Evidence of Universal Temperature Scaling in Self-Heated Percolating Networks

During routine operation, electrically percolating nanocomposites are subjected to high voltages, leading to spatially heterogeneous current distribution. The heterogeneity implies localized self-heating that may (self-consistently) reroute the percolation pathways and even irreversibly damage the material. In the absence of experiments that can spatially resolve the current distribution and a nonlinear percolation model suitable to interpret them, one relies on empirical rules and safety factors to engineer these materials. In this paper, we use ultrahigh resolution thermo-reflectance imaging, coupled with a new imaging processing technique, to map the spatial distribution ΔT(x, y; I) and histogram f(ΔT) of temperature rise due to self-heating in two types of 2D networks (percolating and copercolating). Remarkably, we find that the self-heating can be described by a simple two-parameter Weibull distribution, even under voltages high enough to reconfigure the percolation pathways. Given the generality of the phenomenological argument supporting the distribution, other percolating networks are likely to show similar stress distribution in response to sufficiently large stimuli. Furthermore, the spatial evolution of the self-heating of network was investigated by analyzing the spatial distribution and spatial correlation, respectively. An estimation of degree of hotspot clustering reveals a mechanism analogous to crystallization physics. The results should encourage nonlinear generalization of percolation models necessary for predictive engineering of nanocomposite materials.