Effects of Topological Constraints on Equilibrium Swelling of Polymer Gels

Understanding the swelling behavior of polymer gels is crucial for enhancing their properties in various applications that depend on their capacity to absorb solvents and undergo volume changes. In this work, coarse-grained molecular simulations and scaling theory analysis are employed to investigate how topological constraints, inherited from cross-linking linear and ring polymers at different polymer volume fractions ϕ0, influence swelling as the system changes from the dry to the equilibrated swollen state. The results show that at ϕ0 = 1, the ring polymer gel exhibits a higher swelling ratio Q compared to the linear polymer gel with the same cross-linking density. As ϕ0 decreases, both types of gels show an increase in Q, but their values eventually converge at the lowest ϕ0. The dependence of swelling on ϕ0 and polymer topology stems from the corresponding dependence of entanglements trapped during cross-linking. These trapped entanglements enhance network elasticity and provide greater resistance to the osmotic pressure that drives swelling, thus shifting the swelling equilibrium. At ϕ0 = 1, ring polymers are more compact than linear polymers, and the cross-linking traps fewer entanglements in the gel, resulting in a higher Q. As ϕ0 decreases, the drop in Q for both gel types stems from the reduction in the number of trapped entanglements per network strand. At the lowest ϕ0, both ring and linear polymers are barely entangled, leading to a similar Q dictated by the cross-links. Throughout the range of ϕ0, Q decreases as the combined number density of cross-links and trapped entanglements increases, indicating less swelling when the gel has higher elasticity. Clarifying these effects of topological constraints is expected to benefit the design of polymer gels with tunable swelling behavior by adjusting the preparation conditions.