Adsorption of ions and thickness dependence of conductivity in liquid crystals
It is experimentally shown that, at thicknesses less than 100 μm, conductivity of planar oriented liquid crystals is a function of the thickness. The main reason for this effect is adsorption of ions on the surface of electrodes. The relation for estimation of changes in the conductivity has been...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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| Zitieren: | Adsorption of ions and thickness dependence of conductivity in liquid crystals / O.V. Kovalchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 4. — С. 452-455. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1177982017-05-27T03:04:56Z Adsorption of ions and thickness dependence of conductivity in liquid crystals Kovalchuk, O.V. It is experimentally shown that, at thicknesses less than 100 μm, conductivity of planar oriented liquid crystals is a function of the thickness. The main reason for this effect is adsorption of ions on the surface of electrodes. The relation for estimation of changes in the conductivity has been theoretically obtained, and the value of the characteristic length for distribution of ions in a near-electrode area has been estimated. 2011 Article Adsorption of ions and thickness dependence of conductivity in liquid crystals / O.V. Kovalchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 4. — С. 452-455. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS 61.30.Gd, St; 68.43.-h http://dspace.nbuv.gov.ua/handle/123456789/117798 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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It is experimentally shown that, at thicknesses less than 100 μm, conductivity
of planar oriented liquid crystals is a function of the thickness. The main reason for this
effect is adsorption of ions on the surface of electrodes. The relation for estimation of
changes in the conductivity has been theoretically obtained, and the value of the
characteristic length for distribution of ions in a near-electrode area has been estimated. |
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Article |
| author |
Kovalchuk, O.V. |
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Kovalchuk, O.V. Adsorption of ions and thickness dependence of conductivity in liquid crystals Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kovalchuk, O.V. |
| author_sort |
Kovalchuk, O.V. |
| title |
Adsorption of ions and thickness dependence of conductivity in liquid crystals |
| title_short |
Adsorption of ions and thickness dependence of conductivity in liquid crystals |
| title_full |
Adsorption of ions and thickness dependence of conductivity in liquid crystals |
| title_fullStr |
Adsorption of ions and thickness dependence of conductivity in liquid crystals |
| title_full_unstemmed |
Adsorption of ions and thickness dependence of conductivity in liquid crystals |
| title_sort |
adsorption of ions and thickness dependence of conductivity in liquid crystals |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2011 |
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http://dspace.nbuv.gov.ua/handle/123456789/117798 |
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Adsorption of ions and thickness dependence of conductivity in liquid crystals / O.V. Kovalchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 4. — С. 452-455. — Бібліогр.: 8 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT kovalchukov adsorptionofionsandthicknessdependenceofconductivityinliquidcrystals |
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2025-07-08T12:48:58Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 452-455.
PACS 61.30.Gd, St; 68.43.-h
Adsorption of ions and thickness dependence
of conductivity in liquid crystals
O.V. Kovalchuk
Institute of Physics, NAS of Ukraine, 46, prospect Nauky, 03028 Kyiv, Ukraine;
Kyiv National University of Technologies and Design, 2, Nemirovich-Danchenko str., 01011 Kyiv, Ukraine
E-mail: akoval@iop.kiev.ua
Abstract. It is experimentally shown that, at thicknesses less than 100 μm, conductivity
of planar oriented liquid crystals is a function of the thickness. The main reason for this
effect is adsorption of ions on the surface of electrodes. The relation for estimation of
changes in the conductivity has been theoretically obtained, and the value of the
characteristic length for distribution of ions in a near-electrode area has been estimated.
Keywords: conductivity, planar oriented liquid crystal, adsorption of ions.
Manuscript received 11.07.11; revised manuscript received 30.08.11; accepted for
publication 14.09.11; published online 30.11.11.
1. Introduction
The value of conductivity σ is an important parameter
that should be known when determining suitability of
liquid crystals (LC) for scientific or practical needs.
Therefore, it is important to establish conditions under
which the σ value of LC is measured. In prospectuses of
LC manufacturers, presented in most cases is the value
of alternating current frequency (usually it is 1 kHz), at
which the conductivity is measured. There are not any
standards for the thickness of cells.
Since real measurements of the σ value in liquid
crystals are performed in cells of certain thickness, it is
important to know whether the cell thickness influences
(and how, if there is such influence) on the value of LC
conductivity.
It was shown in [1-3] that, after filling the cell with
liquid crystal, some part of ions is adsorbed on the
electrode surface. So, the total amount of charge carriers
in LC will decrease, which in some way should affect the
value of conductivity. Relative changes in concentration
will be greater the smaller the thickness of the cell.
Therefore, a priori it can be asserted that the value of
change in conductivity should depend on the cell
thickness. Analysis of publications has shown that
detailed studies and theoretical analysis of the
conductivity depending on the thickness of measuring cell
are absent. In a rather long-published paper [4],
considered was a thickness dependence of the
conductivity of homeotropic oriented LC. These obtained
small changes in the conductivity were explained by
anisotropy of the LC conductivity and non-homogeneous
orientation of LC molecules with the cell thickness (tilting
one near the surface and strictly homeotropic in the bulk
sample). A thickness dependence of the conductivity was
obtained in [5] when studying the properties of liotropic
LC. The authors considered injection of charge carriers as
a possible mechanism to explain this effect. But it was
only a hypothesis that was not accompanied by
appropriate models and estimations.
Therefore, the purpose of this work was a detailed
experimental study of the influence of cell thickness on
the value of LC conductivity and theoretical analysis of
these changes taking into account redistribution of the
ion concentration in near-electrode area due to
adsorption of ions.
2. Materials and methods
To measure the conductivity, for these studies we used
standard cells of the sandwich type. Electrodes were
layers of tin oxide transparent in the visible spectral
range. These layers were deposited on glass plates. To
avoid the influence of edge effects, using the etching
procedure each electrode was separated by inner
(measuring) and external (protecting) parts. When
measuring, the protecting electrodes were connected to
each other.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
452
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 452-455.
The thickness of the cell was set by teflon tapes
that were placed on protecting electrodes. Since the cell
thickness was one of the main parameters for the cell, its
value was determined in two ways: the interenferential
one and that based on measurements of cell conductivity
that is not filled with liquid crystal. When measuring the
thickness d by using the interference method, this value
was estimated from place to places over the whole area
of the cell. This enables one not to use a cell of the
wedge shape for these researches.
Filling the cells with liquid crystals occurred due to
forces of surface tension (at small thickness each cell is a
capillary). In this case, when filling cells the LC flow is
directed parallel to the surface, and at a small thickness
independently of orienting surfaces it can create planar
orientation of molecules (immediately after filling the
cell). To eliminate the influence of this effect, studies
were performed with cells in which the orienting
surfaces themselves created the planar orientation of LC
molecules. To create this orienting surface, a thin layer
of polyimide was deposited on the electrode and rubbed
with a cloth of velvet in a certain direction.
For researches, we used three kinds of liquid
crystal mixtures: РКС1282 (НІОПІК, Russia), BL055
(Mark, Germany) and MJ961180 (Mark, Germany). This
made it possible to establish whether the experimentally
obtained dependences of conductivity on the LC
thickness are common to all LCs.
Conductivity determination was based on analyzing
the frequency dependence of the sample resistance. The
value of resistance at various frequencies was
determined by using the oscilloscopic method [6, 7]. The
measuring signal voltage was 0.25 V and was an order
of magnitude lower than the voltage of Fredericks
transition. Therefore, changes in orientation of
molecules with the cell thickness, which can be caused
by electric field of the measuring signal, should not be
taken into account. All measurements were performed at
the temperature 293 K.
3. Results of the experiment
As we have mentioned when formulating the research
problem, when ions are adsorbed on the electrode
surfaces, the conductivity of samples should decrease,
and its changes are the greater the smaller the thickness
of the cell is. In general, it is confirmed by experimental
data of this work. As to compare the results with
theoretical estimations, one should know the relative
change in the conductivity without account of changing
its sign, we analyzed the thickness dependence of the
relative change in the conductivity module ( σσΔ / ).
The value σσΔ / was experimentally found from
the equation
∞
∞
σ
σ−σ
=
σ
σΔ d ,
where σd is the value of conductivity at a given
thickness, σ∞ is the conductivity at an infinite thickness
extrapolated from the experimental data.
Shown in Fig. 1 are the thickness dependences
σσΔ / for РКС1282 (1), BL055 (2), MJ961180 (3). It
is seen that, with increasing the cell thickness, the value
σσΔ / tends to zero. This effect is typical for all the
samples. Our estimations showed that the obtained
changes in the conductivity versus the cell thickness
cannot be explained in the frameworks of the model
proposed in [4]. Therefore, the main factor that defines
the thickness dependence of conductivity was adsorption
of ions on the surface of electrodes. As will be shown
below, this approach made it possible to explain the
presence of the conductivity peak for РКС1282
(curve 1). The presence of this peak cannot be explained
in principle when being based on the work [4].
4. Model and estimation of parameters
Let we have the sample of sandwich type with the
thickness d. Since the electric field is applied
perpendicular to the surface of electrodes, to determine
the dependence ( )d
σ
σΔ
it is important to find the
distribution of charges in this particular direction.
Choose the x axis in this direction and take one of the
electrodes as its origin. To find the charge distribution,
one can use a solution of the Poisson-Boltzmann
equation for symmetric electrolyte [8-10], assuming that
this condition is fulfilled for the LC. Since the sample
thickness is specific, in a general case, one must take
into account possible “overlapping” the distributions of
ions that was formed near each electrode. This effect
may be essential at very small thicknesses and, in
general, can be described only qualitatively.
For quantitative estimations, we will consider the
examples of such thickness, for which the distribution of
ion concentrations near one of the electrodes does not
effect on the distribution of ions near the opposite
electrode. Then, the total distribution of ions with the
thickness of the cell is as follows
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
−+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
AA
S l
xd
l
xnxn expexp)( , (1)
where nS is the surface concentration of adsorbed charge,
lA is the characteristic length that describes distribution
of ions near electrodes.
The total charge of adsorbed ions and ions in the
near-electrode area of the sample equals
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−−== ∫
A
AS
d
s l
dlnSexdxnSeQ exp12)(
0
, (2)
where S is the area of the electrode, e is the charge of
ion.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
453
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 452-455.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
2000 100
0.0
0.1
0.2
0.3
0.4
32
1
IΔ
σI
/σ
d,μm
Fig. 1. The thickness dependence σσΔ / of planar oriented
LC: РКС1282 (1), BL055 (2), MJ961180 (3).
10-1 100 101
0.0
0.2
0.4
0.6
0.8
1.0
IΔσI/σ
d/lA
Fig. 2. Graphical view of the function (4) in the
coordinates d / lA.
Since the total charge of ions in the sample at the
beginning of redistribution is
0SdenQ = (3)
(n0 is the bulk concentration of ions), the relative change
in the conductivity caused by the process of adsorption
of ions takes the form:
.
exp1
2
exp12
0
0
A
AS
A
AS
A
l
d
l
d
n
n
ndSe
l
dlneS
Q
Q
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−−
=
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−−
==
σ
σΔ
(4)
The thickness dependence σσΔ / is expressed by
a function that is in square brackets of the relation (4).
This function is graphically depicted in Fig. 2. As it
follows from this figure, the evident increase in σσΔ /
should be observed when the sample thicknesses lA ≈ 6lA,
and when the thicknesses d ≈ lA the change in σσΔ /
should be quite sharp.
Extrapolation of experimental data based on Eq. (4)
shows that in general these results can be described by
the proposed model. Based on this analysis, estimated is
the value lA for the samples of various types: lA =
6.9 ± 0.6 μm for РКС1282, 3.0 ± 0.3 for BL055, and
6.4 ± 0.4 for MJ961180. As follows from the
estimations, it reaches several micrometers and depends
on the type of liquid crystal. Comparison of the value lA
with the Debay screening length lD shows that it is more
than two orders of magnitude higher than lD.
The model proposed in this paper allows to explain
not only the monotonous increase in the conductivity
with increasing the LC thickness, but presence of the
peak in the thickness dependence of the conductivity in
the samples РКС1282 (Fig. 1, curve 1). In this model,
the amount of ions in the near-electrode area of the
sample is determined by using the distribution function
found on the basis of the balance of diffusion and
migration flows. At rather small thicknesses, these flows
in the near-electrode areas of each electrode will
overlap, which results in equalization of ion
concentrations with the sample thickness and increase of
the influence of the above-described effect of changes in
the conductivity. As up to now these changes can be
described only qualitatively, we will not analyze them in
detail.
5. Conclusions
It is experimentally shown that the conductivity of
planar oriented nematic liquid crystals depends on the
thickness of the cell, and this dependence cannot be
described by changes in orientation of molecules with
the sample thickness. Proposed was the model of this
effect where the main cause of the thickness dependence
of conductivity is the adsorption of ions on electrodes
and associated with this process of redistribution of ions
in the near-electrode area of the sample.
For the sample thicknesses where overlapping the
“tails” of charge distributions near each electrode is yet
absent, considering LC as a symmetric electrolyte we
have obtained the relation for the thickness dependence
of the relative change in conductivity. It is shown that
using this relation one can describe the obtained
experimental results. Estimated was the value of the
characteristic length lA that is included in the function of
distribution of ions in the near-electrode area of the
sample. It has been shown that the value lA reaches
several micrometers and is more than two orders of
magnitude higher than the Debye screening length.
Being based on the proposed model, the maximum
of conductivity observed for РКС1282 at rather small
454
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 452-455.
thicknesses is explained by equalizing the concentration
of ions with the thickness of the sample due to
overlapping the “tails” of charge distributions near each
electrode.
References
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energy: beyond the exponential approximation for
the electric field of ionic origin // Phys. Rev. E, 65,
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2. G. Barbero, L.R. Evangelista, Adsorption
Phenomena and Anchoring Energy in Nematic
Liquid Crystal. Taylor & Francis Group, London,
New York, 2006.
3. A.V. Koval’chuk, Near-electrode adsorption in
isotropic dielectric liquids and liquid crystals: study
method, experimental results, the model //
Functional Materials, 8(3), p. 543-547 (2001)..
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© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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