Energy Evaluation to determine the most compact packing
arrangement of hydrocarbon chains at the interface
As mentioned already, the results of this calculation are shown in
another paper from Peyronel et al. (in review) That paper showed that if
the hydrocarbon chains of TC are rigidly in their all-trans
conformation, then they minimize their free energy when in a solid state
and adopt orientations tilted, at an angle \(\theta_{t}\), with respect
to the (surface) plane formed by their methyl groups. It was shown that
the free energy for a system at the methyl plane interface gives rise to
at least three possible local free energy minimum:\(\theta_{t}\approx 0\), \(\theta_{t}\approx 33\)and\(\theta_{t}\approx 53\). There are other tilts possible at larger
angles. The paper showed that the global minimum was when\(\theta_{t}\approx 33\), followed by \(\theta_{t}\approx 53\).\(\theta_{t}\approx 0\) had the highest energy value, hence it can be
deduced that hydrocarbon chains will packed at a tilt angle of about\(33\) rather that at an angle of \(\theta_{t}\approx 0\). This result
is essentially in acord with the data of Table 1.