Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 2 / Section A(i) / 14 / ii

The gas impingement flux onto a surface follows from the normal component of the Maxwell-Boltzmann distribution:Here $P=0.1\mathrm{Pa}$ and $m=18(1.66\times 10^{-27})=2.99\times 10^{-26}\mathrm{kg}$, givingAssume a conventional monolayer density $N_s=10^{19}{\mathrm{m}}^{-2}$ and unit sticking coefficient. The incident-monolayer time isThus a few milliseconds is the usual contamination-time estimate at this pressure.

The assumed molecular footprint matters: neither $N_s$ nor the sticking coefficient is specified. More generally $t_{\mathrm{ML}}=N_s/(sJ)$ if the sticking probability is $s$ and desorption is negligible. Water can desorb rapidly from clean graphene at room temperature, so the incident-monolayer estimate does not establish that a stable, complete water layer actually forms in that time. Residues and defects can increase local adsorption.