Breaking the Quality–Throughput Trade-Off: A Chaotic Microreactor Enabling Continuous Synthesis of High-Performance High-Entropy Prussian Blue Analogues

Abstract High-entropy Prussian blue analogues (HE-PBAs) for sodium-ion batteries face a quality–throughput trade-off: slow batch addition suppresses [Fe(CN)6]4– vacancies, whereas faster feeding increases defects and water. We develop a continuous recirculation chaotic microreactor integrating a 33-hole crossflow inlet with an oscillating feedback mixing chamber. CFD and dye-tracer tests, supported by Poincaré sections, Lyapunov exponents, Shannon entropy, and engineering metrics, confirm coupled vortex, feedback, and oscillatory flows that create chaotic advection, extreme velocity gradients (∼104 s–1), and subsecond mixing. At a metal-salt feed rate of 5 mL min–1 with ferricyanide recirculation at 300 mL min–1, the reactor continuously yields HE-PBAs with fewer vacancies and less crystalline water than batch products. The resulting cathode delivers 77 mAh g–1 at 5000 mA g–1, retains 61.5% after 2500 cycles, maintains 76.8 mAh g–1 at −20 °C, and achieves 82.8% full-cell retention after 500 cycles, demonstrating scalable chaos-engineered HE-PBA synthesis.