About a century ago, Knudsen derived the groundbreaking theory of gas diffusion through straight pipes and holes, which since then found widespread application in innumerable fields of science and inspired the development of vacuum and related coating technologies, from academic research to numerous industrial sectors. Knudsen's theory can be straightforwardly applied to filter membranes with arrays of extended holes for example, however, for the inverse geometry arrangement, which arises when solid nanowires or fibers are arranged into porous interwoven material (like in carpets or brushes) the derivation of an analytical theory framework was still missing. In this paper, we have identified the specific geometric and thermodynamic parameters that determine the gas diffusion kinetics in arrays of randomly oriented cylinders and provide a set of analytical expressions allowing to comprehensively describe the gas transport in such structures. We confirmed analytical solutions by Monte Carlo simulations. We specify our findings for an atomic layer deposition process, the diffusion of trimethyaluminium molecules into a carbon nanotube array, but highlight the applicability of our derivation for other fields comprising gas diffusion membranes, composite materials, fuel cells and more.

Stability of quantum dot (QD) films is an issue of concern for applications in devices such as solar cells, LEDs, and transistors. This paper analyzes and optimizes the passivation of such QD films using gas-phase deposition, resulting in enhanced stability. Crucially, we deposited alumina at economically attractive conditions, room temperature and atmospheric pressure, on (1,2-ethanediamine) capped PbSe QD films using an approach based on atomic layer deposition (ALD), with trimethylaluminum (TMA) and water as precursors. We performed coating experiments from 1 to 25 cycles on the QD films, finding that alumina formed from the first exposure of TMA. X-ray photoelectron spectroscopy points to the presence of oxygen-rich compounds on the bare QD films, most likely from entrapped solvent molecules during the assembly of the QD films. These oxygenated compounds and the amine groups of the organic ligands react with TMA in the first cycle, resulting in a fast growth of alumina. Using 10 cycles resulted in a QD film that was optically stable for at least 27 days. Depositing alumina at ambient conditions is preferred, since the production of the QD films is also carried out at room temperature and atmospheric pressure, allowing combination of both processes in a single go.