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

RSA Study of Dimers

The first theoretical study of a dimer's adsorption process at homogenous surface is presented. By using the RSA algorithm, we show example monolayers, discuss estimations of random jamming coverage and measure the surface blocking function, which could be used for calculating real systems kinetics. We also found the correlation function for generated coverages and analyzed orientational ordering inside the adsorbed monolayer. Results were compared with theoretical and experimental data. Keywords: adsorption, RSA, monolayer, colloid particlesComment: 13 pages, 13 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

Competitive adsorption of bimodal latex suspension

Competitive deposition of binary mixture of small and large latex particles is studied using Random Sequential Adsorption (RSA) algorithm. We designated the saturated random coverage ratio dependence on small-to-large particle concentration ratio and on particles size ratio. Moreover, the deposition kinetics of the process was calculated numerically. To check validity of the numerical model, the saturated random coverage ratio for 1:1 binary latex particle mixture was measured experimentally using Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM)

Physics of free climbing

Theory of stochastic processes provides theoretical tools which can be efficiently used to explore properties of noise induced escape kinetics. Since noise facilitated escape over the potential barrier resembles free climbing, one can use the first passage time theory in analysis of rock climbing. We perform the analysis of the mean first passage time in order to answer the question regarding the optimal, i.e., resulting in the fastest climbing, rope length. It is demonstrated that there is a discrete set of favorable rope lengths assuring shortest climbing times, as they correspond to local minima of mean first passage time. Within the set of favorable rope lengths there is the optimal rope giving rise to the shortest climbing time. In particular, more experienced climbers can decrease their climbing time by using longer ropes.Comment: 7 pages, 6 figure

Random Sequential Adsorption on Fractals

Irreversible adsorption of spheres on flat collectors having dimension $d<2$ is studied. Molecules are adsorbed on Sierpinski's Triangle and Carpet like fractals ($1<d<2$), and on General Cantor Set ($d<1$). Adsorption process is modeled numerically using Random Sequential Adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e. maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.Comment: 12 pages, 8 figure