Percolation-Mediated Emergence of Computation in Conductive Ionic Polymer Networks: A Quantitatively Constrained Theoretical Framework

Abstract

Scientists have long sought to understand the brain and replicate its computational capabilities, but silicon-based neuromorphic systems remain costly and complex. Motivated by naturally occurring chemical systems, a theoretical framework is developed that links conducting ionic electroactive polymer networks with biological neural networks to explore brain-like computation. Using concepts from non-equilibrium critical phenomena, parallels are drawn between an abiotic polymer blob and a biological brain. Inspired by studies of percolation-based brain function and the demonstration of a polymer hydrogel playing Pong in real time, we examine whether both systems can be described by critical connectivity transitions on random graphs. Analysis of reported current fluctuations in polymer hydrogels reveals scaling behavior consistent with three-dimensional percolation-like critical dynamics, although available evidence is insufficient to uniquely distinguish these phenomena from isotropic universality classes. To connect microscopic transport with macroscopic connectivity, threshold-based conduction rules are replaced by a smooth ionic activation function coupled with a Nernst-Planck-Poisson-mechanical description, enabling a coarse-grained mapping from ionic concentration fields to probabilistic bond formation and motivating a generating-function treatment of network evolution. Performance growth is described by a Weibull-type law whose shape parameter is <inline-formula> <tex-math notation="LaTeX">$k =1.66$ </tex-math></inline-formula> (95% CI [1.58, 1.76]), consistent with <inline-formula> <tex-math notation="LaTeX">$k \approx ~1.8~\pm ~0.3$ </tex-math></inline-formula> obtained for the neural case; the percolation threshold <inline-formula> <tex-math notation="LaTeX">$\lambda _{c} \approx ~0.29$ </tex-math></inline-formula> coincides with the continuum threshold for overlapping spheres, and the derived Rentian exponent spans <inline-formula> <tex-math notation="LaTeX">$\alpha _{Rent} \approx ~0.54$ </tex-math></inline-formula>-0.79, below unity in all cases. Geometry and temperature adjustments are predicted to reduce the memory-acquisition timescale from ~1300 s to ~33 s. Experimentally testable criteria are proposed to validate or falsify the framework and clarify the limits of equivalence between conductive polymer networks and biological neural systems.