Homework: Free Radical Polymerizations
1. Rate constants for termination kt may be of the order of 108 L/mol s in free
radical polymerizations. Let's consider the polymerization of styrene initiated by
di-t-butyl peroxide at 60˚C. For a solution of 0.01 M peroxide and 1.0 M styrene in
benzene, the initial rate of polymerization is 1.5 x 10-7 mol/L s and Mn of the
polymer produced is 138,000.
(a) From the above information, estimate kp for styrene at 60˚C.
(b) What is the average lifetime of a macroradical during the initial stages of
polymerization for this system?
2. For a particular application, the molecular weight of the polymer made in #1 is
too high. What concentration of t-butyl mercaptan should be used to lower the
number average molecular weight of the polymer to 85,000? For this transfer agent
the Ctr is 3.7 in the polymerization of styrene.
3. (a) In a free radical polymerization in solution the initial monomer concentration
is increased by a factor of 10;
(i) How is the rate of polymerization affected quantitatively?
(ii) What change takes place in the number average degree of
polymerization?
(b) If the monomer concentration was not changed but the initiator concentration
was halved instead;
(i) What is the change in the rate of polymerization?
(ii) What is the change in the number average degree of polymerization?
4. If we assume that the polymerization of methyl methacrylate terminates by
coupling, then (kp2/kt) = 0.460 liter/mol s at 60˚C. [This is often the manner in
which kp and kt are given]. If an azo compound with a half-life of 10.0 h at this
temperature is used to initiate polymerization of a solution of 260.0 grams of
monomer in toluene (to make 1.00 liter), what concentration of initiator will give an
initial Mn of 500,000? What will be the initial rate of conversion?