chapter 10. step-reaction and ring-opening...
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Chapter 10. Step-Reaction and Ring-Opening Polymerization
10.2. Step-Reaction Polymerization - KineticsStep-Reaction Polymerization
1. Difunctional monomers Linear polymersAB type, AA and BB
Network polymers2. Polyfunctional monomersFunctionality > 2
3. Polymers retain their functionality as end groupsat the completion of polymerization
4. Single reaction (cf. initiation, propagation,and termination in chain-reaction polymerization)
5. M.W. increases slowlyCarothers equation
p11DP−
= p = extent of reaction
6. High-yield reactions and an exact stoichiometric balance are necessary to obtain high-m-w linear polymer
7. Formation of cyclic byproduct
HOCH2CH2OHH+
O
O
OCH2CH2- H2O
major
polyether
1,4-dioxane
H2NCH2CH2CH2COOH∆
NH
O
NHCH2CH2CH2 C
O- H2O
lactam
majorNylon 4
Kinetics of Step-Growth PolymerizationFlory’s assumption
The reactivity of a functional group is independent of the length of the chain to which it is attached.
Example: dibasic acid + glycol polyester
Assumption 2.• The reactivity of a functional group is unaffected by reactions of other functional groups in the molecule
The probability of chemical reaction with the increase of the MW:
• The rate of molecular diffusion decreases, i.e., larger time intervals between encounters (fewer encounters of functional groups per unit time)
• Greater duration of each encounter (a larger number of collisions of functional groups per encounter)
• Kinetics
1. Catalyzed [cat]k’ = k [cat] is unchanged
If polymerization reaction is first orderw.r.t. each functional group (A & B)
Polymerization rate[ ] [ ][ ]B AkdtAd
=− [ ] ( ) [ ] ktA1
p1A1
oo
=−−
If [A] = [B][ ] [ ]2AkdtAd
=− [ ] [ ] ktA1
ADP
oo
=−
orBy integration
[ ] [ ] ktA1
A1
o
=−[ ] 1ktADP o +=
[ ] kA1DPt
o
−=[ ]
[ ] p11
AADP o
−==
If k is known, time can be calculated.
2. Uncatalyzed (self-catalyzed)
HOOC - COOH + HO – OH → polymer
Carboxylic acid: role of catalyst[ ] [ ] [ ]BAkdtAd 2=−
Assume [A] = [B][ ] ( ) [ ] kt2
A1
p1A1
2o
22o
=−−
( )[ ] 1Akt2
p11 2
o2 +=−
[ ] [ ]3AkdtAd
=−
Integration [ ] 1Akt2DP 2o
2+=
[ ] [ ] kt2A
1A1
2o
2 =−
M.W. increases more graduallythan when acid catalyst is added.[A] = [A]o(1 - p)
Catayzed
[ ] 1ktADP o +=
[ ] 1Akt2DP 2o
2+=
UncatayzedDP
1
t
10.3 Stoichiometric Imbalance
• Three ways to limit M.W. in step polymerization
1. To quench the polymerization reaction by rapid cooling when the desired M.W. is attained.
2. To use an excess of one monomer.
3. To use small amounts of monofunctional reactant
• Stoichiometric imbalance factor
oB
oA
NNr =
whereNA
o = initial # of A functional groupsNB
o = initial # of B functional groups
By conventionr ≤ 1
oA
Ao
A
NNNreaction ofextent p −
==
NA = (1 - p)NAo
( ) ( )r
Npr1Npr1No
AoBB −=−=
# of molecular chains at p
( )
( ) ( )
⎟⎠⎞
⎜⎝⎛ −+=
⎥⎦
⎤⎢⎣
⎡−+−=
+=
p2r11
2N
rNpr1Np1
21
NN21N
oA
oAo
A
BA
oB
oB
oA
oBB prNNpNNN −=−=cf.
# monomers
( )oB
oA
o NN21N +=
Since oB
oA
NNr =
⎟⎠⎞
⎜⎝⎛ +
=⎟⎟⎠
⎞⎜⎜⎝
⎛+=
r1r
2N
rNN
21N
oA
oAo
Ao
Average degree of polymerization
rp2r1r1
p2r11
2N
r1r
2N
NNDP o
A
oA
o
−++
=
⎟⎠⎞
⎜⎝⎛ −+
⎟⎠⎞
⎜⎝⎛ +
==
If r = 1 If p = 1
p11DP−
=r1r1DP
−+
=
If monofunctional reagent is added
Imbalance factor
o'B
oB
oA
N2NN'r−
=
where
NB’o = # of monofunctional B groups
Factor 2 : each B’ molecule is equally as effective as one excess BB monomer in limiting the M.W.
10.4 M.W. Distribution# of total molecules at p = N# of x-mers = Nx
M - (M)x-2 - Mp p 1 - p
p = extent of reaction = probability of reaction
1 – p = probability of finding an unreacted group
where
( )p1NpN 1xx −= −
p1NN
o −= No = initial # of monomers
( ) 1x2ox pp1NN −−=
( ) 1xxx pp1
NNn −−==
nx = mole fraction of x-mers
p = 0.99Monomer: the most abundant species
Wt fraction of x-mers
o
x
oo
oxx N
xNMNMxNw ==
where Mo = mass of repeating unit
( ) 1x2ox pp1NN −−=cf.
Wt fraction distribution
( ) 1x2x xpp1w −−=
The most abundant species
( ) ( )
( ) ( ) 0plnx1pp1
plnxpp1pp1dx
dw
1x2
1x21x2x
=+−=
−+−=
−
−−
pln1x −=
( ) ( )( ) p1
Mp1
1p1Mxpp1MxMnMnM o2o
1xooxxxn −
=−
−=−=== ∑∑∑ −
( )21x
1x
p11xp
−=∑
∞
=
−cf.
( )31x
1x2
p1p1px
−+
=∑∞
=
−
( ) ( )( )
( )p1
p1Mp1p1p1Mpxp1MxMwMwM o
32
o1x22
ooxxxw −+
=−+
−=−=== ∑∑∑ −
Polydispersity index
cf.
p1MM
n
w +=
2MM
n
w →As p →1,
Fig 10.1 Mole fraction distribution in linear step-reaction polymerization
nx
Fig 10.2 Weight fraction distribution in linear step-reaction polymerization
wx
10.5 Network Step PolymerizationEquimolar mixture
COOH
COOHHOOC
O
O
O
HOCH2CHCH2OH
OH
HOCH2CH2OH
Functionality 2 23 3
Average functionality 5.24
3232fav =+++
=
No = initial # of monomers
N = # of molecules at p
# of functional groups reacted = 2(No – N)
Initial # of functional groups = Nofav
( )avavavoavavo
o
fDP2
f2
fNN2
f2
fNNN2p −=−=
−=
NNDP o=cf.
∞=DPAt gel point
avc f
2p = Critical extent of reaction
If fav = 2.5, pc = 80% (cf: difunctional monomers : DP = 5)
If mixture 3 mol of 1, 2 mol of 4
( ) ( ) 4.25
3223fav =×+×
=
%834.2
2pc ==
AfA - A B - B
# of molecules NA NB NC
fA = 2 fB = 2 fC = f > 2Functionality
Imbalance factor
B
CCA
BB
CCAA
N2NfN2
NfNfNfr +
=+
=CCA
CC
CCAA
CC
NfN2Nf
NfNfNf
+=
+=ρ
pA = extent of reaction for A
pB = extent of reaction for B = rPA
Af-1 – A – [B – B A – A]i – B – B A – Af-1
pA (pB(1 - ρ)pA)i
= (r (1 - ρ)pA2)i
pBρ
= rρpA
Branching probability
= probability that a functional group on a branch unitleads to another branch unit
( )[ ]( ) 2
A
2A
A0i
i2AA p1r1
prprp1rpρ−−
ρ=ρρ−=α ∑
∞
=
1
2
3Trifunctionally branched network polymer
i th envelope
Yi branch points on the i th envelope
# of branch points on (i + 1) th envelope
Yi + 1 = 2 Yi α
Criterion for gelationYi + 1 > Yi
21
>αthat is2 Yi α > Yi
21
c =α
1f1
c −=αgenerally
1f1 yprobabilit branching criticalc −
==α
( ) 2c
2c
p1r1pr
1f1
ρ−−ρ
=−
1 – r (1 - ρ) pc2 = (f - 1) r ρ pc
2
1 = (r – r ρ + f r ρ – r ρ) pc2
( )[ ]21c
r2fr
1pρ−+
=
If r = 1
( )[ ]21c
2f1
1pρ−+
=
If ρ = 1No A - AAll Af
If r = ρ = 1
( )[ ]21c
r1f
1p−
=( )2
1c1f
1p−
=
COOHHOOC
CH2
CH
OH
CH2 OH
OH+ At pc = 0.765gelation
αc = pc2 = 0.58
Carothers equation (nonstatistical)Theoretocal (statistical)
( )
( ) ( ) 4.25
3223fav =×+×
=707.021
13
1p21c ==
−=
21
1f1p 2
cc =−
==αav
c f2p = %83
4.22pc ==
Experimental values of pc fall between the values calculated by statistical and nonstatistical methods.
Deviation from statistical method
∵ (1) Intramolecular branching reactions leading to wasted loops (2) Differing reactivities of the functional groups
Reactivity of secondary alcohol < Reactivity of primary alcohol In glycerol
10.6 Step-Reaction CopolymerizationCOOHHOOC
COOHHOOC HOCH2CH2OH
AA BB CC
AA : BB : CC = 1 : 1 : 2 Random copolymer
CC - AA - CCBB
- (CC - AA – CC – BB) -Alternating copolymer
AA + 2 CC
Step polymers : true telechelic polymersHO polyether OH OCN polyurethane NCO
O polyether O NH
polyurethane NH
C
O
C
O
+
C polyester C H2N polyamide NH2
C polyester NH
polyamide NHC
O
+Cl ClO O
O
(AB) multiblock copolymer
HO polyether OH OCN polyurethane NCO
HO polyether O NH
polyurethane NH
C
O
C
O
+2
O polyether OH
ABA triblock copolymer
10.7 Step Polymerization Techniques
1) Bulk polymerization
Free of contaminants
Disadvantage: high viscosity; elevated temp for effective stirringand removal of byproducts
High vacuum to remove byproducts
2) Solvent polymerization
Low viscosity
Removal of byproduct by azeotropic distillationRemoval of water in situ by use of effective dehydrating agent
Necessity of removing solvent
3) Interfacial polymerization
Solutions of two monomers in separate, immiscible solvents(one usually water)
Polymer is formed at the interfacee.g., Schotten – Baumann synthesis“nylon rope trick”
Rapid stirring to maximize the interfacial area increases the yieldof polymer
Characteristics of interfacial polymerization(1) Reaction goes rapidly at low temp.
(2) Reaction is so rapid, diffusion of monomer to the interface is rate determining(3) Monomer reacts with the growing chains at the interface more rapidly than it diffuses through the polymer film to initiate new chains; hence M.W.s tend to be significantly higher.
(4) An exact stoichiometric balance is not necessary.
Interfacial polymerization: the “nylon rope trick”
4) Phase-transfer catalysis (PTC)
Aqueous phase and organic phaseCatalyst: quarternary ammonium salt
Function by transporting a nucleophilic monomerfrom the aqueous phase to organic phase,where its nucleophilicity is greatly enhancedbecause of reduced solvation effects
PhCH2N+(C2H5)3Cl-
CH2ClClH2C NC CH2COOC(CH3)3
CH2 CH2 C
CN
COOC(CH3)3
+
NaOH, H2O / benzene
organic phase aqueous phase ↔ organic phase
organic phase
Aqueous phase
Interface
Organic phase
Q+ X- + M+ Y- Q+ Y- + M+ X-
[Q+, Y-] + R-X[Q+, X-] + R-Y
Q+ = PhCH2N+(C2H5)3 X- = Cl-
M+ = Na+ Y- = NCCHCOOC(CH3)3
-
R-X = CH2ClClH2C
Q+ = R4N+, R4P+ Quarternary onium salt selected due to its highsolubility in the organic phase
Q+ transfers anion Y- into the organic phase as [Q+, Y-], which thenreact with an alkyl halide RX to give the substitution product R-Y
The produced Q+X- is rapidly reconverted into Q+Y-
by anion exchange with nucleophile M+Y- from the aqueous phase.
10.8 Dendritic Polymers
• Potential applications: drug delivery systems, controlled releaseof agricultural chemicals, molecular sensors, rheology modifiers
• Characteristic features of dendrimers
1. Three component parts: a central core, an interior dendritic structure, and an exterior surface
2. Macromolecular dimensions are easily controlled by a repetitive sequence of synthetic steps.
3. More soluble than linear polymers∵ High surface functionality
4. Lack of chain entanglement Low viscosity
5. Supramolecular assemblies by incorporating guest moleculesamong the interior branches of the dendrimer.
• Two approaches to construct dendrimers
1. Divergent synthesis
Branch points are constructed in a stepwise fashion from a central core.
2. Convergent synthesis
Branch segments are constructed separately and then joined to a multifunctional core.
Divergent synthesis
Polyamidoamine (PAMAM) dendrimers
NH3 CH2 CH COOCH3
N(CH2CH2CONHCH2CH2NH2)3
N(CH2CH2COOCH3)3+ 3
H2NCH2CH2NH2
N
NH2
NH2H2N
N
N
NN
NH2
NH2
H2N NH2
NH2
H2NN
N
NN
N
N
N N
N
N
NH2NH2
NH2
NH2
NH2
NH2H2N
H2N
H2N
H2N
H2NNH2
10th generation
# of surface functional groups = 3 x 210 = 3072
Surface area: 100 times
Convergent synthesis
O
OBr
+
HO
HOOH
base
O
OO
OOHO
O
1. CBr4, PPh3
2. HO
HOOH
base
O
OO
OO
O
O
O
O
O
OO
O
OOH
Scheme 10.3 Convergent synthesis of a dendrimerfrom dendritic segments.
Hyperbranched polymers
More random architectures and do not emanate from a central core.
Synthesized from ABx functional monomers
Polymerization occurs via dendritic branching with no possibility of crosslinking
10.9 Ring-Opening Polymerization• Mechanisms
1. Monomer is attacked by ionic or coordination species (X*)Ring opening
2. Monomer is attacked by X* Coordination speciesSecond monomer Ring opening
GX*
X G*G
X G G*G
......
ex
CH2 CH2
O RO-
ROCH2CH2O-CH2 CH2
O
ROCH2CH2OCH2CH2O-CH2 CH2
O
......
GX* G G
G* X G* G X G* G
CH2
CH2O
HA A
CH2
CH2OH
CH2
CH2O
CH2
CH2OHOCH2CH2
ACH2
CH2O
......+
-
+
-ex
Reactivity from ring strain
3 > 4 > 8 > 7 > 5 > 6
6-membered cyclic esters (lactones) polyesters
6-membered cyclic amides (lactams) X polyamides
Cyclic ethers
Reactivity
3 > 4 > 8 > 7 > 5 > 6
OpolyetherX
5-membered cyclic esters (lactones) X polyesters
polyamides5-membered cyclic amides (lactams)
Polyesters
Polyamides
Ring-Opening Polymerization of N-Carboxy Anhydrides
The product polymer is a poly(amino acid) or polypeptide or synthetic protein. This particular reaction is noteworthy because it is a chain reaction that occurs with expulsion of a small molecule (CO2). Such reactions are very rare.
Silicones
An example of an polymer with an inorganic backbonethat can also be made by step polymerization.
Polyphosphazenes
An example of a completely inorganic polymerthat can be functionalized with organic groups after polymerization.