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8/3/2019 Lecture CHAP 3 Part 3
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Chain Reactions
Polymerization Kinetics
Homogeneous Catalysis
Photochemical Reactions
Kinetics of Complex Reactions
Introduction
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Kinetics of Complex Reactions
Polymerization Kinetics
Polymerization Processes
Stepwise polymerization : Polymers build up stepwise
Chain growth polymerization : Addition polymerizationmolecular weights increase successively, one by onemonomer
Ring-opening polymerization may be either stepor chain reaction
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Commonly proceed by condensation reaction Usually small molecule (e.g. H2O) eliminated in
each step
Represented by the following reactions
Monomer + Monomer Dimer + H2OMonomer + Dimer Trimer + H2O
Monomer + Trimer Tetramer + H2O
Dimer + Dimer Tetramer + H2O
Stepwise Polymerization
Kinetics of Complex Reactions
Polymerization Kinetics
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Stepwise Polymerization (cont.)
Based on the assumption that the polymerizationkinetics are independent of molecular size, the
condensation reactions may all be simplified to:
~~~~COOH + HO~~~~ ~~~~COO~~~~ + H2O
Kinetics of Complex Reactions
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Rate law
The condensation expected to be 2nd order in the
concentration of
OH and
COOH (or A) groups
However there is only one
OH group for eachCOOH group, this equation can be written as:
Stepwise Polymerization (cont.)
d [A]
dt= - k [-OH][A]
d [A]
dt
= - k [A]2
Kinetics of Complex Reactions
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Rate law (cont.)
Integrated rate law:
Stepwise Polymerization (cont.)
[A]0
kt +=1
Kinetics of Complex Reactions
kt[A]0 + 1
[A]0=
[A]
[A]
1
1
[A]0
1 + kt [A]0=[A]
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Rate law (cont.)
Fraction (p) of COOH groups that have condensed
at time t is
Stepwise Polymerization (cont.)
[A]0
1 + kt [A]0=[A]
[A]0 [A]
[A]0=p
Kinetics of Complex Reactions
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Stepwise Polymerization (cont.)
[A]0 [A]
[A]0=p
=
Kinetics of Complex Reactions
[A]0 [A]=p[A]0
[A]0
1 + kt [A]0[A]0
= [A]0 (1 + kt [A]0)
1 + kt [A]0
[A]0
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Stepwise Polymerization (cont.)
kt [A]0
1 + kt[A]0=p
Kinetics of Complex Reactions
= [A]0 + kt [A]02
1 + kt [A]0
[A]0
= kt [A]02
1 + kt [A]0
p[A]0
= kt [A]02
[A]0 (1 + kt [A]0 )p
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Degree of polymerization,
Average number of monomer residues per polymer
molecule This quantity is the ratio of initial concentration,
[A]0 to the concentration at the time of interest, [A]
since [A] can be expressed in terms of p, the
average number of monomers per polymer
molecule,
Stepwise Polymerization (cont.)
[A]0
[A]=
Kinetics of Complex Reactions
= 1
1 p
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Degree of polymerization,
In terms of rate constant:
The average length grows linearly with time
The longer a stepwise polymerization proceeds, the
higher the average molar mass of the product
Stepwise Polymerization (cont.)
[A]0
[A]=
Kinetics of Complex Reactions
= 1
1 p
1 + kt [A]0=
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Kinetics of Complex Reactions
Polymerization Kinetics
Polymerization Processes
Stepwise polymerization : Polymers build up stepwise
Chain growth polymerization : Addition polymerizationmolecular weights increase successively, one by onemonomer
Ring-opening polymerization may be either stepor chain reaction
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Kinetics of Complex Reactions
Polymerization Kinetics
Process
Activated monomer, M (chain carriers), attacksanother monomer and links to it Resultant species then attacks new monomer andlinks to it and so on..
Monomer used up slowly Rapid growth of individual polymer chain for each
activated monomer Average molar mass increased by long reaction times
Chain Polymerization
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Occurs by addition of monomers to a growing polymer byradical chain process
Rate of polymerization is proportional to the monomerconcentration and square root of the initiator concentration
rate = k [I] [M]
Chain Polymerization
Kinetics of Complex Reactions
Polymerization Kinetics
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Three basic reaction steps:
1. Initiation :
Chain Polymerization (cont.)
I : initiatorR : radical
M : monomeric radical
Kinetics of Complex Reactions
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1. Initiation (cont.):
Rate determining step: decomposition, formation of
radicals i.e. ka >> ki
We should only consider ki so rate of initiation:
rate = ki [I]
- d [I] .dt
= d [ R]2 dt
= ki [I]
Chain Polymerization (cont.)
Kinetics of Complex Reactions
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- d [ R] .
dt=
d [ M1]
dt= 2 ki [I]
Only a fraction () of radicals initiate chain growth
.d [ M1]
dt= 2 ki [I]
Chain Polymerization (cont.)
.d [ M1]
dt= 2 ki [I] = ri
Kinetics of Complex Reactions
.
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2. Propagation :Chain Polymerization (cont.)
= rp
Kinetics of Complex Reactions
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3. Termination :Chain Polymerization (cont.)
Kinetics of Complex Reactions
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Rate of termination:Chain Polymerization (cont.)
= rt
Kinetics of Complex Reactions
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Total radical concentration is approx. constant
throughout main part of polymerization
This means rate at which radicals are formed by
initiation is approx. the same as the rate at which
they are removed by termination
Chain Polymerization (cont.)
( ri = rt )
Kinetics of Complex Reactions
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2 ki [I] = 2 kt [ M]2.2 ki [I] = [ M]2.2 kt
ki [I] = [ M].kt
Chain Polymerization (cont.)
ri = rt
Kinetics of Complex Reactions
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Rate for propagation = rate of polymerization ~ rate at
which monomer is consumed:
Chain Polymerization (cont.)
rp = kp [M][ M].
Kinetics of Complex Reactions
ki [I]
ktrp = kp [M]
ki [I] [M]kt
rp = kp
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rate = k [I] [M] (rate of polymerization)
Chain Polymerization (cont.)
Kinetics of Complex Reactions
ki
kt
ki [I] [M]kt
rp = kp
k = kp
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Kinetic chain length,
A measure of the efficiency of the chain propagation
mechanism
Defined as ratio of number of monomer units
consumed per active centre produced in the
initiation step:
Chain Polymerization (cont.)
Number of monomer units consumed =Number of active centers produced
Kinetics of Complex Reactions
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Kinetic chain length, (cont.)
It is therefore equal to the ratio of propagation &
initiation rates:
Because initiation rate equal to termination rate
Chain Polymerization (cont.)
Propagation rate (rp) =Initiation rate (ri)
rp =ri or rt
Kinetics of Complex Reactions
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Kinetic chain length, (cont.)Chain Polymerization (cont.)
kp [ M][M] =2 kt [ M][ M]
.. .
kp [M]=2 kt [ M]
Kinetics of Complex Reactions
kp [M]=2 kt ki [I]
kt
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Kinetic chain length, (cont.)Chain Polymerization (cont.)
Kinetics of Complex Reactions
kp [M]
= 2 kt ki [I] kp [M] [I]-=
2 kt
ki
= k [I] - [M] ki -k = kp kt
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Degree of Polymerization,
Average Number of Monomers in a chain, depends on termination mechanism
If it is two radicals combining,
.M
n
+ .Mm
Mm+n
,
is twice the kinetic chain length since twocombine to terminate the reaction
= 2 = 2k [I] - [M]
Chain Polymerization (cont.)
Kinetics of Complex Reactions
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If it is disproportionation,
.M + .M M + :M
is the kinetic chain length termination results intwo chains
= = k [I] - [M]
Chain Polymerization (cont.)
Kinetics of Complex Reactions
Degree of Polymerization,
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The slower initiation of the chain (smaller initiatorconcentration & smaller initiation rate constant), thegreater the kinetic chain length thus higher theaverage molar mass of the polymer
Chain Polymerization (cont.)
Kinetics of Complex Reactions
Degree of Polymerization,