Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle

This study theoretically investigates the force exerted on a nanoparticle (NP) by a clamped semiflexible chain in solution. The force exerted by the semiflexible chain on the NP is related to the chain’s conformational entropy, known as the entropic force. Under the weakly bending approximation, we derive an analytical formula for the entropic force using perturbation theory. This force can be divided into two components: parallel (f_ρ) and perpendicular (f_z, lifting the NP) to the initial vector at the clamped end. These two components are correlated with the local slope of the NP’s cross-section, with the component f_z additionally linked to the local curvature. We compare the magnitude of force f_z with the Euler buckling threshold f_c. The study reveals that as the chain becomes more compressed, f_z initially peaks at a value exceeding the mechanical limit and subsequently decreases to a steady-state value lower than f_c. This behavior significantly differs from the entropic force derived under flat wall confinement. In three dimensions, f_z always stays below the Euler buckling threshold and in two dimensions it is larger than f_c for most of the parameter space.