Adsorption-driven Graphene Oxide SPR Biointerfaces: Coupled Thermodynamic, Kinetic, and Optical Modeling with Effective-layer Validation

Abstract This work presents a theoretical modeling framework for adsorption-driven graphene oxide (GO)-functionalized surface plasmon resonance (SPR) biointerfaces. Rather than describing a specific capture-probe biosensor, the model focuses on the effective optical transduction of molecular accumulation at a GO-modified interface. The framework couples transfer-matrix optical modeling of a prism/TiW/Au/GO multilayer structure with a generalized Langmuir–Hill adsorption formalism, allowing analyte concentration, surface coverage, effective interfacial refractive index, and plasmonic resonance shift to be linked within a unified description. The optical response is evaluated at 633 nm under angular interrogation. Adsorption is represented through effective surface coverage, an optically equivalent biolayer thickness, and a concentration-dependent refractive-index perturbation. Temperature dependence is incorporated using a van’t Hoff-type treatment for enthalpy-driven adsorption, while time-dependent behavior is described using first-order association–dissociation kinetics as an ideal reversible limiting case. Three representative adsorption regimes are considered, corresponding to weak, moderate, and cooperative surface accumulation, with equivalent dissociation constants ranging from approximately 1.67 to 200 μ M. A formal optical optimization identifies Au, TiW, and GO effective thicknesses of 49 nm, 0.20 nm, and 0.20 nm, respectively, producing a deep SPR minimum and a narrow angular linewidth. Because the TiW and GO optima occur at the lower boundary of the optical-thickness scan, they are interpreted as effective interfacial parameters rather than literal physical monolayer thicknesses. Additional simulations using physically realistic GO thicknesses of 0.7–1.5 nm show that the adsorption-driven response is preserved, with low-concentration sensitivities remaining close to 0.037–0.038 deg μ M −1 . For the moderate adsorption regime, the model predicts a resonance shift of approximately 0.79 ∘ over 0–100 μ M, an effective biolayer thickness up to 2.72 nm, and a refractive-index sensitivity of 115.96 deg RIU −1 . The estimated detection limit is shown to depend directly on the assumed angular noise. For an angular resolution of 10 −3 degree, the model-estimated limit of detection is 0.027 μ M, while varying the angular noise from 10 −4 to 10 −2 degree gives limits from 0.0027 to 0.270 μ M. The temperature response is consistent with an exothermic adsorption case with Δ H ≈ − 26 kJ mol −1 , and the kinetic analysis provides characteristic association and dissociation times under the assumed single-rate model. The results establish a mechanism-aware computational framework for connecting adsorption thermodynamics, kinetic parameters, and SPR optical response at GO biointerfaces, while clearly identifying the effective-parameter and experimental-validation limits of the model.