Two Channel Description of Gas Permeability in Polymer-Grafted Nanoparticle Membranes

Abstract

Recent work has demonstrated that polymer-grafted nanoparticle (PGN) melts are spatially heterogeneous media with tunable gas transport properties. In particular, it is thought that the region near the nanoparticle (NP) surface, where the grafted chains are stretched due to crowding effects, as well as the interstitial regions within the NP packing, exhibit distinct transport behaviors. Based on these notions, this work proposes an analytical two channel model with a high-barrier channel akin to the pure polymer melt, and a low-barrier channel with zero activation energy. The model, developed with these simplifying assumptions, has one parameter, the fractional occupancy of the high-barrier channel, which is fit to gas permeability data as a function of chain molecular weight and gas type. Gases as big as CO₂ are present in both channels, while all larger gases primarily occupy the ”high-barrier” channel. Since the model does not distinguish between solubility and diffusivity, it is concluded that the results found for the larger gases are consistent with the experimental findings showing that they have increased solubility within the interstitial spaces of the PGN structure. Similarly, the low channel corresponds to the stretched polymer brush with fast transport for all gases. Despite their higher fractional occupancy in the high-barrier channel, large gases also preferably transport through the low-barrier channel. The distinctions in energy barriers between the two channels manifest through a critical gas size beyond which the model’s effective energy barrier becomes gas size-independent. This highlights the bilinear nature of gas transport in PGNs which results from their heterogeneous spatial structure.