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: $\theta(t) \sim \theta_{jam}-\Delta\theta \exp (-t/\sigma),$ and the values of the parameter $\sigma$ 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.Comment: 11 figures, 2 table

Numerical study of anisotropic irreversible deposition of extended objects on a triangular lattice

The properties of the anisotropic random sequential adsorption (RSA) of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps. Anisotropy is introduced by positing unequal probabilities for orientation of depositing objects along different directions of the lattice. This probability is equa

Adsorption-desorption processes on discrete substrates-optimization of monolayer growth

Kinetics of the deposition process of dimers on a 1D lattice in the presence of desorption is studied by Monte Carlo method. The growth of the coverage θ(t) above the jamming limit to its steady-state value θ∞ is analyzed when desorption probability Pdes decreases both stepwise and linearly (continuously) over a certain time domain. We report a numerical evidence that the process of vibratory compaction of granular materials can be optimized by using a time dependent intensity of external excitations

The effect of UV irradiation on hydrolytic stability of urea-formaldehyde resins filled with thermally modified montmorillonite

The hydrolytic stability of organic-inorganic nano-composites prepared by a two-stage polymerization of urea-formaldehyde resin (UF) filled with thermally activated montmorillonite (MMT) has been assessed before and after UV irradiation. The physical modification of MMT powder (type K10 with surface area 220 – 270 m2/g) was carried out by thermal treatment. The activated samples were designated as TA-K10 and the inactivated as NA-K10. The two types of ureaformaldehyde–MMT composites (UF/TA-K10 and UF/Na-K10) were synthesized. Obtained materials have been irradiated with different wavelengths of UV light (254 and 366 nm) and after that the hydrolytic stability was evaluated on the basis of free and liberated formaldehyde after acid hydrolysis. The free formaldehyde content in sample UF/TA-K10 that was irradiated was 0.60 % and it was smaller compared to the free formaldehyde content before irradiation (0.90 %). The content of the liberated formaldehyde from the modified UF composite which contains unmodified K10 was 2.04% compared to the cross-linked UF/TA-K10 where the content of the released formaldehyde was 2.82%. After UV irradiation of the UF/TA-K10 the content of the liberated formaldehyde decreased to 0.30% (for wavelength 254 nm) and 0.90 % (for wavelength 366 nm).VII International Conference on Radiation in Various Fields of Research : RAD 2019 : book of abstracts; June 10-14, 2019; Herceg Novi, Montenegr

Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice

Monte Carlo simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of linear $k$-mers (also known as rods or needles) on the two-dimensional triangular lattice, considering an isotropic RSA process on a lattice of linear dimension $L$ and periodic boundary conditions. Extensive numerical work has been done to extend previous studies to larger system sizes and longer $k$-mers, which enables the confirmation of a nonmonotonic size dependence of the percolation threshold and the estimation of a maximum value of $k$ from which percolation would no longer occurs. Finally, a complete analysis of critical exponents and universality have been done, showing that the percolation phase transition involved in the system is not affected, having the same universality class of the ordinary random percolation.Comment: 6 figure

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 Ca++ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.Comment: 9 pages, 10 figure

Irreversible deposition of extended objects with diffusional relaxation on discrete substrates

Random sequential adsorption with diffusional relaxation of extended objects both on a one-dimensional and planar triangular lattice is studied numerically by means of Monte Carlo simulations. We focus our attention on the behavior of the coverage θ(t) as a function of time. Our results indicate that the lattice dimensionality plays an important role in the present model. For deposition of k-mers on 1D lattice with diffusional relaxation, we found that the growth of the coverage θ(t) above the jamming limit to the closest packing limit θCPL is described by the pattern θCPL - θ(t) ∝ Eβ[-(t/τ)β], where Eβ denotes the Mittag-Leffler function of order β ∈ (0,1). In the case of deposition of extended lattice shapes in 2D, we found that after the initial “jamming", a stretched exponential growth of the coverage θ(t) towards the closest packing limit θCPL occurs, i.e., θCPL - θ(t) ∝ exp[-(t/τ)β]. For both cases we observe that: (i) dependence of the relaxation time τ on the diffusion probability Pdif is consistent with a simple power-law, i.e., τ ∝ Pdif-δ; (ii) parameter β depends on the object size in 1D and on the particle shape in 2D

Memory effects in vibrated granular systems: Response properties in the generalized random sequential adsorption model

We investigate, by numerical simulation, the dynamical response of a granular system to an abrupt change in shaking intensity within the framework of the reversible random sequential adsorption models. We analyse the two-dimensional lattice model in which, in addition to the adsorption-desorption process, there is diffusion of the adsorbed particles on the surface. Our model reproduces qualitatively the densification kinetics and the memory effects of vibrated granular materials. An interpretation of the simulation results is provided by the analysis of the insertion probability function. The importance of the diffusional relaxation is discussed. We conclude that a complex time-evolution of the density could be explained as a consequence of the variation of the diffusion rate during the compaction. We study the nonequilibrium time-dependent density-density autocorrelation function and show that the model displays out-of-equilibrium dynamical effects such as aging.

Structural Characterization and Statistical Properties of Two-Dimensional Granular Systems During the Compaction

We study the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking, by numerical simulation. Shaking is modeled by a series of vertical expansions of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of the friction coefficient and the coefficient of normal restitution. The granular organization at local level was studied by analyzing the shape factor ξ of the local volumes, associated with a natural way of subdividing the volume into local parts - the Voronoi partition. It gives a clear physical picture of the competition between less and more ordered domains of particles during the compaction. We calculate the distribution of the shape-factor for packings at different stages of the compaction process. We have also investigated a two-dimensional granular medium experimentally. We prepared the granular packings of metallic cylinders of diameters 4, 5, and 6 mm. The distributions of the shape-factor obtained numerically for various tapping intensities are consistent with our experimental results

Linear kinetic equation: long-time behavior of one-particle distribution function

We construct asymptotic (long-time) solution of the linear Boltzmann equation using the time-dependent perturbation theory generalized to non-Hermitian operators. We prove that for times much larger than the relaxation time τ0, t ≫τ0, one-particle distribution function separates into spatio-temporal and velocity dependent parts, and provide the explicit expression for the long-time solution of the linear Boltzmann equation. Our analysis does not assume that relative density gradients n^{-1}(\partial / \partial \mathaccent"017E{r}) n are small. It relates the hydrodynamic form of the one-particle distribution function to spectral properties of operators involved in linear Boltzmann equation