DEPENDENCE OF ROLL FREQUENCY ON DRIVING

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DEPENDENCE OF ROLL FREQUENCY ON DRIVING
FREQUENCY IN NEMATIC LIQUID CRYSTAL MIXTURE  G.
Acharya, J.T. Gleeson  Department of Physics,
Kent State University, Kent, OH 44242 USA
GRC ON LIQUID CRYSTALS 2005
  ABSTRACT We report on the
variation in frequency of traveling rolls with
the variation of driving frequency on
electroconvection of Nematic liquid crystal
mixture driven by ac voltage at given
temperature. The frequency of rolls are found to
be zero at low voltage and driving frequency and
increase with the increase of voltage and
corresponding frequency at given temperature.
However, at higher frequency,instead of normal
traveling rolls,we observed aperiodic oblique
traveling rolls. The driving frequency at onset
was found to be smaller at lower temperature than
that at higher temperature.Also,we did not
observe the traveling rolls when dc was applied
on the sample cell.  
By using Fast Fourier transform(FFT),the
frequency of NT rolls were calculated at
different driving frequency at 60oC. Finally,
graphs of NT roll frequencies were plotted
against the driving frequency(fig.6) The
frequency of rolls were found to be increased
with temperature at fixed onset voltage and
variable driving frequency.
INTRODUCTION Nematic Liquid
Crystal (NLC) molecules have common orientational
order but do not have positional order. As a
result, only diffuse scattering occurs in the
x-ray diffraction pattern. The correlation length
? ? ?-.As compared to isotropic fluids, a
nematic is described by an additional director
field n (nx,ny,nz), n2 1 and n and -n are
indistinguishable. Nematic phase occurs only to
those materials which are achiral' or
racemic1.On heating, some of the
thermodynamic properties like specific heat,
coefficient of thermal expansion and coefficient
of isothermal compression increase rapidly when
the temperature approaches to Nematic-Isotropic(N-
I) point TNI2.At TNI there will be complete
breakdown of orientational order and a weak first
order phase transition takes place .To occur
EHC,the NLC must be doped with ionic impurities
and also the anisotropy in the dielectric
constant ?a ? - ?- must be negative or only
slightly positive3. When ac is applied, in the
conduction regime charge relaxation is faster
than the ac frequency. The sign of the director
deflection remains same, but the charge density
alters its sign with the applied ac. In the
dielectric regime, the director deflection alters
its sign with the applied ac field, but the sign
of charge density remains same4.   When we
increase the ac voltage, beyond certain critical
value Vc, spatiotemporal structures form which
include oblique stationary(fig.1), normal
stationary(fig.2), normal traveling and oblique
traveling rolls. In case of planar arrangement,
if p and q be the components of wave vector
parallel and perpendicular to the director, the
states with q 0 are normal rolls and the states
with q ? 0 are oblique rolls.A point of critical
driving frequency where the system goes from q
0 to q ? 0 is the Lifshitz point. Since the
sample is chemically stable, almost all of the
material properties are known and it is easily
obtained, MV is a suitable material for
EHC5.      
Figure 5 Intensity of single piexl vs time .  
Also, we studied the variation of DC threshold
with temperature (fig.7)for the cell MV 2.7
dopant. No traveling rolls were observed. We had
used 3 cells having roughly area of conducting
cell as 5 by 5 mm2 .
Figure 2 Normal Stationary Rolls taken on a
24.22 µm cell at 60oC,9.85V and 150 Hz. The
rubbing direction is aligned in the vertical
direction of this picture.
 n(O)-Om (CnH2n1)-(O)- -COO
-O-CmH2m1) 4-hexyloxyphenyl-4'-methoxybenzoate
22.0 4-octaphenyl-4'-pentyloxybenzoate
30.3 4-heptyloxyphenyl-4'-hexylobenzoate
13.3 4-butyloxyphenyl-4'-hexylbenzoate
34.4
To control the electrical conductivity, dopant
(mixture of equal weight of p-heptylbenzoic acid
and octyloxyphenol) (3wt) was added to the
sample.The Conductivity varies slightly for
individualal cell7.Difference in conductivity
between individual cell may cause to the
variation of respective threshold4.We observed
temperature dependence of both C- and G- on the
temperature of filled cell (fig.3)
Figure 6 Frequency of Traveling Rolls vs
Driving Frequency in the 23.39 µm sample cell
at 60oC.
F(Hz)
Figure 3 Variation of C- and G- with temperature
in the 24.22 µm sample cell.  
The sample was kept in hot stage FP 82 on the
microscope. The sample showed a Nematic-Isotropic
phase transition at 63oC. A CCD camera was
mounted on the microscope at about 30 cm from the
sample to cast the image on the TV screen and
various image were captured with the help of
snap program. At different driving frequency,ac
voltage at onset were recorded at 600C and
plotted which followed the equation V2(f)
V02/(1- f2/fc2) (fig.4)
Figure 7 Threshold Vdc vs Temperature in the
24.97 µm sample cell .  
CONCLUSION The frequency of
NT rolls at higher frequencies increase with
increase of driving frequency which will apply
only for the liquid crystal sample having
traveling rolls. For normal stationary rolls, the
frequency are zero(the width of the roll roughly
equal to the cell gap) for smaller driving
frequency and increases slowly with increase of
driving frequency(Wavelength of rolls decrease).
The driving frequency at onset was found to be
smaller at lower temperature than that at higher
temperature.   With dc supply, we did not report
the traveling rolls. Instead, we fund the
decrease of onset voltage with increase of
temperature
REFERENCES 1                 P.G.De
Gennes and J.Prost, The physics of liquid
Crystals, Clarendon Press,Oxford(1993). 2        
         S.Chandrashakhar,Liquid
Crystals,Cambridge University Press(1992) 3       
          M.Dannin,Ph.D.thesis,University of
California at Santa Barbara(1995) 4               
  T.John,U.Behn and R. Stannarius,Phys. Rev. E 65
046229 (2002). 5                
J.Shi,C.Wang,V.Surendenatha,K.Kang,J.T.
Gleeson,Liq. Crys. 29,887 (2002). 6               
  E.H.C. Co Tokyo,Japan 7                 T.John
and R. Stannarius,Phys. Rev 70,025202(R) (2004).
Figure 1 Oblique Stationary Rolls taken on a
24.22 µm cell at 60oC,6.22V and 150 Hz. The
rubbing direction is aligned in the vertical
direction of this picture.  
Figure 4 Threshold Voltage vs Driving Frequency
in the 24.22 µm sample cell at different
temperature.


EXPERIMENTAL The experiment was
performed on a mixture of Phenyl Benzoate
derivatives called Mischung V(MV) sandwiched in
the sample cell.The sample had a Nematic range
from below room temperature to 630C.The sample
cell consists of ITO coated Borosilicate. The
electrodes have been treated to induce planar
alignment. Electrical contact between the plates
and the wire were made by using silver epoxy.
The cutoff frequency, Fc(below which the regime
is conductive and above which it is
dielectric)increases with temperature as well as
with conductivity of the sample   By increasing
the driving frequency and simultaneously the
applied voltage, normal stationary(NS) and normal
traveling(NT) rolls were casted on the screen.
Finally central single pixel was recorded at
different time interval.At higher frequency,
instead of NT rolls,we observed oblique
traveling(OT) rolls which were aperoidic.
The space between the electrodes was measured by
using spectrometer and the capacitance(C-) and
conductance(G-) of the cell by using
capbridge.   MV is a four component mixture of
following compounds