HAL Id: jpa-00247631
https://hal.archives-ouvertes.fr/jpa-00247631
Submitted on 1 Jan 1992
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Electrostriction dynamics of blue phase II crystallites
H.-S. Kitzerow, P. Crooker, J. Rand, J. Xu, G. Heppke
To cite this version:
H.-S. Kitzerow, P. Crooker, J. Rand, J. Xu, G. Heppke. Electrostriction dynamics of blue phase II crystallites. Journal de Physique II, EDP Sciences, 1992, 2 (3), pp.279-284. �10.1051/jp2:1992132�.
�jpa-00247631�
Classification Physics Abstracts
61.30 77.60 78.20J
Short Communication
Electrostriction dynaInics of blue phase II crystallites
H.-S. Kitzerow(~>*), P-P- Crooker(~), J. Rand(~), J. Xu(~) and G. Heppke(~)
(~) Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, U-S-A-
(~) Hawaii Institute of Geophysics, University of Hawaii, Honolulu, Hawaii 96822, U-S-A- (~) Iwan-N.-Stranski-Institut, Technische Universitit Berlin, Sekr. ER it, Str. des 17. Juni
135, 1000 Berlin 12, Germany
(Received 11 October 1991, accepted 20 December1991)
Abstract. The dynamics of electrostriction occurring in the cubic blue phase BPII is in-
vestigated. We find that the lattice constants relax exponentially and that the time constants
are independent of the electric field strength. Near the BPI-BPII transition temperature, the
time constants increase with increasing sample thickness. For higher temperatures, the time
constants depend strongly on temperature as a result of the temperature-dependent crystallite dimensions. These results are discussed with respect to recent theories.
1 Introduction.
There has been great interest during the last decade in the blue phases BPI, BPII, and BPIII which occur close to the clearing tempiratures of short-pitch cholesteric liquid crystals [I]. One of the most striking properties of the cubic modifications BPI and BPII is the selective reflection of visible light. This Bragg~like scattering is the signature of a chiral cubic director field with
lattice constants of several hundred nm. It is now well known that these selective reflection
wavelengths are shifted under the influence of ac electric fields [2] due to electrostriction [3, 4].
Not until recently, however, have the dynamics of the electrostriction received experimental [5-7] or theoretical attention [7, 8].
Interestingly, the electrostriction time constants in BPI and BPII have been found to be much longer than those associated with field~induced changes of the refractive index occurring
in the swne samples [9]. The electrostriction time constants of BPI and BPII are also long compared to field-induced intensity changes found in BPIII [7]. In BPII, time constants of () Permanent address: Iwan-N.Stranski-Institut, Technische Universit£t Berlin, Sekr. ER it, Str.
des 17. Juni135, 1000 Berlin 12, Germany.
280 JOURNAL DE PHYSIQUE II N°3
the order often seconds are found for electrostriction, whereas the time constants for both the
change of the refractive index in BPII and the intensity increase in BPIII are in the millisecond range.
A phenomenological description of the dynamics of electrostriction in BPI and BPII has been given by Kitzerow et al. [7]. Starting from a diffusion type of differential equation for the lattice strain and assuming that the boundaries of the crystallite lattice are free, it was found that the BPII director lattice constant relaxed exponentially with time constant
r
=yL~/ (4~~K) (I)
Here y is a viscosity, K is an elastic coefficient, and L is the length of the lattice in the direction of the field.
In the experiments of Kitzerow et al. [7], however, the director lattice filled the entire sample
thickness. This condition, in turn, imposes rigid boundary conditions on the blue phase lattice not accounted for by the theory. In order for such a lattice to expand, lattice planes must be removed, a process which involves defect motion and a corresponding complication of the
dynamics. In such a case equation (I) is not expected to strictly hold. To avoid this situation
we have extented our experiments here to BPII crystallites, which, we have found, can be
conveniently grown in the BPIllisotropic two-phase region. These crystallites are smaller than the sample thickness, thereby removing the rigid boundary condition and allowing for an
electrostriction process which enables us to more realistically satisfy equation (I).
We present here measurements on the electrostriction dynamics of the (100) Bragg line of the BPII phase. The electrostriction processes for this line are particularly simple since, unlike the BPI lines, the lattice constant behaves exponentially in time. We find that this time depends
on sample thickness, but is unaffected by electric field strength, in agreement with equation (I). In addition, we present information on the temperature behavior of the response time and conclude that it is dominated by the temperature dependence of the size L of the BPII
crystallites in the BPlllisotropic two-phase region.
2. Experbnent.
The material under investigation consists of 29 il of the chiral dopant 58 II (Merck, Darmstadt, Germany) and 71 $l of thq nematic mixture EN18 (Chisso Corporation, Japan) exhibiting
negative dielectric anisotropy. With increasing temperature, this material shows the phase
sequence N* BPI BPII BPII/ISO ISO. It is also possible to get a BPIII phase with this mixture [6], but by limiting the amount of chiral material, we were able to ensure that only BPII
appeared at the clearing point. Samples with nominal thickness 6.35 pm, 12.7 pm, 24.5 pm and 50 pm were investigated. Depending on the sample thickness, ac voltages f
=I kllz) up
to 150 Vrr~s were applied in order to obtain electric field strengths between 0 and 3 x 10~ V /m.
The experiments consisted of suddenly applying or removing ac voltages from the sample
and recording the resulting selective reflection spectrum as it evolved in time. The measure-
ments were performed with a polarizing microscope, in reflection, with crossed polarizers. A
Princeton ltesearch optical multichannel analyzer (1024 diodes, 700 of which were intensified
by a multichannel plate) was used in order to rapidly measure the selective reflection spectra and store them in a computer. A triple grating monochromator provided a spectral resolution of about 0.08 nm/diode with
a time resolution of 33 ms/spectrum. For measurements involving
long time constants, however, five spectra were averaged to get a better signal /noise ratio.
3. Ilesults.
The time dependence of the central wavelength of the BPII (100) selective reflection line is shown in figure I for both the field-on and field-off cases. For both cases, I(t) is well fit by an exponential relation
I(t)
=lo + Ale~~/~, (2)
where I and I + Al are related to the field-off and field-on lattice constants, respectively.
The field-off and field~on time constants, ro~ and Ton, are identical within our experimental
accuracy.
5z6
524
Field off
j szz
Field
on518
IO 0 IO 20 30 40 50 60
(s)
Fig. I. Time dependence of the BPII <100> selective reflection wavelength. Solid lines are least square fits to equation (2). Err~s
"50 V/25.4 pm f
=lkHz), T
=44.63°C.
It was possible to explore regimes both with and without rigid boundary conditions by varying the sample temperature and hence the size of the BPII crystallites in the BPII /ISO two-
phase region. Figure 2 shows the time constants as a function of sample thickness just above the BPLBPII transition temperature where the BPII lattice fills the sample completely. In this temperature regime, the sample thickness L is also the crystallite size. In this case the boundary
conditions are not free and equation (I) is not expected to hold, however we nevertheless compare it with our results. To within our experimental accuracy, the time constants are
independent of field strength, as predicted by the theory, and they increase with increasing sample thickness. To test the prediction that r cK L~, two data fits are shown in figure 2. The solid line is a fit to r
=
aL"; we find that n
=
1.6 + 0.I. The dashed line is a fit to r
=
aL~
as
predicted by the theory. Thus, for the case of the sample filling the thickness of the cell, the
theory is qualitatively but not quantitatively correct. This result is not surprising, however,
since the experiment did not meet the theoretical requirement of free boundary conditions.
At higher temperature, in the BPII-ISO two-phase region, the BPII crystallites are smaller than the sample thickness and the boundary conditions are free. Here the time constants
decrease by over two orders of magnitude as the temperature is varied from 44.0°C to 45.0°C
through the two-phase region (Fig. 3). In order to explain this behavior, we must consider the temperature dependence of all the quantities in equation (I). Only the viscosity and
crystallite thickness, however, have significant temperature dependence. The viscosity variation
is negligible: taking the viscosity to be proportional [10] to exp(B/T) with B typically StS
282 JOURNAL DE PHYSIQUE II N°3
35
(.lls)L
1e330
~(0.035)L
o 1.18 V/HIn
25
.
1.18 V/»m
o
I-S? V/HIn
zo
mI-S? V/Hm
Q
'a
2?6 V/HIn
°~)
~~
A2?6
lo
, ,
5
0
0 5 10 15 20 25 30
L (»m)
Fig. 2. Time constants versus sample thickness at constant temperature T
=
TBPI-BPII + 0.05 K for samples lvith different thickness L. The solid and dashed fines are least square fits to their respective
functions.
5.000 K, the variation is only a few percent over our 0.5°C temperature range. The size of the
crystallites is, however, strongly temperature dependent; figure 3 also shows L', the crystallite
width observed in the plane of the sample perpendicular to the electric field. Anticipating that the crystallite width L' is equal to the crystallite length L (along the field), we plot r versus L'
on a log~log plot in figure 4 along with a construction line corresponding to the L'~ dependence
of equation (I). In the region 40 pm < L' < 80 pm the L'~ dependence predicted by equation (I) is reasonable, however above 80 pm the fit is quite poor. The larger crystallites occur near
the low-temperature end of the two phase region, however, and it is possible that the width L' of the crystallites ceases to grow at the same rate as the length L. Unfortunately, a direct
measure of L is not possible, so it is not possible for us to resolve the issue.
io~ loo
1
° 80
lo
60
~
10° L'
(s)
~~ (~m)
10~~ o L'
u T
Field on ~°
. T
Field off
10~ 0
44.4 44.6 44.8 45.0 45.2
T (°c)
Fig. 3. Time constants and crystallite ~Nidths versus temperature in the BPILISO two-phase region.
Solid line8 are guides to the eye. Erms
"
50 V/25.4 pm.
io~
l lllll Ill
lo
,
~~ ~~~ ___-~'~~"'~'~
io~
2TO
