Extension of integral of first passage times towards multi-point polymer adsorption

We present a comprehensive extension of the integral of first passage times (IFS) method to investigate the adsorption kinetics of polymers with multiple binding sites on planar surfaces. While effective for single-point adsorption, the original IFS method was limited in capturing the complex kinetics of multi-point adsorption due to inadequate reaction coordinates and theoretical frameworks. Our approach introduces a center-of-mass-based reaction coordinate and a generalized kinetic model that accounts for multi-barrier free energy landscapes characteristic of collective polymer diffusion and binding. This theoretical advancement, implemented using the adaptive bias force method for efficient sampling, enables prediction of adsorption kinetics across timescales from nanoseconds to seconds. Our results demonstrate that adsorption behavior is governed by two key factors: the number of binding monomers primarily controls desorption barriers and long-term stability, while the configuration of pre-adsorbed layers significantly modulates both adsorption and desorption rates. Polymers with three or more binding sites exhibit effectively irreversible adsorption due to exponentially increasing desorption barriers, whereas different adsorbed layer configurations lead to distinct equilibrium coverages and kinetic profiles. This extended IFS framework provides critical insights for designing functional surfaces in nanoscale sensing, macromolecular recognition, and tailored polymeric coatings where precise control over adsorption kinetics is essential.