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The diffusion of small molecular penetrants through polymeric materials represents an important fundamental problem, relevant to the design of materials for applications such as coatings and membranes. Polymer networks hold promise in these applications, because dramatic differences in molecular diffusion can result from subtle changes in the network structure. In this paper, we use molecular simulation to understand the role that crosslinked network polymers have in governing the molecular motion of penetrants. By considering the local, activated alpha relaxation time of the penetrant and its long-time diffusive dynamics, we can determine the relative importance of activated glassy dynamics on penetrants at the segmental scale versus entropic mesh confinement on penetrant diffusion. We vary several parameters, such as the crosslinking density, temperature, and penetrant size, to show that crosslinks primarily affect molecular diffusion through modification of the matrix glass transition, with local penetrant hopping at least partially coupled to the segmental relaxation of the polymer network. This coupling is very sensitive to the local activated segmental dynamics of the surrounding matrix, and we also show that penetrant transport is affected by dynamic heterogeneity at low temperatures. To contrast, only at high temperatures and for large penetrants or when the dynamic heterogeneity effect is weak does the effect of mesh confinement become significant, even though penetrant diffusion more broadly empirically follows similar trends as established models of mesh confinement-based transport., Comment: Including a main text and a supporting information, for main text: 33 pages, 1 table, and 9 figures; for supporting information: 3 figures and 1 table. Totally, 35 pages, 2 tables, and 12 figures

We generalize and apply a microscopic force-level statistical mechanical theory of the activated dynamics of dilute spherical penetrants in glass-forming liquids to study the influence of permanent crosslinking in polymer networks on the penetrant relaxation time and diffusivity over a wide range of temperature and crosslink density. Calculations are performed for model parameters relevant to recent experimental studies of an nm-sized organic molecule diffusing in crosslinked PnBA networks. The theory predicts the penetrant alpha relaxation time increases exponentially with the crosslink fraction ($f_n$) dependent glass transition temperature, $T_g$, which grows roughly linearly with the square root of $f_n$. Moreover, $T_g$ is also found to be proportional to a geometric confinement parameter defined as the ratio of the penetrant diameter to the mean network mesh size. The decoupling ratio of the penetrant to polymer Kuhn segment alpha relaxation times displays a complex non-monotonic dependence on crosslink density and temperature that can be well collapsed based on the variable $T_g(f_n)/T$. The microscopic mechanism for activated penetrant relaxation is elucidated and a model for the penetrant diffusion constant that combines activated segmental dynamics and entropic mesh confinement is proposed which results in a significantly stronger suppression of mass transport with degree of effective supercooling than predicted for the penetrant alpha time. This behavior corresponds to a new polymer network-based type of decoupling of diffusion and relaxation. In contrast to the diffusion of larger nanoparticles in high temperature rubbery networks, our analysis in the deeply supercooled regime suggests that for the penetrants studied the mesh confinement effects are of secondary importance relative to the consequences of crosslink-induced slowing down of glassy activated relaxation., Comment: 42 pages and 14 figures

The diffusion of molecules (penetrants) of variable size, shape, and chemistry through dense crosslinked polymer networks is a fundamental scientific problem that is broadly relevant in materials, polymer, physical and biological chemistry. Relevant applications include molecular separations in membranes, barrier materials for coatings, drug delivery, and nanofiltration. A major open question is the relationship between molecular transport, thermodynamic state, and chemical structure of the penetrant and polymeric media. Here we address this question by combining experiment, simulation, and theory to unravel the competing effects of penetrant chemistry on its transport in rubbery and supercooled polymer permanent networks over a wide range of crosslink densities, size ratios, and temperatures. The crucial importance of the coupling of local penetrant hopping to the polymer structural relaxation process, and the secondary importance of geometric mesh confinement effects, are established. Network crosslinks induce a large slowing down of nm-scale polymer relaxation which greatly retards the rate of penetrant activated relaxation. The demonstrated good agreement between experiment, simulation, and theory provides strong support for the size ratio variable (effective 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 chemical details. The developed microscopic theory provides a fundamental understanding of the physical processes underlying the behaviors observed in experiment and simulation. Penetrant transport is theoretically predicted to become even more size sensitive in a more deeply supercooled regime not probed in our present experiments or simulations, which suggests new strategies for enhancing selective polymer membrane design., Comment: including a main text and a supporting information. For the main text, 28 pages and 5 figures; For the supporting information, 23 pages and 14 figures. Totally, 51 pages and 19 figures