Modeling of the nanoparticle coagulation in pulsed radio-frequency capacitively coupled C ₂ H ₂ discharges

Abstract

The role of pulse parameters on nanoparticle property is investigated self-consistently based on a couple of fluid model and aerosol dynamics model in a capacitively coupled parallel-plate acetylene (C 2 H 2 ) discharge. In this model, the mass continuity equation, momentum balance equation, and energy balance equation for neutral gas are taken into account. Thus, the thermophoretic force arises when a gas temperature gradient exists. The typical results of this model are positive and negative ion densities, electron impact collisions rates, nanoparticle density, and charge distributions. The simulation is performed for duty ratio 0.4/0.7/1.0, as well as pulse modulation frequency from 40 kHz to 2.7 MHz for pure C 2 H 2 discharges at a pressure of 500 mTorr. We find that the pulse parameters, especially the duty ratio, have a great affect on the dissociative attachment coefficient and the negative density. More importantly, by decreasing the duty ratio, nanoparticles start to diffuse to the wall. Under the action of gas flow, nanoparticle density peak is created in front of the pulse electrode, where the gas temperature is smaller.

Simulation of nanoparticle coagulation in radio-frequency C 2 H 2 /Ar microdischarges

“…4 that a local maximum is presented in front of the showerhead electrode, which is due to the fact that the thermophoretic force moves the nanoparticles away from the showerhead electrode to the presheath region where the gradient of the neutral gas temperature is maximum. Compared with our previous studies, [19] the nanoparticle density in the bulk plasma for MDs is much higher, suggesting that more collisions between background gas and electrons occur due to higher gas pressure, and this leads to the increase of nanoparticles and the shrinking in the sheaths. Therefore, the nanoparticles' profile has a great difference between atmospheric pressure microdischarges and low pressure radio-frequency discharges.…”

“…Therefore, the fluid model is used to describe the particle formation and growth by nucleation to further growth by agglomeration via a coupling to the aerosol dynamics model. [18,19] In this one-dimensional (1D) fluid model, the continuity balances equations are taken into account to describe the electrons, ions, radicals, and molecules mass density, the momentum equations for electrons, ions, and radicals can be estimated by the drift-diffusion approximation. However, ions' masses are much larger than the electrons', hence the effective electric field is introduced to follow the inertia effects.…”

Mode transition induced by gas pressure in dusty acetylene microdischarges: two-dimensional simulation

“…where G j is the particle flux and S j represent the sink and source terms of particle j. The momentum balance equation is estimated by a drift-diffusion approximation, which suggests that the small species (electrons, ions, and molecules) flux terms consist of a drift and a diffusion term [15,16],…”

Mode transition in dusty micro-plasma driven by pulsed radio-frequency source in C 2 H 2 /Ar mixture

“…Fluid models solve the continuity equations for each species j including electrons, ions, radicals, neutral gases, and nanoparticles [20,21] in the C 2 H 2 /Ar MDs plasma is described by…”

“…In this article, we mainly studied the behavior of nanoparticles in C 2 H 2 /Ar pulsed radio-frequency MDs plasma, which are generally produced by a series of chemical reactions. [20,21] The fluid model [9] is extended by adding the neutral gas flow and heat transfer equations, thus the role of thermophoretic force on the nanoparticles formation and growth mechanism is presented. The effects of pulse width, repetition frequency on electrons, ions, radicals as well as nano particles densities, electron temperature, plasma uniformity are our mainly concerned.…”