kinetics of polymer is at ion
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8/7/2019 Kinetics of Polymer is at Ion
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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
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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 .
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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 ?
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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=
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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
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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
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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
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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]
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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)
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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)
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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
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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
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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
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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
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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
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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
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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
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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.
.
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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
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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
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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%
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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
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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
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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
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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_________=
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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
_
_
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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
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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)
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