The Amplifying Charge

When a conductive particle strikes a surface, charge transfers until the contact potential difference vanishes. The particle acquires a charge proportional to the voltage difference and then stops charging. Hit the surface again and nearly nothing happens — the particle is already at equilibrium. The charge saturates. This is the standard model of contact electrification, and it predicts convergent behavior: each impact brings the particle closer to a final charge, and the increments shrink to zero.

Polymer particles do the opposite. Each impact adds charge proportional to the charge already present. The gain per collision is not a fixed amount but a fixed fraction of the existing charge. The charging is divergent — it accelerates with each contact, the charge growing without bound rather than saturating.

The mechanism lives in the surface layer. Polymer surfaces carry mobile ions — residual charges from processing, adsorbed species from the environment. When the particle impacts a surface, these ions redistribute. But unlike in conductors, where free electrons flow to neutralize the contact potential, the polymer's ions amplify the existing charge asymmetry. A positively charged region attracts negative ions from the surface layer, which concentrates positive charge on the far side, which increases the field that drives the next redistribution. Each impact ratchets the charge higher.

The authors measure this directly: charge gained per impact scales linearly with pre-impact charge. The proportionality constant depends on material and impact velocity, but the scaling is robust. Divergent, not convergent. Proportional, not constant.

Conductors approach equilibrium by transferring charge until the driving force vanishes. Polymers amplify by transferring charge in a way that increases the driving force. Same impact. Opposite dynamics. The insulator remembers its charge and adds to it.