Phase transition with nonthermodynamic states in reversible polymerization

We investigate a reversible polymerization process in which individual polymers aggregate and fragment at a rate proportional to their molecular weight. We find a nonequilibrium phase transition despite the fact that the dynamics are perfectly reversible. When the strength of the fragmentation process exceeds a critical threshold, the system reaches a thermodynamic steady state where the total number of polymers is proportional to the system size. The polymer length distribution has a sharp exponential tail in this case. When the strength of the fragmentation process falls below the critical threshold, the steady state becomes nonthermodynamic as the total number of polymers grows sublinearly with the system size. Moreover, the length distribution has an algebraic tail and the characteristic exponent varies continuously with the fragmentation rate.

Figure 1

(Color online) The normalized dimer density ${\rho }_2$ versus the normalized monomer density ${\rho }_1$. The phase transition at ${\lambda }_c=1$ is reflected by the discontinuity in the first derivative at ${\rho }_1=1/2$.

Figure 2

(Color online) The size distribution ${\rho }_k$ versus $k$ for (a) $\lambda =0.9$ and (b) $\lambda =0.5$. The simulation results are for a system of size $N={10}^5$.

Figure 3

(Color online) Fluctuations in the total number of clusters. Shown are the average number of clusters, $⟨N_{\text{tot}}⟩$, and the variance ${\sigma }^2=⟨N_{\text{tot}}^2⟩-{⟨N_{\text{tot}}⟩}^2$ for $\lambda =0.5$.