Numerical simulation of nanoparticles coagulation in RF-discharge
This paper presents the simulation results of nanoscale dust particles coagulation in capacitive radio-frequency discharge of low pressure in argon. Simulations carried out under the self-consistent kinetic model that takes into account the stochastic nature of the process of dust particles chargi...
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irk-123456789-1154612017-04-06T03:02:39Z Numerical simulation of nanoparticles coagulation in RF-discharge Kravchenko, O.Yu. Yushchyshena, Yu.V. Low temperature plasma and plasma technologies This paper presents the simulation results of nanoscale dust particles coagulation in capacitive radio-frequency discharge of low pressure in argon. Simulations carried out under the self-consistent kinetic model that takes into account the stochastic nature of the process of dust particles charging and their coagulation using general dynamic equations for aerosols. We analyze the distribution of dust particles by size and charge at different distances from the electrodes. It is shown that a significant number of dust particles of opposite charges present in sheaths, which improves the process of their coagulation, compared with the central region inter-electrode gap. It is shown that the presence of dust particles increases the concentration of electrons in the discharge, as well as increases the average electric potential drop in sheaths. Представлены результаты компьютерного моделирования коагуляции наноразмерных пылевых частиц в ёмкостном радиочастотном разряде низкого давления в аргоне. Расчёты проведены в рамках самосогласованной кинетической модели, которая учитывает стохастическую природу процесса зарядки пылевых частиц, а также их коагуляцию при помощи общих динамических уравнений для аэрозолей. Анализируется распределение частиц по заряду и размеру на различных расстояниях от электродов. Показано, что на краях приэлектродных слоёв присутствует значительно большее количество пылевых частиц с противоположными зарядами, в сравнении с центральной областью межэлектродного промежутка, что значительно улучшает процесс их коагуляции. Проанализировано влияние пылевых частиц на параметры разрядной плазмы. Показано, что наличие пылевых частиц приводит к увеличению концентраций электронов в разряде, а также к увеличению скачков усреднённого электрического потенциала на приэлектродных слоях. Представлені результати комп’ютерного моделювання коагуляції нанорозмірних пилових частинок в ємнісному радіочастотному розряді низького тиску в аргоні. Розрахунки проведені в рамках самоузгодженої кінетичної моделі, яка враховує стохастичну природу процесу зарядки пилових частинок, а також їх коагуляцію за допомогою загальних динамічних рівнянь для аерозолів. Аналізується розподіл пилових частинок по заряду та розміру на різних відстанях від електродів, а також вплив пилових частинок на властивості розряду. Показано, що в приелектродних шарах присутні значна кількість пилових частинок протилежних зарядів, в порівнянні з центральною областю міжелектродного проміжку, що значно прискорює процес їх коагуляції. Проаналізовано вплив пилових частинок на параметри розрядної плазми. Показано, що наявність пилових частинок приводить до збільшення концентрацій електронів в розряді, а також до збільшення стрибків усередненого електричного потенціалу на приелектродних шарах. 2016 Article Numerical simulation of nanoparticles coagulation in RF-discharge / O.Yu. Kravchenko, Yu.V. Yushchyshena // Вопросы атомной науки и техники. — 2016. — № 6. — С. 272-275. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.27.Lw http://dspace.nbuv.gov.ua/handle/123456789/115461 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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| language |
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| topic |
Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies |
| spellingShingle |
Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies Kravchenko, O.Yu. Yushchyshena, Yu.V. Numerical simulation of nanoparticles coagulation in RF-discharge Вопросы атомной науки и техники |
| description |
This paper presents the simulation results of nanoscale dust particles coagulation in capacitive radio-frequency
discharge of low pressure in argon. Simulations carried out under the self-consistent kinetic model that takes into
account the stochastic nature of the process of dust particles charging and their coagulation using general dynamic
equations for aerosols. We analyze the distribution of dust particles by size and charge at different distances from
the electrodes. It is shown that a significant number of dust particles of opposite charges present in sheaths, which
improves the process of their coagulation, compared with the central region inter-electrode gap. It is shown that the
presence of dust particles increases the concentration of electrons in the discharge, as well as increases the average
electric potential drop in sheaths. |
| format |
Article |
| author |
Kravchenko, O.Yu. Yushchyshena, Yu.V. |
| author_facet |
Kravchenko, O.Yu. Yushchyshena, Yu.V. |
| author_sort |
Kravchenko, O.Yu. |
| title |
Numerical simulation of nanoparticles coagulation in RF-discharge |
| title_short |
Numerical simulation of nanoparticles coagulation in RF-discharge |
| title_full |
Numerical simulation of nanoparticles coagulation in RF-discharge |
| title_fullStr |
Numerical simulation of nanoparticles coagulation in RF-discharge |
| title_full_unstemmed |
Numerical simulation of nanoparticles coagulation in RF-discharge |
| title_sort |
numerical simulation of nanoparticles coagulation in rf-discharge |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2016 |
| topic_facet |
Low temperature plasma and plasma technologies |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/115461 |
| citation_txt |
Numerical simulation of nanoparticles coagulation in RF-discharge / O.Yu. Kravchenko, Yu.V. Yushchyshena // Вопросы атомной науки и техники. — 2016. — № 6. — С. 272-275. — Бібліогр.: 10 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT kravchenkooyu numericalsimulationofnanoparticlescoagulationinrfdischarge AT yushchyshenayuv numericalsimulationofnanoparticlescoagulationinrfdischarge |
| first_indexed |
2025-07-08T08:49:02Z |
| last_indexed |
2025-07-08T08:49:02Z |
| _version_ |
1837067973007769600 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2016. №6(106)
272 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2016, № 6. Series: Plasma Physics (22), p. 272-275.
NUMERICAL SIMULATION OF NANOPARTICLES COAGULATION IN
RF-DISCHARGE
O.Yu. Kravchenko, Yu.V. Yushchyshena
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
E-mail: kay@univ.kiev.ua
This paper presents the simulation results of nanoscale dust particles coagulation in capacitive radio-frequency
discharge of low pressure in argon. Simulations carried out under the self-consistent kinetic model that takes into
account the stochastic nature of the process of dust particles charging and their coagulation using general dynamic
equations for aerosols. We analyze the distribution of dust particles by size and charge at different distances from
the electrodes. It is shown that a significant number of dust particles of opposite charges present in sheaths, which
improves the process of their coagulation, compared with the central region inter-electrode gap. It is shown that the
presence of dust particles increases the concentration of electrons in the discharge, as well as increases the average
electric potential drop in sheaths.
PACS: 52.27.Lw
INTRODUCTION
Low temperature plasmas containing dust particles
are widely studied for fundamental research as well as
technological applications [1]. Plasmas present exciting
opportunities for nanoparticle synthesis. In particular,
for the creation of dust particles having the desired
properties are used radiofrequency discharges. Such
dust particles could find applications in medicine,
materials science, in the production of nanostructured
materials if the formation, growth and transport of theirs
in plasmas can be controlled. In order to control the
morphology, composition and transport of the particles
in the above mentioned and other existent and future
technological applications a better understanding of the
particle formation mechanisms and their influence on
plasma is needed.
Radiofrequency discharges with dust particles
investigated in the framework of the hydrodynamic
model [2], as well as using the method of particles in
cells [3, 4]. In these studies, it was assumed that the size
of the dust particles was constant in time and uniform in
space. However, while monodisperse models may be an
obvious choice for plasmas with dust particles in the
micrometer-size range, they have several shortcomings
for plasmas containing nanoparticles, or so-called
‘nanodusty plasmas’. In the latter case, the coagulation
can broaden size distributions and the discharge
chamber contains particles of different sizes and
charges. Adding to the complexity introduced by
polydispersity in nanodusty plasmas, stochastic
charging causes particles of given size to have a
distribution in terms of the number of charges on each
particle.
The coagulation of dust particles in rf discharges has
been studied in [5, 6]. In these reports, densities and
charge distributions are calculated in the frame of one-
dimensional hydrodynamic model, in addition the
influence of particle charging on coagulation frequency
not taken into account. It should also be noted,
hydrodynamic model is not applicable to describe the
discharge at low gas pressures.
In this paper, we model the rf discharge with dust
nanoparticles in argon gas at low pressures ( 1p Torr )
using PIC/MCC method [7], taking into account the
coagulation of dust particles.
1. MODEL AND SIMULATION METHOD
A one-dimensional RF discharge is considered
between two plane electrodes separated by a gap which
is filled with Ar. Dust particles of a given radius
1dr nm are distributed uniformly at initial time in the
inter-electrode gap. In our model, the dust particles are
assumed unmovable. Simulations have been carried out
with dust densities 13 14 35 10 ... 5 10dn m , the rf
frequency and the amplitude of rf power were set
103,56rf MHz and 150rfV V . In the frame of
Monte-Carlo method, we take in account elastic
collisions of electrons and ions with atoms, an
ionization and excitation of atoms by electrons, the
charge exchange between ions and atoms.
Nanoparticles in the plasma are charged because of
collisions with electrons and ions. The electron and ion
currents collected by a dust particle in the nanometer
regime can be described by the orbital-motion-limited
(OML) probe theory. A particle with radius
dr which
carries a charge
kZ k e (with e the elementary charge
and k an integer) is charged to a surface potential of
0/ 4k k dZ r , with
0 the vacuum dielectric
constant. Using OML theory, expressions for the
frequency with which a particle with charge
kZ is hit by
electrons and ions, respectively, can be derived
,
, , , ,
,
,
, , , ,
,
exp , 0
1 , 0.
e i kk
e i e i e i e i k
B e i
e i kk
e i e i e i e i k
B e i
q
n Sv q
k T
q
V n Sv q
k T
24 dS r is the particle surface area,
1/2
, , ,/ 2 ,e i B e i e iv k T m ,e in stands for the electron
and ion densities, ,e im and ,e iT are the mass and
temperature of electrons and ions, respectively, and
ISSN 1562-6016. ВАНТ. 2016. №6(106) 273
,e iq e is the respective charge,
Bk is Boltzmann
constant.
The charge distribution of particles of a given radius
dr is described by the fraction of particles
kF carrying
a charge k e . It is normalized by 1k
k
F . The rate
equation for a charge state k can then be written as
1 1
1 1.
k k k kk
e k e k i k i k
dF
F F F F
dt
It is assumed that the charging of particles is much
faster than coagulation so the charge distribution can be
considered in steady state [8]. This assumption enables
the use of recursive relations for the charge distribution
1 1
k
i
k kk
e
F F
.
In the present paper, we will focus on the growth of
nanoparticles due to coagulation. Similar to [9], we
suppose that the typically coagulation of particles in a
low-pressure plasma is identical to the coagulation in a
bipolar aerosol. Since the charging time is much shorter
than the typically coagulation time of particles we
separate the problems of charging and coagulation from
each other.
The volume distribution function of dust particles
( )n v is described by the general dynamic equation [9]
0
0
( ) 1
( , ) ( ) ( )
2
( , ) ( ) ( ) ,
v
n v
v v v n v n v v dv
t
v v n v n v dv
where v is the volume of the dust particle, ( )dvn v
denotes the particle number density in a volume range
[ , ]v v dv . Coefficient ( , )v v is the frequency for
coagulation between two particles with a volume v and
v . According to [10], ( , )v v is given
1/2
1/6 1/2
2
1/3 1/3
63 1 1
( , ) ( , )
4
,
B
p
k T
v v v v
v v
v v
where v and v are the volumes of the particles
interacting,
p is the density of the particles, and T is
the temperature of the particles. (v, v ) is a coefficient
which describes that the effective cross section for
coagulation depends on the charge of both particles
( , ) ( ) (v )Q(k,k , v, v )k k
k k
v v F v F
with
2
0
2
0
( , , , ) exp , 0
4
1 , 0.
4
s B
s B
kk e
Q k k v v kk
R k T
kk e
kk
R k T
2. RESULTS AND DISCUSSION
We here present selected results of radio-frequency
discharge numerical simulation. The plasma process
parameters are as follows: electrode spacing is 0.03 m ,
gas pressure is 0.1Torr , and pulse frequency is
13.56 .MHz Initially, neutral nanoparticles having a
radius of 1 nm are uniformly arranged in the
interelectrode gap with density 14 32 10dn m .
Subsequently, the dust particles are charged in the
plasma and have an influence on the discharge
parameters.
Fig. 1,a shows spatial distributions of electron
density averaged over the period of the discharge for
case without dust particles (solid line) and for case with
dust density 14 32 10dn m (dash line).
0,00 0,01 0,02 0,03
0,0
2,0x10
15
4,0x10
15
6,0x10
15
x,m
n
e
,m
-3
n
d
=0
n
d
=2*10
14
m
-3
a
0,00 0,01 0,02 0,03
0
20
40
60
80
n
d
=2e14 m
-3
n
d
=0
x, m
,V
b
Fig. 1. Spatial distributions of electron density (a) and
self-consistent electric potential (b), averaged over the
discharge period
As can be seen, the electron density increases
significantly in the present of dust particles at the same
potential drop across the discharge gap. This is due to
an increase in resistance of the discharge gap.
Fig. 1,b shows spatial distributions electric potential,
averaged over the rf discharge period. Solid and dash
lines correspond to the cases with dust particles and
without dust particles, respectively. It is seen, that
sheaths are formed near electrodes, which are
characterized by a sharp change in potential. The
potential drop in sheaths increases in the presence of
dust particles.
Inhomogeneity of the plasma parameters in the
discharge gap leads to a different charge distributions of
dust particles at different points in space. This is
nd=2х1014 m-3
274 ISSN 1562-6016. ВАНТ. 2016. №6(106)
confirmed figure 2, which shows the charge distribution
of dust particles for different particle volumes V at the
boundary of the sheath (a) and in the centre of the
discharge gap (b). It is seen that the average charge of
the smaller size of nanoparticles in the sheath is
approximately equal to zero, since at this point the
number of positive and negative particles of about the
same. The increasing of particle volume due to
coagulation increases the average charge in magnitude.
-4 -2 0 2 4
0,0
0,2
0,4
k
F(V,k)
V= 4*10
-27
m
3
V= 10
-26
m
3
V= 2 *10
-26
m
3
a
-6 -4 -2 0 2
0,0
0,2
0,4
k
F(V,k)
V= 4* 10
-27
m
3
V= 1 *10
-26
m
3
V= 2 *10
-26
m
3
b
Fig. 2. Charge distributions of nanoparticles for
different sizes (a near the electrodes; b – in the center
of the discharge gap)
However, we can observe an essential fraction of
positively charged particles in these cases too. In the
center of the discharge gap, the charge distribution
significantly differs from one in the sheath. In this case,
we can observe mainly negative dust particles.
Coagulation is a main reason of decrease in dust
particle density as particles grow to larger size. Fig. 3
shows the densities of dust particles at various times
after the ignition of the discharge. The presented
dependences show that the minimum values of the
concentration of dust particles are observed at the edges
of sheaths. This can be explained by the fact that in this
area the coagulation process is most effective. In the
central part of inter-electrode gap coagulation frequency
is lower that at the boundaries of sheaths. This is due to
the presence in that area a significant amount of dust
particles of the opposite sign. Near the electrodes (at
0x and at 0.03x m ) averaged over the period of
the discharge the electron density is much less than the
ions density. Consequently, nanoparticles are here
mainly positive charged and their coagulation rate
decreases. We concluded that interaction of positively
and negatively charged particles is the main reason of
enhance coagulation rate in comparison to the
coagulation rate in the canter of discharge.
0,00 0,01 0,02 0,03
1,2x10
14
1,6x10
14
2,0x10
14
x,m
n
d
, m
-3
t=0s
t=5s
Fig. 3. Spatial distributions of dust density at different
times after the discharge ignition
0,0 2,0x10
-26
4,0x10
-26
10
-1
10
2
10
5
10
8
10
11
10
14
dn
d
/dV
V, m
3
1
2
Fig. 4. Distributions of dust particles by volume at the
sheath boundary (1) and at the center of the discharge
gap (2)
Distributions of dust particles by volume are
presented in Fig. 4. Solid line corresponds to the edge of
the sheath and dash line corresponds to the centre of the
discharge gap.
CONCLUSIONS
In this paper, particle-in cell (PIC) simulations with
Monte-Carlo (MC) collisions have been performed to
investigate the coagulation of nanoparticles in argon
radiofrequency discharge and the their influence on the
discharge. The analysis of the obtained simulation
results indicates that the presence of dust particles in the
discharge leads to increase the ionization rate of atoms,
as well as to increase of electron and ion densities. It is
obtained charge and volume distributions of
nanoparticles at different points of interelectrode gap. It
was shown that the coagulation of the nanoparticles is
more effective in the sheath, since in this region there
are dust particles of opposite charge.
V = 4 x 10-27 m3
V = 2 x 10-26 m3
0.4
0.2
0.0
V = 4 х 10-27 m3
V = 1 х 10-26 m3
V = 2 х 10-26 m3
0.4
0.2
0.0
2.0 х 1014
1.6 х 1014
1.2 х 1014
0.00 0.01 0.02 0.03
0.0 2.0х10-26 4.0х10-26
ISSN 1562-6016. ВАНТ. 2016. №6(106) 275
REFERENCES
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Modelling of nanoparticle coagulation and transport
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7. C.K. Birdsall. Particle-in-Cell Charged-Particle
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8. V.A. Schweigert and I.V. Schweigert. Coagulation in
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particulate coagulation in low pressure plasmas //
Physical Review. 1999, v. 60, p. 887-898.
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Article received 25.10.2016
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ КОАГУЛЯЦИИ НАНОЧАСТИЦ
В РАДИОЧАСТОТНОМ РАЗРЯДЕ
A.Ю. Кравченко, Ю.В. Ющишена
Представлены результаты компьютерного моделирования коагуляции наноразмерных пылевых частиц в
ёмкостном радиочастотном разряде низкого давления в аргоне. Расчёты проведены в рамках
самосогласованной кинетической модели, которая учитывает стохастическую природу процесса зарядки
пылевых частиц, а также их коагуляцию при помощи общих динамических уравнений для аэрозолей.
Анализируется распределение частиц по заряду и размеру на различных расстояниях от электродов.
Показано, что на краях приэлектродных слоёв присутствует значительно большее количество пылевых
частиц с противоположными зарядами, в сравнении с центральной областью межэлектродного промежутка,
что значительно улучшает процесс их коагуляции. Проанализировано влияние пылевых частиц на
параметры разрядной плазмы. Показано, что наличие пылевых частиц приводит к увеличению
концентраций электронов в разряде, а также к увеличению скачков усреднённого электрического
потенциала на приэлектродных слоях.
ЧИСЛОВЕ МОДЕЛЮВАННЯ КОАГУЛЯЦІЇ НАНОЧАСТИНОК
В РАДІОЧАСТОТНОМУ РОЗРЯДІ
О.Ю. Кравченко, Ю.В. Ющишена
Представлені результати комп’ютерного моделювання коагуляції нанорозмірних пилових частинок в
ємнісному радіочастотному розряді низького тиску в аргоні. Розрахунки проведені в рамках самоузгодженої
кінетичної моделі, яка враховує стохастичну природу процесу зарядки пилових частинок, а також їх
коагуляцію за допомогою загальних динамічних рівнянь для аерозолів. Аналізується розподіл пилових
частинок по заряду та розміру на різних відстанях від електродів, а також вплив пилових частинок на
властивості розряду. Показано, що в приелектродних шарах присутні значна кількість пилових частинок
протилежних зарядів, в порівнянні з центральною областю міжелектродного проміжку, що значно
прискорює процес їх коагуляції. Проаналізовано вплив пилових частинок на параметри розрядної плазми.
Показано, що наявність пилових частинок приводить до збільшення концентрацій електронів в розряді, а
також до збільшення стрибків усередненого електричного потенціалу на приелектродних шарах.
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https://scholar.google.com/citations?view_op=view_citation&hl=ru&user=h4MzsJcAAAAJ&citation_for_view=h4MzsJcAAAAJ:u-x6o8ySG0sC
https://scholar.google.com/citations?view_op=view_citation&hl=ru&user=h4MzsJcAAAAJ&citation_for_view=h4MzsJcAAAAJ:u-x6o8ySG0sC
https://scholar.google.com/citations?view_op=view_citation&hl=ru&user=h4MzsJcAAAAJ&citation_for_view=h4MzsJcAAAAJ:u-x6o8ySG0sC
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