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This paper introduces a self-assembly Monte Carlo scheme that overcomes the computational challenges of sampling equilibrium in giant polymer melts by operating in a self-assembly ensemble. This novel approach, utilizing strictly local moves that efficiently propagate backbone reconnections, achieves near-linear scaling of decorrelation time with system size (τeq ~ V1.0) and allows for the equilibration of systems up to 1.1 × 10^9 monomers. Analysis of these large-scale simulations reveals that topological entanglements in polymer melts manifest as localized knots and links, with the Gauss linking integral between neighboring chains growing only as N^1/4.
Giant polymer melts exhibit localized entanglements, not global tangles, with linking integrals scaling sub-linearly with chain length.
Topological entanglements are central to understanding and predicting the properties of polymer melts. Yet, they make equilibrium sampling computationally challenging, as decorrelation times grow rapidly with chain length. Here, we introduce a Monte Carlo scheme that bypasses typical computational bottlenecks by working in a self-assembly ensemble rather than at fixed composition. Strictly local moves efficiently propagate backbone reconnections across scales while conserving the number of linear chains, achieving near-linear scaling of decorrelation time with system size, τeq ~ V1.0. With this method, formulated for a fully-packed lattice, we equilibrate periodic systems totalling up to ≃ 1.1 × 109 monomers, accessing a universal melt regime insensitive to lattice details. We analyze intra- and inter-chain entanglements for chains of up to N ≃ 5 × 105 monomers, revealing that they manifest as localized knots and links rather than as global tangles. Finally, we show that the magnitude of the Gauss linking integral between neighbouring chains grows only as N1/4. Simulating dense polymer melts remains challenging due to the rapid increase in computational cost with chain length. Fornasa et al. report a Monte Carlo scheme that addresses this bottleneck by employing a self-assembly ensemble, achieving linear scaling with system size and typical chain length.