Untangling cation and anion contributions to refractive index changes in electrical double-layer capacitors

Abstract

Label-free optical microscopy and sensing techniques are gaining attention for investigating electrochemical reactions -critical for batteries, fuel cells, corrosion, chemical sensing, and bioelectrochemistry. Several studies have examined how perturbations of electrical double layer capacitors (EDLCs) affect the refractive index at metal-electrolyte interfaces and the consequent sensor output. However, the individual contributions of cations and anions to the overall optical response remain unexplored. We address this gap using coupled electrostatics and electrodiffusion models to simulate the metal-electrolyte interface, with resulting ion concentration profiles used to compute refractive index changes. We develop a mathematical model based on the Lorenz-Lorentz equation to estimate macroscopic refractive index changes using the concentration and molar refractivity of ions. We demonstrate this effect computationally using three optical configurations: Normal Incidence Reflection Modulation (NIRM), Surface Plasmon Resonance (SPR) with the Kretschmann-Raether configuration, and Localised Surface Plasmon Resonance (LSPR) via gold nanoparticles. Each method exhibits sensitivity to refractive index variations due to excess or depletion of cations and anions. For 1:1 sodium chloride electrolyte, we observe an asymmetric optical response upon polarity switching, with enhanced sensitivity at positive potentials due to chloride ions' higher molar refractivity relative to sodium ions. The response increases in inverse proportion to the optical field penetration depth at the sensing interface. These findings inform the design of highly sensitive optical sensors and offer insight into ion dynamics in biological systems, battery charge transport, and metrology of optical properties of ionic species.