Coagulation and dynamics nanoparticles in low pressure plasma jets

One of the most promising methods for creating nanostructured films is the use of plasma jets of low pressure with nanoparticles. In this case, it is important to control the size of the nanoparticles, their temperature and energy to optimize the properties of the films. In this paper, using compute...

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Datum:	2019
Hauptverfasser:	Kravchenko, O.Yu., Maruschak, I.S.
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Sprache:	English
Veröffentlicht:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2019
Schriftenreihe:	Вопросы атомной науки и техники
Schlagworte:	Low temperature plasma and plasma technologies
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spelling	irk-123456789-1947122023-11-29T11:17:27Z Coagulation and dynamics nanoparticles in low pressure plasma jets Kravchenko, O.Yu. Maruschak, I.S. Low temperature plasma and plasma technologies One of the most promising methods for creating nanostructured films is the use of plasma jets of low pressure with nanoparticles. In this case, it is important to control the size of the nanoparticles, their temperature and energy to optimize the properties of the films. In this paper, using computer simulations, a study is conducted on coagulation of nanoparticles in a plasma jet that expands into rarefied gas. In our model, we use a hydrodynamic model for describing the dynamics of a plasma with a multidisperse phase, as well as a sectional method for describing the coagulation of nanoparticles. At the entrance to the plasma torch, the plasma parameters were stationary, and the dust particles were considered the same size. Calculations were made at various concentrations of dust particles in the plasma jet. The simulation results show that nanoparticles of various sizes appear in the plasma stream as a result of coagulation. With increasing distance from the inlet, the average modulus charge and the dispersion of the charge of nanoparticles decreases due to the decrease in the temperature of the ions and, consequently, the ion current on the dust particles. Одним з найбільш перспективних методів створення наноструктурованих плівок є використання плазмових струменів низького тиску з наночастинками. При цьому для оптимізації властивостей плівок важливим є контроль за розміром наночастинок, їх температурою та енергією. У цій роботі за допомогою комп’ютерного моделювання проводиться дослідження коагуляції наночастинок у плазмовому струмені, який розширюється в розріджений газ. У нашій моделі використовуються гідродинамічна модель для описання динаміки плазми з мультидисперсною фазою, а також секційний метод для описання коагуляції наночастинок. На вхідному отворі плазмового факела параметри плазми задавалися стаціонарними, а пилові частинки вважалися одного розміру. Розрахунки проводилися при різних концентраціях пилових частинок у плазмовому струмені. Результати моделювання показують, що в потоці плазми внаслідок коагуляції з’являються наночастинки різних розмірів. Зі збільшенням відстані від вхідного отвору зменшуються середній заряд по модулю та дисперсія заряду наночастинок, що пов’язано із зменшенням температури іонів та, відповідно, іонного струму на пилову частинку. Одним из наиболее перспективных методов создания наноструктурированных пленок является использование плазменных струй низкого давления с наночастицами. При этом для оптимизации свойств пленок важным является контроль за размером наночастиц, их температурой и энергией. В работе с помощью компьютерного моделирования проводится исследование коагуляции наночастиц в плазменной струе, которая расширяется в разреженный газ. В нашей модели используются гидродинамическая модель для описания динамики плазмы с мультидисперсною фазой, а также секционный метод для описания коагуляции наночастиц. На входном отверстии плазменного факела параметры плазмы задавались стационарными, а пылевые частицы считались одного размера. Расчеты проводились при различных концентрациях пылевых частиц в плазменной струе. Результаты моделирования показывают, что в потоке плазмы вследствие коагуляции появляются наночастицы различных размеров. С увеличением расстояния от входного отверстия уменьшаются средний заряд по модулю и дисперсия заряда наночастиц, что связано с уменьшением температуры ионов и, соответственно, ионного тока на пылевую частицу. 2019 Article Coagulation and dynamics nanoparticles in low pressure plasma jets / O.Yu. Kravchenko, I.S. Maruschak // Problems of atomic science and technology. — 2019. — № 1. — С. 172-175. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 52.27.Lw http://dspace.nbuv.gov.ua/handle/123456789/194712 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
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. Maruschak, I.S. Coagulation and dynamics nanoparticles in low pressure plasma jets Вопросы атомной науки и техники
description	One of the most promising methods for creating nanostructured films is the use of plasma jets of low pressure with nanoparticles. In this case, it is important to control the size of the nanoparticles, their temperature and energy to optimize the properties of the films. In this paper, using computer simulations, a study is conducted on coagulation of nanoparticles in a plasma jet that expands into rarefied gas. In our model, we use a hydrodynamic model for describing the dynamics of a plasma with a multidisperse phase, as well as a sectional method for describing the coagulation of nanoparticles. At the entrance to the plasma torch, the plasma parameters were stationary, and the dust particles were considered the same size. Calculations were made at various concentrations of dust particles in the plasma jet. The simulation results show that nanoparticles of various sizes appear in the plasma stream as a result of coagulation. With increasing distance from the inlet, the average modulus charge and the dispersion of the charge of nanoparticles decreases due to the decrease in the temperature of the ions and, consequently, the ion current on the dust particles.
format	Article
author	Kravchenko, O.Yu. Maruschak, I.S.
author_facet	Kravchenko, O.Yu. Maruschak, I.S.
author_sort	Kravchenko, O.Yu.
title	Coagulation and dynamics nanoparticles in low pressure plasma jets
title_short	Coagulation and dynamics nanoparticles in low pressure plasma jets
title_full	Coagulation and dynamics nanoparticles in low pressure plasma jets
title_fullStr	Coagulation and dynamics nanoparticles in low pressure plasma jets
title_full_unstemmed	Coagulation and dynamics nanoparticles in low pressure plasma jets
title_sort	coagulation and dynamics nanoparticles in low pressure plasma jets
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2019
topic_facet	Low temperature plasma and plasma technologies
url	http://dspace.nbuv.gov.ua/handle/123456789/194712
citation_txt	Coagulation and dynamics nanoparticles in low pressure plasma jets / O.Yu. Kravchenko, I.S. Maruschak // Problems of atomic science and technology. — 2019. — № 1. — С. 172-175. — Бібліогр.: 12 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT kravchenkooyu coagulationanddynamicsnanoparticlesinlowpressureplasmajets AT maruschakis coagulationanddynamicsnanoparticlesinlowpressureplasmajets
first_indexed	2025-07-16T22:10:56Z
last_indexed	2025-07-16T22:10:56Z
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fulltext	ISSN 1562-6016. ВАНТ. 2019. №1(119) 172 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2019, № 1. Series: Plasma Physics (25), p. 172-175. COAGULATION AND DYNAMICS NANOPARTICLES IN LOW PRESSURE PLASMA JETS O.Yu. Kravchenko, I.S. Maruschak Taras Shevchenko National University of Kyiv, Kyiv, Ukraine E-mail: kay@univ.kiev.ua One of the most promising methods for creating nanostructured films is the use of plasma jets of low pressure with nanoparticles. In this case, it is important to control the size of the nanoparticles, their temperature and energy to optimize the properties of the films. In this paper, using computer simulations, a study is conducted on coagulation of nanoparticles in a plasma jet that expands into rarefied gas. In our model, we use a hydrodynamic model for describing the dynamics of a plasma with a multidisperse phase, as well as a sectional method for describing the coagulation of nanoparticles. At the entrance to the plasma torch, the plasma parameters were stationary, and the dust particles were considered the same size. Calculations were made at various concentrations of dust particles in the plasma jet. The simulation results show that nanoparticles of various sizes appear in the plasma stream as a result of coagulation. With increasing distance from the inlet, the average modulus charge and the dispersion of the charge of nanoparticles decreases due to the decrease in the temperature of the ions and, consequently, the ion current on the dust particles. PACS: 52.27.Lw INTRODUCTION Plasma-assisted technologies represent important tools for deposition of nanostructured films on substrates. The growth of thin and ultra-thin films may be achieved using a large variety of techniques such as chemical vapour deposition, RF sputtering, pulsed laser deposition or plasma enhanced chemical vapour deposition [1-3]. Recently, a new process, which uses a plasma torch operating at low pressure has been developed with the aim of depositing uniform thin layers on large surfaces [4, 5]. In this plasma spraying process plasma jets are used as a heat sources to melt and accelerate the injected nanoparticles which subsequently impinge and solidify on a substrate. Modelling the nanoparticles, which create and assemble the film it is possible to enhance the physical properties of thin films. As is known, nanoparticles have the ability to coagulate, resulting in a change in their size. This process can be significant in plasma and it must be taken into account when transporting nanoparticles to a substrate in a plasma jet. It is important to be able to control the size of the nanoparticles, their kinetic energy, the temperature and the magnitude of the flow on the substrate. The aim of this work is to simulate the dynamics and coagulation of nanoparticles in a plasma jet expanding through a round hole into a dilute gas. 1. MODEL AND SIMULATION METHOD In this paper, the expansion of an axially symmetric plasma jet with nanoparticles into a rarefied neutral gas is studied. A hydrodynamic model is used to describe a problem that takes into account the processes of coagulation of dust particles. At the initial moment of time, it is assumed that the plasma flows through a circular hole into a space filled with neutral gas. The plasma consists of neutral argon atoms, single charge ions, electrons and dust particles. It was believed that at the initial moment of time dust particles were of the same radius 4dr nm . The plasma flow velocity at the inlet was v0=40 m/s, plasma pressures were in the range of 4 to 80 mbar. To describe the problem, a hydrodynamic model is used, which is described in [6]. This model includes continuity equations for ions, atoms and dust particles   0, n div nw t       / ,i i i d n div n w I n e t        0d d d n div n w t     , momentum equations for heavy plasma particles (ions and atoms) and dust particles     1 ,d r i r i i i nu n fP e div nuw n E t m r m m              1 ,d z i z i i i nv n fP e div nvw n E t m z m m              , d d d d r d d d d d r d d d n u n f qP div n u w n E t m r m m              , d d d d z d d d d d z d d d n v n f qP div n v w n E t m z m m          equations for internal energies ions and atoms  , electrons e and dust particles d     , enei ddiv w Pdiv w Q Q n Q t              , e e e e ei en d ed div w P div w divq t Q Q n Q               d d d d d d d ed iddiv w n Q n Q Q t           . Here , ,d in n n are the sum of ion and neutral atom concentrations, dust particles and ion concentrations respectively;  ,w u v and  ,d d dw u v are drift ISSN 1562-6016. ВАНТ. 2019. №1(119) 173 velocities of plasma and dust component; , eP P are partial pressures of the heavy plasma component and electrons. In these equations , , Qed idQ Q are the energy exchanges between a dust particle and neutral atoms, electrons and ions; eiQ is the energy exchange between electrons and ions; enQ is the energy exchange between electrons and neutrals [6]. In this model, we believe that all dust particles have a single hydrodynamic velocity, since they effectively exchange impulse in collisions. This velocity differs from the hydrodynamic velocity of the plasma component. We also note that due to the low plasma pressure we allow for a difference between the temperature of the electrons and the temperature of the heavy plasma particles (ions and neutrals), as well as the surface temperature of dust particles. The system of hydrodynamic equations is solved numerically by the method of large particles [7]. To determine the distribution of nanoparticles by charge, we use the model proposed in [8, 9]. This model takes into account the stochastic nature of the charging of dust particles associated with the chaos of the thermal motion of electrons and ions. As a result, dust particles with different charges are present in each elemental volume of plasma. 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 [10]. 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 e i kk e i e i e i e i k B e i q n Sv q k T            , , , , , , 1 , 0. e i kk e i e i e i e i k B e i q n Sv q k T            Here 24 dS r is the particle surface area,   1/2 , , ,/ 2e i B e i e iv k T m is the electron (ion) thermal velocity; ,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 ,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 [9]. This assumption enables the use of recursive relations for the charge distribution 1 1 k i k kk e F F      . In addition, in the presented model, coagulation of dust particles is considered, which is described by the model proposed in [11,12]. The volume distribution function of dust particles ( )n v is described by the general dynamic equation 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 [11], ( , )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                 and   1/3 1/3 '1/33 . 4 sR v v         2. RESULTS AND DISCUSSION Fig. 1 shows distributions on the charge of nanoparticles of a radius 4dr nm at different distances from the inlet. Here is the fraction of particles with charge . As can be seen from the figure, with increasing the average charge of the nanoparticles decreases in absolute value. The obtained results are explained by the fact that when the distance from the inlet of the plasma jet increases, the temperature of the ions decreases rapidly, and the electrons temperature remains practically unchanged due to their high thermal conductivity. This leads to an increase in the flow of ions on the surface of the dust particles and, consequently, to a decrease in its negative charge. 174 ISSN 1562-6016. ВАНТ. 2019. №1(119) -10 -5 0 0,0 0,1 0,2 0,3 k F z=0 z=0.005 m z=0.02 m a Fig. 1. Distributions by charge of nanoparticles at different distances from the inlet of plasma jet -20 -10 0 0,0 0,1 0,2 q d /e z=0.01 m  d0 / 0 =0.05  d0 / 0 =0.2 E Fig. 2. Distributions by charge of nanoparticles at z = 0.001 m from the inlet of plasma jet for different dust densities Consider now how the concentration of nanoparticles in the plasma jet affects their charge distributions. In Fig. 2 depicts the charge distributions of nanoparticles with a radius rd = 4 nm for two modes: at d0/0=0.05 and d0/0=0.2. Here d0 is a dust density, 0 is a plasma density at the inlet of the plasma torch. The plasma density in these modes was 0=0.122 kg/m 3 . As can be seen, the decrease in the density of dust particles leads to a shift of the charge distribution of dust particles in the region of negative charges. This result is because when the concentration of negatively charged dust particles increases, the concentration of electrons decreases (due to the quasi- neutrality of the plasma). This leads to a decrease in the electron current to the dust particles. Consider now the coagulation of nanoparticles in a plasma jet. Fig. 3 shows axial profiles along the jet axis of the dust particles densities on a semi-logarithmic scale for different their radii. In this mode of calculation, the concentration of nanoparticles at the inlet was nd = 5∙10 -9 m -3 , and their radius was rd = 4∙10 -9 m. We can see that nanoparticles with rd >4 nm appear in the plasma jet, the maxima of densities which are at a certain distance from the inlet. This can be explained by the coagulation of dust particles in the plasma jet. As a result of this process, the concentration of nanoparticles with a radius exceeds the concentration of particles which are injected through the inlet (with a radius ) at . 0,000 0,025 0,050 10 3 10 8 10 13 10 18 z, m n d , m -3 r d =4 nm r d =4.7 nm r d =5.3 nm r d =7 nm Fig. 3. Axial profiles on jet axis of the dust densities for different their radii Fig. 4 shows the distributions of nanoparticles by their radius at different distances from the inlet. These results correspond to the calculation mode presented in Fig. 3. As can be seen, because of the coagulation, at a distance from the inlet z = 0.001 m in the plasma appear particles of different radii. When increasing the distance to the inlet, the number of particles of larger radii first increases and then decreases. Decrease in concentrations of dust particles is due to the expansion of the plasma jet. 4,0x10 -9 6,0x10 -9 8,0x10 -9 1,0x10 -8 10000 1E9 1E14 1E19 n d , m -3 r d , m z=0.001 m z=0.01 m z=0.03 m Fig. 4. Distributions of dust particles by their radius at different distances from the inlet of plasma jet CONCLUSIONS In this work, a sectional model that is selfconsistently coupled to a plasma fluid model was used to conduct numerical simulations of a low-pressure plasma jet in which nanoparticles grow due to coagulation. The simulation was carried out at different plasma pressures, and the concentration of dust particles at the inlet of the plasma torch. As a result of the calculations, the spatial distributions of the plasma parameters, size and charge distributions of nanoparticles in the different points of space have been obtained. Influence of nanoparticle coagulation on the parameters of a plasma jet and the dynamics of nanoparticles is studied. It is shown that due to coagulation in the jet appear dust particles of larger radii. The maximum concentrations of these particles are at some distance from the inlet. We found that with the increase of the distance from the inlet due ISSN 1562-6016. ВАНТ. 2019. №1(119) 175 to the decrease of the ion temperature, the average charge of dust particles per module and the width of their distribution by charge decreases. When the density of dust particles in the jet increases, their average charge decreases modulo due to a decrease of the electron density in the plasma, which leads to an increase of the coagulation rate of nanoparticles. REFERENCES 1. P. Roca i Cabarrocas, N. Chaabane, A.V Kharchenko, S. Tchakarov. Polymorphous silicon thin films produced in dusty plasmas: application to solar cells // Plasma Phys. Controlled Fusion. 2004, v. 46, p. 235. 2. N.M. Hwang, D.K. Lee. Charged nanoparticles in thin film and nanostructure growth by chemical vapour deposition // J. Phys. 2010, D 43:483001. 3. N. Chaabane, V. Suendo, H. Vach, P. Roca i Cabarrocas. Soft landing of silicon nanocrystals in plasma enhanced chemical vapor deposition // Appl. Phys. Lett. 2006, v. 88, p. 2031111. 4. I. Biganzoli, F. Fumagalli, F. Di Fonzo, R. Barni, C. Riccardi. A Supersonic Plasma Jet Source for Controlled and Efficient Thin Film Deposition // J. Mod. Phys. 2012, v. 3, p. 1626-1638. 5. V. Trifiletti., R. Ruffo, C. Turrini, D. Tassetti, R. Brescia, F. Di Fonzo, C. Riccardi, A. Abbotto // J. Mater. Chem. 2013, v. A 1, p. 11665. 6. O.Yu. Kravchenko, I.S. Maruschak. Dynamics of dust particles in a plasma jet // Problems of Atomic Science and Technology. Ser. “Plasma Physics”. 2017, № 1, p. 159-162. 7. O.M. Belozerkovskiy, Yu.M. Davydov. Metod krupnyh chastiz v gasovoj dinamike. M.: “Nauka”, 1982, 392 p. (in Russian). 8. M.S. Sodha, S.K. Mishra, S. Misra, S. Srivastava. Fluctuation of charge on dust particles in a complex plasma // Physics of Plasmas. 2010, v. 17, p. 073705-7. 9. Themis Matsoukas, Marc Russell, and Matthew Smith. Stochastic charge fluctuations in dusty plasmas // J. Vac. Sci. Technol. 1996, v. A 14, p. 624-630. 10. P.K. Shukla, A.A. Mamun. Introduction to Dusty Plasma Physics. Bristol and Philadelphia: “IoP Publishing Ltd”, 2002. 11. P. Agarwal, S.L. Girshick. Sectional modeling of nanoparticle size and charge distributions in dusty plasmas // Plasma Sources Sci. Technol. 2012, v. 21, p. 055023-12. 12. U. Kortshagen, U. Bhandarkar. Modeling of particulate coagulation in low pressure plasmas // Physical Review. 1999, v. 60, p. 887-898. Article received 15.12.2018 КОАГУЛЯЦИЯ И ДИНАМИКА НАНОЧАСТИЦ В ПЛАЗМЕННЫХ СТРУЯХ НИЗКОГО ДАВЛЕНИЯ А.Ю. Кравченко, И.С. Марущак Одним из наиболее перспективных методов создания наноструктурированных пленок является использование плазменных струй низкого давления с наночастицами. При этом для оптимизации свойств пленок важным является контроль за размером наночастиц, их температурой и энергией. В работе с помощью компьютерного моделирования проводится исследование коагуляции наночастиц в плазменной струе, которая расширяется в разреженный газ. В нашей модели используются гидродинамическая модель для описания динамики плазмы с мультидисперсною фазой, а также секционный метод для описания коагуляции наночастиц. На входном отверстии плазменного факела параметры плазмы задавались стационарными, а пылевые частицы считались одного размера. Расчеты проводились при различных концентрациях пылевых частиц в плазменной струе. Результаты моделирования показывают, что в потоке плазмы вследствие коагуляции появляются наночастицы различных размеров. С увеличением расстояния от входного отверстия уменьшаются средний заряд по модулю и дисперсия заряда наночастиц, что связано с уменьшением температуры ионов и, соответственно, ионного тока на пылевую частицу. КОАГУЛЯЦІЯ І ДИНАМІКА НАНОЧАСТИНОК У ПЛАЗМОВИХ СТРУМЕНЯХ НИЗЬКОГО ТИСКУ О.Ю. Кравченко, І.С. Марущак Одним з найбільш перспективних методів створення наноструктурованих плівок є використання плазмових струменів низького тиску з наночастинками. При цьому для оптимізації властивостей плівок важливим є контроль за розміром наночастинок, їх температурою та енергією. У цій роботі за допомогою комп’ютерного моделювання проводиться дослідження коагуляції наночастинок у плазмовому струмені, який розширюється в розріджений газ. У нашій моделі використовуються гідродинамічна модель для описання динаміки плазми з мультидисперсною фазою, а також секційний метод для описання коагуляції наночастинок. На вхідному отворі плазмового факела параметри плазми задавалися стаціонарними, а пилові частинки вважалися одного розміру. Розрахунки проводилися при різних концентраціях пилових частинок у плазмовому струмені. Результати моделювання показують, що в потоці плазми внаслідок коагуляції з’являються наночастинки різних розмірів. Зі збільшенням відстані від вхідного отвору зменшуються середній заряд по модулю та дисперсія заряду наночастинок, що пов’язано із зменшенням температури іонів та, відповідно, іонного струму на пилову частинку. 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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