How Segmental Dynamics and Mesh Confinement Determine the Selective Diffusivity of Molecules in Cross-Linked Dense Polymer Networks

Abstract

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.

Scaling Perspective on Dynamics of Nanoparticles in Polymers: Length- and Time-Scale Dependent Nanoparticle–Polymer Coupling

“…The research on nanoparticle hopping diffusion in crosslinked polymer networks may be extended to glass forming polymer network, an cutting-edge research topic with applications such as separation membranes, barrier materials, and nanofiltration as the technological background. A recent joint theory-experiment-simulation study 193 on the diffusion of large aromatic molecules ("penetrants") in dense cross-linked polymer networks demonstrated that the motion of the penetrants is primarily determined by the coupling of local penetrant hopping to polymer structural relaxation, with the entropic mesh confinement effects being of secondary importance. More aspects of nanoparticle hopping in crosslinked networks have been revealed by molecular simulations.…”

Reversible Reactions, Mesh Size, and Segmental Dynamics Control Penetrant Diffusion in Ethylene Vitrimers

“…A single exponential function is observed, in distinction to probe diffusion in linear polymers which typically exhibits a Williams–Landel–Ferry (WLF) or nonexponential temperature relationship when approaching T g / T = 1. ,, However, temperature relationships derived here are a result of changing T g with cross-link density, not the experimental temperature. A single exponential form has been observed in experiment, theory, and simulations of dye diffusion in polymers for a broad range of penetrant volumes . The reduction in diffusion coefficient is generally attributed to a slowing down of the segmental dynamics (increased T g ) as well as an entropic mesh confinement term .…”

“…Analogous ethylene networks were prepared with a fast cross-linker reported in prior work and investigated by us for probe diffusion in acrylic vitrimers . The neighboring nitrogen groups accelerate the rate-limiting proton transfer step of the boronic transesterification and increase the exchange rate by a factor of ∼10,000 . The faster cross-linker has six carbons connecting the boronic acids, and thus we only prepare the C 6 network for these comparisons (Scheme ).…”

“…A single exponential form has been observed in experiment, theory, and simulations of dye diffusion in polymers for a broad range of penetrant volumes. 52 The reduction in diffusion coefficient is generally attributed to a slowing down of the segmental dynamics (increased T g ) as well as an entropic mesh confinement term. 52 The concentration of the dye is 10 −5 M to make sure the dye would not self-quench or aggregate.…”

“…52 The reduction in diffusion coefficient is generally attributed to a slowing down of the segmental dynamics (increased T g ) as well as an entropic mesh confinement term. 52 The concentration of the dye is 10 −5 M to make sure the dye would not self-quench or aggregate. The reactive cross-links are in large abundance relative to the dye.…”