Energy Evaluation to determine the most compact packing
arrangement of hydrocarbon chains at the interface (formed by the methyl
groups)
This analysis was carried out in another paper from Peyronel et al. (in
review) Here we summarize the analysis.
The location of each atom in a hydrocarbon chain in 2 D was properly
mapped using Adobe Photoshop. The mapping included the atom’s
corresponding electron density. A minimum of four consecutive
hydrocarbon chains on each side of the interface was considered, and six
immediate neighbors for each atom were used. The interface was given by
the plane formed by the methyl groups. The free energy at the interface
was computed when considering different tilted angles (\(\theta_{t})\)for the hydrocarbon chain. Only those atoms at the interface were
considered because the energies of those atoms not involved at the
interfaces are independent of tilt angle. The free energy was given by
the dispersion energy (see below) between atoms of different hydrocarbon
chains. The local energy minimums were shown to appear when neighboring
molecules are placed in a “lock-in” position of chain-chain close
packing. Any other position causes the atoms to be farther apart.