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.     

Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.     

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.     

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.     

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 .     

Reversible random sequential adsorption on a one-dimensional lattice

We consider the reversible random sequential adsorption of line segments on a one-dimensional lattice. Line segments of length l⩾2 adsorb on the lattice with a adsorption rate K_a, and leave with a desorption rate K_d. We calculate the coverage fraction, and steady-state jamming limits by a Monte Carlo method. We observe that coverage fraction and jamming limits do not follow mean-field results at the large K=K_a/K_d⪢1. Jamming limits decrease when the length of the line segment l increases. However, jamming limits increase monotonically when the parameter K increases. The distribution of two consecutive empty sites is not equivalent to the square of the distribution of isolated empty sites.     

Reversible random sequential adsorption of dimers on a triangular lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca2+ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.     

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.     

Simulation study of random sequential adsorption of mixtures on a triangular lattice

Random sequential adsorption of binary mixtures of extended objects on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding random walks on the lattice. We concentrate here on the influence of the symmetry properties of the shapes on the kinetics of the deposition processes in two-component mixtures. Approach to the jamming limit in the case of mixtures is found to be exponential, of the form: θ(t) ∼ θ_jam - Δθ exp(- t/σ), and the values of the parameter σ are determined by the order of symmetry of the less symmetric object in the mixture. Depending on the local geometry of the objects making the mixture, jamming coverage of a mixture can be either greater than both single-component jamming coverages or it can be in between these values. Results of the simulations for various fractional concentrations of the objects in the mixture are also presented.     

Ground-state and quenched-state properties of a one-dimensional interacting lattice gas in a random potential

We determine the zero-temperature properties of a one-dimensional lattice gas of particles that interact via a nearest neighbor exclusion potential and are subject to a random external field. The model is a special limiting case of the random field Ising chain. We calculate (1) the energy and density of the ground state as well as the local energy-density correlation and (2) the pair correlation function. The latter calculation gives access to all higher order correlations. The structure factor is shown to be a squared Lorentzian. We also compare the ground state to the quenched state obtained by sequentially filling the lowest available energy levels.     

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.     

Coverage and Structure of Films of Spherical Particles Deposited after Diffusing in a Gravitational Field

We investigate the coverage and structure of a layer of particles deposited on a line after diffusion in a gravitational field. The dynamics of the depositing particles is controlled by the gravity number N _G(=d ⁴ g/6k _B T), where d is the diameter of the particles, is the density difference between the particles and the solution, g is the acceleration due to gravity, k _B is Boltzmann's constant, and T is the temperature. The position-dependent flux of particles in a gap formed by two preadsorbed particles is estimated by superposition of solutions of a steady-state convective diffusion equation for the flux in the presence of a single preadsorbed particle. The saturation coverages are found with a recursion relation and are in good agreement with those obtained from Brownian dynamics simulation. The jamming coverage increases rapidly with increasing particle size, particularly for large values of . An algorithm is presented to generate adsorbed configurations from which the structure of the deposit is determined.     

Modeling multilayer adsorption of interacting polyatomic species on heterogeneous surfaces

In the present work, a generalized lattice-gas model to study multilayer adsorption of interacting polyatomic species on heterogeneous surfaces is introduced. Using an approximation in the spirit of the well-known Brunauer-Emmet-Teller (BET) model, a new theoretical isotherm is obtained in one- and two-dimensional lattices and compared with Monte Carlo simulation. In addition, the BET approach is used to analyze these isotherms and to estimate the monolayer volume. In all cases, the application of the BET equation leads to an underestimate of the true monolayer capacity. However, significant compensation effects were observed for heterogeneous surfaces and attractive lateral interactions.     

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.     

Parking on a Random Tree

Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Rényi’s parking problem, alternatively called blocking RSA (random sequential adsorption): at every vertex of the tree a particle (or “car”) arrives with rate one. The particle sticks to the vertex whenever the vertex and all of its nearest neighbors are not occupied yet. We provide an explicit expression for the so-called parking constant in terms of the generating function. That is, the occupation probability, averaged over dynamics and the probability distribution of the random trees converges in the large-time limit to (1−α ²)/2 with .     

The asymptotic behavior of a random walk on a dual-medium lattice

This paper considers the asymptotic distribution for the horizontal displacement of a random walk in a medium represented by a two-dimensional lattice, whose transitions are to nearest-neighbor sites, are symmetric in the horizontal and vertical directions, and depend on the column currently occupied. On either side of a change-point in the medium, the transition probabilities are assumed to obey an asymptotic density condition. The displacement, when suitably normalized, converges to a diffusion process of oscillating Brownian motion type. Various special cases are discussed.     

外力驱动作用下高分子链在表面吸附性质的计算机模拟

采用退火法模拟研究受外力F驱动的高分子链在吸引表面的吸附特性.通过高分子链的平均表面接触数〈M〉与温度T之间的关系计算临界吸附温度T_c,并发现T_c随着F的增加而减小;进而通过高分子链的均方回转半径分析外力驱动作用对高分子链构象的影响,并从回转半径极小值或者垂直外力方向的y和z分量的变化交叉校验临界吸附点T_c.模拟计算了处于吸附状态的高分子链随着外力F的增加是否会发生吸附状态到脱附状态的相变以及发生相变所需施加的外力是否由温度所决定.模拟结果表明:两种不同温度下高分子链的吸附性质和构象性质受外力驱动作用而产生不同现象,在温度区间T*_cTT_c时会发生脱附现象,而在TT*_c时不会发生脱附现象.     

Numerical simulation of the XY-model on a two-dimensional random lattice

We discuss a numerical simulation of the planar XY-model on a two-dimensional random lattice. Results obtained on the random lattice are compared with those obtained using identical methods on a square lattice, which acts as a “control experiment”. Calculations were made of the average energy per spin, susceptibility per spin and magnetization. The specific heat was obtained by a numerical differentiation of the energy curve. Also, the number of positive (or negative) spin vortices in the system at different temperatures was calculated. Particular attention is paid to the way in which these vortices entered the system, since it is their appearance which signals the phase transition. Numerical results computed at high temperatures are compared with the theoretical values obtained from high-temperature expansions; and those computed at low temperatures, with the results of spin-wave theory. We investigate the effect of varying the weights for the field theory on the random lattice.