BME 314 MIDTERM I REVIEW
Created By: Lonnissa Hong Nguyen
1.
Given a polymer sample with the following distribution of polymer molecules.
50 molecules of molar mass 1000
100 molecules of molar mass 3000
80 molecules of molar mass 5000
200 molecules of molar mass 7000
20 molecules of molar mass 10000
A.
Calculate the number average
22
.
5222
450
000
,
350
,
2
20
200
80
100
50
)
10000
20
(
)
7000
200
(
)
5000
80
(
)
3000
100
(
)
1000
50
(
=
=
+
+
+
+
×
+
×
+
×
+
×
+
×
=
=
∑
∑
i
i
i
n
N
M
N
M
The
number average molecular weight
is a way of determining the molecular weight of a polymer.
Polymer molecules, even ones of the same type, come in different sizes (chain lengths, for linear
polymers), so the average molecular weight will depend on the method of averaging. The number
average molecular weight is the common, mean,
average of the molecular weights of the individual
polymers
. It is determined by measuring the molecular weight of
n
polymer molecules, summing the
weights, and dividing by
n
.
The number average molecular weight of a polymer can be determined by vapor pressure osmometry,
endgroup titration, and colligative properties.
B.
Calculate the weight average
59
.
6276
000
,
350
,
2
000
,
000
,
750
,
14
)
10000
20
(
)
7000
200
(
)
5000
80
(
)
3000
100
(
)
1000
50
(
)
10000
20
(
)
7000
200
(
)
5000
80
(
)
3000
100
(
)
1000
50
(
2
2
2
2
2
2
=
=
×
+
×
+
×
+
×
+
×
×
+
×
+
×
+
×
+
×
=
=
∑
∑
i
i
i
i
w
M
N
M
N
M
The
weight average molecular
weight is a way of
describing the molecular weight of a polymer
.
Polymer molecules, even if of the same type, come in different sizes (chain lengths, for linear polymers),
so we have to take an average of some kind.
where
N
i
is the number of molecules of molecular weight
M
i
.
Intuitively, if the weight average molecular weight is
w
, and you pick a random monomer, then the
polymer it belongs to will have a weight of
w
on average.
The weight average molecular weight can be determined by light scattering, small angle neutron
scattering (SANS), Xray scattering, and sedimentation velocity.
C.
Calculate the polydispersity Index (PI)
202
.
1
22
.
5222
59
.
6276
=
=
=
n
w
M
M
PDI
Polydispersity Index (PDI),
is a
measure of the distribution of molecular weights
in a given
polymer sample. The PDI calculated is the weight average molecular weight divided by the number
 1 
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BME 314 MIDTERM I REVIEW
Created By: Lonnissa Hong Nguyen
average molecular weight. It indicates the distribution of individual molecular weights in a batch of
polymers. The PDI has a value always greater than 1, but as the polymer chains approach uniform
chain length, the PDI approaches unity (1).
Effect of Polymerization Mechanism on PDI:
Typical PDI's vary based on the mechanism of
polymerization and can be affected by a variety of reaction conditions. In synthetic polymers, it can
vary greatly due to
reactant
ratio, how close the
polymerization
went to completion, etc. For
typical addition
polymerization
, values of the PDI can range around 10 to 20. For typical step
polymerization, values range around 2 to 3.
Living polymerization
, a special case of addition
polymerization, leads to values very close to 1. Such is the case also in biological polymers, where
the PDI can be very close or equal to 1, indicating only one length of polymer is present.
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 Spring '08
 Frey
 Polymer, Lonnissa Hong Nguyen

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