Local swelling effect of flexible entangled polymer chains in athermal solvents

Solutions of flexible, entangled polymer chains dissolved in athermal solvents have been widely studied; however, the influence of the local swelling effects on the overall dynamics of such systems remains incompletely understood. In this study, we performed coarse-grained simulations to compute the concentration dependence of plateau modulus of such systems. Initially, we examined the concentration dependence of entanglement length, denoted as Ne, through simulations. Our findings revealed a concentration scaling relationship for Ne, demonstrating N e = A Φ − 5 / 4 + B, where A and B are chain length independent constants, and Φ is polymer concentration. To account for the local swelling effects, we employed the concept of blobs to represent the chains confined in athermal solvents. Each blob was characterized by a diameter ξ, a number of connected beads g, and a volume Ω b ∼ ξ 3. Our simulations showed that the blob diameter followed the excluded volume relationship, with ξ ∼ g 3 / 5. By combining the local swelling effect and the non-zero constant B, we derived a concentration scaling relationship for the plateau modulus G of solutions of flexible polymer chains in athermal solvents: G ∼ Φ ( N e / g ) Ω b ∼ Φ 2.30. This scaling exponent aligns with experimental observations ranging from dilute to highly concentrated systems, as well as our simulations, where values of 2.0–2.3 were observed.