Topology-Selected Molecular Pathways in the Ion-Tuned Pinch-Off Dynamics of Weak Polyelectrolyte Drops

Capillarity-driven pinch-off of polyelectrolyte drops underpins transformative technologies from high-resolution biofabrication to the precision processing of complex fluids. While multivalent ions are frequently used to tune these dynamics, the concurrent and often coupled effects of electrostatic screening and coordination-mediated bridging obscure the dominant mechanism governing filament destabilization. Here, we establish a unified framework demonstrating that topological constraint density acts as a fundamental selector of molecular pathways for multivalent-ion interactions. In solutions with weak topological constraints, divalent ions promote intrachain bridging and conformational compaction, accelerating pinch-off beyond electrostatic screening alone. In solutions with strong topological constraints, the response becomes nonmonotonic: divalent ions initially enhance transient interchain bridging and delay pinch-off, but stronger screening at higher ionic strength reduces effective overlap and shifts the dominant pathway back to intrachain compaction, yielding a topology-selected inversion. By reconciling the competition between electrostatic screening, intrachain collapse, and interchain reinforcement, this study reveals the molecular origin of extensional rheology in complex ionic environments. Our findings establish a quantitative basis for the rational design of industrial formulations, enabling the programmable control of fluid instabilities in advanced manufacturing and lab-on-a-chip platforms.