Abstract
We derive an upper limit, imposed by cinematic constraints, for the ratio
of the average density function relative to the local density function for
a freely rotating right circular cylindrical domain made of right circular
spherocylindrical molecules. The derivation is made under the assumption
that the molecules are ridgid, that they are close packed and that their
molecular axes are perpendicular to the base of the domain. For domains
containing more than 100 molecules, the avarage density, evaluated as a
function of domain size, is well approximated by a simple smooth analytical
expression. For smaller domains, on the other hand, the boundary effects
lead to an average density that varies erratically with the size of the
domain. The contribution of the boundary effects to the difference between
the local density and the average domain density, increases with decreasing
domain size. It is negligible for very large domains, it is about
2.5&perc; for domains containing around 10 000 molecules; and it can be as
high as 20&perc; for very small domains. The theoretical results obtaied
here are consistent with the reported discrepancy between the value of the
molecular area obtained from pressure area measurements and that obtained
from X-ray measurements.
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