One-dimensional movement of interacting particles is a challenging problem where the correlation between particles induces non-trivial collective effects. In contrast to the single-file diffusion case, the pure ballistic single-file movement of particles has received less attention. Here, the ballistic file diffusion of hard disks is studied using an adaptative continuum Monte Carlo numerical scheme. Dynamics is studied as a function of the size of the particles, the system size and the number of particles. The mean-square displacement presents three regimes corresponding to independent motion, collective motion and finite-size effects. These regimes and the crossover times between them are analyzed and presented in analogy with the ones observed for the single-file diffusion problem.

An analytical model to explain the mobilities of enantiomer binary mixture in capillary electrophoresis experiment is proposed. The model consists in a set of kinetic equations describing the evolution of the populations of molecules involved in the enantioseparation process in capillary electrophoresis (CE) is proposed. These equations take into account the asymmetric driven migration of enantiomer molecules, chiral selector and the temporary diastomeric complexes, which are the products of the reversible reaction between the enantiomers and the chiral selector. The solution of these equations gives the spatial and temporal distribution of each species in the capillary, reproducing a typical signal of the electropherogram. The mobility, μ, of each specie is obtained by the position of the maximum (main peak) of their respective distributions. Thereby, the apparent electrophoretic mobility difference, Δμ, as a function of chiral selector concentration, [C], can be measured. The behaviour of Δμ versus [C] is compared with the phenomenological model introduced by Wren and Rowe in J. Chromatography 1992, 603, 235. To test the analytical model, a capillary electrophoresis experiment for the enantiomeric separation of the (±)-chlorpheniramine β-cyclodextrin (β-CD) system is used. These data, as well as, other obtained from literature are in closed agreement with those obtained by the model. All these results are also corroborate by kinetic Monte Carlo simulation.

Monte Carlo simulation is used to study the adsorption–desorption kinetics in the framework of the kinetic lattice-gas model. Three schemes of the so-called hard dynamics and five schemes of the so called soft dynamics were used for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and non-equilibrium observable, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and non-equilibrium observables have several problems.

The influence of directing agents in the self-assembly of molecular wires to produce two-dimensional electronic nanoarchitectures is studied here using a Monte Carlo approach to simulate the effect of arbitrarily locating nodal points on a surface, from which the growth of self-assembled molecular wires can be nucleated. This is compared to experimental results reported for the self-assembly of molecular wires when 1,4-phenylenediisocyanide (PDI) is adsorbed on Au(111). The latter results in the formation of (Au-PDI)(n) organometallic chains, which were shown to be conductive when linked between gold nanoparticles on an insulating substrate. The present study analyzes, by means of stochastic methods, the influence of variables that affect the growth and design of self-assembled conductive nanoarchitectures, such as the distance between nodes, coverage of the monomeric that leads to the formation of architectures, and the interaction between the monomeric units. This work proposes an approach and sets the stage for the production of complex 2D nanoarchitectures using a bottom-up strategy but including the use of current state-of-the-art top-down technology as an integral part of the self-assembly strategy.

This paper analyzes the effect of particle-hole symmetry on the behavior of the tracer diffusion coefficient as well as the jump diffusion coefficient. The coefficients are obtained by performing a random walk of individual atoms in a two-dimensional square lattice at monolayer, using the $n$-fold way Monte Carlo simulation. Different hopping mechanisms have been introduced to study the effect of particle-hole symmetry. For hopping kinetics where the initial-state interactions are involved, the diffusion coefficient at high coverage falls several orders of magnitude due to the effect of particle-hole symmetry. For hopping kinetics where the final-state interactions are present, the effect is the opposite. For those involving both initial- and final-state interactions, like the so-called interaction kinetics, the effect of particle-hole symmetry is also discussed. This effect seems to be critical for repulsive lateral interactions, for which the behavior of the diffusion coefficients is modified by introducing the particle-hole symmetry condition.

This paper studies the single-file diffusion process on a linear chain of identical pointlike particles with multiple-site occupation confined in a one-dimensional box. The particles are noninteracting, except that double occupancy is forbidden. When particles are confined in a finite box, the final stage is saturation. By means of combinatorial analysis, an exact numerical evaluation of the saturation values for both the mean-square displacement (MSD) of a tracer particle and the center of mass of the system are obtained. Different initial distributions of particles are introduced. The time dependence of the MSD is obtained by means of Monte Carlo simulations. The values of the MSD for the tracer particles as well as the center of mass of the system depend on the size of the particle, the size of the box, and the initial distribution. Moreover, the transient regime depends on the initial distribution. In fact, the crossover from normal to subdiffusive regime is observed for random and alternate initial distributions, while superdiffusive diffusion appears for any stacked initial distributions. In all cases, it is shown that the collisions between particles do not determine the time exponent of the MSD. A simple expression for the transient regime is also obtained for the especial case of random initial distribution.

The exact expression for the collective diffusion coefficient in one dimension, obtained by Payne and Kreuzer [Phys. Rev. B. 75, 115403 (2007)], is compared with Monte Carlo simulation. Different hopping kinetics are analyzed. For initial-and final-state interaction kinetics no anomalies are observed. However, for the so-called interaction kinetics where both initial-and final-state interactions are involved, it is shown that even when the transition rates satisfy the principle of detail balance, additional constraints are necessary to guarantee the diffusion of particles. These restrictions give rise to a phase diagram that determines the regions where the exact solution of the diffusion coefficient seem to be not physically sound. The Monte Carlo simulation allows us to analyze the mechanism of diffusion in these regions, where in some cases the simulation does not match the exact solution. A possible explanation is presented.

The kinetics of the monomer–dimer mixtures is formulated in the framework of the kinetic lattice gas model. The so-called local evolution rules are used to derive the hierarchy of coupled differential equations for coverage and other correlators, when processes like adsorption, desorption and diffusion are included. The hierarchy of equation is truncated by using mean-field (m,n) closures. Equilibrium properties are analyzed. In particular, adsorption isotherms as a function of the nearest neighbor lateral interaction are presented. The irreversible kinetics are also considered. Temperature-programmed-desorption (TPD) with readsorption is of special interest and this experiment is simulated under different conditions giving different spectra. In these spectra, the influence of adsorbate mobility is analyzed in two dimensions by Monte Carlo simulations.

This work describes a novel mechanism for phase transitions during desorption, involving the formation of lattice size dependent intermediate states when there is enough adsorbate mobility. Monte Carlo simulations are performed to analyze the mechanism of the thermal desorption for adsorbed homonuclear dimers on two-dimensional square lattices. The lattice–gas model with nearest-neighbor repulsive interactions between particles is implemented to study the cases of mobile (with diffusion) and immobile desorption. The number of peaks for the immobile desorption spectra is related to the connectivity of the adsorbed species for both monomer and dimer molecules. However, for the case of mobile desorption, the spectra give information about the desorption mechanism, which differs significantly for monomers and dimers, particularly when the initial temperatures correspond to the critical region.

The coverage dependence of the one-dimensional collective diffusion coefficient is analyzed by using the gradient expansion of the local density. The transition probabilities are written as an expansion of the probabilities of the occupation configurations. Since the detail balance principle determines only a part of the diffusion terms in the expansion, different functional relations are proposed for these terms. The diffusion coefficient is obtained for various choices of these relations. However, some of them seem to be not physically sound and the diffusion coefficient does not behave properly. The range of validity of various expressions for the jump rates is determined and phase diagrams are shown. Besides that, it is shown that the transition state theory guarantees physically suitable behavior of the coefficient of one-dimensional diffusion.

In this work, the adsorption-desorption kinetic in the framework of the lattice gas model is analyzed. The transition probabilities are written as an expansion of the occupation configurations. Due to that, the detail balance principle determine half of the adsorption A{i} and desorption D{i} coefficients, consequently, different functional relations between them are proposed. Introducing additional constrains, it is demonstrated that when those coefficients are linearly related through a parameter gamma , there are values of lateral interaction V , that lead to anomalous behavior in the adsorption isotherms, the sticking coefficient and the thermal programmed desorption spectra. Diagrams for the allowed values of V and gamma are also shown. Alternatively, a more reliable formulation for the adsorption desorption kinetic based on the transition state theory is introduced. In such way the equilibrium and non equilibrium observables do not present anomalous or inconsistent behavior.

The adsorption-desorption kinetics is discussed in the framework of the kinetic lattice-gas model. The master equation formalism has been introduced to describe the evolution of the system, where the transition probabilities are written as an expansion of the occupation configurations of all neighboring sites. Since the detailed balance principle determines half of the coefficients that arise from the expansion, it is necessary to introduce ad hoc, a dynamic scheme to get the rest of them. Three schemes of the so-called hard dynamics, in which the probability of transition from single site cannot be factored into a part which depends only on the interaction energy and one that only depends on the field energy, and five schemes of the so-called soft dynamics, in which this factorization is possible, were introduced for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and nonequilibrium observables, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and nonequilibrium observables have several problems. Some of them can be regarded as abnormal behavior.