Prediction Of Monolayer Adsorption Equilibrium Characteristics On The Basis Of Similarity Theory
Prediction of monolayer adsorption equilibrium characteristics on the basis of similarity theory
V. V. Kutarov
Physical Research Institute, University of Odessa,
27 Pastera St., Odessa, 65026, Ukraine
Nowadays one of the main adsorption theory problems is the correct description of the monolayer adsorption equilibrium characteristics; the most important of which are the adsorption isotherm and the Henry coefficient. Despite the fact that both molecular-statistic and phenomenological models have been obtained for the theoretical adsorption isotherms and the Henry coefficient, it is still very difficult to account a priori all the peculiarities of different configuration molecules interaction with the surface. That is why the reduced parameters have to be introduced into the equilibrium characteristic model.
The given paper contains the methodic of prediction of monolayer adsorption equilibrium characteristics on the theory of similarity basis. As a sample we have considered the Langmure type isotherms i.e. convex to the ordinate axis and tending to saturation.
The prediction methodic based on the application of similarity transformation to the fundamental phenomenological thermodynamic adsorption equation –the Gibbs equation-was spread on the globular type molecules under their adsorption on the surface of heterogeneity of different type. The following formula was obtained for the Henry coefficient prediction
(1)
All the values here, marked with the upper index ”o” relate to the basic i.e. defined experimentally, Henry coefficient; and index “x” relates to the predicted value.
The next universal function was obtained for the isotherm prediction
(2)
In these both formulae is the Henry coefficient; P and PS are the partial pressure and the partial pressure of adsorbate saturation in the volume; FC is the critical adsorbate pressure in adsorbed phase, S is the specific adsorbent surface, ω is the Pitzer factor and N is the adsorption value.
To predict the isotherm according the experimentally obtained basic isotherm, we should build the universal function (2), which is further used for isotherm prediction. The account of the adsorption phase critical pressure is made in the Van der Vaals model frame according to the formula where TС is the critical temperature of the adsorbed phase. Supposing that the globular molecules in the adsorptive phase are arbitrary oriented we can account the constant b2 using the molecule Van der Vaals diameter σ. The critical adsorbed phase temperature depends on the typical adsorptive space size and on the energetic surface characteristics.
If , which determines the merely two dimensional case .
If the critical adsorbed phase temperature will be more than and it can be calculated in the frames of the scaling theory of critical phenomena as where l is the characteristic size of adsorption space, b is the parameter, depending on energetic surface characteristic, λ is the critical index and and are the critical temperatures for adsorbate in the surface with the characteristic size l and the volume phase.
Simultaneously the critical adsorbate temperature in the space with the characteristic size L was analyzed with the help of the model potential U1(Z) of the fluid-wall interaction. The potential sum of the adsorbate molecule interaction with the both walls is defined as U1(Z)=U(Z)+U(l-Z).
The potential (10-4) was used as the interaction potential U(Z). The characteristic adsorption surface size, the width of the active carbon slot-like pore were evaluated according the following formula where φ is the coefficient depended on the adsorbent structure and ρ is the adsorbent density.
We have shown that formulae (1) and (2) can be applied for prediction of monolayer adsorption parameters under the adsorption of organic and inorganic substances on the active carbon with the specific surface S=700-1440 m2/g in the temperature range T=298,2-400,0 K.
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