Kinetics of Polymer is at Ion

8/7/2019 Kinetics of Polymer is at Ion

1/28

P O L YM E R I Z AT I O N K I N E T I C S

THERMODYNAMICS

Tells us where t he syst emwould l ike t o goevent ually !!ie.def ines r elat ionships

bet ween macr oscopicvar iables at equilibr ium

KINETICS

Tells ushow f ast t hesyst em t akes var iousr eact ion pat hs

EXAMPLES

SUGAR + OXYGEN PRODUCTS + ENERGY

CRYSTALLIZATION IS ALSO A PROCESS CONTROLLEDBY KINETICS, AS WE WILL SEE LATER


2/28

P O L Y M E R I Z A T I O N K I NE T I C S

STEP GROWTH - SLOW

Can use st at ist ical met hodsas well as kinet ics t o descr ibemol. wt . dist r ibut ions - mor eon t his lat er

CHAIN Polymerization - FAST

Can apply st at ist ical met hodst o an analysis of t hemicrost r uct ur e of t he pr oduct s,

but not t he polymer izat ionprocess and t hings like mol . wt .


3/28

K I N E T I C S O F ST E P G R O W T H

P O L Y M E R I Z A T I O N

WHY BOTHER ?

How long does it t ake t omake polymer ?

Can we speed up t he r eact ion ?

What is t he relat ionship bet weenkinet ics and t he Mol. Wt . Of t hepr oduct ?


4/28

R E V I S I O N

RATE OFREACTION

= CONSTANT x CONCENTRATION TERMS[ ]n

RATE OF DISAPPEARANCEOF MONOMER = -

dM

dt

__

k x CONCENTRATION TERMS[ ]n=


5/28

K I NE T I C S O F P O L YC O N DE N SAT I O N

KEY ASSUMPTION - FLORY

The reactivity of a functional groupis independent of the length of thechain to which it is attached

EXAMPLE:

DIBASIC ACID + GLYCOL POLYESTER

HO~~~~~~~~~~~~~~~OH

HO~~~~~~OH

HO - C ~~~~~~~~~~~~~~~~~~~~~~ C - OH

O O

HO - C ~~~~~~ C - OH

OO

This group

reacts asreadily asThis group


6/28

W A S F L O R Y R I G H T ?

20151050

0

5

10

15

20

25

Chain Length: N

kAx

10

4

(g

equiv/

l)-1

sec

-1

Redrawn from the data of Flory,P.J.,Principles of Polymer Chemistry,CornellUniversity Press, 1953, p71


7/28

K I N E T I C S O F P O L Y C O N DE N SA T I O N

Kinet ic equat ion f or t his t ype ofr eact ion is usually of t he f or m:

Reaction Rate = -d[A]

dt= k

2[A][B]

N. B. [A] AND [B] ARE THE CONCENTRATIONSOF FUNCTI ONAL GROUPS

However, esterifications are acid catalyzedand in t he absence of added st r ong acid

-d[A]

dt= k

3[A]

2

[B]

A - A + B - B A- AB - B


8/28

M O R E K I N E T I C S

c = [A] = [B]

I f

Hence

3

3 ckdt

dc=

[A] = [B]

=

=t

t

c

c

dtkc

dc

o 0

33

223

112

occ

tk =

-d[A]

dt= k

3[A]

2

[B]


9/28

E X T E NT O F R E AC T I O N

Def ine

p = EXTENT OF REACTION

I n this example

LET p =# OF COOH GROUPS REACTED

# OF COOH GROUPS ORIGINALLY PRESENT____________________________________

200010000

0

100

200

300

400

10000

20

Time (mins)

1

(1 - p)2

Then

And

2 c k t =

1

(1-p) - 1_____

230

2

c = c (1 - p)0

Redrawn from the data of Flory,P.J.,J.A.C.S.,61, 3334 (1939)


10/28

A C I D C AT A L YZ E D R E A C T I O N

d [COOH ]dt

dc

1(1-p)

+ constant

2

0

k' [COOH ] [OH ]- _______ =

- __dt

= k'c

c k't =___

8006004002000

0

20

40

60

80

100

Time (mins)

1(1 - p)

Not e; t he concent r at ion of t he acid

cat alyst (a const ant ) is included in k'

Redrawn from the data of Flory,P.J.,J.A.C.S.,61,3334(1939)


11/28

NU M BE R A VE R AG E D E G R E E

O F P O L YM E R I Z A T I O N

M

c

1

(1-p)

x =

=

n

0__N

n

_

x =n

_

0

c 0__

___ie

= M x =n_

0M__(1-p)

__1.00.80.60.40.20.0

0

100

200

Conversion, p

1(1 - p)=

c 0__(1-p)c 0

N


12/28

K I N E T I C S O F F R E E R A DI C A L

P O L Y M E R I Z A T I O N

We need t o consider t he f ollowing st eps

INITIATION

PROPAGATION

(CHAIN TRANSFER)

TERMINATION


13/28

I N I T I A T I O N

Benzoyl peroxide

C O

O

2

O C

O

C O

O

CH 2 C

H

X

R CH 2 C

H

X

R +

I 2Rk

2

d .

R. + M ki

M 1.

Decomposition

Addition


14/28

I N I T I A T I O N

I 2Rk d .

R. + Mk i

M .

ASSUME DECOMPOSITION IS THERATE LIMITING STEP

i.e. k dk i > >

THEN WE SHOULD ONLY HAVE TO CONSIDER

BUT; ONLY A FRACTION f OF RADICALS INITIATE CHAIN GROWTH

r iMdt

= 2 f k [ I ]1.

=d[ ]___

d

k d

M

d t

1.d[ ]___d[ I ]dt

___ 1__2

k [ I ]d- = =i.e.

1

C O

O

+ CO2

C O

O

+

C

O

O

2


15/28

P R O P A G A T I O N

r Mdt

= k [ M ][ M ]= -d[ ]__

M 1 2

3

. + M M .k p

2M . + M

k p

x

M .

M . + M x+1k p

M.

In general;p p .

Assumption; reactivity isindependent of chain length


16/28

T E R M I N A T I O N

COMBINATION

xM. + x+yMyM.

k tc

DISPROPORTIONATION

xM. + xMyM

.k td

+ yM

CH2 C

H

X

CH2C

H

X

+

CH2 C

H

X X

H

C CH2

ktc

CH2 C

H

X

CH2C

H

X

+

CH C

H

X X

H

C CH2H+ktd


17/28

R AT E O F T E R M I N AT I O N

rMdt

= 2 k [ M ][ M ]= -d[ ]___

t t.

..

Where k = k + ktc td

OBTAINED FROM :

Rat e of r emoval of chain radicals= sum of t he r at es of t he t wot erminat ion r eact ions

.

.Bot h r eact ions ar e second order

t


18/28

S U M M A R Y

riM

dt= 2 f k [ I ]1

.=

d[ ]___d

PROBLEM :

We don' t know [ M ].

SOLUTION :

Assume a st eady st at econcent r at ion oft r ansient species

rMdt

= 2 k [ M ][ M ]= -d[ ]___

t t. .

rMdt

= k [ M ][ M ]= -d[ ]___

p p.

.


19/28

S T E ADY S T AT E AS SUM P T I O N

[ M ]. = CONSTANT

This means t hat r adicalsare consumed at t he samer at e as t hey are generat ed

ri

= rt

2f k [ I ]d

= 2 [ M ]t.k 2

[ M ]. [ ]fk [ I ]d______tk

=1 /2


20/28

R A T E O F P R O P A G AT I O N

RATE OF PROPAGATION = RATE OF POLYMERIZATION

.BUT [ I ] IS NOT CONSTANT

Rr pp =

rp = [ M ]pk [ ]fk [ I ]d______ 1 /2subst it ut ing;tk

tk

d[ I ]dt

= k [ I ]d

__f rom- obt ain [ I ] = [ I ] e- k td

0

HENCE

Rp = [ M ]pk[ [ ] ]f kd____ 1 /2[ I ] e - k t/2d0 [ ]

1 /2


21/28

W H A T D O E S T H I S T E L L U S ?

[ M ] [ I ]pR1 . IF WE WANT TO INCREASE

INCREASE ORBut ; changing [ I ] also changesmol. wt . - mor e on t his lat er !

3. TROMSDORFF EFFECT

k k tp2. pR ~ /1 /2 k k tp /

1 /2

For et hylene at 130 C and1 bar pressure

~ 0.05For et hylene at 200 C and2500 bar pressure

k k tp /1 /2 ~ 3.0

0

0

10005000

0

20

40

60

80

100

Time (mins)

20001500

10%

20%

40%

60%80%

100%


22/28

C O N V E R S I O N

___________

[ M ]pk [ ]fk [ I ]d______tk

1 /2

[ M ] - [ M ]0

[ M ]0

Amount of monomer used up

Amount of monomer at start_______________=DEFINITION ;

in init ial st ages of r eact ion wecan assume [ I ] = [ I ] = const ant

0

d[ M ]dt

= -___

I nt egr at ing

[ M ]___Ln1 /2

= - tpkfk [ I ]d______

tk

0

[ M ]0

[ ]

1.0

t

Conversion


23/28

M A XI M U M C O N VE R SI O N

d[ I ]

dt= - k [ I ]d__i.e.

and

USUALLY THERE IS A FIRST ORDER DECAY IN INITIATOR CONCENTRATION

[ I ] = [ I ] e- k t

0d

[ M ]___Ln

1 /2

= - p2 k fk

[ I ]d______t

k0

[ M ]0 [ ]kd___d- k t[ ]1 - e

hence

CONVERSION =

1 - exp - { }d1 /2

p

2 k f [ I ]______tk

0

[ ]- k t/2

[ ]1 - ekdMAX CONVERSION ( t ) =

1 - exp -1 /2

p2 k f [ I ]______

tk

0[ ]kd

{ }

Conversion

t

1.0


24/28

AV E R AG E C H A I N L E N G T H

DEFINE KI NETI C CHAI N LENGTH

RATE OF MONOMER ADDITION

TO GROWING CHAINS

RATE AT WHICH CHAINSARE STARTED

_____________________________=

This is t he average number ofmonomer s polymer ized perchain r adical at a par t icular

inst ant of t ime dur ing t hepolymer izat ion


25/28

K I N E T I C C H A I N L E NG T H

CONSIDER A TIME PERIOD tlet us say t hat

1. 100 chains are st art ed2. 1, 000, 000 monomers are r eact ed

in t his t ime per iod

Then t he average degr ee ofpolymer izat ion of t hese chainsis

1,000,0001 00

10,000_________=


26/28

K I N E T I C C H A I N L E NG T H

THERE WILL BE SOME OBVIOUS ERRORS (e. g. What about

chains that were initiated, but did not terminate just beforethe start of the chosen period ?), BUT THESE DECREASE ASt SMALL

IN THE LIMIT OF A TIME PERIOD dt

rp

ri= __ =

k [ M ]p_______________2 (f k k )

d t1 /2 [ I ] 1 /2

~[ M ]

[ I ] 1 /2____

i. e. c. f. rp ~ [ M ] [ I ]1 /2

THE DEGREE OF POLYMERIZATION THEN DEPENDS UPONTHE MECHANISM OF TERMINATION

x =

x = 2

- disproportionation- combination

n

n

_

_


27/28

INSTANTANEOUS NUMB ER AVER AGE C HAIN LENGTH

What if t erminat ion occur s by bot h mechanisms ? def ine an

average number of dead chains per t erminat ion r eact ion

=r at e of dead chain f or mat ion

r at e of t er minat ion____________________________

= [ k + k ][ M ]td

td

tc

2

2.

[2 k + k ][ M ]tc.

___________________ =[2 k + k ]

td tc___________

k t

x =n_

HENCE

kp [ M ][ M ].

[2 k + k ][ M ]td tc

2.

____________

=kp [ M ]_______________

[f k k ] [ I ]d t1 /21 /2n

_x


28/28

C H A I N T R A NS F E R

x xrtr

d[ M ]dt

._____ - k [R':H ][ M ].

tr= =

x =n_ k p [ M ]

[f k k ] [ I ] + k [ T ]d t1 /21 /2

tr

_____________________________

R' H + M M H + R'. .:

k [ T ][ M ].trMdt

d[ ]___.

= 2k [ M ] +td . k [ M ]tc .2 2

+-

Chain t r ansf er can occur t o solvent , added agent s,et c.

OR

xn_1___

(x )n

_1___

0

C [ T ]

[ M ]____ C = k / ktr p= + where

CAN THEN OBTAIN

30100

0

40

80

160

200

20

120

Benzene

Toluene

Ethylbenzene

[S]/ [M]

105

xn

Redrawn from the data of R.A.Gregg + F.R.Mayo,

Faraday Soc. Discussions,2,328(1947)

Kinetics of Polymer is at Ion

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