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Equilibrium and kinetics: Water confined in carbon nanotubes as one-dimensional lattice gas
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8.Although it is easy to numerically calculate the exact value of the free energy it is not necessary to do so due to the current objective of the model.
9.As the hydrogen-bond chain is very long, the free energy of each bond of the chain may exist fluctuation. But for a short chain we can use the average value of the free energies, and the fluctuation can further be neglected.
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12.For very long nanotubes with large M, the effect of the additive ending energy is not important, so as changes from >0 to <0 (the external field H changes its direction in the equilvalent Ising model), a sharp transition from empty to filled states comes to appear (the magnetic moment changes its direction sharply).
13.The 27 Å nanotube used in the recent MD simulations has 11 graphene unit cells along its axis and the 13.5 Å nanotube have 5.5 graphene unit cells.
14. in the 25.8 Å nanotube should be far lower than that in the 13.5 Å nanotube. Even though, due to the positive the free energy of the empty state may be still lower than that of the filled state.
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