Jamming Limit Research Articles

Model of correlated sequential adsorption of colloidal particles.

We present results of a model of sequential adsorption in which the adsorbing particles are correlated with the particles attached to the substrate. The strength of the correlations is measured by a tunable parameter sigma. The model interpolates between free ballistic adsorption in the limit sigma-->infinity and a strongly correlated phase, appearing for sigma-->0 and characterized by the emergence of highly ordered structures. The phenomenon is manifested through the analysis of several magnitudes, as the jamming limit and the particle-particle correlation function. The effect of correlations in one dimension manifests in the increased tendency to particle chaining in the substrate. In two dimensions the correlations induce a percolation transition, in which a spanning cluster of connected particles appears at a certain critical value sigma(c). Our study could be applicable to more general situations in which the coupling between correlations and disorder is relevant, as for example, in the presence of strong interparticle interactions.

Perfect Simulation for Random Sequential Adsorption of d-Dimensional Spheres with Random Radii

An efficient simulation algorithm for random sequential adsorption of spheres with radii chosen from a (prior) probability distribution is implemented. The algorithm is based on dividing the whole domain in small subcubes of different edge length. Samples obtained by this algorithm satisfy the jamming limit propertyi.e., no further sphere can be placed in the final configuration without overlapping. Samples for both discrete and continuous radii distributions are simulated and analyzed, especially jamming coverage, pair correlation functions and posterior radii distributions of the obtained sphere configurations.

Random Parking, Sequential Adsorption,¶and the Jamming Limit

Identical cars are dropped sequentially from above into a large parking lot. Each car is positioned uniformly at random, subject to non-overlap with its predecessors, until jamming occurs. There have been many studies of the limiting mean coverage as the parking lot becomes large, but no complete proof that such a limit exists, until now. We prove spatial laws of large numbers demonstrating that for various multidimensional random and cooperative sequential adsorption schemes such as the one above, the jamming limit coverage is well-defined.

Dynamics of Silica Colloid Deposition and Release in Packed Beds of Aminosilane-Modified Glass Beads

The transport and deposition dynamics of colloidal particles in packed porous media were investigated. The colloids were negatively charged silica particles (0.1 and 0.3 μm in diameter), and the packed-bed columns comprised aminosilane-modified glass beads. The glass beads acquired a positive surface charge by anhydrous chemical reaction with aminoethyl(N-aminopropyl)dimethoxymethylsilane. Maximum attainable surface-coverage (θmax) and excluded-area-parameter (β) values were determined for particle deposition experiments under various physicochemical conditions, namely, solution ionic strength, flow velocity, and particle size. The results demonstrated that excluded-area-parameter values increased with decreasing ionic strength and increasing flow velocity and particle size. Observed excluded-area-parameter values smaller than 1.83, the hard-sphere jamming limit according to random-sequential-adsorption (RSA) mechanics, alluded to the occurrence of multilayer deposition. The release of deposited particles after complete breakthrough was also investigated by reducing the ionic strength of the solution and by reversing the collector surface charge with an anionic surfactant (sodium dodecyl sulfate). Because colloid release was predominantly observed following deposition runs with higher values of surface coverage, which suggested the possible presence of multilayer deposition, it could be inferred that particle−particle repulsion was mainly responsible for the observed colloid release.

The influence of the random sequential adsorption of binary mixtures on the kinetics of hydrocarbon hydrogenation reactions

The hydrogenation of unsaturated hydrocarbons by transition metal catalysts demonstrates complex kinetic behavior that cannot be represented by mean-field kinetic models. In this paper, a Monte Carlo model of the Horiuti-Polanyi hydrogenation mechanism is introduced and is applied to the hydrogenation of a number of alkenes of varying chain length. We demonstrate that the origin of this anomalous kinetic behavior can be explained by assuming that the adsorption of the hydrocarbon on the catalyst surface approximates a random sequential adsorption (RSA) process. The model is shown to reproduce the kinetic discontinuities observed experimentally for the hydrogenation of ethene and ethyne. Monte Carlo simulations conducted on square lattices for a number of hydrocarbons indicate that the transition between the two kinetic regimes occurs at the point where the hydrocarbon surface coverage exceeds the dimer jamming limit.

Long-Range-Interaction Induced Ordered Structures in Deposition Processes

We present a new model of sequential adsorption in which the adsorbing particles experience dipolar interactions. We show that in the presence of these long-range interactions, highly ordered structures in the adsorbed layer may be induced at low temperatures. The new phenomenology is manifest through significant variations of the pair correlation function and the jamming limit, with respect to the case of noninteracting particles. Our study could be relevant in understanding the adsorption of magnetic colloidal particles in the presence of a magnetic field.

Effect of Charge Nature on the Adsorption of Single-Stranded DNA Fragments onto Latex Particles

The adsorption of single-stranded DNA fragments (oligonucleotides) onto latex particles is investigated using a series of polymer latexes exhibiting various surface charge and group natures (sulfate, amidine, and amine). The latexes are prepared using free emulsion polymerization. In this work, we study the adsorption of single labeled oligonucleotide polythymidylic acid and of a 35-base-bearing fluorescein group (Fluo-dT35) on four latexes to elucidate certain general principles of oligonucleotide adsorption as a function of surface charge nature. Several results are presented in this paper. It was found that the adsorbed amount of oligonucleotide is strongly dependent on the pH of the medium and the charge density of positively charged latex particles. This indicates that electrostatic forces play a major role in the adsorption process. The maximal adsorbed amount was found to be lower than the one calculated from the jamming limit for the random sequential adsorption of nonoverlapping rigid rods adsorbed in two dimensions. Desorption of the oligonucleotide was also studied by fluorescence measurements, in which both the supernatant and the latex particles were analyzed using the front face analysis method. In addition, attempts were made to correlate the maximum fluorescence emission intensity using the front face analysis with the amount of oligonucleotides adsorbed onto latex particles.

Addition of particles of alternating charge

The maximum attainable coverage of a given type of particle on a smooth planar surface is limited by the shape and size of the particles, and by their electrostatic charge. By alternating the adsorption of one type of particle with another of opposite charge, a composite layer is formed in which the jamming limit is exceeded. The phenomenon was investigated experimentally using negatively charged silica particles and positively charged iron(III) hydroxide, dispersed in water. Silica is not adsorbed at all on a bare silica–titania surface but, after depositing iron(III) hydroxide particles to the jamming limit, a jammed layer of silica may be subsequently deposited, upon which more iron(III) hydroxide may be deposited. The sequence cannot be continued adlib, however, because at each step progressively less material is deposited. Optical waveguide lightmode spectroscopy (OWLS) was used to monitor the precise number of particles adsorbed at each step, and the corresponding layer thickness. Analysis of the results revealed that true multilayers are not formed, because of incomplete charge reversal at each step. The adsorbed silica provides a fresh surface on which the iron(III) hydroxide can be adsorbed, but the amount of silica is limited by interparticle repulsion and, as the interfacial region becomes progressively more basic due to the presence of the iron(III) hydroxide, the silica becomes more and more negatively charged, interparticle repulsion increases, and its jamming limit ineluctably decreases.

Packing of spheroids in three-dimensional space by random sequential addition

Packings of spheroidal particles with semi-axes of length (a,b,b) were generated by random sequential addition (RSA) simulations. As the jamming limit is approached, the volume fraction occupied by particles tends towards an asymptote , which was determined as a function of aspect ratio . This asymptote has a local minimum at (spheres), with local maxima at (prolate spheroids) and (oblate). Values of agree with results from RSA simulations of sphere packings, but lie below volume fractions obtained in simulations of near-spheres packed under gravity. Volume fractions reported for simulations of spheroids packed under gravity vary widely when the aspect ratio is very large or small; differences between these results and the predictions of RSA are discussed.

2-D and 3-D Interactions in Random Sequential Adsorption of Charged Particles

We explore the influence of electrolyte concentration on the adsorption of charged spheres using modeling techniques based on random sequential adsorption (RSA). We present a parametric study of the effects of double layer interactions between the charged particles and between the particle and the substrate on the jamming limit using a two-dimensional RSA simulation similar to that of Z. Adamczyket al.(1990,J. Colloid Interface Sci.140,123) along with a simple method of estimating jamming limit coverages. In addition, we present a more realistic RSA algorithm that includes explicit energetic interaction in three dimensions, that is, particle–particle and particle–surface interactions during the approach of a particle to the substrate. The calculation of interaction energies in the 3-D RSA model is achieved with the aid of a three-body superposition approximation. The 3-D RSA model differs from the 2-D model in that the extent of coverage is controlled by kinetic rather than energetic considerations. Results of both models capture the experimentally observed trend of increased surface coverage with increased electrolyte concentration, and both models require the value of a key model parameter to be specified for a quantitative match to experimental data. However, the 3-D model more effectively captures the governing physics, and the parameter in this case takes on more meaningful values than for the 2-D model.

Monte Carlo analysis of the fluctuations in the random sequential adsorption of aligned and unaligned hard-squares

The fluctuations in the number of aligned and unaligned hard-squares deposited on a subvolume of a finite flat surface through a random sequential adsorption process are analyzed from Monte Carlo computer simulations. Approximate expressions for the coverage dependence of the relative fluctuation are obtained from a fit to simulation data. The influence of both the size of the subvolume and the size of the total adsorbing surface on the relative fluctuation is also examined. Two theoretical probability distributions, binomial and hypergeometric, are tested by comparing them with simulation distributions. A hypergeometric model where the effects of mutual exclusion between squares are incorporated by a coverage dependent effective volume per square is shown to give an excellent agreement with simulation distributions, even at coverages close to the jamming limit.

Role of diffusion in irreversible deposition

The adsorption of spheres onto solid surfaces is investigated using a cellular automaton model of diffusion deposition. Unlike previous models, the diffusive transport of the particles from the bulk to the surface as well as their interaction with adsorbed particles are explicitly considered at a microscopic level. We study the initial time regime, which determines the subsequent evolution and during which the particle flux at the surface is not constant. We observe that diffusion-driven adsorption differs significantly from random sequential adsorption (RSA) when particles diffuse in a two-dimensional bulk and are adsorbed on a one-dimensional substrate. We also find that the microscopic details of the diffusive motion influence both the kinetics of deposition and the jamming limit of the coverage. The RSA model appears to be a good approximation, especially for two-dimensional deposition, but cannot generally represent diffusion deposition. {copyright} {ital 1997} {ital The American Physical Society}

Kinetics and Jamming Coverage in a Random Sequential Adsorption of Polymer Chains.

Using a highly efficient Monte Carlo algorithm, we are able to study the growth of coverage in a random sequential adsorption (RSA) of self-avoiding walk (SAW) chains for up to 10^{12} time steps on a square lattice. For the first time, the true jamming coverage (theta_J) is found to decay with the chain length (N) with a power-law theta_J propto N^{-0.1}. The growth of the coverage to its jamming limit can be described by a power-law, theta(t) approx theta_J -c/t^y with an effective exponent y which depends on the chain length, i.e., y = 0.50 for N=4 to y = 0.07 for N=30 with y -> 0 in the asymptotic limit N -> infinity.

Spontaneous Reconfiguration of Adsorbed Lysozyme Layers Observed by Total Internal Reflection Fluorescence with a pH-Sensitive Fluorophore

By conjugating proteins with a common pH-sensitive fluorescent label, fluorescein isothiocyanate (FITC), and controlling the ionic strength, we provide a means to decrease the characteristic length scale of the total internal reflection fluorescence (TIRF) technique by two orders of magnitude. The usual characteristic length scale for TIRF is an optical length, specifically the evanescent wave penetration depth (on the order of 100 nm). In our experiments the penetration depth is replaced by the Debye screening length as the characteristic length scale. This is readily controlled to match the dimensions of an adsorbed protein layer (on the order of 1 nm). We achieve this length scale reduction by coupling the well-known pH-sensitivity of fluorescence emission by FITC-labeled proteins with the variation of electrostatic potential near a negatively charged surface. Using this fine-resolution TIRF capability in combination with scanning angle reflectometry, we find that lateral repulsions induce a dramatic reconfiguration of adsorbed lysozyme layers on negatively charged silica surfaces. This occurs as the surface concentration approaches the jamming limit for random sequential adsorption. The reconfiguration evidently optimizes electrostatic interactions in the adsorbed layer and decreases the effective excluded area per lysozyme. The decrease in effective excluded area allows adsorption to continue beyond the jamming limit to ultimately attain a hexagonal close packed monolayer of horizontally oriented lysozyme molecules. The adsorption kinetics switch abruptly from being transport-limited to surface-limited after the reconfiguration.

Nearest-neighbor statistics in a one-dimensional random sequential adsorption process.

The probability of finding a nearest neighbor at some radial distance from a reference point in many-particle systems is of fundamental importance in a host of fields in the physical as well as biological sciences. We have derived exact analytical expressions for nearest-neighbor probability functions for particles deposited on a line during a random sequential adsorption process for all densities, i.e., up to the jamming limit. Using these results, we find the mean nearest-neighbor distance \ensuremath{\lambda} as a function of the packing fraction, and discuss it in light of recent theorems derived for general ergodic and isotropic packings of hard spheres. \textcopyright{} 1996 The American Physical Society.

Percus–Yevick-like integral equation for random sequential addition

Random sequential addition is a process that generates nonequilibrium configurations of hard objects. The corresponding spatial pair correlations are investigated via a Percus–Yevick (PY)-like integral equation. Numerical solutions are obtained in one, two, and three dimensions. Comparison with exact results in one dimension and with Monte Carlo data in higher dimensions shows that the PY-like integral equation provides an accurate description of the structure, except close to the jamming limit, where the logarithmic divergence of the correlation function at contact is not reproduced. Using diagrammatic expansions, we show that in one dimension, contrary to its equilibrium counterpart, this equation is only exact up to the second order in density.

Adsorption of colloidal particles in the presence of external fields.

We present a new class of sequential adsorption models in which the adsorbing particles reach the surface following an inclined direction (shadow models). Capillary electrophoresis, adsorption in the presence of a shear or on an inclined substrate are physical manifestations of these models. Numerical simulations are carried out to show how the new adsorption mechanisms are responsible for the formation of more ordered adsorbed layers and have important implications in the kinetics, in particular modifying the jamming limit.

Effect of transport mechanisms on the irreversible adsorption of large molecules.

We consider one-dimensional models for the irreversible adsorption of large molecules on a solid surface. The study is motivated by recent simulations of the diffusion random sequential adsorption process in which hard spheres diffuse above an adsorbing surface. We first consider a generalized parking process in which the rate of deposition of a particle within a gap formed by two preadsorbed spheres depends on the width of the gap, but is uniform within a gap. We demonstrate simply that all generalized parking processes, including simple random sequential adsorption (RSA), have the same jamming limit coverage. As a by-product of this analysis, we obtain a recursion formula for the saturation coverage in gaps of finite length. In the second part of the paper, we consider a parking process in which the rate of deposition within a gap varies with position as well as the gap width. To apply the model to diffusion random sequential adsorption (DRSA) we solve the steady state diffusion equation to find the probability density function for the creation of a free interval of width h upon adsorption of a particle in a gap of size h'. The resulting jamming limit coverage, ${\mathrm{\ensuremath{\theta}}}_{\mathrm{\ensuremath{\infty}}}$=0.7506, is in good agreement with the numerical simulations of the DRSA process (0.7496), but larger than that of simple RSA (0.7476).

Random sequential adsorption on a dashed line

We study analytically and numerically a model of random sequential adsorption (RSA) of segments on a line, subject to some constraints suggested by two kinds of physical situations: - deposition of dimers on a lattice where the sites have a spatial extension; - deposition of extended particles which must overlap one (or several) adsorbing sites on the substrate. Both systems involve discrete and continuous degrees of freedom, and, in one dimension, are equivalent to our model, which depends on one length parameter. When this parameter is varied, the model interpolates between a variety of known situations : monomers on a lattice, "car-parking" problem, dimers on a lattice. An analysis of the long-time behaviour of the coverage as a function of the parameter exhibits an anomalous 1/t^2 approach to the jamming limit at the transition point between the fast exponential kinetics, characteristic of the lattice model, and the 1/t law of the continuous one.

Dynamics of Colloid Deposition in Porous Media: Blocking Based on Random Sequential Adsorption

An improved theoretical model is presented for quantifying the dynamics of colloid deposition in granular porous media. The model characterizes the transient aspects ofirreversible particle deposition onto spherical collector surfaces where repulsive electrostatic forces between colloidal particles limit deposition to monolayer coverage. The transient deposition rate normally associated with particle deposition is depicted in the model by a dynamic blocking function derived from random sequential adsorption (RSA) mechanics. The RSA blocking function has a nonlinear power law dependence on surface coverage, in contrast to the linear Langmuirian blocking function used in previous dynamic deposition models for porous media. A technique involving the calculation of the jamming limit from experimental particle breakthrough curves is utilized for determining the excluded area parameter, an integral component of the dynamic blocking function. Parameter estimation and curve fitting techniques are not required by the model as all parameter values are calculated a priori using available theoretical principles. Parameter values are incorporated into the theoretical model to produce theoretical particle breakthrough curves based on both RSA and Langmuirian dynamic blocking functions. A comparison of theoretical results with experimental particle breakthrough curves demonstrates the utility of RSA mechanics as a means of describing particle blocking dynamics associated with colloid deposition in granular porous media.