### Adsorption of Gases on Heterogeneous Surfaces

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Telles and F. Abstract - The effect of surface topography upon the adsorption of dimer molecules is analyzed by means of grand canonical ensemble Monte Carlo simulations. Heterogeneous surfaces were assumed to consist of a square lattice containing active sites with two different energies. These were distributed in three different configurations: a random distribution of isolated sites; a random distribution of grains with four high-energy sites; and a random distribution of grains with nine high-energy sites.

For the random distribution of isolated sites, the results are in good agreement with the molecular simulations performed by Nitta et al. In general, the comparison with theoretical models shows that the Nitta et al. The molecular simulation results also show that the energy topology of the solid surfaces plays an important role in the adsorption of dimers on solids with large differences in site energies. For these cases, the Nitta et al. Keywords : Adsorption isotherms, heterogeneous surfaces, Monte Carlo simulations. The modeling of adsorption phenomena on solid surfaces is an important tool to predict and correlate the physical adsorption involved in the separation or purification processes and to understand the chemical adsorption adsorption on solids with a broad distribution of energies and irregular surface patterns inherent in catalytic processes.

The diversity of solids used in these processes gives rise to a large number of isotherm models. These are used to describe different observed adsorption characteristics.

## Adsorption of Gases on Heterogeneous Surfaces

Generally, the task of choosing the best model to apply is not an easy one. Molecular simulation techniques can be a useful tool in testing hypotheses and simplifications used to develop isotherms. In particular, surface topography is an important parameter in view of the heterogeneity of solids. The isotherm models presented in the literature fall within one of the following extreme situations: sites distributed in large clusters called patchwise heterogeneous surfaces or randomly distributed sites Rudzinski and Everett, Recently, Nitta et al.

This work was based on studies performed by Riccardo et al.

Ramirez-Pastor et al. The comparison between the molecular simulation results and experimental data demonstrates the potentiality of this technique to describe real systems. The objective of the present work is to systematically analyze the effect of solids energy topography on the adsorption of dimers using Monte Carlo simulations. We also explore the conditions under which the Nitta et al.

For the simulations and models studied here, adsorbate-adsorbate interactions were neglected. Thus, the configurational energy U of the adsorbed phase results from the configuration of occupied sites,.

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In order to minimize the size effect of the solids, the periodic boundary conditions were used. Once the surface structure was defined, the surface coverage due to dimer adsorption was calculated by the Monte Carlo method, given the chemical potential m , temperature T , and number of specified sites M in the lattice. The method is based on three fundamental movements, according to the Metropolis algorithm Allen and Tildesley, and Nitta et al.

The transition probability from a configurational state m to another configurational state n is given as.

Details of each movement are presented below:. Among the adsorbed molecules, one is randomly chosen to rotate around one of its segments. This segment is fixed as a pivot and another random number is generated to choose a new position for the second segment. If this position is already occupied, the movement is rejected the configuration is thermodynamically impossible.

If not, the energy of this new configuration is computed and the new ratio of the probability density of the new configurational state n to that of the old state m is given by Allen and Tildesley, In order to add one molecule, a position in the lattice is chosen to place the first segment of the dimmer, and using another random number, a neighboring site is chosen to complete the addition. If one of these sites is already occupied, the movement is rejected, as its configuration is thermodynamically impossible. If not, the energy of this new configuration is computed and the ratio of the probability density of the new n state to that of the old m Allen and Tildesley, is calculated as follows:.

One of the adsorbed molecules is randomly removed and the energy of this new configuration is calculated and the ratio of the probability density of the new n state to that of the old m Allen and Tildesley, is computed by.

The relationship connecting fugacity, f, and chemical potential is given by the classic equation Smith and van Ness, :. On the other hand, the Henry constant for dimer adsorption on a homogeneous solid exclusively constituted by sites of the b kind is given by Hill, Therefore, the chemical potential is given by.

Periodic boundary conditions were considered for both distributing the acid grains on the solid and moving a molecule in the lattice. The Monte Carlo method is based on a large number of configurations involving these three basic movements. Each simulation cycle starts with the establishment of an initial configuration by randomly placing a specific quantity of dimers in the lattice. With a given initial configuration, the system was first relaxed to equilibrium throughout 10 6 Monte Carlo steps rotation, creation, and destruction.

After equilibration, another 10 6 Monte Carlo steps were performed to compute the thermodynamic properties, such as the coverage fraction and the configurational energy.

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## Adsorption of Gases on Heterogeneous Surfaces by W. Rudzinski, Douglas H. Everett - xomuremaqyhy.cf

The global means and the standard deviation of the thermodynamic properties were calculated using 10 cycles of simulation, each one marked by a different random distribution of acid grains. The scheme of the Monte Carlo method used in this work is summarized in Figure 2. Typical standard deviation of the thermodynamic properties obtained here was, for example, 10 -3 for the coverage fraction of dimers. In the Langmuir isotherm model, it is assumed that every molecule adsorbs on only one effective site, without lateral interactions.

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In these equations, K b is the adsorption equilibrium constant for the dimer molecules adsorbed on the surface composed only of sites b and r a is the relative strength of adsorption on sites a compared to that on sites b. In the Nitta et al. On the other hand, the Flory-Huggins equation is used to estimate the entropic effect due to the adsorption of dimer molecules in the lattice.

In this way, the equation is Nitta et al. The quasi-chemical equation should be solved simultaneously to obtain q and q b by.

## Adsorption of gases on heterogeneous surfaces

In these equations, f is the fugacity for a dimer in the gas phase, K b is the equilibrium constant of the adsorption on the hypothetical homogeneous surface composed only of sites b, and q and q b are fractions of the total coverage and the coverage of nonacid sites, respectively. The Monte Carlo simulation method for a grand canonical ensemble was used to calculate the coverage fraction and configurational energies for adsorption of dimer molecules on heterogeneous surfaces.

Special attention was given to analyzing different topographies of the energy surface heterogeneity.

The results obtained with Monte Carlo simulations were compared to those obtained with the theoretical dual-site Langmuir Mathias et al. Multilayer Adsorption on Heterogeneous Surfaces. Average Review. Write a Review. Related Searches. Adsorption, which occurs when a solid surface is exposed to a gas or liquid, is Adsorption, which occurs when a solid surface is exposed to a gas or liquid, is of great technological importance. Adsorption plays a vital role in heterogeneous catalysis and in many solid state reactions and chromatographic separations. Solid adsorbents are employed View Product. Adsorption From Solution.

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