Modeling Piezoresistive Behavior of Conductive Composite Sensors via Multi-State Percolation Theory

Flexible strain sensors, fabricated from high-elongation polymers and conductive filler particles, are proving an essential tool in the study of biomechanics using wearable technology. It has been previously shown that the resistive response of such composites, relative to the amount of conductive filler material, can be reasonably modeled using a standard percolation-type model. Once a certain critical fraction of filler material is reached, a conductive network across the sample is established and resistance rapidly decreases. However, modeling the more subtle resistance changes that occur while deforming the sensors during operation is more nuanced. Conductivity across the network of particles is dominated by tunneling mechanisms at the interfaces between the filler materials. Small changes in strain at these interfaces lead to relatively large, but nevertheless continuous, changes in local resistance. By assigning some arbitrary value of resistance as a dividing line between ‘low’ and ‘high’ resistance, one might model the piezoresistive behavior using a standard percolation model. But such an assumption is likely to lead to low accuracy. Our alternative approach is to divide the range of potential resistance values into several bins (rather than the usual two bins) and apply a relatively novel multi-state percolation theory. The performance of the multi-state percolation model is assessed using a random resistor model that is assumed to provide the ground truth. The model is applied to predict resistance response with both changes in relative amount of conductive filler (i.e., to help design the initial unstrained sensor) and with applied strain (for an operating sensor). We find that a multi-state percolation model captures the behavior of the simulated composite sensor in both cases. The multicomponent percolation theory becomes more accurate with more divisions/bins of the resistance distribution, and we found good agreement with the simulation using between 10 and 20 divisions.