Role of network connectivity on the mechanical properties of highly cross-linked polymers

The effects of mixed functionality and degree of curing on the stress-strain behavior of highly cross-linked polymer networks are studied using molecular dynamics simulations. The networks are made dynamically in a manner similar to epoxy network formation, and the average functionality of the cross-linker, f(av), is systematically varied from 3 to 6 by mixing cross-linkers with functionalities f = 3, 4, and 6. Stress-strain curves are determined for each system from tensile pull simulations. The range of strain of the plateau region (R-P) in the stress-strain curve, failure strain (is an element of(f)), and failure stress (sigma(f)) for fully cured networks are found to have a power law dependence on f(av) as similar tof(av)(alpha). For R-P and is an element of(f), alpha is determined to be -1.22(3) and -1.26(4), respectively. The failure strain is equal to the strain needed to make taut the maximum of the minimal paths through the network connecting the two solid surfaces. The failure stress, however, shows two distinct regions. For f(av)(alpha) less than or equal to 4, sigma(f) increases with increase in f(av) and alpha = 1.22(5). In this f(av) regime, the work to failure is constant. For f(av)(alpha) greater than or equal to 4, the systems fail interfacially, av sigma(f) becomes a constant, and work to failure decreases with fav. These mechanical properties are also found to depend on the degree of curing. With decrease in percentage of curing, failure stress decreases and failure strain increases. The mode of failure changes from interfacial to bulk.