Electrochemical diffusion potential in a flame plasma: theory and experiment

Abstract

A flame doped with an appropriate additive to produce positive ions and free electrons is a quasineutral, weak, continuum plasma. When bounded by a metallic burner upstream and a metal plate downstream, the two electrodes and flame plasma can be viewed as a gas-phase electrochemical cell. When the ion (and electron) density varies continuously along the flame axis, an expression for the diffusion potential can be derived in terms of the concentration gradient. The familiar logarithmic dependence on the ion concentration is obtained. A plasma sheath develops at the metal plate electrode; it sustains a potential difference which can be modeled by a Boltzmann distribution of the electrons in the sheath. Since the plate has to be cooled in practice, the average sheath temperature is less than the flame temperature because the sheath occurs inside the thermal boundary layer which covers the plate electrode. Inevitably, the reduced sheath temperature affects the sheath voltage. Experimental measurements of the “cell” voltage are made for the two cases of a positive concentration gradient using a sodium plasma, and a negative gradient by doping the flame with methane. As predicted theoretically, the cell voltages have opposite signs. However, the magnitude of the cell voltage seems to depend significantly on the sheath temperature which appears to decrease steadily with increasing distance downstream from the burner. It is also possible that the measured cell voltages involve unknown surface contact potentials. When compared with solution concentration cells, gas-phase flame systems exhibit both similarities and differences.