Expert: Mike Fulcher - 6/27/2006

Question
Hi there,

I need to obtain a curve of % of conversion vs. time for a given polymerization reaction but I just don't know how to derive the ODE and algebraic equations involved on the free radical polymerization in order to solve them numerically.

Thanks in advance.

Answer
Well, it's been a while since I've used this, but the classical rate experession for homogenous free-radical polymerization is:

r = -(d[M]/dt) = kp * ((f*kd*[I])/kt)^0.5 * [M]

where
kp = propagation kinetic constant
kd = initiator decomposition kinetic constant
kt = chain termination kinetic constant
f = active radical fraction
[I] = initiator concentration
[M] = monomer concentration

I will admit that I did not recall this from memory, but found it in the book "Fundamental Principles of Polymeric Materials", by Stephen Rosen, Wiley, 1982.  This was an old textbook from back in the day, but it has proven useful to me over the years when I need polymer related information.  If you'd like your own copy, you can get a used one at Amazon for $5, or the new one for $100.  Here's the link:

http://www.amazon.com/gp/product/0389005118/sr=8-2/qid=1151426192/ref=sr_1_2/104...

I hope this helped.  Thanks for your question.