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, T g. 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 T g, 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 T g, 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.

The diffusion of molecules ("penetrants") of variable size, shape, and chemistry through dense cross-linked polymer networks is a fundamental scientific problem broadly relevant in materials, polymer, physical, and biological chemistry. Relevant applications include separation membranes, barrier materials, drug delivery, and nanofiltration. A major open question is the relationship between transport, thermodynamic state, and penetrant and polymer chemical structure. Here we combine experiment, simulation, and theory to unravel these competing effects on penetrant transport in rubbery and supercooled polymer permanent networks over a wide range of cross-link densities, size ratios, and temperatures. The crucial importance of the coupling of local penetrant hopping to polymer structural relaxation and the secondary importance of mesh confinement effects are established. Network cross-links strongly slow down nm-scale polymer relaxation, which greatly retards the activated penetrant diffusion. The demonstrated good agreement between experiment, simulation, and theory provides strong support for the size ratio (penetrant diameter to the polymer Kuhn length) as a key variable and the usefulness of coarse-grained simulation and theoretical models that average over Angstrom scale structure. The developed theory provides an understanding of the physical processes underlying the behaviors observed in experiment and simulation and suggests new strategies for enhancing selective polymer membrane design.