Kinetic Anomalies in Addition-Aggregation Processes

TL;DR

This paper studies how different reaction rates in irreversible aggregation influence the long-term dynamics, revealing conventional scaling for certain rate ratios and unusual stretched exponential behaviors for others.

Contribution

It introduces a detailed analysis of kinetic anomalies in addition-aggregation processes based on reaction rate ratios, highlighting new scaling behaviors and boundary layer phenomena.

Findings

Conventional linear growth of cluster mass for gamma<2 and epsilon=0.

Stretched exponential decay of cluster concentrations for gamma>=2.

Emergence of boundary layer effects depending on rate ratios.

Abstract

We investigate irreversible aggregation in which monomer-monomer, monomer-cluster, and cluster-cluster reactions occur with constant but distinct rates K_{MM}, K_{MC}, and K_{CC}, respectively. The dynamics crucially depends on the ratio gamma=K_{CC}/K_{MC} and secondarily on epsilon=K_{MM}/K_{MC}. For epsilon=0 and gamma<2, there is conventional scaling in the long-time limit, with a single mass scale that grows linearly in time. For gamma >= 2, there is unusual behavior in which the concentration of clusters of mass k, c_k decays as a stretched exponential in time within a boundary layer k<k* propto t^{1-2/gamma} (k* propto ln t for gamma=2), while c_k propto t^{-2} in the bulk region k>k*. When epsilon>0, analogous behaviors emerge for gamma<2 and gamma >= 2.