Dynamics of polydisperse irreversible adsorption: A pharmacological example

Radek Erban, S. Jonathan Chapman, Kerry D. Fisher, Ioannis G. Kevrekidis, Leonard W. Seymour

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Many drug delivery systems suffer from undesirable interactions with the host immune system. It has been experimentally established that covalent attachment (irreversible adsorption) of suitable macromolecules to the surface of the drug carrier can reduce such undesirable interactions. A fundamental understanding of the adsorption process is still lacking. In this paper, the classical random irreversible adsorption model is generalized to capture certain essential processes involved in pharmacological applications, allowing for macromolecules of different sizes, partial overlapping of the tails of macromolecules, and the influence of reactions with the solvent on the adsorption process. Working in one dimension, an integro-differential evolution equation for the adsorption process is derived, and the asymptotic behavior of the surface area covered and the number of molecules attached to the surface are studied. Finally, equation-free dynamic renormalization tools are applied to study the asymptotically self-similar behavior of the adsorption statistics.

Original languageEnglish (US)
Pages (from-to)759-781
Number of pages23
JournalMathematical Models and Methods in Applied Sciences
Issue number5
StatePublished - May 2007

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics


  • Polydispersity
  • Polymer coating
  • Random sequential adsorption


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