Question

Styrene is polymerized by free radical mechanism in solution. The initial monomer and initiator concentrations are 1 M and 0.001 M, respectively. At the polymerization temperature of 60ºC, the initiator efficiency is 0.30. The rate constants at the polymerization temperature are as follows:

kd= 1.2 x 10-5 s-1

kp= 176 M-1s-1

kt= 7.2 107m-1s-1

Given this information, determine the following;

a. Rate of initiation at 1 min and at 16.6 hrs

b. Steady-state free radical concentration at 1 min

c. Rate of polymerization at 1 min

d.Average free-radical lifetime, t,at 1 min, where t is defined as the radical

concentration divided by the rate of termination.

Answer 1

1) The expression Since the rate of reaction between the initiating radical and a monomer molecule is much faster than the rate of the initiator decomposition,
Ri = fkd[I],

(f * kd is the product of the initiator efficiency 'f' and the initiator decomposition rate constant kd)

Ri = 0.30 x 1.2 x 10^-5  x 1 = 0.36x 10^-5 S^-1 (both 1minute and 16.6 hrs rate of initiation will be same)

2)

=

3) rATE OF Polymerization

The expression kp/kt^1/2 is the ratio of the propagation rate constant to the square root of the termination rate constant. The free radical rate of polymerization equation written with this ratio separated out is

Rp = (kp/kt^1/2) [M] (fkd[I])^1/2.
Again, substitute the information you have to get the kp/kt^1/2 ratio.

(b) The kinetic chain length of a polymer is just the ratio of the rate of propagation over the rate of initiation. However, if termination is by coupling, the actual degree of polymerization Xn is twice the kinetic chain length. If termination is by disproportionation, the actual degree of polymerization Xn equals the kinetic chain length. Since it is assumed that termination occurs by disproportion only, Rp/Ri gives Xn directly. Multiply Xn by the molecular weight of styrene to get the polymer molecular weight.

(c) If Chain transfer to monomer is the dominant transfer mode, the degree of polymerization is simply
1/Xn = Cm.
Just compare this Xn to the Xn previously calculated.