Statistical mechanics of equilibrium charging of metallic aerosol particles with free-electrons at elevated temperatures

Abstract

It was suggested by Mayya (1995, J. Aerosol Sci. 26, 151) that unlike conventional charging, free-electron charging of particles at elevated temperatures under the conditions of thermo-electronic emission and maintained electron concentration would be an experimentally realisable equilibrium charging process. Here we present expressions for the particle charge distributions attained in this process, both using Fermi-Dirac statistics for the partition functions as well as the method of equilibrium kinetics. The resulting theory describes the final state to which charge distributions would tend at a given temperature, complementary to the current non-equilibrium theories of free-electron charging in electropositive gases. The existence of similar equilibrium processes in combustion literature is pointed out. Based on recent developments in cluster physics, it is shown that the free-energy of a charged particle of radius R carrying n ( = 0, ± 1, ± 2, …) excess (or deficient) electrons is − nkT ln( 1 2 CΛ 3 ) − nW + ϵ 2n(n + 1 - 2α) 2R where, C, Λ are the concentration and the thermal de Broglie wavelength of the electrons in the gas respectively, s is the unit charge and α is a parameter that relates the electron work function W∗ of a cluster to that ( W) of its bulk state through the relation, W∗ = W − (1 − α) R . Quantum-mechanical estimates place α in the range of 0.38–0.42.