Skip to main content

Research Repository

Advanced Search

The Becker-Döring equations with monomer input, competition and inhibition

Bolton, Colin D.; Wattis, Jonathan A.D.


Colin D. Bolton

Professor of Applied Mathematics


We investigate the Becker-Döring model of nucleation with
three generalisations; an input of monomer, an input of inhibitor and finally, we allow the monomers to form two morphologies of cluster. We assume size-independent aggregation and fragmentation rates. Initially we consider the problem of constant monomer input and determine the steady-state solution approached in the large-time limit,
and the manner in which it is approached. Secondly, in addition to a constant input of monomer we allow a
constant input of inhibitor, which prevents clusters growing any larger and this removes them from the kinetics of the process; the inhibitor is consumed in the action of poisoning a cluster. We determine a critical ratio of poison to monomer input below which the cluster concentrations tend to a non-zero steady-state solution and the poison concentration tends to a finite value. Above the critical input ratio, the concentrations of
all cluster sizes tend to zero and the poison concentration grows without limit. In both cases the solution in the large-time limit is determined. Finally we consider a model where monomers form two morphologies, but the inhibitor only acts on one morphology. Four cases are identified, depending on the relative poison to monomer input rates and the relative thermodynamic stability. In each case we determine the final cluster distribution and poison concentration. We find that poisoning the less stable cluster type can have a significant impact on the structure of the more stable cluster distribution; a counter-intuitive result. All results are shown to agree with numerical simulation.


Bolton, C. D., & Wattis, J. A. The Becker-Döring equations with monomer input, competition and inhibition. Journal of Physics A: Mathematical and General, 37,,

Journal Article Type Article
Deposit Date Aug 15, 2008
Journal Journal of Physics. A, Mathematical and General
Electronic ISSN 0305-4470
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 37,
Public URL


You might also like

Downloadable Citations