Unveiling the three-dimensional network and deformation mechanism of foamed polyurethane by coarse-grained and graph theory

Non-aqueous reactive foamed polyurethane (PU) has gained widespread applications in engineering trenchless rehabilitation, and the three-dimensional (3D) network formed by crosslinking is the key to their applications through strength and durability. However, there remains a major gap between the general understanding of the 3D network in foamed PU and how it affects the strength of closed cell. Here classical molecular dynamics simulations combined with coarse-grained modeling, X-ray photoelectron spectroscopy and graph theory were employed to characterize the key components and deformations of the 3D network, also the resulting mechanical properties of foamed PU. The results quantified the number and deformations of simple cycles in 3D networks and indicate that the simple cycles are crucial structure that reflect the connectivity and deformation of 3D network. A stronger connectivity results in a higher quantity of shorter simple cycles in the 3D network. These shorter simple cycles impose more limitations on the deformation of the 3D network, manifested as smaller degree of flipping and stretching, resulting from the extension of linear chain segments within soft segments and the flipping of hard segments. Consequently, the stronger connectivity contributes to more uniform deformation and greater tensile strength of PU closed cells. The results can provide a blueprint for future characterization and design of this materials.