SPR sensors enhanced by nanomaterials for monitoring heavy metal ions in water: A mathematical modeling

Surface plasmon resonance (SPR) sensors enable label-free readout of refractive-index (RI) changes at metal–dielectric interfaces and are promising for on-site water monitoring, whereas ICP-MS/AAS lack portability. We model prism-coupled SPR using a CaF 2 prism and a Cu/Si 3 N 4 stack overlaid with graphene-family films at 633 nm. Four overlayers—graphene, semiconducting single-wall carbon nanotubes (s-SWCNTs), graphene oxide (GO), and reduced graphene oxide (rGO)—are compared via a transfer-matrix approach. Metrics include resonance-angle shift (Δθ), angular sensitivity (S), detection accuracy (DA), quality factor (QF), figure of merit (FoM), limit of detection (LoD), and a combined sensitivity factor (CSF) in deionized water and heavy-metal solutions. Simulations reveal a dual-regime design: rGO maximizes raw sensitivity (318.21° RIU −1 for Pb 2+ ) with LoD ≈ 1.57 × 10 −5 RIU, whereas GO provides the sharpest resonances (QF ≈ 195 RIU −1 ; DA ≈ 0.64); graphene and s-SWCNTs are intermediate. Electric-field profiles yield a penetration depth of ≈50–52 nm with the 2D layer at the field maximum. We justify the CaF 2 /Cu choice, map trade-offs across 2D films, and outline functionalization, scalable fabrication, stability, and miniaturization, alongside microfluidic, multi-wavelength, and AI-assisted validation toward meeting WHO/EPA guidelines.