Abstract: The influence of topological constraints on the dynamic behavior of polymer chains constitutes a core scientific challenge in condensed matter physics and soft matter science. Herein, we employed molecular dynamics simulations to systematically investigate how static geometric features and dynamic flexibility of topological constraints regulate the equilibrium conformations and non-equilibrium dynamics of polymer chains within quasi-two-dimensional confinement models, encompassing both regular/disordered topological structures and rigid/flexible topological constraints. Under regular rigid lattice confinement, the diffusion coefficient D and relaxation time t_R vs the chain length N of the test chain adhere to the classical scaling relationships D ～ N^?1.5 and t_R～ N^3 with static dimensions independent of the lattice spacing—a result in excellent agreement with theoretical predictions. For small spacing regimes, the dynamic behavior of polymer chains in disordered rigid lattices is nearly equivalent to that in regular lattice systems, indicating that equilibrium topological fluctuations do not significantly alter the uniformity of the effective confinement tube diameter. This finding revises the expectations of Muthukumar's random medium model. Conformational rearrangements of flexible chains induce a "dynamic constraint enhancement effect": short-time internal motions and long-time overall diffusion of the test chain become decoupled, with the whole-chain relaxation time increasing by approximately 3-fold compared to rigid constraint systems. This effect arises from the additional contribution of topological friction. During constant-velocity stretching, the force on the test chain exhibits a significant overshoot phenomenon, and the whole-chain friction coefficient increases nonlinearly with stretching rate, directly confirming the critical role of topological friction in the nonlinear mechanical response of polymer chains. This work offers insights to deepen the understanding of dynamic laws in complex confined systems and may guide the optimization of polymer material dynamic properties.

Key words: Quasi-two-dimensional confined system, Topological constraint, Molecular dynamics; Topological friction, Tube model