Explosive electric breakdown due to conducting-particle deposition on an insulating substrate

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Electric breakdown in substrates with adsorbed particles is a critical phenomenon.
• The behavior of adsorbed/desorbed particles influenced by electric fields is not fully understood.
• Percolation transitions are fundamental in understanding conductivity and material properties.

Purpose of the Study:

• To develop a theoretical model for electric breakdown of substrates with field-dependent particle adsorption/desorption.
• To investigate how tuning adsorption probability affects the nature of the breakdown transition.
• To establish a connection between this model and established statistical physics models.

Main Methods:

• Introduction of a novel theoretical model incorporating field-dependent adsorption/desorption probabilities.
• Analysis of the model in different limits, including mapping to the q-state Potts model.
• Comparison with the traditional bond percolation model.

Main Results:

• The electric breakdown transition can be tuned from continuous to explosive by adjusting the relative strength (q) of field dependence.
• In a specific limit, the model maps exactly to the q-state Potts model, with a discontinuous transition occurring at q = 4.
• In another limit, the model recovers the behavior of the traditional bond percolation model.

Conclusions:

• The proposed model provides a framework for understanding electric breakdown with tunable transition dynamics.
• It demonstrates a potential experimental realization of a truly discontinuous percolation transition.
• The study highlights the role of local electric fields in governing particle dynamics and macroscopic material properties.