Parameter-free multiscale analysis of hydrogen solubility in Pd nanofilms under hydrogen gas using density functional theory

A parameter-free multiscale analysis of hydrogen solubility, hydrogen coverage, and hydrogen bulk concentration for face-centered-cubic Pd nanofilms with a (111) surface under hydrogen gas conditions is proposed using density functional theory and a simple kinetic model. The calculated solubility is quantitatively comparable to that obtained via experimental observations. Although the Pd surface is fully covered by hydrogen in a short time (microseconds to milliseconds) under exposure to 10–10000 ppm hydrogen gas pressure (1.0 atm), the hydrogen concentration in the subsurface or bulk changes significantly on the experimental time scale depending on gas pressure. We confirmed that the hydrogen concentration in the bulk or subsurface of Pd nanofilms (not the Pd surface) plays a role in the resistance change of Pd through comparison between the calculated hydrogen concentration and experimental observations of an electric resistance change caused by exposure to hydrogen gas. A hydrogen sensor requires a 0.1% change in the hydrogen concentration in the bulk to observe a significant change in the electric resistance. Furthermore, we calculated the time-dependent diffusion coefficient of hydrogen in a Pd nanofilm and compared it with the experimental observed one. We also investigated temperature dependency of the solubility and confirmed that the hydrogen gas pressure determines hydrogen solubility in Pd nanofilms at the equilibrium state, whereas the temperature controls the speed to reach the equilibrium state.