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

Abstract

Abstract. We investigate the Becker-Doring model of nucleation with three generalisations; an input of monomer, an input of inhibitor and nally, 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 nite 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 identied, depending on the relative poison to monomer input rates and the relative thermodynamic stability. In each case we determine the nal cluster distribution and poison concentration. We nd that poisoning the less stable cluster type can have a signicant impact on the structure of the more stable cluster distribution; a counter-intuitive result. All results are shown to agree with numerical simulation. 1.