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(b) Calculate
χ
AB
at 200 K and 600 K based upon their Hildebrand solu-
bility parameters;
(c) Based upon the results obtained in part (b), what conclusion can you
make on the phase behavior of the blend? Why?
5-9 Consider the following empirical expression for the Flory
Huggins inter-
action parameter
χ
10
2
2
3
:
70
3
10
2
10
T
2
χ
5
7
:
64
1
3
T
where T is the absolute temperature.
(a) What are the units of the two constants in the above expression?
(b) What type of phase behavior should one expect from the above
expression? Why?
(c) If a binary polymer blend containing polymers A (M
n
5
275,000 g/
1.06 g/cm
3
; molar volume of a repeating unit (
25 cm
3
/
mol;
ρ
5
υ
A
)
5
1.20 g/cm
3
;
53 cm
3
/mol),
mol) and B (M
n
5
650,000 g/mol;
ρ
5
υ
B
5
χ
critical
based upon the geometric mean of the molar volumes
of the repeating units of polymers A and B;
(d) Plot
calculate
against T over the temperature range of 100 to 500 K and deter-
mine the UCST and LCST of the blend.
χ
5-10 The weight fraction activity coefficient at infinite dilution (i.e., the con-
centration of the solvent in the polymer is very low),
Ω
1
N
, can be mea-
sured by a technique so-called inverse gas chromatography. In a particular
experiment,
Ω
1
N
and the ratio of the specific volume of the solvent to that
of the polymer,
ν
2
,at150
C are measured to be 4.49 and 1.1, respec-
tively. Also, the relationship between
ν
1
/
Ω
1
N
and the Flory
Huggins inter-
action parameter,
χ
, is given by the following equation:
ln
ν
1
Ω
1
5
ln
1
1
χ
ν
2
1
Note that the activity of the solvent in the polymer, a
1
, is given by the
following equation:
a
1
5
Ω
1
w
1
5
γ
1
x
1
where w
1
and x
1
are the weight and mole fractions of the solvent and
γ
1
is
the activity coefficient of the solvent in the polymer.
(a) Are the solvent and polymer miscible under the above described
conditions?
(b) What
is the volume fraction of
the solvent
in the polymer
if
w
1
5
0.002?
