Van der Waals-Driven Network Restructuring Explains Time-Dependent Piezoresistivity in Soft Nanocomposites

TL;DR

The paper addresses the puzzling time-dependent piezoresistivity observed in carbon-elastomer composites, where traditional homogenized or microstructural models fall short. It hypothesizes that van der Waals attractions promote a conductivity-promoting network prior to curing, which deformation disrupts, while viscoelastic relaxation enables partial reformation over time; this interplay yields the observed time-dependent resistivity. A novel network-based microstructural model combines a discrete aggregate representation with a mesh-free, quasi-static viscoelastic scheme inspired by bond-based peridynamics, minimizing the total energy $U_ ext{total} = U_ ext{vdw} + U_ ext{elastic}$ to reach equilibrium. The simulations reproduce key experimental phenomena—long-timescale resistivity decay, non-monotonic secondary peaks upon strain relaxation, and density-dependent amplification—supporting the view that network restructuring governs piezoresistivity beyond simple tunnelling models.

Abstract

Carbon-elastomer composites exhibit complex piezoresistive behaviour that cannot be fully explained by existing macroscopic or microstructural models. In this work, we introduce a network-based modelling methodology to explore the hypothesis that van der Waals interactions between carbon particles contribute to the formation of a conductivity-promoting network structure prior to curing. We combine a discrete aggregate-based representation of filler with a mesh-free, quasi-static viscoelastic model adapted from bond-based peridynamics, resolving equilibrium states through energy minimization. The resulting particle networks are analysed using graph-theoretic measures of connectivity and conductivity. Our simulations reproduce several unexplained experimental phenomena, including long-timescale resistivity decay, non-monotonic secondary peaks upon strain release, and the increasing prominence of these features with higher filler density. Crucially, these behaviours emerge from the interplay between viscoelastic stresses and van der Waals interactions. We show that the resistance response of the network operates over different characteristic timescales to the viscoelastic stress response. The approach has potential for understanding and predicting emergent behaviour in composite materials more broadly, where material characteristics often depend on percolating network structure.

Figures (12)

• Figure 1: Piezoresistive behaviour of a silicone/carbon black composite, tested as described in ritchie2024electromechanical, displaying time dependence and non-monotonic secondary peak of resistivity
• Figure 2: Structure of a network of aggregates (25 aggregates of 15 particles + 25 aggregates of 5 particles) prior to, and post energy minimization under van der Waals interactions
• Figure 3: Graph measures with minimization progress, gradient tolerance represents how close the simulation is to a local minimum (equilibrium). The effect of the van der Waals interactions is to increase network connectivity and decrease resistivity by several orders of magnitude
• Figure 4: Simulation Results - $\frac{1}{\overline{k}}$ and $\overline{\sigma}$ for 25 aggregates of 15 particles and 25 aggregates of 5 particles at various densities under 50% uniaxial strain. Time dependence, non-monotonic secondary peak, and increasing significance of non-monotonicity with filler density is reproduced
• Figure 5: Experimental results for comparison - measured resistivity of Ecoflex 0045 with varying densities Vulcan XC72R carbon black under 50% uniaxial strain, produced and tested as described in ritchie2024electromechanical