Julian Talbot

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.

GENERALIZED RANDOM SEQUENTIAL ADSORPTION

Adsorption of hard spherical particles onto a flat uniform surface is analyzed by using generalized random sequential adsorption (RSA) models. These models are defined by releasing the condition of immobility present in the usual RSA rules to allow for desorption or surface diffusion. Contrary to the simple RSA case, generalized RSA processes are no longer irreversible and the system formed by the adsorbed particles on the surface may reach an equilibrium state. We show by using a distribution function approach that the kinetics of such processes can be described by means of an exact infinite hierarchy of equations reminiscent of the Kirkwood–Salsburg hierarchy for systems at equilibrium. We illustrate the way in which the systems produced by adsorption/desorption and by adsorption/diffusion evolve between the two limits represented by ‘‘simple RSA’’ and ‘‘equilibrium’’ by considering approximate solutions in terms of truncated density expansions.

Random Sequential Addition: A Distribution Function Approach

Random sequential addition (RSA) of hard objects is an irreversible process defined by three rules: objects are introduced on a surface (or ad-dimensional volume) randomly and sequentially, two objects cannot overlap, and, once inserted, an object is clamped in its position. The configurations generated by an RSA can be characterized, in the macroscopic limit, by a unique set of distribution functions and a density. We show that these “nonequilibrium” RSA configurations can be described in a manner which, in many respects, parallels the usual statistical mechanical treatment of equilibrium configurations: Kirkwood-Salsburg-like hierarchies for the distribution functions, zero-separation theorems, diagrammatic expansions, and approximate equations for the pair distribution function. Approximate descriptions valid for low to intermediate densities can be combined with exact results already derived for higher densities close to the jamming limit of the process. Similarities and differences between the equilibrium and the RSAconfigurations are emphasized. Finally, the potential application of RSA processes to the study of glassy phases is discussed.

Influence of bulk diffusion on the adsorption of hard spheres on a flat surface

Irreversible adsorption of hard spheres onto a solid surface is analyzed by using a generalization of the ‘‘random sequential adsorption’’ (RSA) model: ‘‘diffusion random sequential adsorption’’ (DRSA). In addition to the irreversible nature of the adsorption process and exclusion effects of the adsorbed configurations of hard spheres, the new model also considers the interactions between adsorbed particles and particles from the bulk, diffusing toward the surface. It is shown, in particular, that this affects the structure of adsorbed configurations for coverages different from the jamming limit coverage θ∞. Surprisingly, θ∞ appears to be identical for configurations generated by RSA and DRSA algorithms. Moreover, the structures of the configurations, as characterized by the radial distribution function g(r), are also identical at the jamming limit, whereas they differ for lower coverages. The coupling between the bulk diffusion process and the ‘‘adsorption process’’ is also analyzed as a function of the...

Random sequential addition of hard spheres

We study the random sequential addition (RSA) of hard spheres into three-dimensional space. A virial-like expansion for the fractional available volume, φ, (i.e. that volume which is accessible to the centre of a new sphere) is derived up to third order in packing fraction, η. Comparison with numerical simulations shows that, unlike the two-dimensional case, the third order expansion is a poorer representation of the process than the second-order expansion. We attempt to confirm that the jamming limit is approached in the asymptotic regime according to η(∞) — η(t) ∞ t -1/3. In addition we obtain an improved estimate for the jamming limit packing fraction, η(∞). Simple formulae that interpolate between the low and high density regimes are derived which accurately describe the RSA process over the entire density range. Finally, we compare the structure of the RSA configurations with that of the corresponding equilibrium HS fluid.

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...

A comparison between molecular-dynamics and theoretical results for the structure of fluids of hard ellipsoids

For fluids of hard ellipsoids of revolution the pair distribution function can be expressed as an expansion in products of spherical harmonics. In this paper molecular-dynamics results are given for eight coefficients in this expansion and detailed comparisons are made with the hypernetted-chain (HNC) and Percus-Yevick (PY) approximations. Ellipsoids with length-to-breadth ratios of ⅓, 2, 3 and 5 are considered, and in some cases results are reported for different densities. It is shown that both the HNC and PY theories are in reasonable agreement with molecular-dynamics results for prolate particles. The accuracy of the theories improves with decreasing density as expected, but does not depend strongly upon the length-to-breadth ratio for the prolate systems considered. For oblate ellipsoids the HNC theory remains in very good agreement with the molecular-dynamics results but the PY approximation is less accurate, tending to be rather poor for some coefficients.

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...

Molecular rattling in two‐dimensional fluids: Simulations and theory

We have carried out molecular dynamic simulations over a range of densities for two‐dimensional fluids consisting of hard, soft, and Lennard‐Jones disks. For comparison we have also carried out simulations for the corresponding systems in which all but one particle are frozen in position. We have studied the velocity autocorrelation functions and the closely related velocity‐sign autocorrelation functions, and have examined the probabilities per unit time that a particle will undergo a first velocity sign reversal after an elapsed time t measured alternately from the last velocity reversal or from a given arbitrary time. At all densities studied, the first of these probabilities per unit time is zero at t=0 and rises to a maximum at a later time, but as the hardness of the disks is increased, the maximum moves in toward t→0. This maximum can be correlated with the ‘‘negative’’ dip observed in the velocity correlation functions when plotted versus time. Our conclusion is that all these phenomena can be exp...