$P$ and average degree of polymerisation $L$ are given by \[eq9\] P() &=& , and \[eq10\] L() &=& = 2 n\_c -1 for all values of $\kpb$ and $\kmb$. Note that the equilibrium average degree of polymerisation $L(\infty)$ only depends on the critical nucleus size, $n_c \ge 2$, not on the concentration. This, of course, disagrees with the thermodynamic theory but, as we shall see below, this does not preclude very large values of $L(t)$ for intermediate times. [@paul_review] Similar results were obtained by Cohen *et al.* in the absence of *body evaporation and addition*. [@knowles_two_stage]

Lag Time Analysis {#sec3}
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The steady-state solutions of the moment equations clearly indicate that our generalized reaction schemes do not result into the long polymers in the limit of $t \rightarrow \infty$ to be expected for nucleated polymerisation. However, as shown in Fig. \[fig2\], for intermediate times the mean polymer length overshoots and attains very large values. Also, Fig. \[fig2\] shows that the mean polymer length for very large and very small values of recombination rate constant, $k_f^+=10^{8}, 10^{-8}$, $M s^{-1}$ the term $k_f^+ P^2$ has no effect on the early time kinetics for any reasonable value of $k_f^+$. This justifies our approximation 