Carbon dioxide sequestration by carbon nanotubes: Application of graph theoretical approach

A graph theoretical approach is applied to analyze the dynamic evolution of retention of carbon dioxide (CO2) molecules in single-walled carbon nanotubes (SWNTs). The trajectories of the molecules were obtained from the Molecular Dynamics (MD) simulations performed at constant temperature, T = 300 K, with a duration of 10 ns. The simulation box contains four single-walled carbon nanotubes and 408 CO2 molecules with a bulk number density of 0.042 nm−3. Non-bonding interaction distances between CO2 molecules during the simulation were calculated in 1 ns intervals and these values were used to construct 10 dynamic interaction networks, by taking a cut-off value of 0.9 nm for the van der Waals distance. Each of these interaction networks were then analyzed with the two global measures of graph theory: connectivity and clustering coefficient. Our results signified that an increase in the average clustering coefficient in corresponding networks is a reliable indicator for CO2 sequestration in single-walled carbon nanotubes. In addition, the distance distribution for each of the interaction networks revealed that the CO2 molecules retained in carbon nanotubes have a tendency to localize around a distance of 0.48 nm. Consequently, the network representation of CO2 molecules and their encapsulation in SWNTs is in agreement with the actual MD simulation. In summary, the study presented here uses graph theoretical approach to interpret the results received from MD simulations providing a powerful tool to analyze such simulations.