 2 tend vers un par valeurs supkrieures la tension seuil du regime de conduction diverge, ainsi que le champ seuil du rkgime dielectrique. Les deux types d'instabilite disparaissent pour 5 2 = 1.
Pour 5 2 < 1 il existe encore des instabilites qui sont interpretdes comme provenant de l'amplifi- cation de fluctuations de torsion du directeur. Cette amplification peut se produire si le coefficient de friction a s est positif, et si le rapport des conductivitks electriques parallele et perpendiculaire aux molecules all/q est plus petit que un.
Abstract. - We present observatibns on electrohydrodynamic instabilities in materials for which the Helfrich parameter 5 2 is strongly temperature dependent.
For 1;2 de-creasing to one, the threshold voltage of the conduction regime diverges, and both dielectric and conduction regimes disappear for 1 2 = 1, as predicted by the theoretical models.
For 5 2 < 1, we still observe.instabilities, which are interpreted in terms of amplificated twist
fluctuations. Such an amplification,can occur for positive values of the friction coefficient as, and electrical conductivities ratio all/ai, smaller than one.
1. Introduction. - The periodic distortions of, the orientation of a nematic liquid crystal under a. c. elec- trical field have been widely studied both experimen- tally and theoretically [I, 21.
The theoretical model developed by Dubois-Violette, de Gennes, Parodi (D. V. G. P.) [3], following an idea by Carr [4] and Helfrich [5], has pointed out the importance of the parameter
where a l l , ol, &,I, are the conductivities and the dielectric constants respectively parallel and perpen- dicular to the molecules, 8, = ell - cL, and 6 a dimen- sionless parameter involving some friction coefficients of the nematic.
For c2 > 1, both dielectric and conduction regimes can occur.
For 1' < I no instability, arising from an amplifica- tion of bend fluctuations, can occur.
In this paper we present observations on electro- hydrodynamic instabilities in materials for which c2
can be varied continuously from values larger than 1 to values smaller than 1. In section 2, we shall present the experimental conditions. Section 3 will be devoted
(*) Supported by D. R. M. E. under contract no 73 34778004807501.
(**) Permanent address : Laboratoire de Physique des Solides, Bhtiment 510, 91405 Orsay, France.
to the c2 > 1 case with a special attention to the region
C2 very close to 1. The new type of instabilities, which appear for c2 smaller than one, and which are no more relevant to the Carr-Helfrich model, will be presented and tentatively explained in section 4.
2. Experimental conditions. - In order t o vary
c2 one can play with the dielectric constants, but this involve's a rather heavy chemical work and does not allow continuous variations in 1'. A more interesting and powerful method is to play with the electrical conductivities ratio oll/o,. This ratio, which is larger than one in usual nematlcs, can decrease with tempera- ture and become smaller than one in some nematics presenting smectic phases at lower temperatures. Such a behaviour, first pointed out by Rondelez [6], and interpreted by him as due to smectic order fluctuations in the nematic phase, is illustrated on figure 1. In such compounds, one expects 5' to be strongly temperature dependent and to cross the 1 value for a temperature T*
very close to the one at which
We have mainly worked with two compounds (I) : - N-(p-n-butoxybenzy1idene)-n-octylaniline (40.8) which has the following phase diagram :
(1) Cg and 40.8 were synthetized by L. Strzelecki and L. Lie- bert, Orsay.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975141
C1-232 M. GOSCIANSKI AND L. LEGER
Crystal ,--Smectic B = Smectic A Nematic Isotropic
31.1 OC 48.6 OC 62.5 OC 77.8 OC
- di-n-4-4'-octyloxyazoxybenzene (C8) :
crystal 2 Smectic C Nematic L-, Isotropic.
79 OC 107 OC 125 OC
TEMPERATURE ("C I
FIG. 1. - Ratio of the conductivities parallel and perpendi- cular to the long molecular axis, all/aL, versus temperature for 40.8. The mean conductivity at 77 OC is Z7 70 = 2 X 10-9 (C2. cm)-1.
The experimental set-up is a quite conventional one for the study of electrohydrodynamic instabilities, but some special precautions have to be taken :
1. As the temperature is the important parameter we need good temperature control and stability. We have used an electronically regulated oven which has alre- ady been described [7]. The accuracy of the tempe- rature measurements is 10-I OC, and the lateral thermal gradients in the observed area of the sample are evaluated to less than 10-I OC.
2. When working in the temperature range where the anisotropy of electrical conductivity is very low, the effects of charges injection at the electrodes can hide the bulk properties of the material. In order to avoid charges injection, a 3 000 A SiO film is evaporated on the electrodes (conventional In,O, coated glass plates).
3. A strong planar anchoring of the nematic is achieved by the means of a 400 A SiO film evaporated at oblique incidence [8] above the preceding one.
The dielectric constants and the electrical conducti- vities of the two investigated compounds have been measured independently in their whole nematic range [9], and the conductivity a, is measured again on the cells used for the electrohydrodynamic observa- tions in order to remain free of any effects of chemical degradation of the compound between the two measu- rements.
3. 5' > 1 regime. - For the two compounds we have used, the main features are the same :
1. Close to the nematic to isotropic phase transition both dielectric and conduction regimes behave the same as in nematics such as MBBA.
2. As the temperature is decreased, several modifi- cations of the conduction regime appear :
- The instability no longer develops uniformly in the direction normal to the (no, E) plane and takes the typical aspect of figure 2 (no notes the molecular alignment).
- The periodicity of the Williams domains decreases rapidly with decreasing temperature.
- The threshold voltage diverges as T goes to a value T* at which both conduction and dielectric regimes disappear (T* = 65.5 OC for 40.8, T* = 1 16 OC for C,).
- The cut-off frequency goes to zero at T = T*.
FIG. 2. - Typical aspect of a Cg sample in the conduction regime close to the temperature T* at which the Helfrich para- meter 5 2 = 1 (sample thickness : d = 110 pm, t = 118 OC, exci- tation frequency 30 Hz). The Williams domains seem to be broken in the direction normal to (E, no), and, depending on the focusing of the microscope, can take the aspect of undulating focal lines at an angle with respect to the rest direction of the molecules, no. This effect is less pronounced in 40.8 than in Cs.
To compare those observations with the predictions of the D. V. G. P. model, we can first evaluate the temperature T* at which l2 = 1. As eq. (1) involves the friction coefficients ratio 6, which is unknown for the compounds we have used, we have supposed that the D. V. G. P. model is valid near the isotropic phase transition where the instabilities look very usual, and used the cut-off frequency o, = dl2 - 112 as a measurement of 1' (z-I = 4 7ca11/~11 is completely determined by our measurements of and c,,).
Injecting this 5' value in eq. (I), we are able to deter- mine 6 near the isotropic phase. If we now suppose that 6 is temperature independent, we are able to
EHD INSTABILITIES ABOVE A N-SA OR N-Sc TRANSITION C1-233 calculate c2(T) from eq. (1) and our measurements of o
and E . This leads to r2 = 1 for T = 65.8 OC, in rather
good agreement with the temperature T* = 65.5 OC at which the two instabilities are observed to disappear, but this can only give an order of magnitude as 6 has been supposed to be temperature independent.
The temperature dependence of the cut-off frequency shown in figure 3 is also in qualitative agreement with
TEMPERATURE (degree C ) FIG. 4. - Temperature dependence of the threshold voltage of the conduction regime for a 110 pm thick 40.8 sample. The inset gives a plot of --- 1 I
k2(T7 O) , for different
versus --- -
K; CT, W ) K ~ T , 0 ) k 2 v , W ) reduced frequencies.
FIG. 3. - Plot of the cut-off frequency versus temperature for a 40.8 sample (d = 110 pm).
the D. V. G. P. prediction, w, = J-c2 - l/z. It is
observed to go to zero at T* = 65.5 OC. The threshold curves for the conduction regime are more complicated to explain. The cut-off frequency is strongly temperature dependent, and it is necessary to work with reduced frequencies. Figure 4 shows the temperature depen- dence of the threshold voltage for three reduced fre- quencies. We have tried to fit our data-with the D. V. G. P. prediction
1 + (r2 - 1) o2 7 v,2,(T, 0 ) = K;(T 0) o c
o2 (2)
with
' E ~ ~ K 3 k2 d2 1
v,;(q 0) = - - - -
EL E, r2 - 1 E,,
where K , is the bend elastic constant and k the wave vector of the instability.
In the D. V. G. P. model, k is stated to be n/d (d is the sample thickness) and only a qualitative justifica- tion is given. In our case, the wave vector of the insta- bility is temperature and frequency dependent (Fig. 5).
We have no theoretical explanation for this last point which can only come out from a three dimensional computation. In a recent paper [lo], a complete discussion of the instability in the case of square wave
FIG. 5. - Spacing of the domains as a function of temperatiire for three reduced frequencies (40.8, d = 110 pm).
I I
excitation predicts a periodicity smaller than sample thickness and depending on r2 - 1. It should be interesting to extend this calculation to a three dimen- sional model and compare it to our data.
We have not been able to fit eq. (2) without injecting the temperature and frequency dependent wave vector of the instability k2(T, o), i. e .
I I I I I
G5 70 75 TNl 80
TEMPERATURE (degree C )
(21-234 M. GOSCIANSKI AND L. LEGER With our evaluation of - 1 remains much smaller
than 1 throughout the entire interesting temperature range and we have neglected the second term in the numerator. The inset of figure 4 gives a plot of
1 1
versus --- - k2(T, O) , which have been V;(T, m) v,2,(T, 0) k2(T, m)
independently measured, and shows that the frequency dependence predicted by the D. V. G. P. model remains in agreement with the observed one.
4. 5' < 1 regime. - In that region, we were expect- ing that, without injection at the electrodes, no instabi- lity would take place. In fact we were very surprised to observe two regimes of instabilities :
- a low frequency one, which is shown on figure 6, - a high frequency one, which is shown on figure 7.
They are both characterized by a threshold field and by the fact that the distortion always remains in the (E, no) plane (the patterns completely disappear if the incoming polarizatiok is normal to no). In the low fre- quency regime,, the focusing of the light occurs on lines parallel-to no, which completely distinguishes this regime from a usual conduction regime. Moreover, two kinds of hydrodynamic motion are visible if one observes the motion of dust particles : some particles describe cyclic motions between two focal lines, while others are moving parallel to the focal lines. The only distortion of the director which can explain the optical properties of the low frequency instability is a twist distortion. Thus, we have to imagine a mechanism which can amplify some of the thermally excited twist fluctuations of the director.
Such a mechanism is schematically shown on figure 8. We have first to emphasize that it cannot be a
--
FIG. 8. - Proposed mechanism for the amplification of twist fluctuations : as al is larger than ell, the flow induced by the motion of the ions present in the sample is essentially normal to FIG. 6 . - Typical aspect of the sample in the low frequency the molecules. A twist fluctuation distorts the flow lines and gives regime of instability for l;2 > 1. The domains are nearly parallel rise to a velocity gradient in the plane (E, no) which can produce to the rest direction of orientation of the molecules no. The perio- a destabilizing viscous torque for positive 'values of as.
dicity is proportional to the sample thickness (Cs, d = 30 pm, T = 115OC).
one dimensional model ; a uniform (with respect to z) twist distortion is not coupled with the charges present in the sample. Boundary conditions have to be taken into account which strongly complicates the calcula- tions. Thus, we only present here a qualitative argument to make plausible the amplification of twist fluctua- tions. We are in a temperature range where all is smaller than o,. If an electric field is applied, the ions present in the sample tend to move perpendicularly to the molecules. A twist fluctuation distorts the flow lines, if the twist is not uniform in the z direction, and gives rise to a component of the flow in the x direction (parallel to no), and to a velocity gradient in the z direction. If we are dealing with compounds for which
cl, 1111 is negative, such as MBBA, this velocity gra- dient is associated with a stabilizing torque and the fluctuation is not amplificated, but if a, is positive this hydrodynamic torque is destabilizing and an instability FIG. 7. - Bidimensional pattern of the high frequency regime
for 5 2 < 1. The periodicity is of the order of a few microns, and can occur. Independent measurements of the sign of a,,
slightly depends on temperature and frequency (Cs, d = 30 pm, by a method developed by P- Pieranski 1121, have T = 115 OC). shown that a, was positive in a quite large temperature
EHD INSTABILITIES ABOVE A N-SA OR N-Sc TRANSITION Cl-235 range (up to a few degrees below the isotropic-nematic some bend fluctuations of the molecular orientation are transition) for the two compounds we have used. Thus, destabilized by both dielectric and viscous torques.
we think that the low frequency regime we observe for We have observed that other mechanisms can lead to
C2 < 1 comes from the destabilization of twist fluctua- a periodic distortion of the director if an a. c. electrical tions. of the director, which can occur for 01, < O, field is applied to the sample :
and a, 5- 0.
The high frequency regime is probably similar to a dielectric regime with twist oscillations of the director.
Detailed calculations have now to be undertaken to predict the exact behaviour of the thresholds versus frequency and sample thickness, but the problem is much more complicated than in the D. V. G. P. one for it cannot be considered as a one dimensional pro- blem.
If we now come back to the C2 > 1 case, and remember that a, is positive for temperatures much higher than T*, twist fluctuations can also be destabiliz- ed in regions where the flow is parallel to no, and the velocity gradient normal to no, i. e. near the glass plates.
This can explain the fact that the bend instability does not develop uniformly in the direction normal to (no, El.
5. Conclusion. - Up to now, the only recognized mechanism giving rise to electrohydrodynamic insta- bilities in planar samples was the Carr-Helfrich one :
1) If the Helfrich parameter C2 is higher than one, and if the Leslie friction coefficient a, is positive, bend fluctuations can be amplified, but the hydrodynamic flow present in the conduction regime can destabilize twist fluctuations giving rise to cc broken D Williams domains. Despite of that apparently important modifi- cation of the pattern, the main predictions of the D. V. G. P. model remain in agreement with the observed behaviour of threshold voltage and cut-ofF frequency.
2) .If the Helfrich parameter is smaller than one, the bend fluctuations can no longer be amplified, and the observed periodic distortion of the director is due to the destabilization of twist fluctuations which can occur for a, larger than o,, and a, positive.
Acknowledgments. - We want to particularly thank Dr. F. RondeIez who is at the origin of this work and Dr. A. Rapini for fruitful discussions. We are indebted to M. Courdille for technical assistance.
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