Instabilities Across the Isotropic Conductivity Point in a Nematic Phenyl Benzoate under
AC Driving
Pramoda Kumar,
†
Shivaram N. Patil,
‡
Uma S. Hiremath,
†
and K. S. Krishnamurthy*
,†
Centre for Liquid Crystal Research, P. O. Box 1329, Jalahalli, Bangalore 560 013, India, and Garden City
College, Virgonagar Post, Bangalore 560 049, India
ReceiVed: April 5, 2007; In Final Form: May 14, 2007
We characterize the sequence of bifurcations generated by ac fields in a nematic layer held between
unidirectionally rubbed ITO electrodes. The material, which possesses a negative dielectric anisotropy ǫ
a
and
an inversion temperature for electrical conductivity anisotropy σ
a
, exhibits a monostable tilted alignment
near T
IN
, the isotropic-nematic point. On cooling, an anchoring transition to the homeotropic configuration
occurs close to the underlying smectic phase. The field experiments are performed for (i) negative σ
a
and
homeotropic alignment, and (ii) weakly positive σ
a
and nearly homeotropic alignment. Under ac driving, the
Freedericksz transition is followed by bifurcation into various patterned states. Among them are the striped
states that seem to belong to the dielectric regime and localized hybrid instabilities. Very significantly, the
patterned instabilities are not excited by dc fields, indicating their possible gradient flexoelectric origin. The
Carr-Helfrich mechanism-based theories that take account of flexoelectric terms can explain the observed
electroconvective effects only in part.
Introduction
The response of a nematic fluid to an external electric field
is determined by several factors relating to material and field
parameters, and the sample configuration. Much of the vast
literature devoted to electrically driven instabilities in nematics
dwells on one or the other of two different phenomena: First,
purely orientational equilibrium effects such as caused by
dielectric anisotropy, flexoelectric polarization and surface
polarization; second, nonequilibrium dissipative effects, as found
in the vortical flows attributable to anisotropic electrical
conduction, charge injection at the electrodes or surface charge
inhomogeneity.
1-4
Situations involving interplay of different
bifurcation mechanisms are of particular relevance to nonlinear
science and, in recent years, a few significant studies have been
conducted in this area. For instance, Delev et al.
5
have reported
their experimental and theoretical results concerning the cross-
over between flexoelectric and electroconvective distortions
occurring in a homeoplanar nematic subject to a dc field.
Similarly, Dressel et al.
6
have demonstrated the coupling of
homogeneous and vortex modes to generate the so-called splay
and twist normal rolls. More recently, Dressel and Pesch
7
have
reported their rigorous theoretical analysis of the competition
between electroconvection (EC) and the Freedericksz effect
(FE), and we have discussed the experimental results relating
to this competition.
8
In this paper, we report mainly on some
hybrid electroconvective instabilities arising within the Freed-
ericksz distorted state of a nematic.
Nematic EC due to anisotropic material parameters is
principally governed by ǫ
a
) (ǫ
|
- ǫ
⊥
) and σ
a
) (σ
|
- σ
⊥
), |
and ⊥ denoting the directions relative to the nematic director
n. Nematics with negative ǫ
a
, positive σ
a
, and planar alignment
p, conveniently referred to as (-+ p) compounds, taken
between ITO-coated glass plates and driven by a field along
the substrate normal, are established as the ideal candidates to
exhibit a well ordered sequence of hydrodynamic instabilities,
starting with periodic rolls at a threshold voltage and developing
into chaotic flows far from equilibrium.
9
These classic instabili-
ties are understood essentially on the basis of the so-called
Carr-Helfrich (CH) mechanism that addresses, for the applied
dc field, the coupling between σ
a
and the bend curvature
distortion leading to periodic space charges of alternating sign
along the initial director. The body force due to these charges
sets up periodic cellular flows above a voltage threshold V
c
,
which, in turn, is determined by the balance between the
destabilizing hydrodynamic and transverse-field torques, and
the stabilizing dielectric and elastic torques. The corresponding
one-dimensional (1-D) analysis for an ac field of frequency ω
predicts
10
the instability threshold field E
c
(ω) to be
where k
33
denotes the bend elastic constant, λ the period of
stripes, τ the charge relaxation time, and
2
the Helfrich
parameter; R
2
and η
1
are the Leslie and Miesowicz viscosity
coefficients, respectively. The cutoff frequency ω
c
) (
2
-
1)/τ defines the limit of the conduction regime within which
the space charges oscillate at the field frequency while the
director pattern is static. Beyond ω
c
, in the dielectric regime,
the space charges are static, but the director oscillates. The
occurrence of instability in either regime requires (
2
- 1) to
be positive.
Goscianski and Leger
11
were perhaps the first to consider
the effect of varying (
2
- 1) between positive and negative
values via temperature dependent σ
a
in nematics with an
* Corresponding author. E-mail: murthyksk@gmail.com.
†
Centre for Liquid Crystal Research.
‡
Garden City College.
E
c
2
(ω) )
ǫ
|
k
33
λ
2
(1 + ω
2
τ
2
)
ǫ
o
ǫ
a
ǫ
⊥
(1 + ω
2
τ
2
-
2
)
;
2
)
(
1 -
σ
⊥
ǫ
|
σ
|
ǫ
⊥
29 (
1 +
ǫ
|
ǫ
a
R
2
η
1
29
; τ )
ǫ
o
ǫ
||
σ
|
(1)
8792 J. Phys. Chem. B 2007, 111, 8792-8800
10.1021/jp072686o CCC: $37.00 © 2007 American Chemical Society
Published on Web 07/06/2007