First assembly times and equilibration in stochastic coagulation-fragmentation

Maria R. D'Orsogna, Qi Lei, Tom Chou

Research output: Contribution to journalArticlepeer-review


We develop a fully stochastic theory for coagulation and fragmentation (CF) in a finite system with a maximum cluster size constraint. The process is modeled using a high-dimensional master equation for the probabilities of cluster configurations. For certain realizations of total mass and maximum cluster sizes, we find exact analytical results for the expected equilibrium cluster distributions. If coagulation is fast relative to fragmentation and if the total system mass is indivisible by the mass of the largest allowed cluster, we find a mean cluster-size distribution that is strikingly broader than that predicted by the corresponding mass-action equations. Combinations of total mass and maximum cluster size under which equilibration is accelerated, eluding late-stage coarsening, are also delineated. Finally, we compute the mean time it takes particles to first assemble into a maximum-sized cluster. Through careful state-space enumeration, the scaling of mean assembly times is derived for all combinations of total mass and maximum cluster size. We find that CF accelerates assembly relative to monomer kinetic only in special cases. All of our results hold in the infinite system limit and can be only derived from a high-dimensional discrete stochastic model, highlighting how classical mass-action models of self-assembly can fail.

Original languageEnglish (US)
Article number014112
JournalJournal of Chemical Physics
Issue number1
StatePublished - Jul 7 2015

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


Dive into the research topics of 'First assembly times and equilibration in stochastic coagulation-fragmentation'. Together they form a unique fingerprint.

Cite this