Kinetics of Complex Reactions
Introduction Chain Reactions Polymerization Kinetics
Homogeneous Catalysis
Photochemical Reactions
Kinetics of Complex Reactions
Polymerization Kinetics Polymerization Processes
Stepwise polymerization : Polymers build up stepwise Chain growth polymerization : Addition polymerization molecular weights increase successively, one by one monomer Ring-opening polymerization may be either step or chain reaction
Kinetics of Complex Reactions
Polymerization Kinetics
Stepwise Polymerization Commonly proceed by condensation reaction Usually small molecule (e.g. H2O) eliminated in each step Represented by the following reactions
Monomer + Monomer Dimer + H2O Monomer + Dimer Trimer + H2O Monomer + Trimer Tetramer + H2O Dimer + Dimer Tetramer + H2O
Kinetics of Complex Reactions
Stepwise Polymerization (cont.) Based on the assumption that the polymerization kinetics are independent of molecular size, the condensation reactions may all be simplified to:
~~~~COOH + HO~~~~ ~~~~COO~~~~ + H2O
Kinetics of Complex Reactions
Stepwise Polymerization (cont.)
Rate law The condensation expected to be 2nd order in the concentration of OH and COOH (or A) groups
d [A] dt = - k [-OH][A]
However there is only one OH group for each COOH group, this equation can be written as:
d [A] dt =
- k [A]2
Kinetics of Complex Reactions
Stepwise Polymerization (cont.)
Rate law (cont.) Integrated rate law:
1 [A] 1 [A]
= kt +
1 [A]0
kt[A]0 + 1
[A]0
[A]0 1 + kt [A]0
[A] =
Kinetics of Complex Reactions
Stepwise Polymerization (cont.)
Rate law (cont.)
[A] = [A]0
1 + kt [A]0
Fraction (p) of COOH groups that have condensed at time t is
p
= [A]0 [A]
[A]0
Kinetics of Complex Reactions
Stepwise Polymerization (cont.)
p
= [A]0 [A] [A]0
p [A]0 = [A]0 [A]
= [A]0 [A]0
1 + kt [A]0
[A]0
= [A]0 (1 + kt [A]0) 1 + kt [A]0
Kinetics of Complex Reactions
Stepwise Polymerization (cont.)
p [A]0 = [A]0 + kt [A]02 [A]0
1 + kt [A]0
= kt [A]02 1 + kt [A]0 kt [A]02 [A]0 (1 + kt [A]0 )
p p
kt [A]0
1 + kt[A]0
Kinetics of Complex Reactions
Stepwise Polymerization (cont.)
Degree of polymerization, <N> 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, <N>
<N> =
[A]0 [A]
1 = 1 p
Kinetics of Complex Reactions
Stepwise Polymerization (cont.)
Degree of polymerization, <N>
<N> =
[A]0 [A] 1 = 1 p
In terms of rate constant:
<N>= 1 + kt [A]0
The average length grows linearly with time The longer a stepwise polymerization proceeds, the higher the average molar mass of the product
Kinetics of Complex Reactions
Polymerization Kinetics Polymerization Processes
Stepwise polymerization : Polymers build up stepwise Chain growth polymerization : Addition polymerization molecular weights increase successively, one by one monomer Ring-opening polymerization may be either step or chain reaction
Kinetics of Complex Reactions
Polymerization Kinetics Chain Polymerization
Process Activated monomer, M (chain carriers), attacks another monomer and links to it Resultant species then attacks new monomer and links 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
Kinetics of Complex Reactions
Polymerization Kinetics Chain Polymerization
Occurs by addition of monomers to a growing polymer by radical chain process Rate of polymerization is proportional to the monomer concentration and square root of the initiator concentration
rate = k [I] [M]
Kinetics of Complex Reactions
Chain Polymerization (cont.) Three basic reaction steps:
1. Initiation :
I : initiator R : radical M : monomeric radical
Kinetics of Complex Reactions
Chain Polymerization (cont.)
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]
Kinetics of Complex Reactions
Chain Polymerization (cont.)
- d [ .R] d [ .M1] = = dt dt d [ .M1] dt 2 ki [I]
2 ki [I]
Only a fraction () of radicals initiate chain growth
d [ .M1] dt = 2 ki [I] = ri
Kinetics of Complex Reactions
Chain Polymerization (cont.)
2. Propagation :
= rp
Kinetics of Complex Reactions
Chain Polymerization (cont.)
3. Termination :
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Rate of termination:
= rt
Kinetics of Complex Reactions
Chain Polymerization (cont.)
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 )
Kinetics of Complex Reactions
Chain Polymerization (cont.)
ri = rt 2 ki [I] = 2 kt [ . M]2
2 ki [I] = [ . M]2
2 kt ki [I] kt
= [ . M]
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Rate for propagation = rate of polymerization ~ rate at which monomer is consumed:
rp = kp [M][ . M] rp = kp [M] ki rp = kp ki
kt
[I]
kt
[I] [M]
Kinetics of Complex Reactions
Chain Polymerization (cont.)
rp = kp ki
kt
[I] [M]
(rate of polymerization)
rate = k [I] [M] k = kp ki kt
Kinetics of Complex Reactions
Chain Polymerization (cont.)
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
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Kinetic chain length, (cont.) It is therefore equal to the ratio of propagation & initiation rates: = Propagation rate (rp) Initiation rate (ri)
Because initiation rate equal to termination rate rp = ri or rt
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Kinetic chain length, (cont.) = = = kp [ . M][M] 2 kt [ . M][ . M]
kp [M] 2 kt [ . M]
kp [M]
2 kt ki kt
[I]
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Kinetic chain length, (cont.) = kp [M] 2 kt ki kp [M] [I]- 2 kt ki
[I]
= k [I] - [M]
k = kp ki kt -
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Degree of Polymerization, <N> Average Number of Monomers in a chain, <N> depends on termination mechanism If it is two radicals combining, .M + .M M ,
n m m+n
<N> is twice the kinetic chain length since two combine to terminate the reaction <N> = 2 = 2k [I] - [M]
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Degree of Polymerization, <N> If it is disproportionation, .M + .M M + :M <N> is the kinetic chain length termination results in two chains <N> = = k [I] - [M]
Kinetics of Complex Reactions
Chain Polymerization (cont.)
Degree of Polymerization, <N> The slower initiation of the chain (smaller initiator concentration & smaller initiation rate constant), the greater the kinetic chain length thus higher the average molar mass of the polymer
