Лако-красочные материалы — производство

The degree of polymerisation, i, is defined as the number of monomer units in a polymer molecule.

Assuming that little or no transfer occurs then the relationship between v and і will depend on the mode of termination.

a) Termination by combination — two radicals of kinetic chain length v combine to form one molecule with a degree of polymerisation i, that is:

і = 2v

b) Termination by disproportionation — two radicals of kinetic chain length v react to form two molecules each with a degree of polymerisation i, that is:

і = v

Since, as we have seen above

= к2 [M]2 2kt Rp

and for the steady state

Rt = Ri

and

Rp = kp[M](^),/2

it follows that the rate constant for propagation kp (in the early stages of the reaction) will be proportional to [I] 1/2

If f (the initiator frequency or efficiency) is independent of [M] then the rate of propagation is proportional to [M]

that is:

RP a [M]

This holds experimentally where the initiator frequency f is high.

Where f is low then:

f a [M]

and

RP a [Mf2

Plots of Rp versus [I] give a straight line graph with a slope approximately 0.5 as illustrated below:

If the initiator concentration does not vary much during polymerisation (as for example when using a continuous addition or ‘drip feed’ process) and the initiator frequency f is independent of the monomer concentration (as is the case when f approaches 1) then

Rp a [M]

and the polymerisation will proceed in accordance with the principles of first order kinetics.

An example is included here to illustrate this.

Methyl acrylate is polymerised in xylene at 50°C using azo di-isobutyronitrile (AZDN)

If [I] = 1 x 10’3 mole litre"1

Initiation rate constant kd = 1.2 x 10 sec"1

7 -1 -1

Termination rate constant kt = 7.2 x 10 litres mole sec Calculate [M ] when f=l

m

. _ [1 x1.2×10“5×1 хЮ-3]72

[M’j = ———————— Tv————

[7.2 x 10′]’

= 1.28 x 10-8 molelitres-1

Under the conditions of polymerisation [M ] reaches a maximum value within a few seconds of the start of the reaction and thereafter remains constant as illustrated below.

The following table taken from the literature compares [M] and [I] for two monomers commonly encountered in acrylic polymers. The initiator is AZDN and a reaction temperature of 50°C was quoted.