Chemistry Reference
In-Depth Information
The preference for trans conformations in hydrocarbon polymer chains may
be affected by the polymer constitution. Gauche conformations become more
energetically attractive when atoms with lone electron pairs (like O) are present
in the polymer backbone, and polyformaldehyde (or polyoxymethylene), 1-12,
crystallizes in the all-gauche form.
1.14
Molecular Dimensions in the Amorphous State
Polymers differ from small molecules in that the space-filling dimensions of
macromolecules are not fixed. This has some important consequences, one of
which is that certain polymers behave elastically when they are deformed. The
nature of this rubber elasticity and its connection with changes in the dimensions
of elastomeric polymers are explored in Section 4.5.
Portions of polymer molecules that are in crystalline regions have overall
dimensions and space-filling characteristics that are determined by the particular
crystal habit which the macromolecule adopts. Here, however, we are concerned
with the sizes and shapes of flexible polymers in the amorphous (uncrystallized)
condition. It will be seen that the computation of such quantities provides valu-
able insights into the molecular nature of rubber elasticity.
1.14.1
Radius of Gyration and End-to-End Distance of Flexible
Macromolecules
The extension in space of a polymer molecule is usually characterized by
two average dimensions. These are the end-to-end distance d and the radius of
gyration r
g
. The end-to-end distance is the straight-line distance between the
ends of a linear molecule in a given conformation. It can obviously change
with the overall molecular shape and will vary with time if the macromolecule
is dynamically flexible (i.e.,
E is small). The radius of gyration was defined
as the square root of the average squared distance of all the repeating units
of the molecule from its center of mass. This definition follows from the
fact that the r
g
of a body with moment of inertia I and mass m is defined in
mechanics as
Δ
1
=
2
r
g
ð
I
=
m
Þ
(1-19)
If we consider the polymer chain to be an aggregate of repeating units each
with identical mass m
i
and variable distance r
i
from the center of mass of the
macromolecule, then I by definition is
X
m
i
r
i
I
(1-20)
