Kinetic model for BTX adsorption on NiO surface in resistive MEMS gas sensors: determination of the energy components of the model.

We develop a multiscale kinetic model for gas detection by resistive MEMS gas sensors based on NiO. The model couples external mass transfer, multisite Langmuir-type adsorption including a dissociative channel, and surface diffusion on an energetically heterogeneous NiO surface with a flat core-shell grain structure (crystalline core, amorphous shell). Surface heterogeneity is described in two complementary ways. First, an effective medium approximation (EMA) compresses the distribution of adsorption energies and diffusion barriers into effective kinetic parameters. Second, a homotattic patch model explicitly resolves domains with distinct adsorption energies and rate constants. Linearization around equilibrium yields closed-form analytical solutions for local (0D) dynamics, which are extended to surface diffusion via modal analysis. These analytical results validate numerical solutions and quantify EMA accuracy relative to patch description. EMA proves adequate for fast sensor response estimates when energy distributions are narrow, while significant deviations at desorption peaks signal broad energetic heterogeneity requiring explicit patch modeling.