Jump to main content
Jump to site search

Issue 32, 2020
Previous Article Next Article

Smoluchowski equations for linker-mediated irreversible aggregation

Author affiliations


We developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.

Graphical abstract: Smoluchowski equations for linker-mediated irreversible aggregation

Back to tab navigation

Supplementary files

Article information

15 Apr 2020
13 Jul 2020
First published
14 Jul 2020

Soft Matter, 2020,16, 7513-7523
Article type

Smoluchowski equations for linker-mediated irreversible aggregation

J. M. Tavares, G. C. Antunes, C. S. Dias, M. M. Telo da Gama and N. A. M. Araújo, Soft Matter, 2020, 16, 7513
DOI: 10.1039/D0SM00674B

Social activity

Search articles by author