P. Viot

From car parking to protein adsorption: an overview of sequential adsorption processes

Abstract The adsorption or adhesion of large particles (proteins, colloids, cells,…) at the liquid–solid interface plays an important role in many diverse applications. Despite the apparent complexity of the process, two features are particularly important: (1) the adsorption is often irreversible on experimental time scales and (2) the adsorption rate is limited by geometric blockage from previously adsorbed particles. A coarse-grained description that encompasses these two properties is provided by sequential adsorption models whose simplest example is the random sequential adsorption (RSA) process. In this article, we review the theoretical formalism and tools that allow the systematic study of kinetic and structural aspects of these sequential adsorption models. We also show how the reference RSA model may be generalized to account for a variety of experimental features including particle anisotropy, polydispersity, bulk diffusive transport, gravitational effects, surface-induced conformational and orientational change, desorption, and multilayer formation. In all cases, the significant theoretical results are presented and their accuracy (compared with computer simulation) and applicability (compared with experiment) are discussed.

Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior

We study the random sequential adsorption (RSA) of unoriented anisotropic objects onto a flat uniform surface, for various shapes (spherocylinders, ellipses, rectangles, and needles) and elongations. The asymptotic approach to the jamming limit is shown to follow the expected algebraic behavior, θ(∞)−θ(t)∼t−1/3, where θ is the surface coverage; this result is valid for all shapes and elongations, provided the objects have a nonzero proper area. In the limit of very small elongations, the long‐time behavior consists of two successive critical regimes: The first is characterized by Feder’s law, t−1/2, and the second by the t−1/3 law; the crossover occurs at a time that scales as e−1/2 when e→0, where e is a parameter of anisotropy. The influence of shape and elongation on the saturation coverage θ(∞) is also discussed. Finally, for very elongated objects, we derive from scaling arguments that when the aspect ratio α of the objects becomes infinite, θ(∞) goes to zero according to a power law α−p, where p=1/(...

Random sequential adsorption of anisotropic particles. II: Low coverage kinetics

We study the kinetics of random sequential adsorption (RSA) of anisotropic bodies (rectangles, ellipses, spherocylinders or, more precisely, discorectangles, and needles) at low‐to‐intermediate coverages. In this regime, the adsorption probability can be expressed as a power series in the coverage. We calculate numerically the second‐ and third‐order coefficients of the series and compare the results to simulation data. The results for the low‐coverage kinetics are then combined with the asymptotic results of Paper I [J. Chem. Phys. 97, xxxx (1992)] to construct approximate equations for the adsorption probability over the entire coverage range. While the equations provide a reasonably good description of the RSA kinetics, they produce unsatisfactory estimates of the saturation coverages. The effect of particle shape on the adsorption kinetics and surface structure is discussed. Finally, the available surface function is compared with that corresponding to equilibrium configurations of the adsorbed particles.

A kinetic model of partially reversible protein adsorption

We present a kinetic adsorption model for proteins that accounts for the experimentally observed properties of partial reversibility and surface induced conformational change. Particles (proteins) are modeled as disks that adsorb sequentially and without overlap at random positions onto a surface. Following adsorption, a particle can either desorb or spread symmetrically to a larger size. If the latter occurs, it remains adsorbed irreversibly. Both of these events obey first order kinetic rate laws. We derive analytical results in the asymptotic regime and report Monte Carlo results for shorter times. This model yields adsorbed phases that are more dense than those predicted by models of purely irreversible adsorption. We attribute this densification to a fluid structure that is quite liquidlike. We show that a number of experimentally observed kinetic behaviors can be reproduced with this model and that it is in good quantitative agreement with recent experiments.

Irreversible adsorption of macromolecules at a liquid-solid interface: Theoretical studies of the effects of conformational change

The effects of particle conformational changes on the kinetics and saturation coverage of irreversible macromolecular adsorption at liquid–solid interfaces are investigated by computer simulation of a modified random sequential adsorption model. In this model, macromolecules (modeled as disks of diameter σα) adsorb onto a surface at a rate ka. Once adsorbed, the particles spread symmetrically and discretely to a larger diameter σβ at a rate ks. Adsorption or spreading events which result in the overlap of particles on the surface are not allowed. We investigate the effects of changes in spreading magnitude Σ (=σβ/σα) and relative spreading rate Ks (=ks/ka). We observe that the saturation coverage of spread particles decreases while that of unspread particles increases with spreading magnitude. This dependence is most pronounced for small spreading: the derivative of the surface coverage of both spread and unspread particles with respect to Σ diverges logarithmically when Σ→1. An increase in the rate of sp...

Isotropic Raman study of ultrarapid proton‐transfer reactions in aqueous mixtures

A theory is presented to study the exchange broadening of isotropic Raman bands due to ultrarapid proton‐transfer reactions. It represents a generalization of standard theories of Raman band profiles of nonreactive liquids. The variables describing the reaction are assumed to represent a dichotomic Markovian process. The spectral behavior of various AH/H2O mixtures is studied as a function of the exchange rate and the interplay of various band shaping mechanisms is discussed in detail. Finally, the potentialities of the Raman spectroscopy as a tool to measure the rate constant are critically assessed.

The viscous slowing down of supercooled liquids as a temperature-controlled super-Arrhenius activated process: a description in terms of frustration-limited domains

We propose that the salient feature to be explained about the glass transition of supercooled liquids is the temperature-controlled super-Arrhenius activated nature of the viscous slowing down, more strikingly seen in weakly bonded, fragile systems. In the light of this observation, the relevance of simple models of spherically interacting particles and that of models based on free-volume congested dynamics are questioned. Finally, we discuss how the main aspects of the phenomenology of supercooled liquids, including the crossover from Arrhenius to super-Arrhenius activated behaviour and the heterogeneous character of the α-relaxation, can be described by an approach based on frustration-limited domains.

First‐layer formation in ballistic deposition of spherical particles: Kinetics and structure

We present a computer simulation and theoretical study of a ballistic deposition process in which spheres are incident on a planar surface. Each incoming sphere follows a path of steepest descent which may involve rolling over the surface of preadsorbed spheres. All particles reaching a stable, elevated position are removed. The frequency of the various rolling mechanisms are evaluated as a function of coverage. The addition mechanism generates clusters of connected spheres by accretion and coalescence. We evaluate the dependence of the cluster size distribution and coalescence probability on coverage. Various peaks in the radial distribution function of the deposited layer provide a signature for the deposition mechanism. The asymptotic approach to saturation is shown to be of the form θ∞−θ(t) ∝exp[−(4/π)Smt]/t2, where Sm=√3/2 is the smallest possible target area. The expression is shown to be consistent with the simulation results. Interpolants, which accurately describe the time‐dependent coverage over...

New analytical and numerical results on virial coefficients for 2-D hard convex bodies

We present new Monte Carlo calculations of the third and fourth virial coefficients for isotropic systems of different two-dimensional hard convex bodies: ellipses, rectangles and spherocylinders for various aspect ratios, and needles. Our results differ significantly from previously published values. The accuracy of our Monte Carlo method is tested by comparison with the exact value of B 3 for unaligned hard needles, which we have obtained analytically. Finally, the validity of some approximate equations of state is investigated.

Adsorption-desorption model and its application to vibrated granular materials.

We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model that is relevant for compaction of granular materials. The computer simulations use an event-driven algorithm that is particularly efficient at very long times. For a small, but finite desorption rate, the system reaches an equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as 1/t, a logarithmic one where the density varies as 1/ln(t), followed by a terminal exponential approach. The characteristic relaxation time of the final regime, though incorrectly predicted by mean field arguments, can be obtained with a systematic gap-distribution approach. The density fluctuations at equilibrium are also investigated, and the associated time-dependent correlation function exhibits a power law regime followed by a final exponential decay. Finally, we show that denser particle packings can be obtained by varying the desorption rate during the process.