Reaction–Transport Coupling Drives Spatiotemporal Organization in Fuel‐Driven Supramolecular Polymerization

Abstract

ABSTRACT Chemically fueled supramolecular systems provide a versatile platform for generating nonequilibrium structures and dynamical instabilities, including chemical oscillations and traveling waves reminiscent of biological organization. However, a minimal mechanistic framework capable of capturing the emergence of such spatiotemporal order is still lacking. Here, we develop a minimal reaction–transport framework for fuel‐driven supramolecular polymerization that couples activation–deactivation chemistry with cooperative assembly, fragmentation, and polymer length‐dependent diffusion. The model captures autonomous oscillations arising through a Hopf bifurcation and demonstrates how temporal instabilities evolve into spatial self‐organization upon inclusion of transport. We show that the nonlinear interplay between reaction kinetics and state‐dependent mobility gives rise to traveling polymerization fronts, oscillatory wave dynamics, and complex spatiotemporal patterns. The propagating fronts exhibit near‐ballistic dynamics, revealing a fundamentally nonequilibrium transport mechanism emerging from reactive feedback and dynamically evolving diffusivity. These findings establish a minimal physical framework connecting dissipative self‐assembly, nonlinear transport, and active matter, while providing design principles for programmable supramolecular materials capable of autonomous spatiotemporal organization.