Boundary effects in the hexagonal packing of rod‐like molecules inside a right circular cylindrical domain. I. The case of right circular spherocylindrical molecules |
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Authors: | J‐J Max AF Antippa C Chapados |
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Institution: | (1) Département de Chimie‐Biologie, Université du Québec à, Trois‐Rivières, Trois‐Rivières, Québec, Canada, G9A 5H7;(2) Département de Physique, Université du Québec à Trois‐Rivières, Trois‐Rivières, Québec, Canada, G9A 5H7 |
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Abstract: | We derive an upper limit, imposed by kinematic 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 rigid, 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 average 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 on the average domain density, increases with decreasing
domain size. It is negligible for very large domain, it is about 2.5% for domains containing around 10 000 molecules, and
it can be as high as 20% for very small domains. The theoretical results obtained 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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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