Chemistry Reference
In-Depth Information
1-20 Calculate the rms-end-to-end distance for a macromolecule in molten
polypropylene. Take the molecular weight to be 10
5
, tetrahedral carbon
angle
10
2
8
cm. Assume free
109.5
, and the C—C bond length
5
5
1.54
3
rotation.
(a) How extensible is this molecule? (That is, what ratio does its extended
length bear to the average chain end separation?)
(b) Would the real macromolecule be more or less extensible than the
model used for this calculation? Explain briefly.
1-21
Polymer A contains x freely oriented segments each of length l
a
, and poly-
mer B contains y freely oriented segments with length l
b
. One end of A is
attached to an end of B. What is the average end-to-end distance of the
new molecule?
1-22 Using the data of polyethylene given in the hindered rotation model
(
Section 1.14.2.3
) calculate factions of C
a
C bonds in the trans and gauche
) states in a polyethylene molecule at 200
C. Determine its
corresponding characteristic ratio and Kuhn length.
(g
and g
2
1
1-23
For polyethylene, the trans conformation signifies the lowest energy state
for the dihedral angles of the skeletal bonds. This leads to the experimental
observation that chain dimension of polyethylene decreases with increas-
ing temperature. On the other hand, for silicone polymers, the lowest
energy conformations of the skeletal bonds are gauche conformations.
What would you expect the temperature dependence of the chain dimen-
sion for silicon polymers to be? Briefly explain your answer.
1-24
In the Gaussian chain model, the end-to-end distance of a polymer mole-
cule follows Gaussian statistics. This means that the probability that one
end lies in the volume element dV
5
π
r
2
dr at r from the other end is
4
given by the following expression:
3
=
2
3
e
2
3r
2
P
ð
r
Þ
5
2nl
2
π
nl
2
2
where n is the number of bonds; l
2
is the average squared bond length;
and r is the straight line distance between the two ends of the polymer
molecule.
(a) Sketch qualitatively the Gaussian distribution function (i.e., P(r)) and
the radial distribution function (i.e., 4
π
r
2
P(r)) of the end-to-end dis-
tance r for a polymer chain with a (2nl
2
/3) value of 900 nm
2
;
(b) If the mean square end-to-end distance
r
2
,
.5
ð
N
ð
N
r
2
P
ð
r
Þ
π
r
2
dr
=
π
r
2
dr
;
4
P
ð
r
Þ
4
0
0
