Polyethylene in Dead-End Silica Nanopores: Forces and Mobility from Non-Equilibrium Statistical Mechanics and Exchange Spectroscopy Nuclear Magnetic Resonance

Billions of tons of plastic have been produced, and only a small fraction of this has been recycled. Tennakoon et al. [Nature Catalysis 3, 893 (2020)] developed a catalyst that repeatedly cleaves C₁₀-C₃₀ hydrocarbons from the end of a polyethylene chain. The reaction occurs at a Pt nanoparticle at the base of a cylindrical silica mesopore with a diameter of 2 nm and a length of 110 nm. Portions of the polymer situated inside the pore can be differentiated from those outside using ¹³C nuclear magnetic resonance (NMR), allowing the dynamics and extent of polymer threading to be monitored using two-dimensional (2D) exchange spectroscopy NMR. We construct a Fokker-Planck equation for the polymer dynamics by assuming a reptation diffusivity and a graduated adsorption free energy that depends linearly on the depth of polymer penetration in the pore. The solutions allow us to predict the intensities of the 2D NMR resonances as a function of time. We use the solutions to extract a polymer diffusivity at each temperature and estimate the per-segment desorption free energy, enthalpy, and entropy. Random and systematic errors are examined to test key assumptions in the theory and interpretation of the experiments.