Thermal Radiation from Nanoparticles

Abstract

The thermal radiation of small conducting particles was investigated in the region where the Stephan-Boltzmann law is not valid and strongly overestimates radiation losses. The new criterion for the particle size, at which black body radiation law fails, was formulated. The critical radius r c is expressed through a combination of temperature T and particle conductivity σ: thus r c = c(ћ/2πσkT) 1/2 . The approach is based on the magnetic particle polarization, which is valid until very small sizes (cluster size) where due to drop of particle conductivity the electric polarization prevails over the magnetic one. It was also shown that the radiation power of clusters, estimated on the basis of the experimental data, is lower than that given by theStephan-Boltzmann law.In the last years the amount of research in the field of nanotechnology, nanomaterials and nanosystems tremendously increased [1]. One of the most important trends in the nanotechnology is obtaining and using of nanopowders, which can be used in metallurgy, microelectronics, and medicine and food industry. Production and processing of nanopowders are frequently dealt with heating of nanoparticles to high temperatures when intensive thermal radiation can be expected.The problem is close related to dust plasma [2], and to the role of dust in fusion devices [3], where micro-and nano-particles are heated to high temperatures and radiation energy losses can play decisive role in the energy balance of the particles. The effect of metal clusters on emission spectra was discussed in [4].

On the thermal vacuum radiation of nanoparticles and their ensembles

“…In addition, we use more exact elec tric and magnetic polarizabilities computed within the Mie theory [6]. As a result, we come to the conclusion that the value of W/W SB reaches a maximum value of 95% for graphite particles with radii of 150-200 nm at a temperature of about 3000 K. The value of W/W SB sharply decreases with decreasing radius, which agrees with [4], whereas with increasing radius moderate fad ing is observed, in contrast to the "plateau" in [4]. For…”

“…For nanoparticles with radius r ≤ 1 μm and temperature T ~ 10 3 K, the condition r < λ is fulfilled, when the use of Stefan-Boltzmann's law leads to great errors. For such particles, the assess ment of PTR W based on the Kirchhoff law and the expression for the absorption cross section of equilib rium electromagnetic radiation by dipole particles [3] was carried out in [4]. It was established that for con ductive graphite and copper particles W ~ r 3 T 5 .…”

“…More over, W/W SB Ӷ 1 at r Ӷ 100 nm and W/W SB 1 for graphite at r > 1 μm and T > 10 3 K. This work aims at a numerical calculation of W for graphite and gold particles at temperatures of ~10 3 K and particle radii ranging from 100 to 1000 nm. In contrast to [4], we take into account real dielectric characteristics [5] and possible cooperative effect in the case of an ensemble of nanoparticles. In addition, we use more exact elec tric and magnetic polarizabilities computed within the Mie theory [6].…”

“…They can be significant when calculating direct heat exchange between particles with different material properties (SiC and Au particles in [9]), while the effects of mul tiple scattering are insignificant even for particles of micrometer size, as shown in [9]. Note also that the calculation in [4] was based on the first integral term (1) without the contribution of electric polariza tion. This is relatively well justified for good conduc tors (gold, copper), but for graphite particles both dielectric and magnetic polarizations are significant.…”

Influence of emissivity on behavior of metallic dust particles in plasmas

“…This is due to prevalence of the magnetic dipole component of the absorption efficiency factor for highly conductive metals at the low temperatures, which is proportional to the dust radius cubed. 25,42 For the temperatures above 2000 K, the electric dipole component can dominate in the absorption efficiency since the dust material becomes less conductive. That causes more gradual decrease of the emissivity with the dust radius at the high temperatures, because the electric dipole absorption efficiency is proportional to the radius.…”