Lecture CHAP 3 Part 3

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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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




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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



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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:


d [A]

dt= - k [-OH][A]

d [A]

dt

= - k [A]2



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Rate law (cont.)

Integrated rate law:


[A]0

kt +=1


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


[A]0

1 + kt [A]0=[A]

[A]0 [A]

[A]0=p



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[A]0 [A]

[A]0=p

=


[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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kt [A]0

1 + kt[A]0=p


= [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,


[A]0

[A]=


= 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


[A]0

[A]=


= 1

1 p

1 + kt [A]0=


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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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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




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Three basic reaction steps:

1. Initiation :

Chain Polymerization (cont.)

I : initiatorR : radical

M : monomeric radical



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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]




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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]


.d [ M1]

dt= 2 ki [I] = ri


.


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2. Propagation :Chain Polymerization (cont.)

= rp



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3. Termination :Chain Polymerization (cont.)



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Rate of termination:Chain Polymerization (cont.)

= rt



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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


( ri = rt )



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2 ki [I] = 2 kt [ M]2.2 ki [I] = [ M]2.2 kt

ki [I] = [ M].kt


ri = rt



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Rate for propagation = rate of polymerization ~ rate at

which monomer is consumed:


rp = kp [M][ M].


ki [I]

ktrp = kp [M]

ki [I] [M]kt

rp = kp


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rate = k [I] [M] (rate of polymerization)



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:


Number of monomer units consumed =Number of active centers produced



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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


Propagation rate (rp) =Initiation rate (ri)

rp =ri or rt



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Kinetic chain length, (cont.)Chain Polymerization (cont.)

kp [ M][M] =2 kt [ M][ M]

.. .

kp [M]=2 kt [ M]


kp [M]=2 kt ki [I]

kt


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Kinetic chain length, (cont.)Chain Polymerization (cont.)


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]




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If it is disproportionation,

.M + .M M + :M

is the kinetic chain length termination results intwo chains

= = k [I] - [M]





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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




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Lecture CHAP 3 Part 3