Chemistry Reference
In-Depth Information
where w
i
is the weight fraction of polymer with degree of polymerization i
and i can take any value between 1 and 10, inclusively.
(a) Calculate the number average degree of polymerization.
(b) What is the standard deviation of the weight distribution?
(c) Calculate the z average degree of polymerization.
(d) If
the formula wei
ght
of
the repeating unit
in this oligomer
is
100 g mol
2
1
, what is M
z
of the polymer?
2-12 Molecular weight distributions of polymers synthesized using the tech-
niques of living polymerization and condensation polymerization can be
described by the Poisson and exponential distributions, respectively, as
shown in the following equations:
e
2
a
a
i
i
!
n
i
n
5
ð
i
5
0
;
1
;
2
; ...Þð
Poisson distribution
Þ
n
i
n
5 ð
2
b
Þ
b
i
2
1
ð
i
5
;
; ...Þð
Þ
1
1
2
Exponential distribution
where n
i
is the number of chains having a degree of polymerization of i
and n is the total number of chains. Here, a and b are constant. Note that
M
i
5
iM
1
where M
1
is the monomer molecular weight. In the case of the
Poisson distribution, M
n
and M
w
can be shown as follows:
M
n
5
M
1
a
w
5
M
1
ð
1
1
a
Þ
while the corresponding expressions for the exponential distribution are:
M
1
M
1
ð
1
1
b
Þ
M
n
5
M
w
5
ð
1
2
b
Þ
ð
1
2
b
Þ
(a) Show that the polydispersity indices of the polymers prepared by the
aforementioned polymerization techniques approach different limiting
values as M
n
increases.
(b) Using the standard deviation of the number distribution of molecular
weight, show that polymers synthesized by the living polymerization
technique exhibit a considerably narrower molecular weight distribu-
tion than those by the condensation polymerization when M
n
is large.
(c) Given that two samples of oligomers synthesized, respectively, by liv-
ing and condensation polymerization techniques have the same M
n
and M
w
values of 500 and 900, calculate the molecular weights of
their monomers.
2-13 Given that the number distribution of the molecular weight of a polymer
(f
N
(M)) is given by the following expression:
f
N
ð
M
Þ 5
k
1
e
2
k
2
M
