Page 17 - Synthesis of Functional Nanoparticles Using an Atmospheric Pressure Microplasma Process - LiangLiang Lin
P. 17

å dt 1 j=1
b n + 1jj
å j=2
(1+d )E n 2jjj
(1.3)
Introduction - Plasma and Microplasma-assisted Nanofabrication
Where J is the nucleation rate, β is the collision-frequency function for collisions between molecules, ns is the equilibrium saturation monomer concentration at temperature T, S is the saturation ratio, and Θ is the dimensionless surface tension and can be calculated as below:
Q=ss1 (1.2) kT
Where σ is surface tension, s1 is the surface area, k is Boltzmann's constant and T is the nucleation temperature.
In the second one, instead of using the nucleation rate, particle formation is simulated by applying the aerosol general dynamic equation to a discrete representation of the particle size spectrum for monomers and small clusters. In this model, the rate of change in the monomer concentration is writen below:
 dn
1 =-n
¥¥
 Where nj is the equilibrium saturation concentration of molecules, β is the collision-frequency function between molecules, δ2j is the Kronecker delta function, and E is the evaporation coefficient. In the particle nuclestion process, it is reasonable to assume all gas-phase particles are much smaller than the mean free path for collisions, together with an assumption of Boltzmann distribution at equilibrium, the evaporation coefficient can be expressed below:
Eg =b1,g-1ns exp{Q[g2/3 -(g-1)2/3]} (1.4)
Discrete model presumably treats exactly the subcritical cluster dynamics. However, it was limited by the accuracy of the numerical solution method as well as the physical modeling of coagulation and evaporation coefficients. By contrast, the nucleation-coupled model inherently neglects cluster-cluster coagulation and cluster scavenging of stable particles. As a result, it has an apparent advantage in computational economy: it is easily executed on a microcomputer, whereas the discrete model in the condensation/evaporation-controlled regime typically requires a supercomputer.
1.3 Microplasma-assisted Nanomaterials Synthesis
1.3.1 Microplasma
According to the Paschen’s law, the breakdown voltage of a discharge for a certain operating gas is a function of the pressure and the gap length between two electrodes. Thus, it becomes possible to ignite and sustain confined plasmas at high pressures even at the atmospheric pressure by applying a relatively low voltage. New experimental findings, reported recently, provide increasing evidence that the confining of plasmas to small dimensions will lead to new physical behaviors.65–67 Microplasma, as a special category of plasma, refers to a discharge which is confined within submillimeter length scale in at least one dimension. Due to the increased surface-to-volume ratio and the decreased electrode spacing of plasmas at
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