J. Talbot

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.

Molecular thermodynamics of binary mixture adsorption: A scaled particle theory approach

We examine the thermodynamic properties of two-dimensional fluid mixtures of hard convex particles using scaled particle theory (SPT). Analytic expressions are obtained for the excess area, Gibbs free energy, and excess entropy of a binary mixture. For typical fluid densities and for a range of area and perimeter ratios of the two species the fluid mixtures exhibit small negative deviations from ideality. The excess quantities are smaller than the corresponding bulk (three dimensional) mixtures which offers some explanation for the success of the ideal adsorbed solution (IAS) theory. According to the SPT, binary mixtures of hard particles are stable for all compositions and no fluid-fluid demixing transition is possible. The SPT equations are used to examine the adsorption equilibrium between an ideal bulk phase and an adsorbed phase. Adsorption isotherms and selectivities are computed for a range of area and perimeter ratios, equilibrium constant ratio, and bulk mole fraction. Unlike the widely used mult...

Mass and size effects in three-dimensional vibrofluidized granular mixtures

We examine the steady state properties of binary systems of driven inelastic hard spheres. The spheres, which move under the influence of gravity, are contained in a vertical cylinder with a vibrating base. We computed the trajectories of the spheres using an event-driven molecular dynamics algorithm. In the first part of the study, we chose simulation parameters that match those of experiments published by Wildman and Parker. Various properties computed from the simulation including the density profile, granular temperature, and circulation pattern are in good qualitative agreement with the experiments. We then studied the effect of varying the mass ratio and the size ratio independently while holding the other parameters constant. The mass and size ratio are shown to affect the distribution of the energy. The changes in the energy distributions affect the packing fraction and temperature of each component. The temperature of the heavier component has a nonlinear dependence on the mass of the lighter component, while the temperature of the lighter component is approximately proportional to its mass. The temperature of both components is inversely dependent on the size of the smaller component.

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.

Enhanced saturation coverages in adsorption–desorption processes

Many experimental studies of protein deposition on solid surfaces involve alternating adsorption/desorption steps. In this paper, we investigate the effect of a desorption step (separating two adsorption steps) on the kinetics, the adsorbed-layer structure, and the saturation density. Our theoretical approach involves a density expansion of the pair distribution function and an application of an interpolation formula to estimate the saturation density as a function of the density at which the desorption process commences, ρ1, and the density of the depleted configuration, ρ2. The theory predicts an enhancement of the saturation density compared with that of a simple, uninterrupted random sequential adsorption (RSA) process and a maximum in the saturation density when ρ2=(2/3)ρ1. The theoretical results are in qualitative and semiquantitative agreement with the results of numerical simulations.

Aging and response properties in the parking-lot model

Abstract:An adsorption-desorption (or parking-lot) model can reproduce qualitatively the densification kinetics and other features of a weakly vibrated granular material. Here we study the the two-time correlation and response functions of the model and demonstrate that their behavior is consistent with recently observed memory effects in granular materials. Although the densification kinetics and hysteresis are robust properties, we show that the aging behavior of the adsorption-desorption model is different from other models of granular compaction. We propose an experimental test to distinguish the possible aging behaviors.

Sluggish kinetics in the parking lot model

We investigate, both analytically and by computer simulation, the kinetics of a microscopic model of hard rods adsorbing on a linear substrate. For a small, but finite desorption rate, the system reaches the equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as , a logarithmic one where the density varies as , followed by a terminal exponential approach. A mean-field approach fails to predict the relaxation rate associated with the latter. We show that the correct answer can only be provided by using a systematic description based on a gap-distribution approach.

Angular velocity distribution of a granular planar rotator in a thermalized bath

The kinetics of a granular planar rotator with a fixed center undergoing inelastic collisions with bath particles is analyzed both numerically and analytically by means of the Boltzmann equation. The angular velocity distribution evolves from quasi-Gaussian in the Brownian limit to an algebraic decay in the limit of an infinitely light particle. In addition, we compare this model to that of a planar rotator with a free center and discuss the prospects for experimental confirmation of these results.

Optimum Monte Carlo simulations: some exact results

We obtain exact results for the acceptance ratio and mean squared displacement in Monte Carlo simulations of the simple harmonic oscillator in D dimensions. When the trial displacement is made uniformly in the radius, we demonstrate that the results are independent of the dimensionality of the space. We also study the dynamics of the process via a spectral analysis and obtain an accurate description for the relaxation time.

Anisotropic energy distribution in three-dimensional vibrofluidized granular systems.

We examine the energy flows in a three-dimensional model of a granular system consisting of N inelastic hard spheres contained in an open cylinder of radius R under the influence of gravity. Energy is supplied to the system in the vertical direction by a vibrating base and is transferred to the perpendicular directions through particle-particle collisions. We examine how the local and global dissipation of energy by particle-particle and particle-wall collisions depends on the number of particles, the velocity of the vibrating base, and the restitution coefficients.