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.

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S 0 ( T ) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S 0 ( T ) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S 0 ( T ) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Butyl acrylate polymer networks were synthesized to understand the effect of permanent cross-links on large, anisotropic dye diffusion. The average degree of polymerization between cross-links (N x ) was decreased from 92 to 2, leading to a 2 order of magnitude decrease in the probe translational diffusion coefficient (D). The mesh size (a x ) was determined from Young’s modulus, and D showed a weakening single exponential decay dependence on the ratio of the probe long axis (d long) to a x with increasing experimental temperature (T 0). Cross-linking led to a significant increase in the glass transition temperature (T g) of the networks and its breadth determined by both calorimetry and dielectric spectroscopy. Segmental relaxation times and inverse diffusion coefficients exhibited weakening single exponential relationships with d long/a x and T g/T 0 at lower measurement temperatures. These results provide new insights regarding the effect of covalent cross-links on probe diffusion necessary for the design and development of separation membranes.

Polymer membranes are commonly pursued for passive separations, which require less energy than distillation. Typically, glassy materials are chosen for gas separations due to extreme sensitivity to size differences in penetrants, whereas rubbers are used for liquid separations due to solubility differences. Vitrimers, dynamic polymer networks with associative bond exchange, are an emerging class of polymers that have gained much attention as self-healing and recyclable materials. Here, in a new direction for vitrimers, we demonstrate the utility of the dynamic bond for eliciting large differences in molecular transport through dense polymer networks. Specifically, permanent and dynamic polymer networks with boronic ester crosslinks are synthesized across a broad range of dynamic bond densities, and the diffusion of a large aromatic dye is measured using fluorescence recovery after photobleaching. When dynamic bond exchange is accelerated by the presence of neighboring nitrogen groups, penetrant transport is enhanced relative to permanent networks by a factor that increases with increasing dynamic bond density and can exceed 1 order of magnitude. Dynamic bonds without the neighboring group effect produce no enhancement of diffusion. These results are interpreted in terms of the ratio of the bond exchange time (inferred from small-molecule experiments) to the hopping time of the penetrant (extracted from the diffusion coefficients). Our results point to a general route for imparting selectivity into polymer membranes through dense crosslinking and dynamic covalent chemistry.