Phase Transition with Non-Thermodynamic States in Reversible Polymerization
arXiv:0803.2875 · doi:10.1103/PhysRevE.77.061132
Abstract
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 non-thermodynamic as the total number of polymers grows sub-linearly with the system size. Moreover, the length distribution has an algebraic tail and the characteristic exponent varies continuously with the fragmentation rate.
9 pages, 4 figures
References in corpus (17)
- Statistical mechanics of complex networks
- Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
- Particles and fields in fluid turbulence
- Scaling Theory and Exactly Solved Models In the Kinetics of Irreversible Aggregation
- The Scaling Window of the 2-SAT Transition
- Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation
- Borderline Aggregation Kinetics in ``Dry'' and ``Wet'' Environments
- Kinetic Theory of Random Graphs: from Paths to Cycles
- Exact Phase Diagram of a model with Aggregation and Chipping
- Hot String Soup
- Size of Outbreaks Near the Epidemic Threshold
- Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term
- Influence of Island Diffusion on Submonolayer Epitaxial Growth
- Stationary states and energy cascades in inelastic gases
- Cluster-Cluster Aggregation as an Analogue of a Turbulent Cascade : Kolmogorov Phenomenology, Scaling Laws and the Breakdown of self-similarity
- Logarithmic Clustering in Submonolayer Epitaxial Growth
- Solution of an infection model near threshold
Cited by in corpus (15)
- Thermoreversible Associating Polymer Networks: I. Interplay of Thermodynamics, Chemical Kinetics, and Polymer Physics
- Stability of a Giant Connected Component in a Complex Network
- Pattern formation mechanisms in motility mutants of Myxococcus xanthus
- Oscillations in aggregation-shattering processes
- Numerical Solutions of the Isotropic 3-Wave Kinetic Equation
- Driven Brownian coagulation of polymers
- Kinetics and thermodynamics of reversible polymerization in closed systems
- Non-extensive super-cluster states in aggregation with fragmentation
- Kinetics of Ring Formation
- Hopf bifurcation in addition-shattering kinetics
- Aggregation-fragmentation-diffusion model for trail dynamics
- Aggregation and fragmentation dynamics in random flows: From tracers to inertial aggregates
- Simple evolving random graphs
- Jamming and Tiling in Aggregation of Rectangles
- Kinetics of Aggregation with Choice