Reversible thermal fusing model of carbon black current-limiting thermistors

Composites of carbon black particles in polyethylene exhibit an unusually rapid increase in resistivity as the applied electric field is increased, making this material commercially useful as current-limiting thermistors, also known as automatically resettable fuses, in this application the composite is in series with the circuit it is protecting: at low applied voltages the circuit is the load, but at high applied voltages the composite becomes the load. limiting the current to the circuit. We present a simple model of this behavior in terms of a network of nonlinear resistors. Each resistor has a resistance that depends explicitly and reversibly on its instantaneous power dissipation. This model predicts that in the soft fusing, or current-limiting, regime, where the current through the composite decreases with increasing voltage, a platelike dissipation instability develops normal to the applied held, in agreement with experimental observations, which is solely due to fluctuations in the microstructure.