Transiently amplified fluctuations assemble dissipative materials

Abstract

Chemical reactions assemble supramolecular materials with finite lifetimes, responsiveness to stimuli, and the capacity to self-heal after perturbation. These dynamic behaviors arise from a reaction cycle that switches a molecule between associating and nonassociating states via two independent pathways, each driven by a distinct chemical reagent. Here, we show that this same network architecture can transiently amplify small concentration fluctuations, leading to a pronounced, spontaneous increase in the yield of assembled material. Following a small perturbation in reagent supply, the chemical kinetics do not immediately relax toward a steady state; instead, they initially evolve farther from equilibrium and promote the assembly of thermodynamically unstable products. For a model supramolecular system, this dynamical effect produces a strong transient amplification of assembled material above its steady-state level. By analyzing the conditions for transient growth and its maximum, we find that steady states farther from detailed balance can exhibit stronger amplification and higher transient yields. Although these excursions are short-lived, accumulating experimental evidence suggests that analogous dynamics already occur in chemically active supramolecular materials. The mathematically precise conditions identified here suggest opportunities to amplify fluctuations in the design of responsive materials.