We observe and study the reflection and interference in the two-layer thin film composed of a conductive
layer of ITO and dispersed particles of magnetic fluid (magnetite). In an electric field the equivalent
thickness of the membrane is increased by varying the thickness of the second layer. At a certain value of
the electric field the layer becomes unstable, its thickness varies periodically, autowave process leading to
the characteristic active centers (pacemakers), spiral waves (reverberators) was observed

Chekanov, V.S.

Chekanov, V.V.

Kandaurova, N.V.

English

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 7 No 4, 04041(3pp) (2015) Том 7 № 4, 04041(3cc) (2015) 
 
 
2077-6772/2015/7(4)04041(3) 04041-1  2015 Sumy State University 
Calculation of the Membrane Thickness of Magnetite Nanoparticles on the Surface of the 
Transparent Conductive Electrode in the Electric Field 
 
V.V. Chekanov, N.V. Kandaurova*, V.S. Chekanov† 
 
North Caucasus Federal University 2, Kulakova Prosp., 355029 Stavropol, Russia 
 
(Received 29 September 2015; published online 10 December 2015) 
 
We observe and study the reflection and interference in the two-layer thin film composed of a conduc-
tive layer of ITO and dispersed particles of magnetic fluid (magnetite). In an electric field the equivalent 
thickness of the membrane is increased by varying the thickness of the second layer. At a certain value of 
the electric field the layer becomes unstable, its thickness varies periodically, autowave process leading to 
the characteristic active centers (pacemakers), spiral waves (reverberators) was observed. 
 
Keywords: Magnetic fluid, Electroreflection, Thin membrane, Reflectance, Reflected light intensity,  
Instability, Autowaves. 
 
 PACS numbers: 75.50.Mm, 79.60.Jv 
 
 
                                                          
* candaur18@yandex.ru 
† oranjejam@mail.ru 
1. INTRODUCTION 
 
In this paper we investigate the optical properties of 
a thin membrane consisting of a transparent indium-
titanium coating (ITO) and a concentrated layer of solid 
particles of magnetic fluid – packed magnetite nano-
particles. 
Magnetic fluid (MF) is a stable single-domain fer-
romagnetic colloidal particles (magnetite), dispersed in 
various liquids (kerosene, water and others) [1]. As a 
stabilizer for preventing coagulation of the colloidal 
solution we used surfactants, which are adsorbed on 
the surface of the solid particles to form a protective 
coating. In this paper was used for the experiments 
ferrofluid type «magnetite in kerosene» oleic acid (mo-
lecular length of ~ 1.5 nm) as the surfactant. In the 
absence of an electric field, the magnetic fluid is uni-
form, but when the field is on, the particles of the solid 
phase under the effect of the MF electrophoresis and 
dypolophoresis start to migrate to the electrodes, and 
the thin membrane of the solid particles of the magnet-
ic fluid forms on the electrode surface. The approximate 
time of formation of the film is from 0.2 s. to 1 s., de-
pending on the applied electric field, the thickness is 
from 10 to 100 nm. Reflection from the surface of the 
film and variety of the reflection parameters in an elec-
tric field, including interference at the border with the 
electrode has been studied previously in [2-4]. Ability to 
control the thickness of two-layer thin film «magnetite 
nanoparticles – ITO» with the help of an external elec-
tric field and the possible practical applications of this 
phenomenon [5] determines the relevance of research 
carried out in this paper. 
 
2. THE EXPERIMENTAL DEVICE AND METH-
ODS OF THE EXPERIMENT 
 
The device for monitoring changes in the intensity of 
the reflected light in the electric field is a cell (Fig. 1), 
consisting of two electrodes, one of which – a transparent 
conductive glass coated ITO (Manufacturer – SPC «Poly-
tech», St. Petersburg). In order to eliminate glare from 
the surface of the cell it is installed on a glass prism. 
Optical contact with the glass side of the prism made 
immersion liquid (epoxy resin without plasticizer 
n  1,523). With a scanning probe microscope Integra 
Prima been found that the surface layer of ITO is rough. 
 
 
 
Fig. 1 – Experimental device for observing changes in the 
intensity of the reflected light. 1 – magnetic fluid; 2 – plate 
Micarta foil; 3, 16 Isolate pads made of polystyrene; 4 – glass 
coated with a conductive transparent ITO; 5 – angled isosceles 
prism; 6, 11 – aperture; 7, 10, 13, 15 – Polaroids; 8, 9 – photo-
diodes; 12, 14 – laser pointers; 17 – electrodes; Θ1, Θ2 – angles 
of incidence 
 
We measured the roughness parameter Ra – arith-
metic mean of the absolute values of the roughness at 
the «glass-to-air» – is 2 nm, and on the border «ITO-air» 
is 10-12 nm. Optical parameters of the ITO-film was 
measured by spectroscopic ellipsometer SE 800 
SENTECH ten points at a distance of 5 mm from each 
other at the wavelength   650 nm. The average re-
fractive index was equal to 1,78 ± 0,05, the absorption 
coefficient is 0,08 ± 0,02 at a coating thickness of 
200 ± 10 nm. 
 V.V. CHEKANOV, N.V. KANDAUROVA, V.S. CHEKANOV J. NANO- ELECTRON. PHYS. 7, 04041 (2015) 
 
 
04041-2 
Between the electrodes there is a magnetic fluid 
(MF). The experiments used magnetic fluid type «mag-
netite in kerosene». Bulk solids concentration was cal-
culated from the density of the magnetic fluid. For MF 
density   930 kg/m3 the concentration of the solid 
phase was about 3.2 %. The refractive index of MF in 
the amount of cell n3  1,47 refractive index MF concen-
tration of 27 % (near-electrode layer) n2  1,78 ± 0,05, 
the absorption coefficient – 0.07. 
On the face of the prism (Fig. 1) fall rays from a 
2 mm diameter laser pointers (  650 nm) with angles 
α1 and α2, so that the angles of incidence on the surface 
of ITO are 30 and 45 degrees (Fig. 2). The rays are re-
flected from the surface of the «glass film ITO» and 
«film ITO – magnetic fluid» and interfere. Reflect rays 
enter through the diaphragm – 6, 11 and Polaroids – 7, 
10 in the photodiodes PD-256. The photodiodes are 
connected to the input of a two-beam oscilloscope GDS-
71022. The rays reflected from the boundaries of the 
«prism-glass» and from the layer «ITO – magnetic fluid» 
spatially separated ~ 4 mm. In order to avoid stray light 
photodiodes front polarizers 7 and 10 diaphragms about 
1 mm were placed. Lasers and polaroids can rotate rela-
tive to the rays. The plane of polarization of the polariz-
ers 13 and 14 coincides with the plane of polarization of 
the laser beams. Polaroids serve to reduce the depolar-
ized component of laser light. Turning lasers polaroids 
we make the s-component (TE-wave) perpendicular to 
the plane of incidence. Turning polaroids 7, 10 we weak-
en light to photodiodes operated in the linear mode. The 
surface area of the electrodes S  36  30 mm2, the layer 
thickness l MF – 250 microns. 
 
 
 
 a 
 
 
 
 b 
 
Fig. 2 – Waveform of voltage time changes on photodiodes (a), 
type of voltage applied to the electrodes of the cell with a 
magnetic fluid (b) 
 
On the electrode is applied slowly varying voltage of 
0-20 V – (Fig. 2b). Voltage change period – 9.8 seconds. 
Curve 1 – change in reflectance R on the surface of 
«ITO – a layer of solid particles of magnetic fluid» in 
the fall of the laser beam at an angle of 30 degrees, 
curve 2-45 degrees. In the early period of zero voltage 
(the points A and B on the curve 1 and 2) fixed to the 
optical response. Then, with the increase in voltage, the 
reflectance decreases (portion on the curve AC 1 and 
BD portion of the curve 2) to a minimum, which is typi-
cal for interference in thin films. 
Measurements of spectroscopic ellipsometer SE 800 
SENTECH showed that the values of the refractive indi-
ces of ITO-coating and concentrated particle layer MF are 
close in value, and therefore can be considered as ITO 
layer and concentrated MFs optically equivalent to the 
incident light wave. With the increase of the electric field 
an increase in the thickness of the layer of optically equiv-
alent «particle MF + layer ITO» can be stated. 
Please note that in the ITO-coating a transition lay-
er whose properties, including refractive index change 
(1.8-1.7 – data SE 800 SENTECH). Roughness is com-
parable with the size of «trapped» MF particle layer 
(layer thickness about 200 nm and an average particle 
diameter of 10 nm). Speaking of optically equivalent to 
the total thickness of the layer (ITO + MF particles), we 
mean a layer of flat geometric borders and the average 
refractive index. 
 
3. DISCUSSION OF THE RESULTS 
 
We calculate the dependence of R on the thickness 
of the two-layer film «ITO + layer concentrated MF» at 
angles of incidence of 30 ° and 45 ° for the s-
components by the method described in [6]. 
The scheme of multilayer structure with two 
boundaries is shown in Fig. 3. The first medium – glass 
with a refractive index n1  1,52, medium 2 – two-layer 
film «ITO – concentrated MF» variable thickness h0 of 
no electric field to h  Δh + h0 in electrical field having 
a refractive index n2  1.78 ± 0.05. Third environment – 
magnetic fluid with a refractive index n3  1,45 (with-
out taking into account the absorption coefficient). 
Voltage proportional to the intensity of the oscillo-
scope reflected from the surface of the beam which 
strikes the photo diodes 8 and 9, is equal to U1 (V), 
where V  V (t) – the voltage applied to the electrodes 
17 (curve b in Fig. 2). 
 
 
Fig. 3 – The circuit of the multilayer structure with two 
boundaries 
 
Since the photodiode operates in the linear mode, 
the voltage on the oscilloscope is directly proportional 
to the intensity of reflected rays. It was possible to cal-
culate the index and film thickness on the intensity of 
the reflected beams at different angles of incidence as 
described in [4]. 
 CALCULATION OF THE MEMBRANE THICKNESS…  J. NANO- ELECTRON. PHYS. 7, 04041 (2015) 
 
 
04041-3 
 
 
a 
 
 
 
b 
 
Fig. 4 – Autowaves with characteristic leading centers (pace-
makers) (a). Spiral waves (reverb) (b) 
 
After calculations, we obtained the following values: 
film thickness h  h0 + Δh at the maximum value of the 
electric field above which the instability surface ap-
proximates 200 + 300  100 nm, the refractive index of 
the two-layer film n2  1,78, which meaning is close to 
the refractive index of the ITO. 
By adjusting the value supplied to the electrodes of 
the electric field, it is possible to control the thickness 
«adhering» to the electrode layer of the solid particles. 
Given the equality of the refractive index and absorp-
tion of the ITO layer of the particles of the magnetic 
fluid, we get electrically increase in optical thickness 
bilayer film «ITO-magnetite nanoparticles». 
With further increase in voltage observed fluctua-
tions in the intensity of the reflected light. Apparently, 
a layer of solid particles of the magnetic fluid becomes 
unstable; its thickness varies periodically, as shown by 
the oscillograms of the voltage on reaching ~ 15 V. Re-
placing a source of visible laser light in the experi-
mental device (Fig. 1) at a certain critical value of the 
voltage with typical autowave leading centers – pace-
makers, spiral waves – reverberators were observed 
(Fig. 4). A thin layer of the magnetic fluid in the elec-
tric field represents a unique active environment, 
where in the in laboratory conditions we can investi-
gate and easily reproduce the autowave process. Its 
uniqueness lies in the fact that commonly autowave 
processes are difficult to reproduce (population dynam-
ics), or too short-lived, or proceed with a limited num-
ber of repeats (Belousov-Zhabotinsky reaction). 
 
4. СONCLUSIONS 
 
We have investigated the optical properties of a thin 
membrane composed of a conductive coating (Indium 
tin oxide – ITO) and a layer of densely packed particles 
of magnetite. It was found that the refractive index of 
the conductive coating (ITO) layer and the magnetite 
particles are close in value, so the thin film bilayer 
«ITO - magnetite particles» can be regarded as an opti-
cally homogenous to incident light. An increase in the 
thickness of the two-layer membrane depending on the 
applied electric field. Membrane thickness h was calcu-
lated. Given equality of the refractive indices of layers 
of thin membrane, it is shown that the magnitude of h 
may be controlled by varying the electric field. 
 
 
REFERENCES 
 
1. V.E. Fertman, Magnetic Fluids: A Reference Guide (Minsk: 
High school: 1988). 
2. V.V. Chekanov, A.A. Butenko, Y.L. Larionov, L.V. Nikitin, 
A.A. Tulinov, Bull. Russ. Academy Sci.: Phys. 55 No 6, 
1141 (1999). 
3. V.V. Chekanov, N.V. Kandaurova, V.S. Chekanov, Tech. 
Phys. 59 No 9, 1286 (2014). 
4. V.V. Chekanov, N.V. Kandaurova, V.S. Chekanov, 
V.V. Romantcev, J. Opt. Technol. 82 No 1, 43 (2015). 
5. V.V. Chekanov, N.V. Kandaurova, Yu.A. Rachmanina, 
V.S. Chekanov, Pat. 2449382, Russian Federation, IPC 
G09F 9/30 G02F 1/167, publ. 27.04.2012 bull. №12. 
6. M. Born, E. Wolf. Principles of Optics (M.: Nauka: 1973). 
 


Calculation of the Membrane Thickness of Magnetite Nanoparticles on the Surface of the Transparent Conductive Electrode in the Electric Field

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Calculation of the Membrane Thickness of Magnetite Nanoparticles on the Surface of the Transparent Conductive Electrode in the Electric Field

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