Turbulence to turbulence transition in homeotropically aligned nematic liquid crystals
D. E. Lucchetta, N. Scaramuzza, G. Strangi, and C. Versace*
Dipartimento di Fisica dell’Universita ` della Calabria and Istituto Nazionale per la Fisica della Materia, I-87036 Rende, Cosenza, Italy
Received 22 January 1999
In this paper, a study of the electrically driven turbulent-turbulent transition in a homeotropically oriented
nematic sample is reported. The transition has the characteristics of a nucleation process, and its threshold has
been experimentally determined. The nucleation rate and the growth velocity of the new turbulent nuclei are
also reported. S1063-651X9905807-9
PACS numbers: 61.30.-v
INTRODUCTION
The transition between two different turbulent regimes is
not a very common phenomenon in nature 1. Among the
best known systems are the turbulent-turbulent transition in
superfluid helium 2 and the dynamic scattering mode1–
dynamic scattering mode 2 DSM1-DSM2 transition in
nematic liquid crystals NLC under a planar anchoring con-
dition 3. Lately the transition between turbulent states
driven by an external voltage has also been observed in a
homeotropic aligned nematic liquid crystal sample 4.
In the last few years, electrodynamic instabilities in ho-
meotropically oriented layers of negative dielectric anisot-
ropy nematics have attracted the interest of a discrete number
of authors 5–9; in fact, although the homeotropic orienta-
tion shows a less rich scenario it differs dramatically from
the planar case. The electroconvective rolls occur as a sec-
ondary instability after the Fre
´
edericksz one 10. Further-
more, because at the Fre
´
edericksz transition the nematic di-
rector spontaneously chooses a bend direction, a spontaneous
breaking of the isotropic symmetry occurs, which makes
possible a direct transition to the spatial chaos 8,11.
From a strictly phenomenological point of view, when a
low frequency electric voltage is applied to a homeotropic
sample of NLC with a negative dielectric anisotropy and
positive conductive anisotropy, above a certain voltage
threshold, the well-known Fre
´
edericksz transition is ob-
served. At a higher value of the applied voltage, it is possible
to observe several structures constituted by extremely com-
plex and irregular patterns that are quite different from those
observed in a planar sample of the same liquid crystal mate-
rial. In spite of this, even in this case it is easy to observe the
transition between turbulent states. These two turbulent
states are optically similar to DSM1 and DSM2 regimes
found in the planar case so, for simplicity, we keep the same
notation to refer to them.
EXPERIMENTS AND RESULTS
The sample cell consisted of two parallel square ( L 30
30 mm
2
) glass plates spaced by two Mylar strips ( d
36 m). The cell surfaces were coated with transparent
electrodes of indium tin oxide ITO and, in order to obtain
homeotropic alignment, were treated by the surfactant
N , N - dimethyl- N - 3- trimethoxysilylpropyl-1-octadecana
minium chloride DMOAP. Then the cells were filled by
capillary action with the nematic liquid crystal
N -( p -methoxybenzilidene)- p - n -butylaniline MBBA, and
mounted in a thermally insulated oven, the temperature of
which could be kept at 24 °C by a HAAKE F3 water bath
thermostat. Finally, an ac voltage has been applied across the
cell z direction. The experimental procedure consisted of
two steps: a to measure the threshold voltage for the
DSM1-DSM2 transition by the experimental setup shown in
Fig. 1; and b to observe by means of an optical microscope
the nucleation of the DSM2 areas, record their growth on
videotape, and subsequently to calculate the nucleation rate
and the growth velocity from the recorded images.
The experiment was performed at the fixed ac voltage
frequency of 70 Hz, but the results do not change qualita-
tively if the frequency is varied in the conductive regime of
the nematic material 10.
In order to check the existence of a threshold voltage for
the DSM1-DSM2 transition, V
0
was swept with various rates
r mV/s in the neighborhood of the DSM1-DSM2 transition.
In Fig. 2 the voltage dependence of the light transmittance is
shown as a function of both increasing and decreasing ap-
plied voltage.
On increasing the voltage, the light transmittance has a
sudden change in the slope at the voltage V
J
. Above V
J
the
DSM2 nuclei rise and grow spontaneously and a greater and
greater amount of light is scattered out from the transmitted
beam in the homeotropic case we did not observe the strong
dependence on the polarization of the incident light which
has been found for the planar case. The voltage V
J
de-
creases as r increases; therefore, we can consider it as an
*Author to whom correspondence should be addressed.
FIG. 1. The experimental setup. L, He-Ne laser; PH, pinhole;
BS, beam splitter; PD, photodiode; PAM, photoacoustic modulator;
L, lens; S, NLC sample; O, oven, A, amplifier; WG, wave form
generator; LA, lock-in amplifier; PC, personal computer.
PHYSICAL REVIEW E JULY 1999 VOLUME 60, NUMBER 1
PRE 60 1063-651X/99/601/6103/$15.00 610 ©1999 The American Physical Society