Statistical Thermodynamics of Irreversible Aggregation and Gelation

Abstract

Binary aggregation is known to lead, under certain kinetic rules, to the coexistence of two populations, one consisting of finite-size clusters (sol), and one that contains a single cluster that carries a finite fraction of the total mass (giant component or gel). The sol-gel transition is commonly discussed as a phase transition by qualitative analogy to vapor condensation. Here we show that the connection to thermodynamic phase transition is rigorous. We develop the statistical thermodynamics of irreversible binary aggregation in discrete finite systems, obtain the partition function for arbitrary kernel, and show that the emergence of the gel cluster has all the hallmarks of a phase transition, including an unstable van der Waals loop. We demonstrate the theory by presenting the complete pre- and post-gel solution for aggregation with the product kernel, $k_{ij}=ij$.

References in corpus (2)

• Scaling Theory and Exactly Solved Models In the Kinetics of Irreversible Aggregation
• Statistical Thermodynamics of Clustered Populations

Cited by in corpus (5)

• Dynamic Networks that Drive the Process of Irreversible Step-Growth Polymerization
• The Smoluchowski Ensemble: Statistical Mechanics of Aggregation
• Thermodynamics Beyond Molecules: Statistical Thermodynamics of Distributions
• Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework
• Fragmentation instability in aggregating systems