I've been thinking a lot about the kinetics of my radical reactions this morning. Even modelling the initation is tricky, since my method uses the slow addition of initiator via syringe pump, which gives rise to a differential equation that I don't know how to solve:
d[In]/dt = k1(t) - kd[In] where k1 is the rate of addition and kd the rate of decomposition.
The thing that has become overwhelmingly apparent is that my abilities in the solution of differential equations (which were never very extensive) have diffused away over the last six years, and trying to skim through the big maths for physical scientists books doesn't seem to be much help.
Given that I also add the chain carrier and the electrophile via syringe pump, I think that this is going to be a nightmare of analysis. It is interesting that the kinetics texts never seem to treat chain reactions in any depth. Maybe it is too hard a problem.
Not going to be beaten yet, though.
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