Chemistry Reference
In-Depth Information
1
) at the same temperature and pressure. And it is shown that
(i.e.,
μ
1
2μ
where
V
1
is the molar volume of the solvent.
(a) Since the intermolecular interaction between solvent and polymer
molecules can be quantified by the Flory-Huggins interaction parame-
ter
χ
, derive an expression relating
π
and
χ
.
(b) Given that the Taylor's series expansion of ln(1
1
V
1
π
μ
1
2μ
52
2
x
2
2
x
2
)
5 x
2
1
3
x
2
3
, show that at very low concentrations (i.e., ignoring
second-order and higher terms),
...
1
RTc
2
M
2
where
c
2
and
M
2
are the
concentration of the polymer expressed as mass of polymer per unit
volume of the solution and its number average molecular weight,
respectively.
(c) Ignoring third-order and higher terms in the expression obtained in
part (b), show that solvent-polymer pairs exhibiting
π5
χ
values greater
than 0.5 would yield negative osmotic pressure.
3-5 The relative flow times (
t/t
0
) of a poly(methyl methacrylate) polymer in
chloroform are given below.
(a) Deter
m
ine [
η
] by plotting
η
sp
/c
and
η
inh
aga
ins
t
c
.
10
2
5
M
0
:
80
v
(b) Find
M
v
for this polymer. [
η
]
5
3.4
3
(dL/g).
Concentration (g/dL)
t/t
0
0.20
1.290
0.40
1.632
0.60
2.026
3-6 The Mark
Houwink
Sakurada constants for polystyrene in tetrahydrofu-
10
2
3
cm
3
/g and
a
ran at 25
C are
K
0.766. The intrinsic vis-
cosity of poly(methyl methacrylate) in the same solvent is given by
5
6.82
3
5
10
2
2
M
0
:
69
v
cm
3
½η 5
1
:
28
3
=
g
Show how this information can be used to construct a calibration curve
for poly(methyl methacrylate) in gel permeation chromatography, using
anionic polystyrenes as calibration standards.
3-7
A
polymer with true molecular weight averages
M
n
5
430
;
000 and
M
w
5
1000000 is contaminated with 3% by weight of an impurity with
molecular weight 30,000. What effects does this contamination have on
the average molecular weights determined by light scattering and by mem-
brane osmometry?
3-8
Polyisobutene A has a molecular weight around 3000 and polyisobutene B
has a molecular weight ar
ou
nd 70
0,0
00. Which techniques would be best
for direct measurement of
M
n
and
M
w
of each sample?
