our particular choice of molecular pathways, the resulting linearised equations always yield simple exponential time dependence that in turn result into a linear time dependence of early times.

![Time evolution of the polymerised mass fraction $M(t)/M(\infty)$ and the polymer concentration $P(t)/P(\infty)$ obtained by numerically solving Eqs. \[eq6\] and \[eq7\] for $\kpf=0$ $M^{-1} s^{-1}$. The remainder of the system parameters are $k_n^+=10^{-5} s^{-1}$, $\kpe=10^{5} M^{-1} s^{-1}$, $\kme=10^{-2} s^{-1}$, $\kpb=10^{5} M^{-1} s^{-1}$, $\kmb=10^{-2} s^{-1}$, $\kmf=10^{-4} s^{-1}$, $\mtot=10^{-5} M$, $M(0)=\mtot \times 10^{-5}$ and $P(0)=\mtot \times 10^{-6}$, where, $M$ is moles per liter and $s$ is in seconds. The inset shows the early time behaviour of the number of polymers $P(t)$, which remains essentially constant during the relaxation of the polymerised monomeric mass, $M(t)$, and only relaxes after that. This figure highlights our claim of separation of time scales between the time evolution of the polymerised mass fraction and that of the polymer concentration. See the main text.[]{data-label="fig3"}](Fig3.eps){width="6.5in"}

Although the dynamical equations Eqs. \[eq11\] and \[eq12\] contain the polymer scission term, we can reduce the effect of polymer scission on the kinetics of the polymerised monomeric mass, $M$, by choosing a very small value for the scission rate constant $\kmf$. The value of $\kmf=10^{-4}$ 