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Understanding the phase behavior and dynamics of multi-component polymeric systems is essential for designing materials used in applications ranging from biopharmaceuticals to consumer products. While computational tools for understanding the equilibrium properties of such systems are relatively mature, simulation platforms for investigating non-equilibrium behavior are comparatively less developed. Dynamic self-consistent field theory (DSCFT) is a method that retains essential microscopic thermodynamics while enabling a continuum-level understanding of multi-component, multi-phase diffusive transport. A challenge with DSCFT is its high computational complexity and cost, along with the difficulty of incorporating thermal fluctuations. External potential dynamics (EPD) offers a more efficient approach to studying inhomogeneous polymers out of equilibrium, providing similar accuracy to DSCFT but with significantly lower computational cost. In this work, we introduce an extension of EPD to enable efficient and stable simulations of multi-species, multi-component polymer systems while embedding thermodynamically consistent noise. We validate this framework through simulations of a triblock copolymer melt and spinodally decomposing binary and ternary polymer blends, demonstrating its capability to capture key features of phase separation and domain growth. Furthermore, we highlight the role of thermal fluctuations in early stage coarsening. This study provides new insights into the interplay between stochastic and deterministic effects in the dynamic evolution of polymeric fluids, with the EPD framework offering a robust and scalable approach for investigating the complex dynamics of multi-component polymeric materials. 

Supramolecular polymer networks exhibit unique and tunable thermodynamic and dynamic properties that are attractive for a wide array of applications, such as adhesives, rheology modifiers, and compatibilizers. Coherent states (CS) field theories have emerged as a powerful approach for describing the possibly infinite reaction products that result from associating polymers. Up to this point, CS theories have focused on relatively simple polymer architectures. In this work, we develop an extension of the CS framework to study polymers with reversible bonds distributed along the polymer backbone, opening a broad array of new materials that can be studied with theoretical methods. We use this framework to discern the role of reactive site placement on sol–gel phase behavior, including the prediction of a microstructured gel phase that has not been reported for neutral polymer gels. Our results highlight the subtleties of thermodynamics in supramolecular polymers and the necessity for theories that capture them.