Kinetics of Diffusion-Controlled Adsorption of Colloid Particles and Proteins

Abstract

A theoretical model was developed for describing localized adsorption kinetics of proteins and colloid particles at solid/liquid interfaces. In contrast to previous approaches the adsorption and desorption rate constants as well as the surface blocking function were evaluated explicitly without using empirical parameters. It was also predicted that irreversible adsorption kinetics can unequivocally be characterized in terms of the adsorption rate constant ka and the maximum (jamming) coverage Θmx known for various particle shapes from previous Monte-Carlo simulations. The dimensionless constant ka was shown to be inversely proportional to the concentration of particles which is usually very low for protein and colloid adsorption measurements. From the theoretical model it was also deduced that in this case the asymptotic adsorption law for large dimensionless time τ can be expressed as Θmx−Θ ∼ 1/τ1/(n−1) (where n=3 for spheres, n=4 for side-on adsorption of spheroids, n=5 for randomly oriented spheroid adsorption). It was also shown that this limiting adsorption regime occurs for proteins at surface coverage Θl very close to the jamming value Θmx, becoming therefore difficult to detect due to limited experimental accuracy. These analytical predictions were found to be in agreement with numerical calculations performed by using the finite-difference scheme, valid for an arbitrary range of adsorption time. Moreover, it was demonstrated that these numerical results adequately reflected the experimental results of Johnson and Lenhoff who determined the kinetics of colloid particle adsorption using atomic force microscopy. Previously used approaches assuming that particle adsorption flux is reduced by the factor B(Θ) were found to be inadequate. It was also demonstrated that due to the similarity of underlying parameters the results obtained for colloid systems can be exploited as well-defined reference data for estimating the adsorption kinetics of proteins.