The time response of plasmonic sensors due to binary adsorption: analytical versus numerical modeling

In order to allow for multiscale modeling of complex systems, we focus on various approaches to modeling binary adsorption. We consider multiple methods of modeling the temporal response of general plasmonic sensors. We start from the analytical approach. The kinetics of adsorption and desorption is modeled both as a first order reaction and as a second-order reaction. The criteria for their validity and the choice between them in the case of two-component adsorption are established. Due to the nonlinearities of the second-order reactions and the lack of their analytical solutions, computer-aided modeling is considered next, also in multiple ways: the employment of numerical solvers, fitting of experimental results, the stochastic simulation algorithms and the employment of artificial neural networks (ANN). The examples we present illustrate the advantages and disadvantages of the particular approaches. The goal is to aid the concurrent multiscale modeling of adsorption-based devices. Machine learning in ANN performed here is used to estimate the equilibrium values of adsorbed quantities. The obtained results show that to train an ANN for the estimation of the equilibrium adsorption quantities the Levenberg–Marquardt and the Bayesian regularization algorithms are less efficient than the quasi-Newton BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm.