Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies.

We rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes. While gas permeabilities depend specifically on the chemistry of the polymers considered, we focus here on permeabilities relative to the corresponding pure polymer which show interesting, "universal" behavior. For a given NP radius, Rc, and for large enough areal grafting densities, σ, to be in the dense brush regime we find that gas permeability enhancements display a maximum as a function of the graft chain molecular weight, Mn. Based on a recently proposed theory for the structure of a spherical brush in a melt of GNPs, we conjecture that this peak permeability occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The corresponding brush thickness is predicted to be h max = 3 R c , independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕNP, ϕNP,max = [Rc/(Rc + hmax)]3 ≈ 0.049. Motivated by this conclusion, we measured CO-2 and CH4 permeability enhancements across a variety of Rc, Mn and σ, and find that they behave in a similar manner when considered as a function of ϕNP, with a peak in the near vicinity of the predicted ϕNP,max. Thus, the chain length dependent extension free energy appears to be the critical variable in determining the gas permeability for these hybrid materials. The emerging picture is that these curved polymer brushes, at high enough σ behave akin to a two-layer transport medium - the region in the near vicinity of the NP surface is comprised of extended polymer chains which speed-up gas transport relative to the unperturbed melt. The chain extension free energy increases with increasing chain length, up to a maximum, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that is akin to an unperturbed melt with slow gas transport. The permeability maximum and decreasing permeability with increasing chain length then follow naturally.

Local Structure of Polymer-Grafted Nanoparticle Melts.

Polymer-grafted nanoparticle (GNP) membranes show unexpected gas transport enhancements relative to the neat polymer, with a maximum as a function of graft molecular weight (MWg ≈ 100 kDa) for sufficiently high grafting densities. The structural origins of this behavior are unclear. Simulations suggest that polymer segments are stretched near the nanoparticle (NP) surface and form a dry layer, while more distal chain fragments are in their undeformed Gaussian states and interpenetrate with segments from neighboring NPs. This theoretical basis is derived by considering the behavior of two adjacent NPs; how this behavior is modified by multi-NP effects relevant to gas separation membranes is unexplored. Here, we measure and interpret SAXS data for poly(methyl acrylate)-grafted silica NPs and find that for very low MWgs, contact between GNPs obeys the two-NP theory─namely that the NPs act like hard spheres, with radii that are linear combinations of the NP core sizes and the dry zone dimensions; thus, the interpenetration zones relax into the interstitial spaces. For chains with MWg > 100 kDa, the interpenetration zones are in the contact regions between two NPs. These results suggest that for MWgs below the transition, gas primarily moves through a series of dry zones with favorable transport, with the interpenetration zone with less favorable transport properties in parallel. For higher MWgs, the dry and interpenetration zones are in series, resulting in a decrease in transport enhancement. The MWg at the transport maximum then corresponds to the chain length with the largest, unfavorable stretching free energy.

Unusual High-Frequency Mechanical Properties of Polymer-Grafted Nanoparticle Melts.

Brillouin light spectroscopy is used to measure the elastic moduli of spherical polymer-grafted nanoparticle (GNP) melts as a function of chain length at fixed grafting density (0.47 chains/nm^{2}) and nanoparticle radius (8 nm). While the moduli follow a rule of mixtures (Wood's law) for long chains, they display enhanced elasticity and anomalous dissipation for graft chains <100 kDa. GNP melts with long polymers at high σ have a dry zone near the GNP core, surrounded by a region where the grafts can interpenetrate with chain fragments from adjacent GNPs. We propose that the departures from Wood's law for short chains are due to the effectively larger silica volume fraction in the region where sound propagates-this is caused by the short, interpenetrated chain fragments being pushed out of the way. We thus conclude that transport mechanisms (of gas, ions, sound, thermal phonons) in GNP melts are radically different if interpenetrated chain segments can be "pushed out of the way" or not. This provides a facile new means for manipulating the properties of these materials.

Controlling toughness of polymer-grafted nanoparticle composites for impact mitigation.

Toughness in an entangled polymer network is typically controlled by the number of load-bearing topological constraints per unit volume. In this work, we demonstrate a new paradigm for controlling toughness at high deformation rates in a polymer-grafted nanoparticle composite system where the entanglement density increases with the molecular mass of the graft. An unexpected peak in the toughness is observed right before the system reaches full entanglement that cannot be described through the entanglement concept alone. Quasi-elastic neutron scattering reveals enhanced segmental fluctuations of the grafts on the picosecond time scale, which propagate out to nanoparticle fluctuations on the time scale 100s of seconds as evidenced by X-ray photon correlation spectroscopy. This surprising multi-scale dissipation process suggests a nanoparticle jamming-unjamming transition. The realization that segmental dynamics can be coupled with the entanglement concept for enhanced toughness at high rates of deformation is a novel insight with relevance to the design of composite materials.

Tuning Selectivities in Gas Separation Membranes Based on Polymer-Grafted Nanoparticles.

Polymer membranes are critical to many sustainability applications that require the size-based separation of gas mixtures. Despite their ubiquity, there is a continuing need to selectively affect the transport of different mixture components while enhancing mechanical strength and hindering aging. Polymer-grafted nanoparticles (GNPs) have recently been explored in the context of gas separations. Membranes made from pure GNPs have higher gas permeability and lower selectivity relative to the neat polymer because they have increased mean free volume. Going beyond this ability to manipulate the mean free volume by grafting chains to a nanoparticle, the conceptual advance of the present work is our finding that GNPs are spatially heterogeneous transport media, with this free volume distribution being easily manipulated by the addition of free polymer. In particular, adding a small amount of appropriately chosen free polymer can increase the membrane gas selectivity by up to two orders of magnitude while only moderately reducing small gas permeability. Added short free chains, which are homogeneously distributed in the polymer layer of the GNP, reduce the permeability of all gases but yield no dramatic increases in selectivity. In contrast, free chains with length comparable to the grafts, which populate the interstitial pockets between GNPs, preferentially hinder the transport of the larger gas and thus result in large selectivity increases. This work thus establishes that we can favorably manipulate the selective gas transport properties of GNP membranes through the entropic effects associated with the addition of free chains.

Accelerated Local Dynamics in Matrix-Free Polymer Grafted Nanoparticles.

The tracer diffusion coefficient of six different permanent gases in polymer-grafted nanoparticle (GNP) membranes, i.e., neat GNP constructs with no solvent, show a maximum as a function of the grafted chain length at fixed grafting density. This trend is reproduced for two different NP sizes and three different polymer chemistries. We postulate that nonmonotonic changes in local, segmental friction as a function of graft chain length (at fixed grafting density) must underpin these effects, and use quasielastic neutron scattering to probe the self-motions of polymer chains at the relevant segmental scale (i.e., sampling local friction or viscosity). These data, when interpreted with a jump diffusion model, show that, in addition to the speeding-up in local chain dynamics, the elementary distance over which segments hop is strongly dependent on graft chain length. We therefore conclude that transport modifications in these GNP layers, which are underpinned by a structural transition from a concentrated brush to semidilute polymer brush, are a consequence of both spatial and temporal changes, both of which are likely driven by the lower polymer densities of the GNPs relative to the neat polymer.