Polyethylene in
Dead-End Silica Nanopores: Forces
and Mobility from Non-Equilibrium Statistical Mechanics and Exchange
Spectroscopy Nuclear Magnetic Resonance
posted on 2022-12-21, 17:05authored byZiqiu Chen, Alexander L. Paterson, Frédéric
A. Perras, Baron Peters
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.