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The different flow regimes in a two-dimensional silo with a vibrated base are studied in terms of the usual statistical techniques and information theory. The passage of granular material through the mouth of the silo is analyzed by real-time analysis of images captured by a standard video camera. The brightness of these images is measured and recorded at very small time intervals (100 frames per second). The experiment is repeated for different values of the vibration intensity. Data recognizer wlzip directly treats the resulting b(t) files (brightness time series) based on data compressor techniques, yielding the information content measured by the mutability μ function. μ has not previously been considered as part of the conventional treatment of flow in granular media. The results obtained here clearly demonstrate the usefulness of mutability as a tool for distinguishing between different flowing regimes directly from the brightness sequence, with no manipulation of the series. This shows that information theory techniques can provide a complementary description of the discharge of granular materials and its control through data compression algorithms. [ABSTRACT FROM AUTHOR]

A simple model to study the effect of on top coadsorption of anions in underpotential deposition is formulated. It considers a lattice-gas model with pair potential interactions between nearest neighbors. As test system, the electrodeposition of silver on gold is studied by means of grand canonical Monte Carlo simulations. The influence of anions on the adsorption isotherms is analyzed. It is found that as the interaction between silver atoms and anions increases, the monolayer adsorbs at more negative chemical potentials. For large interactions between silver atoms and anions, a expanded structure occurs for the silver monolayer. [ABSTRACT FROM AUTHOR]

In this paper, the percolation of (a) linear segments of size k and (b) k-mers of different structures and forms deposited on a square lattice contaminated with previously adsorbed impurities have been studied. The contaminated or diluted lattice is built by randomly selecting a fraction of the elements of the lattice (either bonds or sites) which are considered forbidden for deposition. Results are obtained by extensive use of finite size scaling theory. Thus, in order to test the universality of the phase transition occurring in the system, the numerical values of the critical exponents were determined. The characteristic parameters of the percolation problem are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited. A phase diagram separating a percolating from a nonpercolating region is determined as a function of the parameters of the problem. A comparison between random site and random bond percolation in the presence of impurities on the lattice is presented. [ABSTRACT FROM AUTHOR]

Monte Carlo (MC) simulations have been carried out tostudy theadsorption on square and triangular lattices of particles with twobonding sites that, by decreasing temperature or increasing density,polymerize reversibly into chains with a discrete number of alloweddirections and, at the same time, undergo a continuous isotropic–nematic(IN) transition. The process has been monitored by following the behaviorof the adsorption isotherms (chemical potential μ as a functionof the surface coverage θ) for different values of lateral interactionenergy/temperature. The numerical data were compared with mean-fieldanalytical predictions and exact functions for noninteracting and1D systems. The obtained results revealed the existence of three adsorptionregimes in temperature. (1) At high temperatures, above the criticalone characterizing the IN transition at full coverage Tc(θ = 1), the particles are distributed at randomon the surface and the adlayer behaves as a noninteracting 2D system.(2) At very low temperatures, the asymmetric monomers adsorb, formingchains over almost the entire range of coverage, and the adsorptionprocess behaves as a 1D problem. (3) In the intermediate regime, thesystem exhibits a mixed regime and the filling of the lattice proceedsaccording to two different processes. In the first stage, the monomersadsorb isotropically on the lattice until the IN transition occursin the system and, from this point, particles adsorb, forming chainsso that the adlayer behaves as a 1D fluid. The two adsorption processesare present in the adsorption isotherms, and a marked singularitycan be observed that separates both regimes. Thus, the adsorptionisotherms appear as sensitive quantities with respect to the IN phasetransition, allowing us (i) to reproduce the phase diagram of thesystem for square lattices and (ii) to obtain an accurate determinationof the phase diagram for triangular lattices. [ABSTRACT FROM AUTHOR]

Random sequential adsorption of k-mers of different sizes and shapes deposited on two types of fractal surfaces (deterministic and statistical) is studied. These kinds of substrates present intrinsic heterogeneities. As a consequence, the average coordination number depends on the topology that characterizes the adsorbent. For discrete models, at the late stage the surface coverage evolves according to θ(t) = θj - A exp[-t/σ], where θj is the jamming coverage while A and σ are fitting parameters. A detailed analysis of how these main quantities [θj, σ] depend on the relationship between the geometry of the adsorbate and the adsorbent is presented. The results obtained suggest that the symmetry of the substrate may exert a decisive influence on the adsorption kinetics of polyatomic species. [ABSTRACT FROM AUTHOR]

In this review, we present our recent results concerning accurate calculations of configurational entropy in generalized lattice-gas models. The calculations are based on the use of the thermodynamic integration method. Different applications (or systems) have been considered. Namely, systems in presence of (i) anisotropy, (ii) energetic heterogeneity, (iii) geometric heterogeneity, and (iv) multisite-occupancy adsorption. Total energy is calculated by means of the Monte Carlo simulation. Then the entropy is obtained by using thermodynamic integration starting at a known reference state. In case (iv), the method relies upon the definition of an artificial Hamiltonian associated with the system of interest for which the entropy of a reference state can be exactly known. Thermodynamic integration is then applied to obtain the entropy in a given state of the system of interest. A rich variety of behaviors is found and analyzed in the context of the lattice-gas theory. [ABSTRACT FROM AUTHOR]

The adsorption of gases onto heterogeneous surfaces has been reviewed, highlighting models capable of taking energetic topography effects into account. The basic ideas are contained in the fundamental Generalized Gaussian Model (GGM) developed to represent mobile adsorption onto heterogeneous surfaces at low coverage, where the energetic topography is considered through an adsorptive energy distribution with a spatial correlation function. Adsorbate molecules interact amongst them via Lennard-Jones interactions. Model predictions have been compared to Monte Carlo simulations of adsorption onto heterogeneous solids obtained by doping a pure crystalline solid with different concentrations of impurities. Energetic topography effects were shown to be important, being predicted correctly by the model at low coverage. In addition, a simplified patchwise model was also considered. The adsorption of particles with nearest-neighbour attractive and repulsive interactions was studied using Monte Carlo simulation on bivariant surfaces characterized by patches of weak and strong adsorbing sites of size "i". Patches were considered to have either a square or a strip geometry, arranged either in a deterministic ordered structure or in a random way. Quantities have been identified which scale obeying power laws as a function of the scale length "l". The consequences of this finding for the determination of the energetic topography of a surface from adsorption measurements were discussed. [ABSTRACT FROM AUTHOR]

In this paper, the percolation of (a) linear segments of size k and(b) k-mers of different structures and forms deposited on a square lattice have been studied. In the latter case, site and bond percolation have been examined. The analysis of results obtained by using finite size scaling theory is performed in order to test the universality of the problem by determining the numerical values of the critical exponents of the phase transition occurring in the system. It is also determined that the percolation threshold exhibits a exponentially decreasing function when it is plotted as a function of the k-mer size. The characteristic parameters of that function are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited. [ABSTRACT FROM AUTHOR]

Adsorption of particles with repulsive nearest-neighbor interactions is studied through Monte Carlo simulation on bivariate surfaces characterized by patches of weak and strong adsorbing sites of size l. Patches can be either arranged in a deterministic chessboard structure or in a random way. Quantities are identified which scale obeying power laws as a function of the scale length l. Consequences of this finding are discussed for the determination of the energetic topography of the surface from adsorption measurements. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The configurational entropy of interacting linear molecules (k-mers) absorbed on a regular lattice is addressed through analytical as well as numerical methods. The general definitions for computational exact calculations of k-mers lattice-gas entropy are presented. In addition, theoretical basis for accurate analytical estimations of the entropy of reference states are given. The coverage and temperature dependence of the configurational entropy of interacting adsorbed dimers on one and two-dimensional lattices are obtained. A novel phase behavior of k-mers lattice-gas is shown and discussed. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Percolation and jamming of k×k square tiles (k²-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k²-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θj,k was determined for a wide range of k values (2≤k≤100 with many intermediate k values to allow a fine scaling analysis). θj,k exhibits a decreasing behavior with increasing k, being θj,k=∞=0.5623(3) the limit value for large k²-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent νj was measured, being νj≈1. On the other hand, the obtained results for the percolation threshold θc,k showed that θc,k is an increasing function of k in the range 1≤k≤3. For k≥4, all jammed configurations are nonpercolating states and, consequently, the percolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapid increase with k of the number of surrounding occupied sites needed to reach percolation, which gets larger than the sufficient number of occupied sites to define jamming. In the case of k=2 and 3, the percolation thresholds are θc,k=2(∞)=0.60355(8) and θc,k=3=0.63110(9). Our results significantly improve the previously reported values of θNakac,k=2=0.601(7) and θNakac,k=3=0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)]. In parallel, a comparison with previous results for jamming on these systems is also done. 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 ordinary random percolation, regardless of the size k considered. [ABSTRACT FROM AUTHOR]

The percolation problem of irreversibly deposited dimers on honeycomb and triangular lattices is studied. A dimer is composed of two segments, and occupies two adjacent adsorption sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Three types of dimers are considered: AA, BB, and AB. The connectivity analysis is carried out by accounting only for the conductive segments (segments type A), whereas the B segments occupy a site in the lattice but are not taken into account in the percolation study. Different cases were investigated, according to the types of dimers involved in the process. By means of numerical simulations and finite-size scaling techniques, the complete phase diagram separating the percolating from the nonpercolating regions was determined for each considered lattice. The present results are compared with the previous study of deposition of defective dimers on square lattices. [ABSTRACT FROM AUTHOR]

The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SARRs) model, the surface is represented by a two-dimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular, and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Peierls analytical predictions about the orientational transition for the square and triangular lattices. The analysis of the phase diagrams, along with the behavior of the critical average rod lengths, showed that the critical properties of the model do not depend on the structure of the lattice at low temperatures (coverage), revealing a quasi-one-dimensional behavior in this regime. Finally, the universality class of the SARRs model, which has been subject of controversy, has been revisited. [ABSTRACT FROM AUTHOR]

In a previous paper [F. Romá, A. J. Ramirez-Pastor, and J. L. Riccardo, Phys. Rev. B 72, 035444 (2005)], the critical behavior of repulsive rigid rods of length k (k-mers) on a square lattice at half coverage has been studied by using Monte Carlo (MC) simulations. The obtained results indicated that (1) the phase transition occurring in the system is a second-order phase transition for all adsorbate sizes k; and (2) the universality class of the transition changes from 2D Ising-type for monomers (k = 1) to an unknown universality class for k ≥ 2. In the present work, we revisit our previous results together with further numerical evidences, resulting from new extensive MC simulations based on an efficient exchange algorithm and using high-performance computational capabilities. In contrast to our previous conclusions (1) and (2), the new numerical calculations clearly support the occurrence of a first-order phase transition for k ≥ 2. In addition, a similar scenario was found for k-mers adsorbed on the triangular lattice at coverage k/(2k+1). [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of self-assembled rigid rods on triangular and honeycomb lattices at intermediate density has been studied. The system is composed of monomers with two attractive (sticky) poles that, by decreasing temperature or increasing density, polymerize reversibly into chains with three allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the IN transition belongs to the q=1 Potts universality class. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results. [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of attractive rigid rods of length k (k-mers) on square lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel k-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density θc. Our study allowed us (1) to determine the dependence of θc on the size of the rods and the magnitude of the lateral interactions and (2) to obtain the critical exponents, which indicate that the transition belongs to the 2D Ising universality class. [ABSTRACT FROM AUTHOR]

In this work we study a simple model of multilayer adsorption of noninteracting polyatomic species on homogeneous and heterogeneous surfaces. A new approximate analytic isotherm is obtained and validated by comparing with Monte Carlo simulation in one- and two-dimensional lattices. Then, we use the well-known Brunauer–Emmet–Teller (BET) approach to analyze these isotherms and to estimate the monolayer volume, vm. In this way, we confirm previous observations that the value of the vm obtained by the BET equation depends strongly on adsorbate size and surface heterogeneity. In all cases, we find that the use of the BET equation leads to an underestimate of the true monolayer capacity. Nevertheless, a compensation effect is found for the adsorption on a patchwise bivariate surface, but this is not enough to eliminate the decrease of vm caused by the molecular size. In addition, we consider also the possibility to use the model to study the adsorption on nanotube bundles. [ABSTRACT FROM AUTHOR]

In the present paper, the multicomponent adsorption of polyatomic species is described as a fractional statistics problem, based on Haldane’s statistics. Site exclusion is characterized by a “mutual exclusion matrix” g, which relates to the sizes of the different species and lattice geometry. The adsorption process has been monitored through total and partial isotherms, energy of adsorption and configurational entropy of the adsorbed phase. The thermodynamic functions calculated for a monomer-dimer mixture were applied to describe the adsorption of methane-ethane mixtures in zeolites. In the case of zero lateral interactions, the present approach was compared to the well-known ideal adsorbed solution theory. The results show that the treatment of this complex problem can be significantly simplified if looked up from the new theoretical perspective. [ABSTRACT FROM AUTHOR]

The critical behavior of long straight rigid rods of length k (k-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel k-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at an intermediate density θc. Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of θc on k, being θc(k)∝k-1. The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of k (kmin=7), which allows the formation of a nematic phase on a triangular lattice. [ABSTRACT FROM AUTHOR]

In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in the presence of repulsive interactions have been considered. Namely, monomers on honeycomb, square, and triangular lattices, and dimers (particles occupying two adjacent adsorption sites) on square substrates. By using Monte Carlo simulation and finite-size scaling analysis, we obtain the percolation threshold θc of the adlayer, which presents an interesting dependence with w/kBT (w, kB, and T being the lateral interaction energy, the Boltzmann constant, and the temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a nonpercolating region is determined. [ABSTRACT FROM AUTHOR]

The configurational entropy of interacting particles adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure is studied by combining Monte Carlo simulation and thermodynamic integration method. Three different energies have been considered in the adsorption process: (1) εo, constant interaction energy between a monomer and an adsorption site; (2) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel, and (3) wT, interaction energy between particles adsorbed across nearest-neighbor channels. Special attention is devoted to the case of repulsive transversal interactions (wT>0), for which a rich variety of ordered phases are observed in the adlayer, depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. The influence of each ordered structure on the configurational entropy of the adlayer has been analyzed and discussed in the context of the lattice-gas model. [ABSTRACT FROM AUTHOR]

A generalization of the site-bond percolation problem was studied, in which pairs of neighboring sites (site dimers) and bonds are occupied irreversibly, randomly, and independently on homogeneous square surfaces. A dimer is composed of two segments and occupies two adjacent sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Two types of dimers are considered, AA and AB, and the connectivity analysis is carried out by accounting only for the conductive segments (segments type A) in combination with bonds. For the combination of dimers and bonds, two different criteria were analyzed: the union or the intersection between the adsorbed percolating particles and the bonds. By means of numerical simulations and finite-size scaling analysis, the complete phase diagram separating a percolating from a non-percolating region was determined. [ABSTRACT FROM AUTHOR]

The percolation problem of irreversibly deposited heteronuclear dimers on square lattices is studied. A dimer is composed of two segments, and it occupies two adjacent adsorption sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Three types of dimers are considered: AA, BB, and AB. The connectivity analysis is carried out by accounting only for the conductive segments (segments type A). The model offers a simplified representation of the problem of percolation of defective (nonideal) particles, where the presence of defects in the system is simulated by introducing a mixture of conductive and nonconductive segments. Different cases were investigated, according to the sequence of deposition of the particles, the types of dimers involved in the process, and the degree of alignment of the deposited objects. By means of numerical simulations and finite-size scaling analysis, the complete phase diagram separating a percolating from a nonpercolating region was determined for each case. Finally, the consistency of our results was examined by comparing with previous data in the literature for linear k-mers (particles occupying k adjacent sites) with defects. [ABSTRACT FROM AUTHOR]

The statistical thermodynamics of straight rigid rodsof length kon triangular lattices was developedon a generalization in the spirit of the lattice-gas model and theclassical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtzfree energy and its derivatives were written in terms of the orderparameter, δ, which characterizes the nematic phase occurringin the system at intermediate densities. Then, using the principleof minimum free energy with δ as a parameter, the main adsorptionproperties were calculated. Comparisons with Monte Carlo simulationsand experimental data were performed in order to evaluate the outcomeand limitations of the theoretical model. [ABSTRACT FROM AUTHOR]

The phase behavior of interacting rigid rods of length k (k-mers) on two-dimensional square and triangular lattices has been studied by theoretical calculations in the framework of the lattice-gas model. The process was analyzed by comparing the dependence on coverage of the free energy per site of an isotropic submonolayer of interacting k-mers fiso(θ) with that corresponding to a fully aligned (nematic) system fnem(θ). The existence of an intersection point between the curves fiso(θ) and fnem(θ) which is indicative of the occurrence of an isotropic-nematic phase transition in the adlayer, allowed us to obtain the complete (temperature, coverage, k-mer size) phase diagram of the system. [ABSTRACT FROM AUTHOR]

The percolation behavior of aligned rigid rods of length k (Armers) on two-dimensional square lattices has been studied by numerical simulations and finite-size scaling analysis. The Ainers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The process was monitored by following the probability RL,K(p) that a lattice composed of L x L sites percolates at a concentration p of sites occupied by particles of size k. The results, obtained for k ranging from 1 to 14, show that (i) the percolation threshold exhibits a decreasing function when it is plotted as a function of the fcmer size; (ii) for any value of k (k > 1), the percolation threshold is higher for aligned rods than for rods isotropically deposited; (iii) the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value oik considered; and (iv) in the case of aligned Amers, the intersection points of the curves of RL,K(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the Amer size. This behavior is completely different to that observed for the isotropic case, where the crossing point of the curves of RL,K(p) do not modify their numerical value as k is increased. [ABSTRACT FROM AUTHOR]

The statistical thermodynamics of straight rigid rods of length A (A-mers) with nonadditive lateral interactions was developed on a generalization in the spirit of the lattice-gas model and the classical Bragg-Williams approximation (BWA) and the quasichemical approximation (QCA). The new theoretical framework is obtained by combining (i) the exact analytical expression for the partition function of noninteracting linear A-mers adsorbed in one dimension and its extension to higher dimensions, and (ii) a generalization of BWA and QCA in which the adsorbate can occupy more than one adsorption site. The traditional assumption of a strictly pairwise additive nearest-neighbors interaction is replaced by a more general one, namely that the bond linking a certain atom with any of its neighbors depends considerably on how many of them are actually present (or absent) on the sites in the first coordination shell of the atom. The coverage and temperature dependence of the Helmholi/ tree energy, chemical potential, configurational entropy, and differential heat of adsorption are given. The formalism (i) reproduces the classical results for monomers, (ii) leads to the exact statistical thermodynamics of nonadditive interacting A-mers adsorbed in one dimension, and (iii) provides a close approximation for two-dimensional systems, taking into account multisite occupancy and nonadditive lateral interactions. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. Significant quantitative differences are shown and discussed. In all cases, the QCA appears to be the more accurate approach. [ABSTRACT FROM AUTHOR]

The adsorption of polyatomics on one- and two-dimensional lattices is studied by combining theoretical modeling, Monte-Carlo (MC), simulations and their correspondence with experimental results. In one dimension, the rigorous statistical thermodynamics of interacting chains has been presented. With respect to two-dimensional adsorption, six different models to study non-interacting adsorbates have been discussed: (i) an extension to two dimensions of the exact thermodynamic functions obtained in one dimension; (ii) the Flory–Huggins's approximation and its modification to address linear adsorbates; (iii) the well-known Guggenheim–DiMarzio approximation; (iv) the fourth one is a new description of adsorption phenomena, based on Haldane's fractional statistics; (v) the so-called Occupation Balance, based on the expansion of the reciprocal of the fugacity; and (vi) a simple semi-empirical model obtained by combining exact one-dimensional calculations and Guggenheim–DiMarzio approach. In addition, the statistical thermodynamics of interacting polyatomics has been developed on a generalization in the spirit of the Bragg–Williams and the quasi-chemical approximations. Comparison with MC simulations and experimental adsorption isotherms are used to test the accuracy and reliability of the proposed models. Finally, applications to heterogeneous systems and multilayer adsorption are discussed. [ABSTRACT FROM AUTHOR]

A generalization of the pure site and pure bond percolation problems in which pairs of nearest neighbor sites (site dimers) and linear pairs of nearest neighbor bonds (bond dimers) are independently occupied at random on a square lattice is studied. We called this model as dimer site-bond percolation. Motivated by considerations of cluster connectivity, we have used two distinct schemes (denoted asand) for dimer site-bond percolation. In(), two points are said to be connected if a sequence of occupied sitesand(or) bonds joins them. By using finite-size scaling theory, data fromandare analyzed in order to determine i) the phase boundary between the percolating and non-percolating regions and ii) the numerical values of the critical exponents of the phase transition occurring in the system. The results obtained are discussed in comparison with the corresponding ones for classical monomer site-bond percolation. [ABSTRACT FROM AUTHOR]

The critical behavior of self-assembled rigid rods on a square lattice was recently reinvestigated by Almarza et al. [Phys. Rev. E 82, 061117 (2010)]. Based on the Binder cumulants and the value of the critical exponent of the correlation length, the authors found that the isotropic-nematic phase transition occurring in the system is in the two-dimensional Ising universality class. This conclusion contrasts with that of a previous study [López et al, Phys. Rev. E 80, 040105(R) (2009)] which indicates that the transition at intermediate density belongs to the q = 1 Potts universality class. Almarza et al. attributed the discrepancy to the use of the density as the control parameter by López et al. The present work shows that this suggestion is not sufficient, and that the discrepancy arises solely from the use of different statistical ensembles. Finally, the necessity of making corrections to the scaling functions in the canonical ensemble is discussed. [ABSTRACT FROM AUTHOR]

In this paper, a two-dimensional lattice-gas model is applied to study the stability and lattice distortion of sI clathrate hydrates of ethylene. Two levels of approximation are considered for the lateral interactions between the adsorbed molecules. By using Monte Carlo simulations, adsorption isotherm (coverage of the cavities as a function of the chemical potential), degree of deformation of the sI structure, and free energy of the adsorbed phase are obtained. A direct relationship between cell distortion and cell occupancy is observed. In addition, the minimum distortion coincides with the minimum value of the free energy. Accordingly, the stability phase diagram can be calculated from the values of the chemical potential at the minimum deformation. The obtained results indicate that the most stable condition of the system occurs for values of the cavity density ranging between 0.35 and 0.4. Finally, MC results are compared with data from experiments and more complex simulations. [ABSTRACT FROM AUTHOR]

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 θj,k is a decreasing function with increasing k, with θj,k→∞=0.7299(21) the limit value for infinitely long k-mers and (2) the jamming exponent νj 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 θc,k as a function of k is also determined, with θc,k=A+Bexp(-k/C), where A=θc,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. [ABSTRACT FROM AUTHOR]

Irreversible multilayer adsorption of semirigid k-mers on one-dimensional lattices of size L is studied by numerical simulations complemented by exhaustive enumeration of configurations for small lattices. The deposition process is modeled by using a random sequential adsorption algorithm, generalized to the case of multilayer adsorption. The paper concentrates on measuring the jamming coverage for different values of k-mer size and number of layers n. The bilayer problem (n≤2) is exhaustively analyzed, and the resulting tendencies are validated by the exact enumeration techniques. Then, the study is extended to an increasing number of layers, which is one of the noteworthy parts of this work. The obtained results allow the following: (i) to characterize the structure of the adsorbed phase for the multilayer problem. As n increases, the (1+1)-dimensional adsorbed phase tends to be a "partial wall" consisting of "towers" (or columns) of width k, separated by valleys of empty sites. The length of these valleys diminishes with increasing k; (ii) to establish that this is an in-registry adsorption process, where each incoming k-mer is likely to be adsorbed exactly onto an already adsorbed one. With respect to percolation, our calculations show that the percolation probability vanishes as L increases, being zero in the limit L→∞. Finally, the value of the jamming critical exponent νj is reported here for multilayer adsorption: νj remains close to 2 regardless of the considered values of k and n. This finding is discussed in terms of the lattice dimensionality. [ABSTRACT FROM AUTHOR]

In the present paper, the adsorption thermodynamics of a lattice-gas model which mimics a nanoporous environment is studied by considering nonadditive interactions between the adsorbed particles. It is assumed that the energy linking a certain atom with any of its nearest neighbors strongly depends on the state of occupancy in the first coordination sphere of such an adatom. By means of Monte Carlo (MC) simulations in the grand canonical ensemble, adsorption isotherms and differential heats of adsorption were calculated. Their striking behaviors were analyzed and discussed in terms of the low temperature phases formed in the system. Finally, the results obtained from MC simulations were compared with the corresponding ones from Bragg-Williams approximation. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas which mimics a nanoporous environment. In this model, the adsorbent is modeled as one-dimensional channels of equivalent adsorption sites arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) wL interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) wT interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse (wT>0) and attractive longitudinal (wL<0) lateral interactions, where a rich variety of structural orderings are observed in the adlayer depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. The results reveal the existence of a first-order phase transition in the adlayer between a low-temperature “condensed” phase and a high-temperature “disordered” phase. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas of interacting monomers adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) wT, interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse interactions (wT>0), where a rich variety of structural orderings are observed in the adlayer, depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. For wL/wT=0, successive planes are uncorrelated, the system is equivalent to the triangular lattice, and the well-known (3×3) [(3×3)*] ordered phase is found at low temperatures and a coverage, θ, of 1/3 [2/3]. In the more general case (wL/wT≠0), a competition between interactions along a single channel and a transverse coupling between sites in neighboring channels leads to a three-dimensional adsorbed layer. Consequently, the (3×3) and (3×3)* structures “propagate” along the channels and new ordered phases appear in the adlayer. Each ordered phase is separated from the disordered state by a continuous order-disorder phase transition occurring at a critical temperature, Tc, which presents an interesting dependence with wL/wT. The Monte Carlo technique was combined with the recently reported free energy minimization criterion approach (FEMCA) [F. Romá et al., Phys. Rev. B 68, 205407 (2003)] to predict the critical temperatures of the order-disorder transformation. The excellent qualitative agreement between simulated data and FEMCA results allows us to interpret the physical meaning of the mechanisms underlying the observed transitions. [ABSTRACT FROM AUTHOR]

The percolation behavior of aligned rigid rods of length k (k-mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The k-mers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability RL,k(p) that a lattice composed of L×L sites percolates at a concentration p of sites occupied by particles of size k. The results, obtained for k ranging from 2 to 80, showed that the percolation threshold pc(k) exhibits a increasing function when it is plotted as a function of the k-mer size. The dependence of pc(k) was determined, being pc(k)=A+B/(C+√k), where A=pc(k→∞)=0.582(9) is the value of the percolation threshold by infinitely long k-mers, B=-0.47(0.21), and C=5.79(2.18). This behavior is completely different from that observed for square lattices, where the percolation threshold decreases with k. In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered. [ABSTRACT FROM AUTHOR]

Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of k×k square tiles (k²-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then the system is diluted by removing k²-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, pc,k, for which the connectivity disappears. This particular value of the concentration is called the inverse percolation threshold and determines a well-defined geometrical phase transition in the system. The results obtained for pc,k show that the inverse percolation threshold is a decreasing function of k in the range 1≤k≤4. For k≥5, all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent νj was measured, being νj=1 regardless of the size k considered. In addition, the accurate determination of the critical exponents ν, β, and γ reveals that the percolation phase transition involved in the system, which occurs for k varying between one and four, has the same universality class as the standard percolation problem. [ABSTRACT FROM AUTHOR]

A new distribution for systems of particles in equilibrium obeying the exclusion of correlated states is presented following Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. Haldane's statistics and Wu's distribution are recovered in the limit of noncorrelated states of the multiple exclusion statistics. In addition, an exclusion spectrum function G(n) is introduced to account for the dependence of the state exclusion on the occupation number n. The results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size k (k-mers) where the multiple exclusion occurs. Remarkable agreement is found with grand-canonical Monte Carlo simulations from k=2 to 10 where the multiple exclusion dominates as k increases. [ABSTRACT FROM AUTHOR]

In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 073211] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates (k-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions g1(π) and g2(π) with zero overlap and mean values π1 and π2, respectively; and (ii) g1(π) and g2(π) are unimodal distributions that are symmetric with respect to the middle point (π1+π2)/2. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear k-mers on square and triangular lattices, S-shaped k-mers on square lattices and k²-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method. [ABSTRACT FROM AUTHOR]

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse bond percolation of straight rigid rods on square lattices. In the case of standard percolation, the lattice is initially empty. Then, linear bond k-mers (sets of k linear nearest-neighbor bonds) are randomly and sequentially deposited on the lattice. Jamming coverage pj,k and percolation threshold pc,k are determined for a wide range of k (1≤k≤120). pj,k and pc,k exhibit a decreasing behavior with increasing k, pj,k→∞=0.7476(1) and pc,k→∞=0.0033(9) being the limit values for large k-mer sizes. pj,k is always greater than pc,k, and consequently, the percolation phase transition occurs for all values of k. In the case of inverse percolation, the process starts with an initial configuration where all lattice bonds are occupied and, given that periodic boundary conditions are used, the opposite sides of the lattice are connected by nearest-neighbor occupied bonds. Then, the system is diluted by randomly removing linear bond k-mers from the lattice. The central idea here is based on finding the maximum concentration of occupied bonds (minimum concentration of empty bonds) for which connectivity disappears. This particular value of concentration is called the inverse percolation threshold pc,ki, and determines a geometrical phase transition in the system. On the other hand, the inverse jamming coverage pj,ki is the coverage of the limit state, in which no more objects can be removed from the lattice due to the absence of linear clusters of nearest-neighbor bonds of appropriate size. It is easy to understand that pj,ki=1-pj,k. The obtained results for pc,ki show that the inverse percolation threshold is a decreasing function of k in the range 1≤k≤18. For k>18, all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed bonds pj,ki is reached. In terms of network attacks, this striking behavior indicates that random attacks on single nodes (k=1) are much more effective than correlated attacks on groups of close nodes (large k's). Finally, the accurate determination of critical exponents reveals that standard and inverse bond percolation models on square lattices belong to the same universality class as the random percolation, regardless of the size k considered. [ABSTRACT FROM AUTHOR]

The orientational phase transitions that occur in the deposition of longitudinal polymers of length k (in terms of lattice units) are characterized by information theory techniques. We calculate the absolute value of an order parameter δ, which weights the relative orientations of the deposited rods, which varies between 0.0 (random orientation) and 1.0 (fully oriented in either of the two equivalent directions in an L×L square lattice). A Monte Carlo (MC) algorithm is implemented to induce a dynamics allowing for accommodation of the rods for any given density or coverage θ (ratio of the occupied sites over all the sites in the lattice). The files storing δ(t) (with time t measured in MC steps) are then treated by data recognizer wlzip based on data compressor techniques yielding the information content measured by a parameter η(θ). This allows us to recognize two maxima separated by a well-defined minimum for η(θ) provided k≥7. The first maximum is associated with an isotropic-nematic (I-N) phase transition occurring at intermediate density, while the second maximum is associated with some kind of nematic-isotropic transition at high coverage. In the cases of k<7, the curves for η(θ) are almost constant, presenting a very broad maximum which can hardly be associated with a phase transition. The study varies L and k, allowing for a basic scaling of the found critical densities towards the thermodynamic limit. These calculations confirm the tendency obtained by different methods in the case of the intermediate-density I-N phase transition, while this tendency is established here in the case of the high-density phase transition. [ABSTRACT FROM AUTHOR]

A computational and experimental screening of hypothetical and real compounds exhibiting different degrees of ethylenediamine grafted to the CPO-27-Mg or Mg-DOBDC skeleton is performed in order to determine the target composition that optimizes the CO2 adsorption properties under flue gas and air filtering conditions. On the basis of the [Mg2(dobdc)] formula, eighteen hypothetical models involving 15–100% of functionalization of the coordinatively unsaturated sites (CUS) were considered by means of Grand Canonical Monte Carlo simulations to evaluate the CO2 adsorption at 298 K. In addition, post-synthesis modification was applied to CPO-27-Mg leading to three kinds of samples exhibiting 15, 50, and 60% of CUS functionalization with ethylenediamine, named CPO-27-Mg-a, CPO-27-Mg-b and CPO-27-Mg-c. Compounds were characterized using elemental analysis, TGA, FTIR spectroscopy, PXRD and DSC. Finally, bare and functionalized CPO-27-Mg materials were evaluated using gas adsorption and microcalorimetry in the 0.001–1 bar range, which is pertinent for the mentioned applications. Valuable information related to design criteria for synthesis of tuned CO2 adsorbents is derived through this computational and experimental investigation. [ABSTRACT FROM AUTHOR]

Percolation of site trimers (k-mers with k=3) is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem. Results are compared to those obtained here by means of extensive computer simulations. Five different deposition possibilities for site trimers are included according to shape and orientation of the depositing objects. Analytical results for the percolation threshold pc are all close to 0.55, while numerical results show a slight dispersion around this value. A comparison with pc values previously reported for monomers and dimers establishes the tendency of pc to decrease as k increases. Critical exponent ν was also obtained both by analytical and numerical methods. Results for the latter give values very close to the expected value 4/3 showing that this percolation case corresponds to the universality class of random percolation. [ABSTRACT FROM AUTHOR]

Adsorption thermodynamics of interacting particles adsorbed on icosahedral and truncated octahedral nanoparticles was studied by a detailed mean-field approximation and Monte Carlo simulations. The nanoparticle is tackled as a multivariate surface, where different types of adsorption sites occur according to coordination with nearest neighbors. In addition, lateral couplings between the adsorbed particles are considered. The analysis covers a wide range of interactions, extending from physical to strong chemical bonds, and different sizes and shapes of nanoparticles. [ABSTRACT FROM AUTHOR]

The localized monolayer adsorption of interacting particles onto heterogeneous surfaces has been studied through Monte Carlo simulation in the framework of the lattice-gas model. The substrate was modelled as a collection of finite homotatic patches, each one characterized by an adsorption energy arising from a discrete energy density function. Patches were distributed spatially, either in a deterministic alternate way (ordered topography) or in a non-overlapping random way (random topography). The adsorption process was analyzed by following the behaviour of surface coverage versus chemical potential (adsorption isotherm) and the differential heat of adsorption as a function of the coverage. These quantities depend on the size of the patch as well as on the topological distribution of the patches on the surface. The consequences of these findings are discussed for the determination of the energetic topography of the surface from adsorption measurements. [ABSTRACT FROM AUTHOR]