Inhomogeneous random sequential adsorption on a lattice

We study idealized random sequential adsorption on a lattice, with adsorption probabilities inhomogeneous both in space and in time, and including the possibility of cooperativity. Attention is directed to the mean occupancy of a given site as a function of time, which is represented by a weighted random walk on the lattice. In the special case of nearest neighbor exclusion, the walk is transformed to one in which only neighbors of occupied sites can be occupied, but with a renormalized probability. Reduction theorems are presented, with which the general case of a tree lattice is completely solved in inverse form.     

Computer simulation of random sequential adsorption of two interacting species on a lattice

A computer-simulation model is introduced to study the variation in the coverage and porosity in a binary system by random sequential adsorption on a periodic square lattice. We study the effects of the range of the repulsive interaction between unlike species and of the probability of deposition of each particle type. For all choices of the interaction range there is a minimum in the total coverage of the lattice which occurs for equal deposition probability of the two species. The saturation coverage decreases on increasing the range of the interaction. For proper choices of the parameters of the model, regimes exist in which either pores or particles of one type form an infinite percolating network.     

Review of new experimental techniques for investigating random sequential adsorption

Burgeoning interest in random sequential adsorption (RSA) processes has led to a surge of theoretical results, but experimental work is lagging behind, due to a dearth of suitable techniques. This article reviews integrated-optical techniques for investigating the kinetics of RSA and related processes. The basic idea is to measure the phase shifts of guided waves, due to the adsorption of particles at the surface of a planar waveguide. The technique is very well suited to investigating 2-dimensional RSA, and can yield high-quality kinetic adsorption data, precise enough for rigorously testing theoretical predictions. The current state of the art allow adsorbed mass to be measured quasicontinuously with a precision of at least 1 ng/cm².     

An overlapping detection algorithm for random sequential packing of elliptical particles

Random sequential packing of particles is a subject of intense research in many branches of physics and engineering. The preponderance of preview work has focused on spherical particles and little is known about non-overlapping elliptical particles. In the present work, a new numerical algorithm is developed to detect overlapping of ellipses by a series of sequential coordinate transformations and a novel golden section search algorithm. The accuracy and efficiency of the numerical algorithm are tested and compared with algorithms developed in previous literature. Its stability is verified by visualizations of random sequential packing of monodispersed and polydispersed ellipses with different boundary conditions. Then, the algorithm is applied to investigate the influence of the shape of ellipses on the random packing fraction, as well as to study the influence of the shape and size of ellipses on the wall effect in the particle packing structure, and some numerical results are demonstrated. Finally, the reliability of the numerical algorithm extended to the three-dimensional space is also evaluated by checking overlapping of ellipsoidal particles.     

Scaling of spatial correlations in cooperative sequential adsorption with clustering

We examine solvable cooperative sequential adsorption models on a linear lattice where adsorption rates produce strong clustering or island formation. We show that the spatial pair correlations in this regime assume a scaled form for separations comparable to a characteristic length (which diverges in the strong clustering limit). This scaled form is also determined directly from consideration of appropriate solvable continuum grain growth models.     

Kinetics of random sequential parking on a line

We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the known car-parking problem and we present an alternate solution to this problem. We also consider the general homogeneous case when the parking distribution varies asx ^–1 atx 1 with the lengthx of the filling interval. We develop a scaling theory describing such mixture-deposition processes and show that the scaled hole-size distribution(), with =xt ^z a scaling variable, decays with the scaled mass as ^–exp(—const·¹⁺) as . We determine scaling exponentsz and, and find that at large times the coverage(t) has a power-law form 1 – (t)t ^–v with nonuniversal exponent =(2–)/(1+) depending on the homogeneity index .     

Random sequential adsorption of polydisperse spherical particles: An integral-equation theory

Our previously developed integral-equation theories were applied to incorporate the effect of polydispersity in the study of the random sequential addition of spherical particles. By using the simplest uniform size distribution, we found that results from theories were in consistence with the Monte Carlo simulation results. Some deviations were seen, which resulted from the exclusion effects of polydisperse particles. It was found in the simulations that with increasing densities, small particles adsorbed preferentially and the size distribution skewed towards the smaller particles. Therefore, to accurately predict the correct radial distribution functions, the more appropriate size distributions are needed. For all size ranges, which were 0.40d–1.60d, 0.75d–1.25d, and 0.90d–1.10d, the radial distribution functions from theory at number densities of 0.2, 0.4 and 0.65 were in good agreements with those from the simulations.     

Random and cooperative sequential adsorption on infinite ladders and strips

We analyze various processes where particles are added irreversibly and sequentially at the sites of infinite ladders or broader strips (i.e., on terraces) of adsorption sites. For sufficiently narrow strips or ladders, exact solution in closed form is possible for a variety of processes. Often this is most naturally achieved by mapping the process onto an equivalent one-dimensional process typically involvingcompetitive adsorption. We demonstrate this procedure for sequential adsorption with nearest-neighbor exclusion on a 2× square ladder. For other select processes on strips slightly too broad for exact solution, almost exact analysis is possible exploiting an empty-site shielding property. In this way, we determine a jamming coverage of 0.91556671 for random sequential adsorption of dimers on a 2× square ladder. For broader strips, we note that the complexity of these problems quickly approaches that for × lattices.     

Random Sequential Adsorption: Relationship to Dead Leaves and Characterization of Variability

A new construction for the planar unbounded random sequential adsorption (RSA) model is presented, which allows for a direct comparison with Matheron's dead leaves model. Furthermore, for the case of disks with random radii the problem of statistical determination of the proposal radius distribution is discussed. Finally, second order characteristics related to the pair correlation function are suggested for describing the variability of the RSA disk systems.     

Effects of particle size distribution,shape and volume fraction of aggregates on the wall effect of concrete via random sequential packing of polydispersed ellipsoidal particles

Concrete can be viewed as granular materials at the mesoscopic level. A specific distribution of aggregate particles in boundary layers, known as the wall effect, plays an important role in the mechanical properties and durability of concrete. However, the detailed and systematic experimental and simulated data about the wall effect of concrete is hardly adequate yet. Specially, the modeling study of spherical and two-dimensional (2D) elliptical aggregates distribution for the wall effect has been focused on in previous work, little is known about three-dimensional (3D) ellipsoidal aggregates. In the present work, based on a mesostructure model of concrete, the wall effect of concrete is quantified by configuration parameters such as the volume fraction, the specific surface area and the meaning free spacing of the solid phase. In addition, the influences of ellipsoidal particle size distribution (EPSD), shape and volume fraction (_Vf$V_f$) of ellipsoidal aggregates on the configuration parameters are evaluated by stereological methods and serial section analysis technique. Furthermore, the effect mechanisms of EPSD, shape and _Vf$V_f$ are analyzed and discussed in this paper. The reliability of the statistical results is verified by experimental data and theoretical analytical results.     

The random parking problem

A new approach to the random parking problem is given.     

Random walk in random environment: A counterexample without potential

We describe a family of random walks in random environment which have exponentially decaying correlations, nearest neighbor transition probabilities which are bounded away from 0, and are subdiffusive in any dimensiond<. The random environments have no potential ind>1.     

Blocking effects in irreversible adsorption of linear macromolecules

A new variant of random sequential adsorption (RSA), namely random sequential ballistic adsorption (RSBA), is proposed to explore the possible role of blocking effects in the adsorption dynamics of ballistically arriving objects. These objects upon adsorption can protrude outside the substrate and in turn can obstruct and hence reject the adsorption of newly arriving objects. Adsorption of linear macromolecules (modeled as infinitesimally thin needles), on a two-dimensional continuum substrate is studied using RSBA model. It is shown analytically that in late time regime, the number n(t) of adsorbed objects at time t follows a power law n(t) ∼ t^α, as in RSA, but with a different exponent, α = 2/3. Computer simulations are also carried out. The simulation results are found to be in close agreement with the analytical results. The exponent behavior for real experimental conditions is also analyzed.     

Surface pore tension and adsorption characteristics of polluted sediment

Most natural sediment particles have numerous pores and a complex surface texture which facilitates their adsorption of contaminants. Particle surface structure, therefore, is an important instrumental factor in the transport of contaminants, especially in water environments. This paper reports on the results of adsorption-desorption experiments to analyze polluted sediment surface pore tension characteristics performed on samples from the bottom of Guanting Reservoir. In our analysis, the Frenkel-Halsey-Hill (FHH) equation is applied to calculate the fractal dimensions of particles to quantify the surface roughness and pore tension characteristics. The results show that the surface fractal dimensions of sediment particle surfaces normally measure from 2.6 to 2.85. The volume of pores smaller than 10 nm changes significantly after being contaminated with pollutants and the fractal dimension decreases because the pores adsorb the contaminants. Supported by the National Science Fund for Distinguished Young Scholars (Grant No. 50325929) and the National Key Technology R&D Program during the 11th Five-Year Plan Period (Grant No. 2006BAB05B05)     

Time-dependent correlation functions for random walks on bond disordered cubic lattices

For hopping models on cubic lattices with a fractionc of impurity bonds, time-dependent transport properties and correlation functions (long-time tails) are calculated through a systematicc-expansion (in the percolation literature referred to as high-density expansion), using a method developed in an earlier paper. The time-dependent diffusion coefficient, velocity autocorrelation function (VACF), and Burnett functions are calculated exact toO(c) for allt, and exact toO(c ₂ ) for long times only. A comparison is made with the results of the effective medium approximation, and numerical results are given for the square lattice.     

A random covering interpretation for the phase transition of the random energy model

The random energy model is related to a random covering of the real line. The phase transition is interpreted as the passage from a regime where a family of random intervals covers the line (high temperature) to a noncovering regime (low temperature).     

Random Packing of Small Blocks: Pressure Effects,Orientational Correlations and Application to Polymer‐Based Composites

Packing is a complex phenomenon of prominence in many natural and industrial processes (liquid crystals, granular materials, infiltration, melting, flow, sintering, segregation, sedimentation, compaction, etc.). A variety of computational methods is available in particular for spheroid particles. Our aim is to apply the principle of the random sequential addition algorithm but with small blocks of varying size and orientation. Here the main purpose is to reproduce the observed arrangement of graphitic assemblies in polymeric matrices. Random packing is improved by applying an external pressure implemented with a drifted diffusive motion of the fillers. Attention is also paid to the emergence of structural and orientational order. Interestingly, mixtures of fillers of irregular shapes can be dealt with efficiently using the proposed algorithm.     

A first-order phase transition defines the random close packing of hard spheres

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ∼64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit. Here we show that RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the “freezing point” in a first-order phase transition between ordered and disordered packing phases. Despite the athermal nature of granular matter, we show the thermodynamic character of the transition in that it is accompanied by sharp discontinuities in volume and entropy. This occurs at a critical compactivity, which is the intensive variable that plays the role of temperature in granular matter. Our results predict the experimental conditions necessary for the formation of a jammed crystal by calculating an analogue of the “entropy of fusion”. This approach is useful since it maps out-of-equilibrium problems in complex systems onto simpler established frameworks in statistical mechanics.