An LSPR-Based Kinetic Framework for Polyelectrolyte Molecular Weight Determination: A Proof-of-Concept Study

Determining the molecular weight of polyelectrolytes remains a persistent challenge because conventional techniques such as size-exclusion chromatography (SEC) often require added salt, calibration against neutral polymers, and complex optimization to overcome chain-column interactions. Here we introduce a kinetics-based method that employs Localized Surface Plasmon Resonance (LSPR) to measure the real-time electrostatic complexation of poly(ethylenimine) (PEI) and poly[1-[4-(3-carboxy-4-hydroxyphenylazo)benzenesulfonamido]-1,2-ethanediyl, sodium salt] (PAZO). By extracting association and dissociation rate constants from concentration-dependent binding transients, we establish a calibration-free approach to determining the number-average molecular weight (M_n) of polyelectrolytes under dilute, salt-free conditions. Using the known M_n of PEI, the M_n of PAZO was calculated as 257,400 g mol^-1, corresponding to a degree of polymerization of 642. This analysis assumes symmetry of the association rate constant (k_on) across binding orientations, an assumption justified by the reciprocal nature of electrostatic interactions. The results highlight LSPR-based kinetics as a powerful, surface-sensitive alternative to traditional methods, offering a broadly adaptable strategy for characterizing charged polymers and other biomolecular systems. This study is presented as a proof-of-concept demonstration, emphasizing the novelty and feasibility of the LSPR-based kinetic framework rather than exhaustive validation of molecular weight determinations. By focusing on methodological innovation, the work highlights a generalizable strategy for polyelectrolyte characterization that can be extended and refined in future investigations.