Investigation of Markovian and Non-Markovian Search Processes of Monomers of a Rouse Chain Confined in a Spherical Cavity

We study the process of monomers of a Rouse chain confined in a spherical cavity of radius Rb to search for a small opening of radius a on the cavity surface by combining scaling analysis and Langevin dynamics simulations. We show that the search process is nearly Markovian when the radius of gyration Rg of the chain is much smaller than Rb and becomes non-Markovian for Rg ≥ Rb. For the non-Markovian search process, we first derive a general scaling relation for the mean search time ⟨τ∞⟩ in the long chain limit and then explicitly determine the scaling exponents based on simulation results, ⟨τ∞⟩ ∼ Rb4a–1DH–3/2 and ⟨τ∞⟩ ∼ Rb5a–1DH–2 for the end and middle monomers, respectively, where DH is a generalized diffusion coefficient associated with the monomer motion. We further find that the Hurst exponent, which characterizes the persistence of the dynamics, decreases exponentially from approximately 1/3 to about 1/4 as the monomer position changes from the end to the middle. This result implies that the subdiffusion of monomers depends considerably on their positions in the chain under confinement, providing insight into the anomalous dynamics of confined polymeric systems.