Developments in Multi-Chain Coarse-Grained Models for Entangled Polymer Dynamics

This review describes the development and applications of multi-chain coarse-grained simulations for entangled polymer dynamics. The mean-field tube model has long served as the standard paradigm for describing the many-body entanglement problem as the motion of a single chain in a static field; it faces intrinsic limitations when addressing spatial correlations, fluctuations, and complex topological rearrangements. To overcome these limitations, "multi-chain" approaches -- specifically the primitive chain network and multi-chain slip-spring models -- were developed. These simulations explicitly resolve the force balance and topological coupling between multiple chains in three-dimensional space. This review covers the primitive chain network model, which emphasizes real-space force balance, and the multi-chain slip-spring model, which is derived from a well-defined free-energy functional. Linear and nonlinear rheology predictions are discussed, along with molecular mechanisms such as constraint release and stretch/orientation-induced reductions in friction. Extensions to branched polymers, wall-slip phenomena, and network polymers are also mentioned.