Fa (polymer composition)

Macromolecular Chemistry Macromolecular Chemistry

Lecture 08 Lecture 08

CH R

H₂C + CO CH₂ CH

R

C O

Free Radical Copolymerization Free Radical Copolymerization

What happens when we initiate a

polymerization in a mixture of monomers???

Random Copolymers

Random Copolymers MM_{1 1}MM_{2 2}MM_{1 1}MM_{1 1}MM_{2 2}MM_{2 2}MM_{2 2}MM_{1 1}MM_{1 1}MM₂₂ Block Copolymers

Block Copolymers MM_{1 1}MM_{1 1}MM_{1 1}MM_{1 1}MM_{2 2}MM_{2 2}MM_{2 2}MM_{2 2}MM_{2 2}MM₂₂ Alternating Copolymers

Alternating Copolymers MM_{1 1}MM_{2 2}MM_{1 1}MM_{2 2}MM_{1 1}MM_{2 2}MM_{1 1}MM_{2 2}MM_{1 1}MM₂₂

M M _{1 1} + M + M _{2 2} → → - - [( [( M M _{1 1} ) ) _{x x} - - (M (M _{2 2} ) ) _{y y} ] ] _{n n} - -

AIBNAIBN

Free Radical Copolymerization Free Radical Copolymerization

~

~

~

~

~

~

~

~

Assume chain end concentrations are constant at “steady state”

Free Radical Co-polymerization

a b

is a/b

If r1 > 1 means M

If r₁ >1 this means that ~M₁ • adds M₁ more readily than M₂ . If r₁ is zero then M₁ does not undergo

homopolymerization!!

This important relationship can be expressed in This important relationship can be expressed in

terms of mole fractions rather than concentrations terms of mole fractions rather than concentrations

This gives the Instantaneous mole fraction of M₁ in the copolymer

Finemann-Ross Equation

Finemann – Ross Equation

Let’s actually calculate r ₁ and r ₂ from some data

We run the copolymerization for a very short time starting with different weight ratios of 2 monomers.

The assumption is that f does not change in this experiment

We isolate the small amount of polymer generated and determine the ratio of monomers

incorporated….by nmr, for example

We apply the Fineman-Ross analysis and extract the reactivity ratios.

A Few Cases to Remember…

3)

4)

r

> 1, r

< 1 or r

< 1, r

> 1

10

5

0.5

0.1

If r₁ > 1 (k11 > k12) and r₂ < 1 (k22 < k21) then M₁ is more active than M₂ whether either ~M₁^• and ~M₂^•. F₁ is always larger than f₁ and the curve is always above the diagonal.

The situation is similar for

r₁ < 1, r₂ > 1 but the curve is below the diagonal.

as r

x r

= 1 (r

=1/r

), it becomes an “ideal copolymerization”

] [M

] r [M

] d[M

] d[M

2 1 1

2

1

=

In this case ~M

and ~M

have the same preference for adding either of the two monomers.

Ideal copolymerization

F

f

Condition under which F, the mole fraction of monomer in the polymer and f, the mole fraction in the feed

remain constant through the whole polymerization….that is, these ratios are not a function conversion

0.0 0.2 0.4 0.6 0.8 1.0 0.0

0.2 0.4 0.6 0.8 1.0

A = styrene B = butadiene

ra = 0.75, rb = 1.3

Fa (polymer composition)

fa (monomer composition)

Ideal copolymer

0.0 0.2 0.4 0.6 0.8 1.0 0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

A = styrene

B = maleic anhydride ra = 0.05, rb = 0.0

Fa (polymer composition)

fa (monomer composition)

Alternating Copolymer

0.0 0.2 0.4 0.6 0.8 1.0 0.0

0.2 0.4 0.6 0.8 1.0

A = vinyl acetate B = styrene

ra = 0.01, rb = 50

Fa (composition of polymer)

fa (Composition of monomer)

Rich in one monomer

0.0 0.2 0.4 0.6 0.8 1.0 0.0

0.2 0.4 0.6 0.8 1.0

A = Acrylonitrile B = Butadiene

ra = 0.046, rb = 0.36

Fa (polymer composition)

fa (monomer composition)

Typical copolymerization

Azeotropic Composition r₁ =0.046, r₂ = 0.36

Poly(styrene-alt-maleic anhydride)

O O

O

δ+ δ

O O

+ O

O O O

[ ]_n

Charge transfer complex

Charge transfer complex polymerization (alternating copolymer).

H₂C CH R

+ SO₂ CH₂ CH

R

SO₂ CH

R

H₂C + CO CH₂ CH

R

C O

Estimating Reactivity Ratios

Estimating Reactivity Ratios

measurement of r₁ and r₂ is possible by applying the Fineman Rose equation but it is a bit tedious!

Q and e Q and e

z Generalizations:

– This is a purely empirical relationship

– Q and e come from measurements of r

and r

– Ideal condition is same Q and e values

– Proceeds poorly if Q

and Q

are very different

– Tends toward alternating if Q’s are the same and

e’s arelarge but of opposite sign.

I+IV or II+III → alternating

I+III, II+IV and same → Statistical Copolymers

Χ

Χ

Copolymerization

Conclusions-radical copolymers

z

Co-polymers are important

– Properties depend on composition

z

In general, these materials are heterogeneous

z

Mayo equation allows calculation of composition knowing r

and r

z

Finemann Ross approach allows determination of r

and r

z

Alfrey – Price allows estimate of r

and r