Bridging Molecular Mechanochemistry and Network Fracture Mechanics

Abstract

The fracture of polymer networks is usually perceived macroscopically and is considered as a mechanical engineering problem. However, to advance a crack in a polymer network, lots of polymer strands that bridge the crack need to be broken, thus network fracture is molecular as well. In the past 80 years, scientists have been trying to build up quantitative connections between network fracture mechanics and the molecular details of the networks, but to date, there is still no well-accepted quantitative molecular model for network fracture. This is due to the lack of understanding of the molecular details (i.e., strand scission reaction, network topology, etc.) in polymer networks. Developments in polymer mechanochemistry and polymer physics open the door to understanding network fracture from the molecular level. With the concepts of polymer mechanochemistry and polymer physic, this dissertation investigates the correlations between bond/strand scission reaction and the network fracture mechanics theoretically and experimentally.The Lake-Thomas theory is the most well-known molecular theory of network fracture which connects the network critical tearing energy to the scission of polymer strands. Although it has been widely used to explain experimental data, the energy parameter in this theory does not capture the correct chemistry of strand scission and the physics of polymer networks. We provided a conceptual framework to modify the molecular energy parameter in the Lake-Thomas theory by considering the force-coupled reactivity of polymer strand scission reaction (SSR) and network connectivity. First, we consider the strand scission during crack propagation as a mechanochemical reaction of polymer strands, the kinetics of which is dictated by the force on the strands instead of the bond dissociation energy of the repeating monomers. By incorporating the data reported from the single-molecule force spectroscopy experiments, we found the elastic energy stored per bond when typical hydrocarbon polymers break is ca. 60 kJ ∙ mol-1, which is well below the typical carbon-carbon bond dissociation energy (ca. 350 kJ ∙ mol-1). This modification introduced the concept of strand scission reaction into the molecular fracture model of polymer networks and explained the underlying criteria of chain scission. Next, we consider the energy contribution of unbroken strands in the polymer networks during crack propagation. This modification includes not only the energy stored in the breaking network strands (bridging strands) but also the energy stored in the tree-like structure of the strands connecting the bridging strands to the network continuum, which remain intact as the crack propagates. We show that the tearing energy stored in each of the generations of this tree depends non-monotonically on the generation index due to the nonlinear elasticity of the stretched network strands. We further show that the energy required to break a single bridging strand is not necessarily dominated by the energy stored in the bridging strand itself but in the higher generations of the tree. To verify our theoretical modification of the Lake-Thomas theory, we designed and synthesized covalent polymer gels in which the macroscopic fracture “reaction” is controlled by mechanophores embedded within mechanically active network strands. The gels were prepared through the end-linking of azide-terminated tetra-arm PEG (Mn = 5 kDa) with different bis-alkyne linkers under identical conditions, except that the bis-alkyne was varied to include either a cis-diaryl or cis-dialkyl linked cyclobutane mechanophore that acts as a mechanochemical “weak link” through a force-coupled cycloreversion. A control network featuring a bis-alkyne without cyclobutane (non-mechanophore) was also synthesized. The networks show the same small strain elasticity and swelling, but they exhibit tearing energies that span a factor of 8 (3.4, 10.6, and 27.1 J ∙ m-2 for networks with cis-diaryl, cis-dialkyl cyclobutane mechanophores, and non-mechanophore control, respectively). The difference in fracture energy is well-aligned with the force-coupled scission kinetics of the mechanophores observed in single-molecule force spectroscopy (SMFS) experiments, implicating local resonance stabilization of a diradical transition state in the cycloreversion of cis-diaryl cyclobutane mechanophore as a key determinant of the relative ease with which its network is torn. The connection between macroscopic fracture and a small-molecule reaction mechanism suggests that the fracture of polymer networks is a chemical reaction. Further characterizations of the force-coupled kinetics of cis-diaryl and cis-dialkyl cyclobutane mechanophores with SMFS suggest opportunities for constructing quantitative correlations between strand scission reaction and network fracture mechanics. Although the tearing energy of polymer networks is highly dependent on the strand scission reaction of network strands, how the networks with mixed strand scission reactions behave remains unclear. Hence, the impact of mixed strand scission reaction is studied through the synthesis of networks with varied ratios of cis-diaryl cyclobutane mechanophore (“weak”) and non-mechanophore (“strong”) control linkers. The strands with mechanophore linkers are about 4 ~ 5 times weaker than the strands with non-mechanophore linkers according to SMFS experiments. Tearing energy versus strong linkers percentage demonstrate the existence of plateau regions for < 40% strong linker at 2 ~ 3 J∙m-2 and >75% strong linker at ~20 J∙m-2. These regions correspond somewhat closely to the expected Flory-Stockmayer percolation thresholds for a tetra-functional network, pc (strong) = 0.67 and pc (weak) = 0.33. From the classical point of view (e.g., Lake-Thomas theory), the crack propagation is usually assumed to be path-determined instead of reactivity-determined. These data suggest the path-determined mechanism, which predicts that the tearing energy should vary linearly with the average strength of the bonds, does not correctly capture the trend in tearing energy, and the reactivity-determined mechanism is likely to be correct. Ongoing experiments on the actual percolation threshold of either weak or strong chains in the networks would provide more understanding of the reactivity-determined mechanism. Our current work on end-linked networks suggests that the network is weak with incorporated weak mechanophores. However, incorporating weak mechanophores as crosslinkers in radically polymerized networks yields an opposite result: the network is tougher with incorporated weak mechanophores. A cis-diaryl cyclobutane-mechanophore is developed as a mechanochemically weak covalent crosslinker and incorporated into controlled radical-polymerized networks. The networks consist of crosslinkers that are mechanochemical weak and long primary chains that are mechanochemically strong. The activation force of the covalent crosslinker is estimated to be ca. 5 times weaker than the corresponding control crosslinkers and the polymer backbone bonds. However, the networks made from the weak crosslinkers are 2 ~ 9 times tougher than the networks made from the corresponding control crosslinkers (non-mechanophore) while the former exhibit the same small strain elasticity as the latter. By altering the degree of polymerization (DP) of primary chains while keeping the crosslinking density similar, we found that, with primary chains that have DP ≈ 1300 and larger, the networks made from the weak crosslinkers are 6 ~ 9 times tougher than that made from control crosslinkers. With primary chains that have DP ≈ 300, the tearing energies of these two types of networks have no significant difference. This suggests that having long enough primary chains is critical for the toughening effect. The underlying principles of this toughening effect are the weak crosslinkers can be activated before the primary chain breaks, and the inherent topological loopy structures of the network can be released as “stored-length”. Such change in topological structures of the networks after weak crosslinker activation can redistribute the load and toughen the networks.