Coverage Dependent H$_2$ Desorption Energy: a Quantitative Explanation Based on Encounter Desorption Mechanism

Recent experiments show that the desorption energy of H$_2$ on a diamond-like carbon (DLC) surface depends on the H$_2$ coverage of the surface. We aim to quantitatively explain the coverage dependent H$_2$ desorption energy measured by the experiments. We derive a math formula to calculate an effective H$_2$ desorption energy based on the encounter desorption mechanism. The effective H$_2$ desorption energy depends on two key parameters, the desorption energy of H$_2$ on H$_2$ substrate and the ratio of H$_2$ diffusion barrier to its desorption energy. The calculated effective H$_2$ desorption energy qualitatively agrees with the coverage dependent H$_2$ desorption energy measured by the experiments if the values of these two parameters in literature are used in the calculations. We argue that the difference between the effective H$_2$ desorption energy and the experimental results is due to the lacking of knowledge about these two parameters. So, we recalculate these two parameters based on experimental data. Good agreement between theoretical and experimental results can be achieved if these two updated parameters are used in the calculations.