TY - JOUR
T1 - Dynamics of polydisperse irreversible adsorption
T2 - A pharmacological example
AU - Erban, Radek
AU - Chapman, S. Jonathan
AU - Fisher, Kerry D.
AU - Kevrekidis, Ioannis G.
AU - Seymour, Leonard W.
N1 - Funding Information:
This work was supported by the Biotechnology and Biological Sciences Research Council (grant Ref. BB/C508618/1). I.G.K. gratefully acknowledges a Guggenheim fellowship.
PY - 2007/5
Y1 - 2007/5
N2 - 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.
AB - 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.
KW - Polydispersity
KW - Polymer coating
KW - Random sequential adsorption
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U2 - 10.1142/S0218202507002091
DO - 10.1142/S0218202507002091
M3 - Article
AN - SCOPUS:34147152056
SN - 0218-2025
VL - 17
SP - 759
EP - 781
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 5
ER -