Fe2O3-SiO2 composites were prepared by impregnation (sample FeIMP) or doping (sample FeDOP) in the structure of porous silica. The dye removal capacity of the materials was investigated through adsorption and oxidation studies of methylene blue and rhodamine B. N2 adsorption/desorption measurements on FeIMP and FeDOP resulted in specific areas of 27 and 235 m2 g−1, respectively. Mössbauer spectroscopy and XRD data detected hematite and maghemite as the iron phases in the samples FeIMP and FeDOP, respectively. Adsorption isotherms and kinetic studies of the dyes were better fitted in DKR model for FeDOP, where the process follows a pseudo-second order with the interparticle diffusion step being the rate-limiting step. On the other hand, FeIMP has better fit in the Langmuir model. Photocatalytic activity was observed in FeDOP under UV irradiation by the presence of reaction-hydroxylated intermediates for MB (m/z = 301) and RhB (m/z = 459). However, the photocatalytic activity was strongly influenced by the adsorption affinity between dye/catalyst. Photogenerated holes are the species responsible for the dye degradation when the adsorption is too strong, while hydroxyl radical action will be favored when the adsorption is not vigorous as detected by ESI-MS.

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.

This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and 1/t algorithms. The classical algorithms are modified by the use of m-independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number π by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, t; then, the average over m walkers is performed. It is observed that the error goes as 1/sqrt[m]. However, if the number of walkers increases above a certain critical value m>m_{x}, the error reaches a constant value (i.e., it saturates). This occurs for both algorithms; however, it is shown that for a given system, the 1/t algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value m_{x}, since it does not reduce the error in the calculation. Therefore, the number of walkers does not guarantee convergence.

We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang-Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f -> f/2) each time the flat-histogram condition is satisfied, in the second f similar to 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1, ..., L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E, t) -> const. as t -> infinity, so that the standard deviation sigma(g) of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases sg saturates at long times. In the 1/t algorithm, by contrast, sigma(g) decays proportional to 1/root t. Modified TS and 1/t procedures, in which f proportional to 1/t(alpha), converge for alpha values between 0 < alpha <= 1. There are two essential facets to convergence of flat-histogram methods: elimination of initial errors in g(E) and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f similar to 1/t(alpha) with 0 < alpha <= 1. Convergence is optimal for alpha = 1. For alpha <= 0 the sampling noise never decays, while for alpha > 1 the initial error is never completely eliminated.

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.

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.

In this work we have analyzed the adsorption-desorption kinetics in the framework of the lattice gas model. We have shown that the coefficients representing the transition probabilities must be carefully chosen even when they fulfill the principle of detailed balance, otherwise the observables arising from the kinetics present anomalous behavior. We have demonstrated that when the adsorption Ai and desorption Di coefficients are linearly related through a parameter γ, there are values of lateral interaction, V , that lead to bad behavior in the kinetics. We have shown a phase diagram for the allowed values of V and γ, concluding that detailed balance does not guarantee a correct physical behavior of the observables obtained from the rate equations like adsorption isotherms, sticking coefficients and thermal desorption spectra. Alternatively, we have introduced a description of the adsorptiondesorption processes based in a simple but consistent energetic argument that leads to a correct behavior of the observables without physical inconsistencies. † e-mail: smanzi@unsl.edu.ar

In this Brief Report, the convergence of the 1t and Wang-Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two, and higher dimensions. The efficiency and accuracy of both algorithms are determined by the dynamical behavior of the errors between the exact and the calculated values of the integral. It is observed that the time dependence of the error calculated with the 1t algorithm varies as N;{-12} [with N the number of Monte Carlo (MC) trials], in quantitative agreement with the simple sampling Monte Carlo method. In contrast, the error calculated with the Wang-Landau algorithm saturates in time, evidencing the nonconvergence of this method. The sources of error for both methods are also determined.

In this work we have analyzed the adsorption-desorption kinetics in the framework of the lattice gas model. We have shown that the coefficients representing the transition probabilities must be carefully chosen even when they fulfill the principle of detailed balance, otherwise the observables arising from the kinetics present anomalous behavior. We have demonstrated that when the adsorption $A_i$ and desorption $D_i$ coefficients are linearly related through a parameter $γ$, there are values of lateral interaction, $V$, that lead to bad behavior in the kinetics. We have shown a phase diagram for the allowed values of $V$ and $γ$, concluding that detailed balance does not guarantee a correct physical behavior of the observables obtained from the rate equations like adsorption isotherms, sticking coefficients and thermal desorption spectra. Alternatively, we have introduced a description of the adsorption-desorption processes based in a simple but consistent energetic argument that leads to a correct behavior of the observables without physical inconsistencies.

interacciones laterales repulsivas puede observarse en las isotermas de adsorciy los espectros de DTP. Descriptores: Modelos de cin´ etica superficial; cinde adsorci´ on; espectros de desorci´ on t´ The equilibrium and kinetics properties of interacting dimmers adsorbed on square lattice are analyzed by using statistical and kinetic methods. A new adsorption model is introduced, the homonuclear dimmers only are adsorbed parallel to one of the lattice orientations (aligned dimmers). Monte Carlo simulation, exact calculation of the partition function on finite cluster, and the exact solution of the equations of motion in a finite cluster are implemented to obtain the equilibrium (adsorption isotherms) and kinetics throughout the study of the thermal desorption spectra. The presence of structural order for repulsive lateral interactions can be observed in the adsorption isotherms and TPD

An algorithm to calculate the density of states, based on the well-known Wang-Landau method, is introduced. Independent random walks are performed in different restricted ranges of energy, and the resultant density of states is modified by a function of time, F(t) proportional to t-1, for large time. As a consequence, the calculated density of state, gm(E,t) , approaches asymptotically the exact value g(ex)(E) as proportional to t-1/2, avoiding the saturation of the error. It is also shown that the growth of the interface of the energy histogram belongs to the random deposition universality class.

In this work we present a theoretical analysis of the convergence of the Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced years ago to calculate the density of states in statistical models. We study the dynamical behavior of the error in the calculation of the density of states. We conclude that the source of the saturation of the error is due to the decreasing variations of the refinement parameter. To overcome this limitation, we present an analytical treatment in which the refinement parameter is scaled down as a power law instead of exponentially. An extension of the analysis to the N-fold way variation of the method is also discussed.

Se analizan las propiedades de equilibrio y la cinetica de dimeros interactuantes sobre redes cuadradas utilizando metodos estadisticos y cineticos. Se introduce un nuevo modelo de adsorcion de dimeros, el cual permite que los dimeros homonucleares solo se adsorban paralelos a una de las orientaciones de la red (dimeros alineados). Se implementan simulaciones de Monte Carlo, calculo exacto de la funcion de particion en clusters finitos, y la solucion exacta de las ecuaciones de movimiento en un cluster finito para obtener las propiedades de equilibrio (isotermas de adsorcion) y la cinetica a traves de los espectros de desorcion termica. La presencia de estructuras ordenadas para interacciones laterales repulsivas puede observarse en las isotermas de adsorcion y los espectros de DTP.

The equilibrium and kinetics properties of interacting dimmers adsorbed on square lattice are analyzed by using statistical and kinetic methods. A new adsorption model is introduced, the homonuclear dimmers only are adsorbed parallel to one of the lattice orientations (aligned dimmers). Monte Carlo simulation, exact calculation of the partition function on finite cluster, and the exact solution of the equations of motion in a finite cluster are implemented to obtain the equilibrium (adsorption isotherms) and kinetics throughout the study of the thermal desorption spectra. The presence of structural order for repulsive lateral interactions can be observed in the adsorption isotherms and TPD spectra.