Hello there, I am a chemical engineering student working on an undergraduate thesis. For my thesis I am attempting to model various chemical reactions, apply some mathematical tests on them and record observations made. One of the chemical systems I have found nice kinetic data for is the Atom Transfer Radical Polymerization.
I have looked over several papers that describe the differential equation model for ATRP. In models there are a few mass balance differential equations and several moment balance differential equations. Several of the papers I have looked at have the differential moment equations such that every moment is fully dependent on other moments.
i.e. 0th moment for dormant chains: d(L0)/dt = -ka[C][L0]+kda[CX][M0]
The papers, and my understanding of the system also suggest that the initial value at time close to zero of all moments should be zero. Here is where I believe I am missing something basic. Since all moment depend on other moments and all moments start at zero the moments are completely unchanged, remaining at 0 throughout the reaction. If I could get some guidance to understand what I am missing to reconcile these two facts it would be much appreciated. This is the first time I have looked at/ gotten to work on ATRP so forgive me if I lack understanding.