Industrial applications of polymer solutions
In many of these applications the phase separation behaviour of a
polymer solution is manipulated in order to create a desired effect.
GCH 6101- Phase separation: solutions
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Example: Viscosity control of motor oils
• In order for motor oils to be effective year round they must have a
viscosity that is insensitive to temperature (especially in Canada!)
• Pure oils are much too sensitive to temperature…the viscosity decreases
exponentially as the temperature increases
• In order to reduce the temperature sensitivity, block copolymers of
polystyrene-hydrogenated polyisoprene are added
At low temperatures the PS blocks phase
separate from the oil forming micelles,
while the H-PI blocks remain dissolved
in the oil. This is a dilute solution and
the viscosity is increased above that of
the oil only slightly.
GCH 6101- Phase separation: solutions
At high temperatures the PS
blocks become soluble in the oil.
This is a concentrated solution
and the viscosity is increased
significantly above that of the oil.
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Thermodynamics of phase separation
• In order for 2 phases to be in equilibrium the chemical
potential (partial molar free energy) of each component
must be equal in both phases
• This requires that the first and second derivatives of μ1
with respect to φ2 be zero.
[
]
μ1 = RT ln (1 − φ 2 ) + (1 − 1 x )φ 2 + χ1φ 22 + μ10
• Therefore the critical conditions for phase separation are
2
given by:
1
(1 + x )
φ =
2c
χ1c =
1+ x
2x
• The critical temperature is the highest temperature of
phase separation:
1
1 ⎡
1 ⎛ 1
1 ⎞⎤
TC
GCH 6101- Phase separation: solutions
=
+
⎟⎥
⎢1 + ⎜
Tθ ⎣ ψ1 ⎝ x 2 x ⎠⎦
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Example: Phase diagrams for PS in cyclohexane
Sample
Mv
PSA
43 600
PSB
89 000
PSC
250 000
PSD
1 270 000
Tθ = 34.5°C
= Tc for a polymer
of infinite M
φ2
GCH 6101- Phase separation: solutions
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Regions of the
polymer-solvent
phase diagram
v=1-2χ
Shows the 5 stable
solution regimes.
GCH 6101- Phase separation: solutions
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• Notation for previous figure
GCH 6101- Phase separation: solutions
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Solution regimes
• Dilute solution regime: delimited by the
overlap volume fraction, φov and vc. In this
state the chains are very far apart and do
not feel each other.
• Ideal solution regime: θ-solvent condition
• Transition region: where φ ≅ φov
• Semi-dilute regime: φ > φov In this state
the chains overlap each other forming
entanglements
φOV
⎤
⎡C
= ⎢ ∞ (1 − 2χ )⎥
⎣ 6
⎦
GCH 6101- Phase separation: solutions
−3 5
x −4 5
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Scaling law theories
• Used to predict the form of the behaviour of polymeric
systems and to predict transitions between regimes of
behaviour
• Based upon the idea of polymer behaviours being
dependant on the topology of the chains (i.e. length and
long branches) in a more complex way than the
dependency on monomer chemistry
m
• Usually look like:
⎛ y⎞
S = S0 f ⎜⎜ ⎟⎟
⎝ yc ⎠
where S is a property of the polymer system, S0
contains the dependence on monomer chemistry, y is a
parameter of the system (often related to chain topology),
yc is the critical value of y when S changes the form of its
dependency on y through the exponent m which changes
value at yc.
GCH 6101- Phase separation: solutions
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Overlap concentration:
Transition from dilute to semi-dilute
• Concentration when the polymer coils begin to just touch
each other:
N coil 3
1=
Rg
V
• We can substitute in: N coil = φOV N A K1 and: R 3g = K 2 x γ
V
• We find: φOV = K 3 x1−3γ
M
Note: In a good solvent γ = ⅗
and in a θ solvent γ = ½.
• In a good solvent:
φOV
⎛ C ∞ [1 − 2χ] ⎞ − 54
≅⎜
⎟ x
6
⎝
⎠
GCH 6101- Phase separation: solutions
− 53
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Radius of gyration in a good solvent in the
semi-dilute regime
• Using a similar procedure we can find:
1
2
R g ,s ∝ x φ
− 18
• This indicates that the radius of gyration decreases slowly
as concentration increases and the dependency of radius of
gyration on chain length is as in a θ solvent.
GCH 6101- Phase separation: solutions
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