Polymerisation kineticsMAT5002

Polymerisation kinetics

Thermodynamics

• Tells us where the system would like to go eventually, i.e. it defines relationships between macroscopic variables at equilibrium

Kinetics

• Tells us how fast the system takes various reaction paths

EXAMPLESSUGAR + OXYGEN → PRODUCTS + ENERGY

CRYSTALLISATION IS ALSO A PROCESS CONTROLLED BY KINETICS

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Polymerisation kinetics

• Step growth SLOW• Can use statistical methods as well as kinetics to describe mol. wt.

distributions

• Chain growth FAST• Can apply statistical methods to an analysis of the microstructure of the

products, but not the polymerisation process and things like mol. wt.

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Kinetics of step-growth polymerisation

• Why bother?• How long does it take to make polymer ?

• Can we speed up the reaction ?

• What is the relationship between kinetics and the mol. wt. of the product ?

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Revision

Rate of reaction = constant x [concentration]n terms

Rate of disappearance of monomer = −𝑑𝑀

𝑑𝑡= k x [concentration]n terms

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Kinetics of polycondensation

• Key assumption – Flory• The reactivity of a functional group is independent of the length of the chain

to which it is attached

• Example: dibasic acid + glycol → polyester

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Was Flory right?

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Kinetics of polycondensation

• Kinetic equation for this type of reaction is usually in the form of

• N.B. [A] and [B] are concentrations of functional groups

• However, esterification reactions are acid catalysed and in the absence of added strong acid

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More kinetics

• If [A] = [B]

• Hence

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Extent of reaction

• Define p = extent of reaction

• In this example let

• Then

• And

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Acid catalysed reaction

• Note the concentration of the acid catalyst (a constant) is included in k’

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Number average degree of polymerisation

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Kinetics of free radical polymerisation

• We need to consider the following steps;• Initiation

• Propagation

• (chain transfer)

• Termination

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Initiation

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Initiation

• Assume decomposition is the rate limiting step, i.e. ki >> kd

• Then we only have to consider kd

• But only a fraction of f radicals initiate chain growth

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f – efficiency factor

Propagation

• In general

• Assumption: reactivity independent of chain length

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Termination

Combination Disproportionation

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Rate of termination

• Where

• Obtained from • Both reactions are 2nd order

• Rate of removal of chain radicals = sum of the 2 termination reactions

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ktc – combinationktd - disproportionation

Summary

• Problem:• we don’t know [M∙]

• Solution:• Assume steady-state concentration of transient species

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Steady-state assumption

• [M∙] = constant

• This means that the radicals are consumed at the same rate as they are generated

• ri = rt

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f – efficiency factor

Rate of propagation

• Rate of propagation = rate of polymerisation

• Substituting

• But [I] is not constant

• From obtain

• So

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What does this tell us?

1. If we want to increase Rp

increase [M] or [I]

2.

3. Trommsdorff effect

• But changing [I] also changes mol. wt.

• For ethylene at 130 ˚C and 1 bar pressure

• For ethylene at 200 ˚C and 2500 bar pressure

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Trommsdorff effect (auto-acceleration)

• A dangerous reaction behaviour that can occur in free-radical polymerisation systems. It is due to the localised increases in viscosity of the polymerising system that slow down termination reactions.

• The removal of reaction obstacles causes a rapid increase in the overall rate of reaction, leading to possible reaction runaway and altering the characteristics of the polymers produced.

• Normally, Rp decreases with time because [M] and [I] drop with extent of conversion

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Conversion

• Definition:

• In initial stages of the reaction we can assume [I]=[I]0 = constant

• Integrating

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Maximum conversion

• Usually there is a 1st order decay in the initiation concentration

• i.e.

• and

• So conversion =

• Max. conversion t→∞ =

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Average chain length

• Define kinetic chain length

• This is the average number of monomers polymerised per chain radical at a particular instant of time during the polymerisation reaction

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Kinetic chain length

• Consider a time period t

• Let us say that1. 100 chains are started

2. 1,000,000 monomers are reacted in this time period

• Then the average degree of polymerisation of these chains is

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Kinetic chain length

• There WILL be some obvious errors, e.g. what about chains that were initiated but not terminated just before the start of the selected period of time?, but these are less significant with smaller time intervals.

• In the limit of time interval dt

• So

• The degree of polymerisation then depends on termination mechanism

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Instantaneous number average chain length

• What if the termination occurs by both mechanisms? Define an average number of dead chains per termination reaction

• Hence

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Chain transfer

• Chain transfer may occur to solvent, added agents, etc.

• Can then obtain

• Or

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Energetic characteristics

• Activation energies and frequency factors

• Assume that all rate constants (kd, kp, kt) are Arrhenius-like.

A – frequency factorE – activation energy

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Energetics: rate of polymerisation

This is the key!

Composite activation energy, usually ~ 80-90 kJ mol-1

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Energetics: degree of polymerisation

This is the key!

Overall activation energy

Coupling

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Temperature dependence of rate of polymerisation and degree of polymerisation

T-1

Rat

e o

f p

oly

mer

isat

ion

Weigh

t-average mo

lecular m

ass

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