Abstract
We study the organization of spherocylindrical molecules inside a freely
rotating right circular cylindrical domain at the gas/liquid interface.
The analysis is made under the assumption that the molecules are rigid and
close packed, and that they are oriented parallel to each other. The
direction and angle of their common orientation are completely arbitrary.
We obtain exact analytic expressions for the lattice of molecular centers
and its boundaries as a function of molecular dimensions, molecular
orientation, and domain size. As a first application, we derive the number
of molecules in a domain, and the packing fraction. The results obtained
are essential when attempting to analytically model a Langmuir film where
the global order of the film is less than the local order of the domains.
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