[ Laboratory | <= S.B.Vrhovac ]
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Abstract: Reversible random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The growth of the coverage $\rho(t)$ above the jamming limit to its steady-state value $\rho_{\infty}$ is described by a pattern $\rho(t)= \rho_{\infty} - \Delta\rho E_\beta [-(t/\tau)^\beta]$, where $E_\beta$ denotes the Mittag-Leffler function of order $\beta\in(0,1)$. The parameter $\tau$ is found to decay with the desorption probability $P_-$ according to a power law $\tau=A\;P_-^{-\gamma}$. The exponent $\gamma$ is the same for all shapes, $\gamma = 1.29 \pm 0.01$, but the parameter $A$ depends only on the order of symmetry axis of the shape. Finally, we present the possible relevance of the model to the compaction of granular objects of various shapes.
Abstract: 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.
Abstract: Reversible 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 adsorption-desorption processes in two-component mixtures. We provide a detailed discussion of the significance of collective events for governing the time coverage behavior of component shapes with different rotational symmetries. We also investigate the role that the mixture composition plays in the deposition process. For the mixtures of equal sized objects, we propose a simple formula for predicting the value of the steady-state coverage fraction of a mixture from the values of the steady-state coverage fractions of pure component shapes.
Abstract: We study random sequential adsorption of polydisperse mixtures of extended objects both on a triangular and on a square lattice. The depositing objects are formed by self-avoiding random walks on two-dimensional lattices. Numerical simulations were performed to determine the influence of the number of mixture components and length of the shapes making the mixture on the kinetics of the deposition process. We find that the late stage deposition kinetics follows an exponential law $\theta(t) \sim \theta_{jam} - A\exp(-t/\sigma)$ not only for the whole mixture, but also for the individual components. We discuss in detail how the quantities such as jamming coverage $\theta_{jam}$ and the relaxation time $\sigma$ depend on the mixture composition. Our results suggest that the order of symmetry axis of the shape may exert a decisive influence on adsorption kinetics of each mixture component.
Abstract: Kinetics of the deposition process of $k$-mers in the presence of desorption or/and diffusional relaxation of particles is studied by Monte-Carlo method on a one-dimensional lattice. For reversible deposition of $k$-mers, we find that after the initial "jamming", a stretched exponential growth of the coverage $\theta(t)$ towards the steady-state value $\theta_{eq}$ occurs, i.e., $\theta_{eq} - \theta(t) \propto \exp[-(t/\tau)^\beta]$. The characteristic timescale $\tau$ is found to decrease with desorption probability $P_{des}$ according to a power-law, $\tau\propto P_{des}^{-\gamma}$, with the same exponent $\gamma = 1.22\pm 0.04$ for all $k$-mers.For irreversible deposition with diffusional relaxation, the growth of the coverage $\theta(t)$ above the jamming limit to the closest packing limit $\theta_{CPL}$ is described by the pattern $\theta_{CPL} - \theta(t) \propto E_\beta [-(t/\tau)^\beta]$, where $E_\beta$ denotes the Mittag-Leffler function of order $\beta\in(0,1)$. Similarly to the reversible case, we found that the dependence of the relaxation time $\tau$ on the diffusion probability $P_{dif}$ is consistent again with a simple power-law, i.e., $\tau\propto P_{dif}^{-\delta}$.
When adsorption, desorption and diffusion occur simultaneously, coverage always reaches an equilibrium value $\theta_{eq}$, which depends only on the desorption/adsorption probability ratio. The presence of diffusion only fastens the approach to the equilibrium state, so that the stretched exponential function gives a very accurate description of the deposition kinetics of these processes in the whole range above the jamming limit.
Abstract: 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 $\theta(t)$ 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 $\theta(t)$ above the jamming limit to the closest packing limit $\theta_{CPL}$ is described by the pattern $\theta_{CPL}-\theta(t) \propto E_\beta [-(t/\tau)^\beta]$, where $E_\beta$ denotes the Mittag-Leffler function of order $\beta\in(0,1)$. 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 $\theta(t)$ towards the closest packing limit $\theta_{CPL}$ occurs, i.e., $\theta_{CPL} - \theta(t) \propto \exp[-(t/\tau)^\beta]$. For both cases we observe that: (i) dependence of the relaxation time $\tau$ on the diffusion probability $P_{dif}$ is consistent with a simple power-law, i.e., $\tau\propto P_{dif}^{-\delta}$; (ii) parameter $\beta$ depends on the object size in 1D and on the particle shape in 2D.
Abstract: Generalized random sequential adsorption (RSA) of polydisperse mixtures of $k$-mers on a one-dimensional lattice is studied numerically by means of Monte Carlo simulations. Kinetics of the deposition process of mixtures is studied for the irreversible case, for adsorption-desorption processes and for the case where adsorption, desorption and diffusion are present simultaneously. We concentrate here on the influence of the number of mixture components and the length of the $k$-mers making the mixture on the temporal behavior of the coverage fraction $\theta(t)$. Approach of the coverage $\theta(t)$ to the jamming limit $\theta_{jam}$ in the case of irreversible RSA is found to be exponential $\theta_{jam}-\theta(t) \propto \exp (-t/\sigma)$ not only for a whole mixture, but also for the individual components. For the reversible deposition of polydisperse mixtures, we find that after the initial "jamming", a stretched exponential growth of the coverage $\theta(t)$ towards the steady-state value $\theta_{eq}$ occurs, i.e., $\theta_{eq} - \theta(t) \propto \exp[-(t/\tau)^\beta]$. The characteristic timescale $\tau$ is found to decrease with desorption probability $P_{des}$. When adsorption, desorption and diffusion occur simultaneously, coverage of a mixture always reaches an equilibrium value $\theta_{eq}$, but there is a significant difference in the temporal evolution of the coverage with and without diffusion.
Abstract: 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, whereby the first step determines the orientation of the object. Anisotropy is introduced by positing unequal probabilities for orientation of depositing objects along different directions of the lattice. This probability is equal $p$ or $(1-p)/2$, depending on whether the randomly chosen orientation is horizontal or not, respectively. Approach of the coverage $\theta(t)$ to the jamming limit $\theta_{\text{jam}}$ is found to be exponential $\theta_{\text{jam}}- \theta(t) \propto \exp (-t/\sigma)$, for all probabilities $p$. It was shown that the relaxation time $\sigma$ increases with the degree of anisotropy in the case of elongated and asymmetrical shapes. However, for rounded and symmetrical shapes, values of $\sigma$ and $\theta_{\text{jam}}$ are not affected by the presence of anisotropy. We finally analyse the properties of the anisotropic RSA of polydisperse mixtures of $k$-mers. Strong dependences of the parameter $\sigma$ and the jamming coverage $\theta_{\text{jam}}$ on the degree of anisotropy are obtained. It is found that anisotropic constraints lead to the increased contribution of the longer $k$-mers in the total coverage fraction of the mixture.
Abstract: Kinetics of the deposition process of dimers in the presence of desorption is studied by Monte-Carlo method on a one-dimensional lattice. The aim of this work is to investigate how do various temporal dependences of the desorption rate hasten or slow down the deposition process. The growth of the coverage $\rho(t)$ above the jamming limit to its steady-state value $\rho_{\infty}$ is analyzed when the desorption probability $P_{des}$ decreases both stepwise and linearly (continuously) over a certain time domain. We report a numerical evidence that the time needed for a system to reach the given coverage $\theta$ can be significantly reduced if $P_{des}$ decreases in time. Finally, a self-consistent optimization procedure, when the probability $P_{des}$ depends on the current coverage density $\theta(t)$, is formulated and tested. The present model reproduces qualitatively the densification kinetics and the memory effects of vibrated granular materials. Our results suggest that the process of vibratory compaction of granular materials can be optimized by using a time dependent intensity of external excitations.
Abstract: Adsorption-desorption processes of polydisperse mixtures on a triangular lattice are studied by numerical simulations. Mixtures are composed of the shapes of different number of segments and rotational symmetries. Numerical simulations are performed to determine the influence of the number of mixture components and length of the shapes making the mixture on the kinetics of the deposition process. We find that above the jamming limit, the time evolution of the total coverage of a mixture can be described by the Mittag-Leffler function $\theta(t) = \theta_{\infty} - \Delta \theta E_{\beta}(-(t/\tau)^{\beta})$ for all the mixtures we have examined. Our results show that the equilibrium coverage decreases with the number of components making the mixture and also with the desorption probability, via corresponding stretched exponential laws. For the mixtures of equal sized objects, we propose a simple formula for predicting the value of steady-state coverage fraction of a mixture from the values of the steady-state coverage fractions of pure component shapes.
Abstract: The random sequential adsorption (RSA) approach is used to analyze adsorption of spherical particles of a fixed radius on nonuniform flat surfaces covered by rectangular cells. The configuration of the cells (heterogeneities) was produced by performing RSA simulations to a prescribed coverage fraction $\theta_0^{\text{(cell)}}$. Adsorption was assumed to occur if the particle (projected) center lies within a rectangular cell area, i.e., if sphere touches the cells. The jammed-state properties of the model were studied for different values of cell size $\alpha$ (comparable with the adsorbing particle size) and density $\theta_0^{\text{(cell)}}$. Numerical simulations were carried out to investigate adsorption kinetics, jamming coverage, and structure of coverings. Structural properties of the jammed-state coverings were analyzed in terms of the radial distribution function $g(r)$ and distribution of the Delaunay `free' volumes $P(v)$. It was demonstrated that adsorption kinetics and the jamming coverage decreased significantly, at a fixed density $\theta_0^{\text{(cell)}}$, when the cell size $\alpha$ increased. The predictions following from our calculation suggest that the porosity (pore volumes) of deposited monolayer can be controlled by the size and shape of landing cells, and by anisotropy of the cell deposition procedure.
Abstract: The out-of-equilibrium dynamical processes during the reversible random sequential adsorption (RSA) of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. We focused on the influence of the order of symmetry axis of the shape on the response of the reversible RSA model to sudden perturbations of the desorption probability $P_d$. We provide a detailed discussion of the significance of collective events for governing the time coverage behavior of shapes with different rotational symmetries. We calculate the two-time density-density correlation function $C(t,t_w)$ for various waiting times $t_w$ and show that longer memory of the initial state persists for the more symmetrical shapes. Our model displays nonequilibrium dynamical effects such as aging. We find that the correlation function $C(t,t_w)$ for all objects scales as a function of single variable $\ln(t_w)/\ln(t)$. We also study the short-term memory effects in two-component mixtures of extended objects and give a detailed analysis of the contribution to the densification kinetics coming from each mixture component. We observe the weakening of correlation features for the deposition processes in multicomponent systems.
Abstract: The properties of the random sequential adsorption 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, whereby the size of the objects is gradually increased by wrapping the walks in several different ways. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density $\theta_\text{J}$ and on the temporal evolution of the coverage fraction $\theta(t)$. Our results suggest that the order of symmetry axis of a shape exerts a decisive influence on adsorption kinetics near the jamming limit $\theta_\text{J}$. The decay of probability for the insertion of a new particle onto a lattice is described in a broad range of the coverage $\theta$ by the product between the linear and the stretched exponential function for all examined objects. The corresponding fitting parameters are discussed within the context of the shape descriptors, such as rotational symmetry and the shape factor (parameter of nonsphericity) of the objects. Predictions following from our calculation suggest that the proposed fitting function for the insertion probability is consistent with the exponential approach of the coverage fraction $\theta(t)$ to the jamming limit $\theta_\text{J}$.
Abstract: The random sequential adsorption (RSA) approach is used to analyze adsorption of spherical particles of fixed diameter $d_0$ on nonuniform surfaces covered by square cells arranged in a square lattice pattern. To characterize such pattern two dimensionless parameters are used: the cell size $\alpha$ and the cell-cell separation $\beta$, measured in terms of the particle diameter $d_0$. Adsorption is assumed to occur if the particle (projected) center lies within a cell area. We focus on the kinetics of deposition process in the case when no more than a single disk can be placed onto any square cell ($\alpha < 1/\sqrt{2} \approx 0.707$). We find that the asymptotic approach of the coverage fraction $\theta(t)$ to the jamming limit $\theta_\text{J}$ is algebraic if the parameters $\alpha$ and $\beta$ satisfy the simple condition, $\beta+\alpha/2 < 1$. If this condition is not satisfied, the late time kinetics of deposition process is not consistent with the power law behavior. However, if the geometry of the pattern approaches towards ``noninteracting conditions'' ($\beta > 1$), when adsorption on each cell can be decoupled, approach of the coverage fraction $\theta(t)$ to $\theta_\text{J}$ becomes closer to the exponential law. Consequently, changing the pattern parameters in the present model allows to interpolate the deposition kinetics between the continuum limit and the lattice-like behavior. Structural properties of the jammed-state coverings are studied in terms of the radial distribution function $g(r)$ and spatial distribution of particles inside the cell. Various, non-trivial spatial distributions are observed depending on the geometry of the pattern.
Abstract: The properties of the Random Sequential Adsorption (RSA) of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are ``lattice animals'', made of a certain number of nearest neighbour sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density $\theta_\text{J}$ and on the temporal evolution of the coverage fraction $\theta(t)$. We analyzed all lattice animals of size $n=$1, 2, 3, 4, and 5. A significant number of objects of size $n \geqslant 6$ were also used to confirm our findings. Approach of the coverage $\theta(t)$ to the jamming limit $\theta_{\text{J}}$ is found to be exponential, $\theta_{\text{J}}- \theta(t) \sim \exp (-t/\sigma)$, for all lattice animals. It was shown that the relaxation time $\sigma$ increases with the number of different orientations $m$ that lattice animals can take when placed on a cubic lattice. Orientations of the lattice animal deposited in two randomly chosen places on the lattice are different if one of them can not be translated into the other. Our simulations performed for large collections of 3D objects confirmed that $\sigma \cong m \in \{1, 3, 4, 6, 8, 12, 24\}$. The presented results suggest that there is no correlation between the number of possible orientations $m$ of the object and the corresponding values of the jamming density $\theta_\text{J}$. It was found that for sufficiently large objects, changing of the shape has considerably more influence on the jamming density than increasing of the object size.
Abstract: Random Sequential Adsorption (RSA) of mixtures of objects of various shapes on a three-dimensional (3D) cubic lattice is studied numerically by means of Monte Carlo simulations. Depositing objects are ``lattice animals'', made of a certain number of nearest neighbour sites on a lattice. We analyzed binary mixtures composed of the shapes of equal size, $n=$3,\;4,\;5. We concentrate here on the influence of geometrical properties of the shapes on the jamming coverage $\theta_\text{J}$ and on the temporal evolution of the density $\theta(t)$. Approach of the coverage $\theta(t)$ to the jamming limit $\theta_{\text{J}}$ is found to be exponential, $\theta_{\text{J}} - \theta(t) \sim \exp (-t/\sigma)$, both for the mixtures and their components. The values of the relaxation time $\sigma$ are determined by the number of different orientations $m$ that lattice animals can take when placed on a cubic lattice. The value of the relaxation time $\sigma$ for a mixture is approximate twice the relaxation time for the pure component shape with a larger number $m$ of possible orientations. Depending on the local geometry of the objects making the mixture, jamming coverage of a mixture $\theta_\text{J}$ can be either greater than both single-component jamming coverages or it can be in between these values. The first case is the most common, while in the second case, the jamming density of the mixture is very close to the higher jamming density for the pure component shapes. For a majority of the investigated mixtures, a component with larger number of orientations $m$ has a larger value of the fractional jamming density.
Abstract: Percolation aspect of random sequential adsorption (RSA) of extended objects on a triangular lattice is studied by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps on the lattice. Jamming coverage $\theta_{jam}$, percolation threshold $\theta_p^*$ and their ratio $\theta_p^* / \theta_{jam}$ are determined for objects of various shapes and sizes. We find that the percolation threshold $\theta_p^*$ may decrease or increase with the object size, depending on the local geometry of the objects. We demonstrate that for various objects of the same length the threshold $\theta_p^*$ of more compact and rounded shapes exceeds the $\theta_p^*$ of elongated ones. In addition, we study the polydisperse mixtures in which the size of line segments making the mixture gradually increases with the number of components. It is found that the percolation threshold decreases, while the jamming coverage increases with the number of components in the mixture.
Abstract: Random sequential adsorption on a triangular lattice with defects is studied by Monte Carlo simulations. The lattice is initially randomly covered by point-like impurities at certain concentration $p$. The depositing objects are formed by self-avoiding random walks on the lattice. For a wide range of impurity concentrations $p$ jamming coverage $\theta_{\text{jam}}$ and percolation threshold $\theta_\text{p}^*$ are determined for various object shapes . Rapidity of the approach to the jamming state is found to be independent on the impurity concentration. The jamming coverage $\theta_{\text{jam}}$ decreases with the impurity concentration $p$ and this decrease is more prominent for objects of larger size. For a certain defect concentration, decrease of the jamming coverage with the length of the walk $\ell$ making the object is found to obey an exponential law, $\theta_{\text{jam}}=\theta_{0} + \theta_{1}e^{-\ell/r}$. The results for RSA of polydisperse mixtures of objects of various sizes suggest that in the presence of impurities, partial jamming coverage of small objects can have even larger values than in the case of an ideal lattice. Percolation in the presence of impurities is also studied and it is found that the percolation threshold $\theta_\text{p}^*$ is practically insensitive to the concentration of point defects $p$. Percolation can be reached at highest impurity concentrations with angled objects, and the critical defect concentration $p_c$ is lowest for the most compact objects.
Abstract: In the preceding paper, Budinski-Petkovi\'{c} \emph{et~al.} [J. Stat. Mech.: Theory and Experiment, 053101, (2016)] studied jamming and percolation aspects of random sequential adsorption of extended shapes onto a triangular lattice initially covered with point-like impurities at various concentrations. Here we extend this analysis to needle-like impurities of various lengths $\ell$. For a wide range of impurity concentrations $p$, percolation threshold $\theta_\text{p}^*$ is determined for $k$-mers, angled objects and triangles of two different sizes. For sufficiently large impurities, percolation threshold $\theta_p^*$ of all examined objects increases with concentration $p$, and this increase is more prominent for impurities of larger length $\ell$. We determine the critical concentrations of defects $p_c^*$ above which it is not possible to achieve percolation for a given object, for impurities of various length $\ell$. It is found that the critical concentration $p_c^*$ of finite-size impurities decreases with the length $\ell$ of impurities. In the case of deposition of larger objects exception occurs for point-like impurities when critical concentration $p_c^*$ of monomers is lower than $p_c^*$ for the dimer impurities. At relatively low concentrations $p$, the presence of small impurities (but not point-like) stimulates the percolation for larger depositing objects.
Abstract: Percolation properties of two-component mixtures are studied by Monte Carlo simulations. Objects are deposited onto a substrate according to the random sequential adsorption model. Various shapes making the mixtures are made by self-avoiding walks on a triangular lattice. Percolation threshold $\theta_p$ for mixtures of objects covering the same number of sites is always lower than $\theta_p$ for the more compact object, and it can be even lower than $\theta_p$ for both components. Mixtures of percolating and non-percolating objects almost always percolate, but the percolation threshold is higher than $\theta_p$ for the percolating component. Adding a shape of high connectivity to a system of compact non-percolating objects, makes the deposit percolate. Lowest percolation thresholds are obtained for mixtures with elongated angled objects. Dependence of $\theta_p$ on the object length exhibits a minimum, so it could be estimated that the angled objects of length $6 \leq \ell \leq 10$ give the largest contribution to the percolation.
Abstract: The percolation properties in anisotropic irreversible deposition of extended objects are studied by Monte Carlo simulations on a triangular lattice. Depositing objects of various shapes and sizes are made by directed self-avoiding walks on the lattice. Anisotropy is introduced by imposing unequal probabilities for placing the objects along different directions of the lattice. Degree of the anisotropy is characterized by the order parameter $p$ determining the probability for deposition in the chosen (horizontal) direction. For each of the other two directions adsorption occurs with probability $(1-p)/2$. It is found that the percolation threshold $\theta_p$ increases with the degree of anisotropy, having the maximum values for fully oriented objects. Percolation properties of the elongated shapes, such as $k$-mers, are more affected by the presence of anisotropy than the compact ones.Percolation in anisotropic deposition was also studied for a lattice with point-like defects. For elongated shapes a slight decrease of the percolation threshold with the impurity concentration $d$ can be observed. However, for these shapes , $\theta_p$ significantly increases with the degree of anisotropy. In the case when depositing objects are triangles, results are qualitatively different. The percolation threshold decreases with $d$, but is not affected by the presence of anisotropy.
Abstract: We consider the percolation model with nucleation and simultaneous growth of multiple finite clusters, taking the initial seed concentration $\rho$ as a tunable parameter. Growing objects expand with constant speed, filling the nodes of the triangular lattice according to rules that control their shape. As growing objects of predefined shape, we consider needle-like objects and ``wrapping'' objects whose size is gradually increased by wrapping the walks in several different ways, making triangles, rhombuses, and hexagons. Growing random walk chains are also analyzed as an example of objects whose shape is formed randomly during the growth. We compare the percolation properties and jamming densities of the systems of various growing shapes for a wide range of initial seed densities $\rho < 0.5$. In order to gain a basic insight into the structure of the jammed states, we consider the size distribution of deposited growing objects. The presence of the most numerous and the largest growing objects is recorded for the system in the jamming state. Our results suggest that at sufficiently low seed densities $\rho$, the way of the object growth has a substantial influence on the percolation threshold. This influence weakens with increasing $\rho$ and ceases near the value of the site percolation threshold for monomers on the triangular lattice, $\rho_\text{p}^* = 0.5$.
Abstract: Percolation model with nucleation and object growth is studied by Monte Carlo simulations on a triangular lattice with point-like impurities. Growing objects are needle-like objects and self-avoiding random walk chains. In each run through the system the lattice is initially randomly occupied by point-like impurities at given concentration $\rho_{imp}$. Then the seeds for the object growth are randomly distributed at given concentration $\rho$. The percolation properties and the jamming densities are compared for the two classes of growing objects on the basis of the results obtained for a wide range of densities $\rho$ and $\rho_{imp}$ up to the percolation threshold for the monomer deposition on a triangular lattice. Values of the percolation thresholds $\theta_p^*$ have lower values for the needle-like objects than for the self-avoiding random walk chains. The difference is largest for the lowest values of $\rho$ and $\rho_{imp}$, and ceases near the values of the site percolation threshold for monomers on the triangular lattice, $\rho_p^* \simeq 0.5$. Values of the jamming coverage $\theta_J$ decrease with $\rho_{imp}$ for given $\rho$. This effect is more prominent for the growing random walk chains.
Abstract: Percolation properties of an adsorbed polydisperse mixture of extended objects on a triangular lattice are studied by Monte Carlo simulations. The depositing objects of various shapes are formed by self-avoiding walks on the lattice. We study polydisperse mixtures in which the size $\ell$ of the shape making the mixture increases gradually with the number of components. This study examines the influence of the shape of the primary object defining a polydisperse mixture on its percolation and jamming properties. The dependence of the jamming density and percolation threshold on the number of components $n$ making the mixture is analyzed. Determining the contribution of the individual components in the lattice covering allowed a better insight into the deposit structure of the $n$-component mixture at the percolation threshold. In addition, we studied mixtures of objects of various shapes but the same size.
Abstract: Percolation properties of the Random Sequential Adsorption (RSA) of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are ``lattice animals'', made of a certain number of nearest neighbour sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the values of percolation threshold $\theta_\text{p}^*$. We analyzed all lattice animals of size $n\leqslant 5$.Thanks to an extensive database of studied objects, we found that the number of nearest neighbors $N_1$ and the radius of gyration $R_g$ of the objects are correlated with the values of percolation threshold $\theta_\text{p}^*$. For lattice animals of the same size, the percolation threshold $\theta_\text{p}^*$ decreases with an increase in the number of the object's nearest neighbors $N_1$. If objects of the same size $n$ have the same number of nearest neighbors $N_1$, their percolation threshold $\theta_\text{p}^*$ decreases with an increase in the radius of gyration $R_g$.
Abstract: Percolation model with nucleation and object growth is studied by Monte Carlo simulations on a triangular lattice with finite size impurities. Growing objects are needle-like objects and self-avoiding random walk chains. Results are obtained for three different shapes of impurities covering three lattice sites - needle-like, angled and triangular. In each run through the system the lattice is initially randomly occupied by impurities of a specified shape at given concentration $\rho_{imp}$. Then the seeds for the object growth are randomly distributed at given concentration $\rho$. Percolation and jamming properties of the growing objects are compared for the three different shapes of impurities. For all impurity shapes percolation thresholds $\theta_p^*$ have lower values for the growing needle-like objects than for the growing self-avoiding random walk chains. In the presence of needle-like and angled impurities, percolation threshold increases with the impurity concentration for a fixed seed density. The percolation thresholds have the highest values in the case of needle-like impurities, and somewhat lower values in the case of angled impurities. On the other hand, in the presence of the triangular impurities, percolation threshold decreases with the concentration of impurities.
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<= S.B.Vrhovac ]