Numerical tool for estimating the dielectric constant, the thickness, and the coverage of immobilized inhomogeneous protein films on gold in aqueous solution

A numerical simulation tool is reported for nanometer thin and inhomogeneous immobilized protein films on gold in aqueous solution. It allows for the first time, to the best of our knowledge, the simultaneous assessment of refractive index, film thickness, and surface coverage. The model relies on and combines the convective diffusion equation, the Langmuir adsorption isotherm, and the Helmholtz equation, with appropriate boundary conditions. These three differential equations were jointly solved using a multiphysics software. The physical film parameters were extracted employing an optimization procedure for immobilized bovine serum albumin, hemoglobin, and neutravidin films. The relatively good agreement between the extracted values for the refractive index, film thickness, and surface coverage and the corresponding values reported in the open literature show the correctness of the proposed methodology.