A. Ben Lamine

New theoretical expressions for the five adsorption type isotherms classified by BET based on statistical physics treatment

New theoretical expressions to model the five adsorption isotherm types have been established. Using the grand canonical ensemble in statistical physics, we give an analytical expression to each of five physical adsorption isotherm types classified by Brunauer, Emett, and Teller, often called BET isotherms. The establishment of these expressions is based on statistical physics and theoretical considerations. This method allowed estimation of all the mathematical parameters in the models. The physicochemical parameters intervening in the adsorption process that the models present could be deduced directly from the experimental adsorption isotherms by numerical simulation. We determine the adequate model for each type of isotherm, which fixes by direct numerical simulation the monolayer, multilayer, or condensation character. New equations are discussed and results obtained are verified for experimental data from the literature. The new theoretical expressions that we have proposed, based on statistical physics treatment, are rather powerful to better understand and interpret the various five physical adsorption type isotherms at a microscopic level.

Statistical Physics Modelling of Dye Adsorption on Modified Cotton

Experimental adsorption isotherms for four anionic dyes (Acid Blue 25, Acid Yellow 99, Reactive Yellow 23 and Acid Blue 74) on to cationized cotton have been analyzed using a multilayer adsorption model. For such purpose, the double-layer model showed the best fit with a high correlation coefficient R2. The analytical expression of the model has been established from an application of the grand canonical ensemble of statistical physics. This method allowed an estimation of all the mathematical parameters in the model. Thus, the receptor site density and the half-saturation concentration have been related to physicochemical variables such as the chemical potential, the adsorption energy, the anchorage number, etc. A physical interpretation of the model parameters has been provided and some results relating to the adsorption process discussed.

Dye Adsorption by Modified Cotton. Steric and Energetic Interpretations of Model Parameter Behaviours

The variations of the three parameters, viz. anchorage number, receptor site density and half-saturation concentration, as determined theoretically (Khalfaoui et al. 2002) and related to the adsorption energy, exhibited different behaviours when examined in terms of the adsorption of various dyes on to modified cotton. When plotted against the percentage nitrogen content of these cottons, variations in the effective receptor site density and the inverse of the adsorbed molecules anchorage number allowed the adsorption process to be described topographically in terms of the parallel or perpendicular adsorption of the dye molecule on to the adsorbent surface. The presence of ionic or van der Waals forces in such adsorption was also considered. The values of the model parameters were found to be related to the magnitude of the steric hindrance arising from the anchorage geometry of the dye molecule. Where the site density was high, a form of dimerization of the dye molecules was favoured. The best conditions for obtaining a high adsorption capacity, necessary for textile dyeing and wastewater depollution, were considered. Through the use of the half-saturation capacity, c1/2, it was possible to determine the change in the adsorption energy when the receptor site spacing was decreased and to relate such variation to the rate of steric hindrance, τ.

Statistical thermodynamics of adsorption of dye DR75 onto natural materials and its modifications: double-layer model with two adsorption energies

In this article, adsorption modelling was presented to describe the sorption of textile dye, Direct Red 75 (DR75), from coloured wastewater onto the natural and modified adsorbent, Posidonia oceanica. The formulation of the double-layer model with two energy levels was based on statistical physics and theoretical considerations. Thanks to the grand canonical ensemble in statistical physics some physico-chemical parameters related to the adsorption process were introduced in the analytical model expression. Fitting results show that the dye molecules are adsorbed in parallel position to the adsorbent surface. The magnitudes of the calculated adsorption energies show that the DR75 dye is physisorbed onto Posidonia. Both Van der Waals and hydrogen interactions are implicated in the adsorption process. Despite its simplicity, the model fits a wide range of experimental data, thereby supporting the underlying data that the grafted groups facilitate the parallel anchorage of the anionic dye molecule. Thermodynamic parameters, such as adsorption energy, entropy, Gibbs free adsorption energy and internal energy were calculated according to the double-layer model. Results suggested that the DR75 adsorption onto Posidonia was a spontaneous and exothermic process.

Application of Statistical Physics on the Modeling of Water Vapor Desorption Isotherms

The sorption isotherms give information about the interaction of biopolymers with water vapor. These isotherms are extremely important in the modeling of the drying processes and in the prediction of the humidity changes during the product storage. An analytical expression for modeling of water vapor sorption isotherms of agricultural products was developed using the statistical physics formalism. The statistical model was further used to fit and interpret desorption isotherms of Tunisian olive leaves and some food products. In this model, five parameters in relation to the desorption process intervene, such as the number of water molecules per site n, the receptor sites density N M , the energetic parameters a 1 and a 2, and the number of multilayers N 2. The fitting results are discussed to explain the behavior of different parameters versus temperature. The statistical model was used to investigate thermodynamics functions that govern in the desorption mechanism, such as entropy, internal energy, and Gibbs free enthalpy.

Interpretation of psychophysics response curves using statistical physics

Experimental gustatory curves have been fitted for four sugars (sucrose, fructose, glucose and maltitol), using a double layer adsorption model. Three parameters of the model are fitted, namely the number of molecules per site n, the maximum response RM and the concentration at half saturation C1/2. The behaviours of these parameters are discussed in relationship to each molecules characteristics. Starting from the double layer adsorption model, we determined (in addition) the adsorption energy of each molecule on taste receptor sites. The use of the threshold expression allowed us to gain information about the adsorption occupation rate of a receptor site which fires a minimal response at a gustatory nerve. Finally, by means of this model we could calculate the configurational entropy of the adsorption system, which can describe the order and disorder of the adsorbent surface.

Energetic and Thermodynamic Analysis of Adsorption Isotherm Type VI of Xenon on Graphite Nanotubes

New theoretical expressions for the modeling of adsorption isotherms of Xenon on Graphite at 110 K have been established. The establishment of these new expressions is based on statistical physics formalism and some working assumptions. This method allowed estimation of physico-chemical parameters in the theoretical model. The parameters intervening in the adsorption process have been deduced directly from experimental adsorption isotherm by numerical simulation. The proposed models allow a good correlation to Type VI experimental isotherms. We mainly introduce three parameters affecting the adsorption process, namely, the density of Xenon receptor sites NM, the number of molecules per site n and the Xenon adsorption energy. Then we apply the model to calculate thermodynamics functions which govern the adsorption mechanism such as entropy, free enthalpy and internal energy.

Models for Type VI Adsorption Isotherms from a Statistical Mechanical Formulation

In this study, two theoretical expressions for the Type VI isotherm in the IUPAC classification are presented. The formulation of these new expressions is based on a rigorous statistical mechanical description. The expressions allow for the estimation of physicochemical parameters within the theoretical model. The proposed models allow a good correlation to Type VI experimental isotherms taken from the literature such as adsorption isotherms for adsorption of methane onto MgO (100) and onto an exfoliated graphite surface. The parameters intervening in the adsorption process have been deduced directly from experimental adsorption isotherms by numerical simulation. The theoretical expressions provide an understanding and interpretation of the adsorption isotherms at the microscopic level.

On the use of the Hill's model as local isotherm in the interpretation of the behaviour of the adsorption energy distributions

Activated carbons are reported to show promise for separation processes and natural gas storage, since they have a strongly heterogeneous surface. In that context, a thorough investigation of the energetic heterogeneity of activated carbon surfaces is essential for the development and improvement of materials designed for specific applications. We have carried out this study, to determine the Adsorption Energy Distribution (AED) corresponding to the adsorption of methane, ethane, and nitrogen on activated carbon at different temperatures by using the Hill model as local isotherm. At first, the integral equation itself is deduced by a reasoning based on the local adsorption isotherm. Then, to solve the integral equation a numerical method is proposed. The Hill isotherm was established by applying the grand canonical ensemble in a statistical physics treatment. This treatment allowed us to define the parameter n, which represents the number of molecules adsorbed per site. We have supposed as a first approach that the energy distribution function has the shape of the normal Gaussian distribution. The influence of the adsorbate type and the values of parameter n at different temperatures on the behaviour of the AED, have been studied. Keywords: Adsorption energy distribution; Activated carbon; Statistical physics; Integral equation; Hill isotherm.

On the statistical physics of finite multilayer adsorption model on gaseous phase

The grand canonical ensemble in statistical physics has enabled us to develop a theoretical model that is an interesting application for adsorption in gaseous phase. The present approach turns out that is promising to the characterization to the adsorbent material surface. Indeed, the theoretical model contains physicochemical parameters that enable us a detailed investigation of the adsorption process. Particularly, our model allows the study of anchorage effect, the receptor sites densities at the adsorbent surface, the number of adsorbed layers and this is possible form the adsorption isotherms. All these parameters reached via a numerical simulation of the experimental adsorption isotherms, allow us to well describe and understand the physical process at molecular level. Modeling of adsorption isotherms has to offer microscopic interpretations for energy storage. The configurational entropy at various temperatures has been studied. This parameter allowed to deduce some results related to the evolution of the disorder during the adsorption process.