10.569 Synthesis of Polymers
Prof. Paula Hammond
Lecture 21: Living Anionic Polymerization, Effects of Initiator and Solvent
Living Polymerization
Rp = −
d [M ]
= k p M − [M ]
dt
[ ]
[M ] ≅ [I ]
−
o
(assumes all initiator is active and available)
⇒ R p = k p [M ][I ]
o
⇒ ln
[M ]o
[M ]
[ ]
= k p M − t = k p [I ]t
constant
log
log
[M]o
[M]
slope = kp[I]
time
tim
e
pn =
[M ] = π [M ]o
[I ]
[I ]
pn
pn
polymer grows at exactly
the same rate (monomer
initiated at exactly the
same time)
⇒
-
0
∴ for complete conversion
PDI:
Mw
Mn
= 1+
ν
(ν + 1)2
linear with time
pn =
[M]
[I]
time
[M ]o
[I ]
(not real PDI, but for statistical purposes)
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
Where ν = kinetic chain length
Mw
→1
⇒ as ν↑,
Mn
⇒ predicts PDI ∼ 1.01 → 1.001
Poisson distribution instead of Gaussian distribution
Solvent Characteristics
Most common solvents
pentane
hexane
cyclohexane
benzene
dioxane
O
increasing
polarity
O
1,2 dimethoxyethane
CH3OCH2CH2OCH3
tetrahydrofuran
O
dimethyl formamide
O
H3C
N
C
H
CH3
• solvent must solvate monomer + polymer
⇒ function of polarity
• important solvent effects in anionic polymerization
- rate of polymerization highly dependent on accessibility
(propagating anion)
of
- association effects
- degree of counterion/ion dissociation
1. Association Effects:
Low dielectric (nonpolar) solvents are poor environments for ions:
Possible to form micelle-like aggregates:
- + + +
- + -
nonpolar
solvent
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
nonpo
nonp
olar
cha
ch
ains
aggregation probabilities ↑
as polarity of solvent ↓
and as counterion size ↓
dependency on concentration:
as conc ↑, agg ↑
Lecture 21
Page 2 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
- + + +
- + -
equilibrium
−
n
Ke
−
let n = # of chains per aggregate
(assume all aggregates have same number of chains)
bracket denotes
aggregate
Ke =
[M ]
[{M ]
− n
−
“unimer”
this species can
propagate
dynamic
structure
{M } ←⎯
⎯→ nM
+
Li
equilibrium constant
n
[M ] = K [{M } ]
−
−
1/ n
e
Rp = −
1/ n
n
d [M ]
= k p K e1/ n [M ] M −
dt
[{
]
1/ n
n
see 1/n dependency in rate of propagation with respect to [M-] [{M } ] ∝ [M ] = [I ]
−
−
n
[{ } ]
can assume [I] ∼ M −
n
⇒ R p ≅ k p K e1/ n [M ][I ]1/ n
If aggregation number is 2, (n=2)
[{
R p = k p K e1/ 2 [M ] M −
≅ k p K e1/ 2 [M ][I ]1/ 2
]
1/ 2
2
aggregate form
2. Degrees of dissociation of counterion and chain
(happens much more frequently)
different degrees of dissociation:
Free ions:
-
+
Na
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 21
Page 3 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
ions are fully dissociated from
negative charge
⇒ assume full availability of charge to react with monomer
Versus … 2 types of ion pairs
a) unsolvated ion pairs (tight pairs)
-+
“contact ion pairs”
b) solvent separated ion pairs (loose ion-ion connections)
- SS
S+
S SS
S
solvent molecules separate ions
thin layer of solvent that separates counterion from + charge
reaction rates of species are going to be different
kp- ⇒ rate constant for free ions
kpI ⇒ rate constant for all ion pairs
and kpI = ykpll + (1-y)kpc
parallel sign
kpll = solvent separated pair y = fraction of solvent separated pair Equilibrium between free and dissociated ion pairs:
-
KD
+
Na
kpI
-
+
Na
kp-
poly
po
lyme
merrize
poly
po
lyme
merrize
Dissociated rate constant
KD =
- ][ Na+ ]
[
[
-
+ ]
Na
+
- ]
⇒ assume [ Na ] = [
(no addition of NaCl that drives up [Na+])
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 21
Page 4 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.
KD =
=
- ]2
[
-
[
[
+ ]
Na
Given that [M-] = concentration of all ionic sites (free and associated)
# of dissociated (free) ions
α≡
all ions
[ ]
[ ]
[ ]
2
KD =
α2 M −
α2 M −
=
1−α
(1 − α ) M −
solve for α:
⎛ K
⎞
1/ 2
α ≅ ⎜⎜ D− ⎟⎟
⎝ M ⎠
[ ]
assuming that α = small
→ neglect 1-α term in denominator
k p = αk p− + (1 − α )k pI
⎛ K
d [M ] ⎡⎢
⇒ RP = −
= k pI + ⎜⎜ D−
dt
⎢
⎝ M
⎣
[ ]
⎞
⎟
⎟
⎠
1/ 2
⎤
(k p− − k pI )⎥[M − ][M ]
⎥
⎦
[I]
10.569, Synthesis of Polymers, Fall 2006
Prof. Paula Hammond
Lecture 21
Page 5 of 5
Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT
OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.