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.