Structural Relaxation and Vitrification in Dense Cross-Linked Polymer Networks: Simulation, Theory, and Experiment

We present a coordinated experimental, simulation, and theoretical study of how polymer network permanent cross-links impact the segmental relaxation time over a wide range of temperatures and different criteria for defining the glass transition temperature, Tg. The simulations adopt a coarse-grained model calibrated to represent the specific polymer chemistry of interest. The elastically collective nonlinear Langevin equation (ECNLE) theory of activated segmental relaxation is extended to explicitly treat chain semiflexibility and network cross-linkers, with the latter modeled as locally pinned or vibrating sites. Our key findings include the following: (i) tight cross-linking leads to very large increases of the segmental relaxation time and elevation of Tg, which grows roughly linearly with cross-link fraction beyond a low threshold, (ii) a remarkably good (but not perfect) collapse of Angell plots of the alpha relaxation time for all cross-link densities studied based on using the cross-link fraction dependent dynamic Tg, which applies for very different dynamic vitrification time scale criteria, and (iii) construction of a microscopic understanding of the experimental and simulation observations based on the central idea of ECNLE theory that activated structural relaxation involves cross-link fraction dependent coupled local cage and nonlocal collective elastic barriers. Overall, excellent agreement between experiment, theory, and simulation is found. We suggest that our study of how quenched chemical cross-links strongly modify the alpha relaxation is more generally valuable as a distinct probe of the basic physics of glassy polymer dynamics and as a flexible tool to manipulate small-molecule diffusion in membrane applications.