description that formally includes all the aforementioned pathways. This is also the reason why we implement *primary nucleation*. To make the problem mathematically tractable we work in the limit of strongly nucleated systems, where for the time domain of our interest the primary nucleation step is not functional and hence can be ignored for all practical purposes. This said, we will explain in detail all of our approximations and limitations, as and when they come in this paper.

To derive a closed form of the moment equations, we start with the discrete master equation for the reaction schemes defined above. For the polymers, this yields \[eq2\] &=& k\_n\^+ x(t)\^[n\_c]{} \_[i,n\_c]{} + 2 x(t) y\_[i-1]{}(t) - 2 x(t) y\_[i]{}(t) + 2 y\_[i+1]{}(t) - 2 y\_i(t)\
& & + (i-2) x(t) y\_[i-1]{} - (i-1) x(t) y\_[i]{} + (i-1) y\_[i+1]{} - (i-2) y\_i\
& & - (i- 2 n\_c +1) y\_i(t) + 2 \_[j=i+n\_c]{}\^ y\_j(t) + \_[k+l=i]{} y\_k(t) y\_l(t)\
& & - 2 y\_i (t) \_[j=n\_c]{}\^ y\_j, where the first term on the right-hand-side of Eq. \[eq2\] accounts for the formation of the critical nucleus, the next four terms stem from the *end evaporation and addition* pathway, and terms six to nine represent 