title: Diffusion of dilute gas in arrays of randomly distributed, vertically aligned, high-aspect-ratio cylinders.
abstract: In this work we modelled the diffusive transport of a dilute gas along arrays of randomly distributed, vertically aligned nanocylinders (nanotubes or nanowires) as opposed to gas diffusion in long pores, which is described by the well-known Knudsen theory. Analytical expressions for (i) the gas diffusion coefficient inside such arrays, (ii) the time between collisions of molecules with the nanocylinder walls (mean time of flight), (iii) the surface impingement rate, and (iv) the Knudsen number of such a system were rigidly derived based on a random-walk model of a molecule that undergoes memoryless, diffusive reflections from nanocylinder walls assuming the molecular regime of gas transport. It can be specifically shown that the gas diffusion coefficient inside such arrays is inversely proportional to the areal density of cylinders and their mean diameter. An example calculation of a diffusion coefficient is delivered for a system of titanium isopropoxide molecules diffusing between vertically aligned carbon nanotubes. Our findings are important for the correct modelling and optimisation of gas-based deposition techniques, such as atomic layer deposition or chemical vapour deposition, frequently used for surface functionalisation of high-aspect-ratio nanocylinder arrays in solar cells and energy storage applications. Furthermore, gas sensing devices with high-aspect-ratio nanocylinder arrays and the growth of vertically aligned carbon nanotubes need the fundamental understanding and precise modelling of gas transport to optimise such processes.
authors.affiliation: Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, 3602 Thun, Switzerland; AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. A. Mickiewicza 30, 30-059 Krakow, Poland; now working at: FHNW University of Applied Sciences and Arts Northwestern Switzerland, Institute of Polymer Engineering, Klosterzelgstrasse 2, 5210 Windisch, Switzerland.
authors.forename: Wojciech
authors.initials: W
authors.lastname: Szmyt
authors.affiliation: Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, 3602 Thun, Switzerland.
authors.forename: Carlos
authors.initials: C
authors.lastname: Guerra
authors.affiliation: Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, 3602 Thun, Switzerland.
authors.forename: Ivo
authors.initials: I
authors.lastname: Utke
keywords: dilute gas; gas transport; molecular diffusion; nanocylinders; random walk