Ben-Naim E, Krapivsky P L
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 1):061132. doi: 10.1103/PhysRevE.77.061132. Epub 2008 Jun 24.
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.
我们研究了一种可逆聚合过程，其中单个聚合物以与其分子量成正比的速率聚集和断裂。尽管动力学是完全可逆的，但我们发现了一种非平衡相变。当断裂过程的强度超过临界阈值时，系统达到热力学稳态，此时聚合物的总数与系统大小成正比。在这种情况下，聚合物长度分布具有尖锐的指数尾部。当断裂过程的强度低于临界阈值时，随着聚合物总数随系统大小呈亚线性增长，稳态变为非热力学的。此外，长度分布具有代数尾部，且特征指数随断裂速率连续变化。
