Path integral simulation of hydrogen adsorption in single-walled carbon nanotubes at low temperatures

Path integral Monte Carlo simulation (PIMC) in the canonical ensemble is applied to study hydrogen properties at low temperatures. Energies, pressures and radial distribution functions are obtained. The simulation results of the quantum system are compared with those of the classical system at the same temperatures. It is found that at the temperature and pressure ranges studied, hydrogen molecules have significant quantum effects. In addition, two energy estimators in path integral simulation are compared. The phase diagram of bulk hydrogen is also calculated by PIMC in the Gibbs ensemble. Reasonable agreement between the calculated and experimental results is obtained. PIMC in the Gibbs ensemble is also used to calculate the phase separation of hydrogen in a single-walled carbon nanotube. However, the co-effects of the quantum nature of hydrogen and the strong attractive potential inside the cylinder tube suppress the critical temperature and the corresponding phase separation in the small confined space. Consequently, phase separation ceases to occur unless the temperature is below 10 K. Adsorption isotherms of tubes with different diameters at temperature of 36.7 K are obtained. When the temperature is continuously decreased, the US Department of Energy (DOE) target is found to be realized at 18.35 K. This temperature is unfortunately lower than the corresponding temperature of bulk liquid hydrogen with the same density. In addition, path integral molecular dynamics (PIMD) in the canonical ensemble is applied to give the equilibrium configuration of the phase separation.