Continuum random sequential adsorption of polymer on a flat and homogeneous surface

Random sequential adsorption (RSA) of polymer, modeled as a chain of identical spheres, is systematically studied. In order to control precisely anisotropy and number of degrees of freedom, two different kinds of polymers are used. In the first one, monomers are placed along a straight line, whereas in the second, relative orientations of particles are random. Such polymers fill a flat homogeneous surface randomly. The paper focuses on maximal random coverage ratio and adsorption kinetics dependence on polymer size, shape anisotropy, and numbers of degrees of freedom. Obtained results were discussed and compared with other numerical experiments and theoretical predictions.Comment: 13 pages, 7 figure

Properties of random sequential adsorption of generalized dimers

Saturated random packing of particles built of two identical, relatively shifted spheres in two and three dimensional flat and homogeneous space was studied numerically using random sequential adsorption algorithm. The shift between centers of spheres varied from 0.0 to 8.0 sphere diameters. Numerical simulations allowed determine random sequential adsorption kinetics, saturated random coverage ratio as well as available surface function and density autocorrelation function.Comment: 5 pages, 8 figure

Scaling properties of the number of random sequential adsorption iterations needed to generate saturated random packing

The properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied. Numerical results obtained for one, two, and three dimensional packings were supported by analytical calculations valid for any dimension $d$. It has been shown that the number of iterations needed to generate finite saturated packing is subject to Pareto distribution with exponent $-1-1/d$ and the median of this distribution scales with packing size according to the power-law characterized by exponent $d$. Obtained resultscan be used in designing effective RSA simulations.Comment: 7 pages, 3 figure

Random packing of regular polygons and star polygons on a flat two-dimensional surface

Random packing of unoriented regular polygons and star polygons on a two-dimensional flat, continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine saturated random packing ratio as well as its density autocorrelation function. Additionally, the kinetics of packing growth and available surface function are measured. In general, stars give lower packing ratios than polygons, but, when the number of vertexes is large enough, both shapes approach disks and, therefore, properties of their packing reproduce already known results for disks.Comment: 5 pages, 8 figure

Domain structure created by irreversible adsorption of dimers

Structure of monolayers built during adsorption process is strongly related to the properties of adsorbed particles. The most important factor is their shape. For example, adsorption of elongated molecules on patterned surfaces may produce certain orientational order inside a covering layer. This study, however, focuses on random adsorption of dimers on flat, homogeneous surfaces. It has been observed that despite the lack of global orientational ordering, adsorbed dimers may form local, orientationally ordered structures [1, 2]. Our investigations focus on the dependence between domain size distribution and environmental parameters such as ionic strength, which affects the range of electrostatic interaction between molecules.Comment: 8 pages, 5 figures, Presented at the XXV Marian Smoluchowski Symposium on Statistical Physics, Krak\'ow, Poland, September, 201

Random sequential adsorption of trimers and hexamers

Adsorption of trimers and hexamers built of identical spheres was studied numerically using the Random Sequential Adsorption (RSA) algorithm. Particles were adsorbed on a two dimensional, flat and homogeneous surface. Numerical simulations allow to establish the maximal random coverage ratio, RSA kinetics as well as the Available Surface Function (ASF), which is crucial for determining kinetics of the adsorption process obtained experimentally. Additionally, the density autocorrelation function was measured. All the results were compared with previous results obtained for spheres, dimers and tetramers.Comment: 11 pages, 6 figure

Boundary conditions in random sequential adsorption

The influence of different boundary conditions on the density of random packings of disks is studied. Packings are generated using the random sequential adsorption algorithm with three different types of boundary conditions: periodic, open, and wall. It is found that the finite size effects are smallest for periodic boundary conditions, as expected. On the other hand, in the case of open and wall boundaries it is possible to introduce an effective packing size and a constant correction term to significantly improve the packing densities.Comment: 9 pages, 7 figure

Multimodal stationary states under Cauchy noise

A L\'evy noise is an efficient description of out-of-equilibrium systems. The presence of L\'evy flights results in a plenitude of noise-induced phenomena. Among others, L\'evy flights can produce stationary states with more than one modal value in single-well potentials. Here, we explore stationary states in special double-well potentials demonstrating that a sufficiently high potential barrier separating potential wells can produce bimodal stationary states in each potential well. Furthermore, we explore how the decrease in the barrier height affects the multimodality of stationary states. Finally, we explore a role of the multimodality of stationary states on the noise induced escape over the static potential barrier.Comment: 10 pages, 11 figure