Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice (original) (raw)
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Jamming and percolation of linear k -mers on honeycomb lattices
Physical Review E
Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of elongated objects deposited on two-dimensional honeycomb lattices. The depositing particle is modeled as a linear array of length k (so-called k-mer), maximizing the distance between first and last monomers in the chain. The separation between k-mer units is equal to the lattice constant. Hence, k sites are occupied by a k-mer when adsorbed onto the surface. The adsorption process starts with an initial configuration, where all lattice sites are empty. Then, the sites are occupied following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. Jamming coverage θ j,k and percolation threshold θ c,k were determined for a wide range of values of k (2 k 128). The obtained results shows that (i) θ j,k is a decreasing function with increasing k, being θ j,k→∞ = 0.6007(6) the limit value for infinitely long k-mers; and (ii) θ c,k has a strong dependence on k. It decreases in the range 2 k < 48, goes through a minimum around k = 48, and increases smoothly from k = 48 up to the largest studied value of k = 128. Finally, the precise determination of the critical exponents ν, β, and γ indicates that the model belongs to the same universality class as 2D standard percolation regardless of the value of k considered.
The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear kkk-mers (particles occupying kkk adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical random sequential adsorption (RSA) model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model LK$_d$ is a generalized variant of the RSA model for both kkk-mers and a lattice with defects. Some of the occupying kkk adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long kkk-mers. The second model is the cooperative sequential adsorption (CSA) one, where, for each new kkk-mer, only a restricted number of lateral contacts zzz with previously deposited kkk-mers is allowed. Deposition occurs in the case when zleq(1−d)zmz\leq (1-d)z_mzleq(1−d)zm where zm=2(k+1)z_m=2(k+1)zm=2(k+1) ...
Jamming and percolation for deposition ofk2-mers on square lattices: A Monte Carlo simulation study
Physical Review E, 2019
Jamming and percolation of square objects of size k × k (k 2-mers) isotropically deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The k 2-mers were irreversibly deposited into the lattice. Jamming coverage θ j,k was determined for a wide range of k (2 ≤ k ≤ 200). θ j,k exhibits a decreasing behavior with increasing k, being θ j,k→∞ = 0.4285(6) the limit value for large k 2-mer sizes. On the other hand, the obtained results shows that percolation threshold, θ c,k , has a strong dependence on k. It is a decreasing function in the range 2 ≤ k ≤ 18 with a minimum around k = 18 and, for k ≥ 18, it increases smoothly towards a saturation value. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation, regardless of the size k considered.
Random sequential adsorption of partially oriented linear k-mers on a square lattice
Physical Review E, 2011
Jamming phenomena on a square lattice are investigated for two different models of anisotropic random sequential adsorption (RSA) of linear k-mers (particles occupying k adjacent adsorption sites along a line). The length of a k-mer varies from 2 to 128. Effect of k-mer alignment on the jamming threshold is examined. For completely ordered systems where all the k-mers are aligned along one direction (e.g., vertical), the obtained simulation data are very close to the known analytical results for 1d systems. In particular, the jamming threshold tends to the Rényi's Parking Constant for large k. In the other extreme case, when k-mers are fully disordered, our results correspond to the published results for short k-mers. It was observed that for partially oriented systems the jamming configurations consist of the blocks of vertically and horizontally oriented k-mers (v-and h-blocks, respectively) and large voids between them. The relative areas of different blocks and voids depend on the order parameter s, k-mer length and type of the model. For small k-mers (k 4), denser configurations are observed in disordered systems as compared to those of completely ordered systems. However, longer k-mers exhibit the opposite behavior.
Random surface deposition of diffusing dimers in two dimensions* 1
Physics Letters A, 1997
Random sequential deposition of diffusing dimers onto a two-dimensional lattice is investigated by Monte Carlo simulation. We find that the jamming occupation for the static case is surpassed; however, the completely filled state is not reached due to the appearance of "dynamically jammed structures". The conjectured time dependence law ( l/t) In I for the hole population fails to fit the simulations.
Random surface deposition of diffusing dimers in two dimensions
Physics Letters A, 1997
Random sequential deposition of diffusing dimers onto a two-dimensional lattice is investigated by Monte Carlo simulation. We find that the jamming occupation for the static case is surpassed; however, the completely filled state is not reached due to the appearance of “dynamically jammed structures”. The conjectured time dependence law () 1n t for the hole population fails to fit the simulations.
Percolation and jamming in structures built through sequential deposition of particles
Journal of Colloid and Interface Science, 2005
The strength of attractive interaction among particles on a surface, which was studied in our previous work, leads to different degrees of clustering and ordering. A growing structure percolates when all clusters connect and become one and finally the structure is jammed when there is no space large enough to accommodate one more particle. The lowest jamming limit reported is for structures from the random sequential adsorption. We studied here, by means of Monte Carlo simulation, structures built through sequential deposition of particles, into which surface diffusion and various degrees of attractive forces are incorporated and reported jamming limits along with the percolation thresholds. The higher the strength of attractive interactions, the larger the percolation densities and jamming limits are. These results were shown in a diagram as a function of temperature (or equivalently the strength of attractive interaction), ranging from very low temperature to very high temperature (RSA limit).
Physical Review E
Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of straight semirigid rods adsorbed on two-dimensional square lattices. The depositing objects can be adsorbed on the surface forming two layers. The filling of the lattice is carried out following a generalized random sequential adsorption (RSA) mechanism. In each elementary step, (i) a set of k consecutive nearest-neighbor sites (aligned along one of two lattice axes) is randomly chosen and (ii) if each selected site is either empty or occupied by a k-mer unit in the first layer, then a new k-mer is then deposited onto the lattice. Otherwise, the attempt is rejected. The process starts with an initially empty lattice and continues until the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. A wide range of values of k (2 k 64) is investigated. The study of the kinetic properties of the system shows that (1) the jamming coverage θ j,k is a decreasing function with increasing k, with θ j,k→∞ = 0.7299(21) the limit value for infinitely long k-mers and (2) the jamming exponent ν j remains close to 1, regardless of the size k considered. These findings are discussed in terms of the lattice dimensionality and number of sites available for adsorption. The dependence of the percolation threshold θ c,k as a function of k is also determined, with θ c,k = A + B exp(−k/C), where A = θ c,k→∞ = 0.0457(68) is the value of the percolation threshold by infinitely long k-mers, B = 0.276(25), and C = 14(2). This monotonic decreasing behavior is completely different from that observed for the standard problem of straight rods on square lattices, where the percolation threshold shows a nonmonotonic k-mer size dependence. The differences between the results obtained from bilayer and monolayer phases are explained on the basis of the transversal overlaps between rods occurring in the bilayer problem. This effect (which we call a "cross-linking effect"), its consequences on the filling kinetics, and its implications in the field of conductivity of composites filled with elongated particles (or fibers) are discussed in detail. Finally, the precise determination of the critical exponents ν, β, and γ indicates that, although the increasing in the width of the deposited layer drastically affects the behavior of the percolation threshold with k and other critical properties (such as the crossing points of the percolation probability functions), it does not alter the nature of the percolation transition occurring in the system. Accordingly, the bilayer model belongs to the same universality class as two-dimensional standard percolation model.
Random sequential adsorption of straight rigid rods on a simple cubic lattice
Physica A: Statistical Mechanics and its Applications, 2015
Random sequential adsorption of straight rigid rods of length k (k-mers) on a simple cubic lattice has been studied by numerical simulations and finite-size scaling analysis. The calculations were performed by using a new theoretical scheme, whose accuracy was verified by comparison with rigorous analytical data. The results, obtained for k ranging from 2 to 64, revealed that (i) in the case of dimers (k = 2), the jamming coverage is θ j = 0.918388(16). Our estimate of θ j differs significantly from the previously reported value of θ j = 0.799(2) [Y. Y. Tarasevich and V. A. Cherkasova, Eur. Phys. J. B 60, 97 ]; (ii) θ j exhibits a decreasing function when it is plotted in terms of the k-mer size, being θ j (∞) = 0.4045(19) the value of the limit coverage for large k's; and (iii) the ratio between percolation threshold and jamming coverage shows a non-universal behavior, monotonically decreasing with increasing k.
Irreversible Deposition of Line Segment Mixtures on a Square Lattice: Monte Carlo Study
International Journal of Modern Physics B, 1998
We have studied kinetics of random sequential adsorption of mixtures on a square lattice using Monte Carlo method. Mixtures of linear short segments and long segments were deposited with the probability p and 1-p, respectively. For fixed lengths of each segment in the mixture, the jamming limits decrease when p increases. The jamming limits of mixtures always are greater than those of the pure short- or long-segment deposition. For fixed p and fixed length of the short segments, the jamming limits have a maximum when the length of the long segment increases. We conjectured a kinetic equation for the jamming coverage based on the data fitting.