Many soft materials, such as elastomers and hydrogels, are made of long chain molecules crosslinked to form a three-dimensional network. Their mechanical properties depend on network parameters such as chain density, chain length distribution and the functionality of the crosslinks. Understanding the relationships between the topology of polymer networks and their mechanical properties has been a long-standing challenge in polymer physics.
In this work, we focus on so-called “near-ideal” networks, which are produced by the cross-coupling of star-like macromolecules with well-defined chain length. We developed a computational approach based on random discrete networks, according to which the polymer network is represented by an assembly of non-linear springs connected at junction points representing crosslinks. The positions of the crosslink points are determined from the conditions of mechanical equilibrium. Scaling relations for the elastic modulus and maximum extensibility of the network were obtained. Our scaling relations contradict some predictions of classical estimates of rubber elasticity and have implications for the interpretation of experimental data for near-ideal polymer networks.
Reference: G. Alame, L. Brassart. Relative contributions of chain density and topology to the elasticity of two-dimensional polymer networks. Soft Matter 15, 5703 (2019).