Graph-Based Kirchhoff Modeling of Non-Ohmic Electron Transport in Self-Assembled Nanonecklace Networks

Gold nanonecklace networks are promising platforms for single-electron switching, chemical sensing, and biogating devices because of their nonlinear current--voltage ($I$--$V$) characteristics arising from collective Coulomb-blockade transport. However, the mechanisms governing this macroscopic behavior remain poorly understood because experimental measurements are generally limited to the network topology and global $I$--$V$ response. To address this, we developed a graph-based Kirchhoff framework that represents a self-assembled nanonecklace network as a graph, with nodes corresponding to junctions between necklace segments and edges to the conducting segments themselves. The solver returns the active nodes, conducting subgraph, nodal potentials, and edge currents at each applied bias, while allowing the activation-voltage statistics, network density, and structural topology to be varied independently. The model reproduces the experimentally observed non-Ohmic response, $I \propto (V-V_T)^{\zeta}$, and shows that this behavior emerges from the collective, staggered activation of threshold junctions and voltage-driven percolation of the conducting subgraph. Independent parameter sweeps reveal that the mean activation voltage shifts the threshold $V_T$ while leaving $\zeta$ nearly unchanged, increasing network density raises $\zeta$ from approximately 1.9 to 3.1 and enhances current, and topology controls the response even at fixed density and node characteristics. These trends agree qualitatively with experimental observations and establish the model as a design tool for engineering collective transport in self-assembled nanonecklace devices.