The influence of the material and the form on the charge of a dust particle in a plasma

The world of dusty plasmas is simple: dust particles are perfect spheres, electrons from the plasma that reach the particle are all absorbed, and the charge of the particle q can be determined from its floating potential Φ_f using q = C · Φ_f , where C is the electrical capacitance of the particle, equivalent to that of a spherical capacitor.

However, this is not the case in the real world. Dust particles have arbitrary, non-spherical shapes and are made of a wide variety of electrically conductive or insulating materials. A key material property that distinguishes conductive from dielectric particles is the electron-sticking coefficient s_e. Theoretical calculations predict s_e to be significantly less than 1 for dielectric particles. Measurement of s_e is very difficult, as it involves electron energies below 5 eV, and measurement techniques based on electrical conductivity do not work for insulating materials.

We have developed a dusty plasma-based method for measuring s_e. Using this method, we were able to demonstrate that s_e is in fact significantly less than 1 for Silica. This is relevant because it affects the secondary electron emission of glass walls. Moreover, previously unexplained observations, such as the selefpropelled motion of the so-called Janus particles, can be explained by this finding.

To determine s_e for materials such as MgO or Al₂O₃, which are not spherical, the electrical capacitance of these particles must be known. Through experiments with small clusters of spheres and ZnO tetrapods and simulations of charging of aggregates of monomers, we have shown that the formula q = C · Φ_f always yields the correct charge if the electrical capacity of the dust particle is used for C. The so-called "orientation-averaged equivalent sphere" provides a very good approximation for calculating the capacitance- However, the "smallest enclosing sphere" approximation is never accurate.