Abstract
The studies of strongly coupled complex plasmas are of significant in the area of science and technology. The plasma thermal conductivity strongly coupled (complex) plasmas is of significant in scientific technology, because it behaves as complex fluids. The two-dimensional (2D) plasma thermal conductivity of strongly coupled complex dusty plasmas (SCCDPs) has been investigated by using the homogenous nonequilibrium molecular dynamics (HNEMD) simulations, proposed by Evan-Gillan scheme, at higher screening parameter к. In our case, we have chosen particularly higher screening strength (к) for calculating plasma thermal conductivity. The new simulations of plasma thermal conductivity are computed over an extensive range of plasma states (Г, к) for suitable system sizes by applying the HNEMD simulation method at constant external force field strength (F*). It is found that the plasma thermal conductivity of SCCDPS decreases by increasing plasma states (Г, к). The calculations show that the kinetic energy of SCCDPS depends upon the system temperature (1/Г) and it is independent of к for higher screening parameter. The new results of thermal conductivity obtained from an improved HNEMD algorithm are in satisfactory agreement with earlier known numerical results and experimental data for 2D SCCDPS. It is depicted that the HNEMD method is a powerful tool to calculate an accurate plasma thermal conductivity of 2D SCCDPS.
Keywords
- plasma thermal conductivity
- strongly coupled
- homogenous nonequilibrium molecular dynamics
- force field strength
- system size
1. Introduction
The thermophysical properties or physical properties of complex fluids are changed with the variation of pressure, temperature, and composition of the material, but the chemical properties remain unchanged. The phase transition of simple and complex liquids is explained by thermophysical properties [1]. Thermophysical properties consist of both thermodynamic and transport properties of fluid materials. Thermodynamic properties define the equilibrium conditions of the system which consist of temperature, heat capacity, entropy, pressure, internal energy, enthalpy and density whereas the transport properties include thermal conductivity, diffusion viscosity and waves with its instabilities. These transport properties tell the transfer of energy and momentum to the system under consideration. The transport and thermodynamic properties contain information about the physical phenomena and help to design a system [2]. The thermal properties are calculated through experimentally, computer simulations and can predict through theoretically. The essential transport coefficient of dusty plasma is thermal conductivity and depends upon the internal energy of the particles. The thermal properties of dusty plasmas are computed for a wide combination of dusty plasma parameters by employing different computational techniques. It is a sensitive and complex parameter from the computational point of view because it directly depends on the internal energy of particles. At low temperature and high density, the thermal property of complex liquids/nonideal gases (dusty plasma) is dissimilar from ideal gases (H2, O2, N2, and H2O) at same higher system parameters. For the calculation of transport properties, particular numerical models are proposed in order to investigate thermal properties for an extensive range of system temperature and density values (Γ,
1.1 Significance of thermal conductivity
Thermal conductivity is the measurement of heat transfer rate in materials; the experimental parameter gives the information at the microscopic level. It has treated via theoretically based on kinetic theory, Boltzmann equation and linear response theory. The management of thermal transport is in increasing demands in the field of modern technologies. It plays a critical role in a wide variety of practical applications, such as well-organized heat dissipation in nanoelectronics and heat conduction hindering in solid-state thermoelectric. It is well established that heat transport in semiconductors and insulators efficiently modulated by materials processing or structural engineering. Though, practically all the existing approaches include altering the original atomic structure of materials that would delay due to either irreversible structure change or limited tunability of thermal conductivity. The inherent relationship between phonon behaviors and interatomic electrostatic interaction is the efficiently manipulating by thermal transport in materials fundamental thermal physical problems. Electronics cooling or high performance thermal management systems here higher thermal conductivity is needed. Phonons play a dominant role in the thermal transport of semiconductors and insulators [3]. Thermal conductivity and mass transmission over a stretched heated surface with different effects have an abundant and extensive range of applications in various engineering and industrial disciplines. These include glass blowing, extrusion process, melt-spinning, design of heat exchangers, wire and fiber coating, glass fiber production, manufacturing of plastic and rubber sheets, etc. Dusty plasma complex liquids have used in various industries such as semiconductors, energy-powered engineering industries, and microelectronics, and currently, they have vastly used in the field of nanotechnology. It is very necessary to increases thermal conductivity, which increases heat transfer rates. The main concept of the thermal conductivity of different materials and fluids is to increase the transfer heat quickly [4].
1.2 Plasma
Plasma is an ionized gas that contains neutral particles (such as molecules, radicals, and atoms) electrons and positively charged ions. In the universe, 99% of physical matter is in the plasma state and the rest part of the world is only about 1% [5]. In science and technology, plasma has extensive applications and exists in various forms. In space, most of the visible things are in the plasma state, sun and stars are the significant examples of plasma in our universe. Constitutes of plasma show different behaviors such as quasi-neutrality that comes when positive charges and negative charges density becomes equal. Criteria of plasma at the laboratory level must satisfy three conditions by which we can say that gas is in plasma state or not at a given temperature and number of particles per centimeter cubic. These are three conditions are: (i)
1.2.1 Types of plasmas
Plasma can be described based on different characteristics, such as density, temperature, and degree of ionization of ionized gas. Based on these characteristics, we can differentiate plasma into different types, which have succinctly discussed below. The ratio between charged particles to the total number of particles, including ions and neutrals, is proportional to the degree of ionization of plasma. The charged particle collisions dominate in plasma if the degree of ionization is high. It is low if the collisions between charged particles and neutrals have not dominated. These types are given as (i)
1.2.2 Role of nonideal (complex) plasma
In nonideal plasmas, the Coulomb collisions are not negligible. The mean energy of interparticle interactions increases by increasing the density. Nonideal plasmas become when the mean K.E and the mean power of the interparticle interactions become comparable. It can occur in the dense planetary atmosphere during the hypersonic motion of bodies, as a result of simulation of matter by sharp shock, concentrated laser radiations, detonation, and electric explosion waves and under the powerful chemical and nuclear explosion conditions and electron and ion fluxes. Because Coulomb collisions are active in nonideal plasmas, so, on the bases of Coulomb coupling, the nonideal (complex) plasmas have categorized in two classes. (i) Strongly coupled dusty plasma (SCDP) and (ii) weakly coupled dusty plasma (WCDP). These two terms have described by using the plasma coupling parameter Г of a collection of charged particles, which is the ratio between potential energy to kinetic energy. Mathematically Coulomb coupling parameter is given as, Г = <P.E>/<K.E> ≡
1.3 Complex (dusty) plasma and applications
Plasma consists of electrons, ions, and neutral atoms; in addition to dust particles is known as dusty (complex) plasma. Due to dust particles, the physical properties of the plasma become complicated; that is why we call them also complex plasma. The study of dusty plasmas has become a developing branch of plasma physics in the field of sciences, technologies, and space. The study of dusty plasmas had become interesting for research of laboratory plasma when the formation of dust and dust trapping was observed during the plasma etching of silicon wafers and to limit the deposition rate when powder formation in plasma-enhanced CVD was identified. Dust is present everywhere in the space, such as interplanetary dust in planetary rings and in comet tails, and also it have present in the atmosphere and earth magnetosphere. These charged particles interact with each other and with the plasma constituents such as electrons, ions, and neutral atoms due to which plasma behavior becomes complicated [8]. These charged dust particles change the properties of plasma by electric and magnetic fields. The value of the Coulomb coupling parameter between dust particles is high due to the massive dust charge, which leads to the liquid and solid phase of the dust system at room temperature. For study the phase transitions and structural properties of solids, Yukawa balls and plasma crystals are appropriate systems. Plasma with dust particles can be termed as either “dust in plasma” or “dusty plasma” depending on the ordering of several characteristic lengths and radius between interacting particles (
In industrial applications, dust particles distributed in the plasma and produced disturbing effects in plasma. This contamination in the plasma has devastating effects on the fabricated circuits. On the other side, applications such as surface processing make the use of dust particles that have spread in the plasma. For example, the growth of carbon-based nanostructures on the surface used for electronic devices such as sensors, silicon-based films which have used in solar cells, and flat-panel displays illustrates an enhanced performance of nanoparticles produced in the plasma through chemical reactions, are inserted into the film. Through plasma processing, the coating of particles has produced. Plasma-based materials processing technologies have widely used in the manufacturing of integrated circuits. To etch, sputter, or modify the surface properties of silicon wafer, chemically reactive plasma have used. The fine dust particles created in plasma chemical systems have useful and exciting features that also control their compositions and size. It has used to grow or modify existing materials.
1.3.1 Merits and demerits of dust particles
Initially, the dust has not considered a useful technological consequence in the plasma. It has simply considered an unwanted pollutant in the plasma. To minimize the negative influences of dust particles in the plasma leads to the development of material science. The nanoparticles have considered as the basic building blocks of nanotechnology in plasma discharges. There are many advantages of dust particles in dusty plasmas such that nanocrystalline silicon particles have used to enhance the lifetime and efficiency of silicon solar cells, which have developed in silane plasmas. Dust particles have used to improve the surface properties of materials by applying plasma-enhanced CVD systems. The thin films produced by PECVD systems of TiN in an amorphous Si3N4 matrix have very high elastic modulus and hardness. In hydrocarbon plasmas such as methane or acetylene, carbon-based nanostructures have developed to govern thin carbon films, which lead to materials of high hardness, wear-resistance, and chemical inertness. In Ar/CH4 plasmas, the fabrication of nanocrystalline diamond films has done. These films have unique properties such as high hardness, chemical inertness, and extreme smoothness [9]. Dust particles are also used in the ceramic industry for sintering and in the fabrication of hard coatings, and also used in optical devices. Dust particles decrease the performance and the yield of many electronic devices. In the semiconductor industry, dust particles reduced the performance and yield of semiconductors. Dust particle contamination in the medical field during the production of different kinds of medicines has serious issues. The dust particles are of micron-sized, which reduces the adhesion of thin films of different materials due to deposition on the surfaces and also creates dislocations. In industrial applications, dust particles contamination in the plasma creates many defects in the manufacturing of microchips and fabricated circuits. Dust particles disturb the stability and the safety of the plasma in fusion reactors.
2. Molecular dynamics simulations
Over the last seven decades, the computer performance’s speed to elementary calculations has increased by 1015 factor. The computer memories, data storage also increased at a similar speed. Nowadays, by using computer simulation, we can save both time and money. The fundamental purpose of computer simulation is to guide the real experiment more precisely. Computer simulations used to predict various properties of gases, liquids, solids, and biological organisms. It is very useful for checking theoretical results, understanding experimental observation for the case where no academic data available. It also allows us to the identification of essential processes and visualization of the system [10]. The molecular dynamics simulations (MDS) one of the computer simulations techniques, in these technique atoms and molecules, are assumed to follow Newton’s law as
2.1 Numerical model and algorithm
NEMDS is used to obtain the trajectory of dust particles’ motion of a system [13] that interacts with each other through an interparticle Yukawa potential [14]. Homogeneous nonequilibrium molecular dynamic simulation (HNEMDS) approach have used for the calculation of thermal conductivity of complex (dusty) plasma liquids, which are molded, using a most common Yukawa (screened Coulomb) potential for charged particles [15] and has the following form,
Here “
where in Eq. (2),
Where
Where
In Eq. (6),
When an external force field parallel to the z-axis is of the form
In Eq. (8),
In this study we have used the same method as employed in our earlier work of 3D strongly coupled dusty plasmas [11, 12]. The most computational time consuming part of used algorithm is to compute the interparticle interactions (force and internal energy). It has been shown in our previous work that the proposed method has advantage to calculate Yukawa forces and relevant energy in appropriate computational time with reasonable computational power. In our present case, the HNEMD method is used to compute the thermal conductivity of 2D plasma systems and production stage of thermal conductivity is obtained between 106/ωp and 2 × 106/ωp time units for each plasma states. It shows that the used method is computational time cost-effective and power saving as compared to earlier methods based on different numerical schemes [12, 14, 26, 27].
3. Simulation results and discussion
In this section, the processing of the data of our computer simulation gave us the numerical results of the thermal conductivity of 2D complex (dusty) plasmas. We have used HNEMD simulations over the wide range of plasma Coulomb Couplings Г (═10, 500) and four higher Debye screening strengths
Figures 1 and 2 present the simulation results obtained by applying the Evan-Gillan HNEMD approach of thermal conductivity (
Figures 1 and 2 display the normalized thermal conductivity (
It has proposed from these figures that measured results of
4. Summary
In this work, we have derived the plasma thermal conductivity of 2D SCDPs liquids over a suitable range of plasma couplings (10 ≤ Γ ≤ 500) and screening strengths (4.5 ≤
Acknowledgments
The authors thank Z. Donkó (Hungarian Academy of Sciences) for providing his thermal conductivity data of Yukawa Liquids for the comparisons of their simulation results, and useful discussions. They are grateful to the National Advanced Computing Center of National Center of Physics (NCP), Pakistan, for allocating computer time to test and run their MD code.
Abbreviations
SCCNPs | strongly coupled complex nonideal plasmas |
HNEMD | homogeneous nonequilibrium molecular dynamics |
Γ | Coulomb coupling |
κ | Debye screening length |
F* | external force field strength |
HNEMD | homogenous nonequilibrium molecular dynamics |
NEMD | nonequilibrium molecular dynamics |
MD | molecular dynamics |
InHNEMD | inhomogenous nonequilibrium molecular dynamics |
SCP | strongly coupled plasma |
EMD | equilibrium molecular dynamics |
λ | thermal conductivity |
λ0 | normalized thermal conductivity |
PBCs | periodic boundary conditions |
VP | variance procedure |
HPMD | homogenous perturbed MD |
N | number of particles |
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