Divergent Impact Charging of Polymer Particles

TL;DR

The paper challenges the conventional view that contact charging between dissimilar materials converges to a fixed polarity by showing that insulating polymers exhibit divergent charging, where the impact charge $\Delta q$ scales linearly with the pre-impact charge $q_i$ and features a divergence point $q_{i,0}$. Using single-particle collisions with precisely controlled impact conditions via acoustic levitation, the authors measure both $q_i$ and $\Delta q$ across multiple material pairings, revealing that $\Delta q = \Delta q_0 - \beta q_i$ with $\beta>0$ for insulators (divergent) and $\beta<0$ for conductors (convergent), including a near-unit slope for steel–steel. They propose a phenomenological mechanism in which adsorption of surface ions with polarity opposite to $q_i$ dominates charge transfer, combining a fixed bound charge and a loosely bound surface charge whose quantity scales with $q_i$. This framework accounts for the observed divergence in polymers and the convergence in conducting particles, and is supported by reanalysis of prior data when velocity/impact-number effects are controlled. The findings have broad implications for understanding contact electrification, challenging established models and offering a unified view in which conductivity governs the transition between divergent and convergent charging, with practical impact on processes involving polymer powders and triboelectric applications.

Abstract

When a particle contacts a surface of another material, it is commonly believed that the particle acquires an impact charge that scales inversely with its pre-impact charge and whose polarity is set by the materials. We show that this belief holds for conductive particles but fails for polymers. For polymers, the impact charge increases linearly with the particle's pre-impact charge. Its polarity is not determined by the materials but by the pre-impact particle charge relative to a divergence point at which the net charge transfer reverses. We attribute this divergence to the attraction of surrounding ions to the particle surface. These attracted ions carry polarity opposite to that of the particle, and their amount scales with the particle charge. They transfer to the opposing surface during contact, thereby defining the impact charge. We propose a phenomenological model for the divergent impact charge arising from this mechanism. Finally, we reexamine previous measurements and show that they support this mechanism.

Figures (5)

• Figure 1: (a) Schematic of the experimental apparatus and the levitated particle. (b) Example electrometer recording for a PS particle impacting a PTFE target. The red curve shows the charge signal ($q$) as a function of time ($t$) after background subtraction and correction for drift due to charge leakage (see End Matter for details). The levitator releases the particle at $t=1.0~\mathrm{s}$. The particle contacts the target at approximately $t=1.3~\mathrm{s}$, marked by the negative peak in the charge signal. The difference between the charge at release and at impact defines the particle’s pre-impact charge ($q_i$). After rebounding, the particle leaves the Faraday cage at approximately $t=1.6~\mathrm{s}$. The additive inverse of the difference between the charge at release and at exit from the Faraday cage defines the particle’s impact charge ($\Delta q$).
• Figure 2: Impact charge ($\Delta q$) against pre-impact charge ($q_i$). Impacts of (a) PMMA particles versus a PMMA target, (b) PS particles versus a PTFE target, (c) PMMA particles versus an aluminum target, (d PMMA particles versus a steel target, and (e) steel particles versus a steel target. (f) Summary of the regression lines of (a)-(e). The impact charge of steel (conductive) particles converges, whereas the impact charge of all polymer (insulating) particles diverges.
• Figure 3: Phenomenological explanation for (a) divergent charging of insulating and (b) convergent charging of conducting particles. Both particles have a positive pre-impact charge. The insulating particle loses negative charge during impact, thus obtaining a positive impact charge. The insulating particle loses positive charge during impact, thus obtaining a negative impact charge.
• Figure 4: Impact charge ($\Delta q$) of $200$ µm-sized PMMA particles in a cascade experiment. Each particle undergoes several successive impacts on steel plates at decreasing velocity. (a) Originally published scattered impact-charge distribution GROSSHANS2022117623. The impact charges filtered for normal velocities between (b) 30 m/s and 50 m/s and (c) above 50 m/s diverge. (d) Particle charge versus impact number ($n$) for two individual particles. One starts positively charged and remains positive; the other starts negatively charged and remains negative throughout subsequent impacts.
• Figure 5: Details of the experimental apparatus. (a) Gor’kov potential of the standing acoustic wave that traps the particle. (b) Unity-gain response of the analog section for sampling frequencies up to 1 kHz. (c) Red: raw electrometer signal during the first 0.4 s; blue: fitted 50 Hz grid-noise component using \ref{['eq:50Hz']}. (d) Signal after subtraction of the 50 Hz component. (e) Blue: raw electrometer signal after 1.0 s; red: filtered signal with grid noise removed. (f) Time-lapse composite of a particle collision. (g) Particle velocity before and after impact (red bar) as a function of the time since entering the camera window.