Surfaces, heterogeneous, thermodynamics adsorption

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Both extreme models of surface heterogeneity presented above can be readily used in computer simulation studies. Application of the patch wise model is amazingly simple, if one recalls that adsorption on each patch occurs independently of adsorption on any other patch and that boundary effects are neglected in this model. For simplicity let us assume here the so-called two-dimensional model of adsorption, which is based on the assumption that the adsorbed layer forms an individual thermodynamic phase, being in thermal equilibrium with the bulk uniform gas. In such a case, adsorption on a uniform surface (a single patch) can be represented as... 

In the limit of a - 0, the ideal Langmuir adsorption isotherm is obtained. See - Frumkin isotherm, and for the role of surface heterogeneity - Temkin isotherm. Refs. [i] Horanyi G (2002) Specific adsorption. State of art Present knowledge and understanding. In Bard A], Stratmann M, Gileadi M, Urbakh M (eds) Thermodynamics and electrified interfaces. Encyclopedia of electrochemistry, vol. I. Wiley-VCH Verlag, Weinheim, pp 349-382 [ii] Calvo EJ (1986) Fundamentals. The basics of electrode reactions. In Bamford CH, Compton RG (eds) Comprehensive chemical kinetics, vol. 26. Elsevier, Amsterdam, pp 1-78... 

G. D. Halsey, Advances in Catalysisy 4 (1952), presents an excellent critique of the various theories of adsorption in the light of surface heterogeneity. T. L. Hill in the preceding chapter outlines the statistical mechanical and thermodynamics of the different sorption theories. 

Similar problems arise with the surface excess Gibbs energy G°, which is defined in table 1.2 in sec. 1.3. However, a number of enthalpy changes (upon adsorption, immersion, etc.) can be obtained and from them useful thermodynamic information can be deduced, see sec. 1.3. Some of these measurements contribute to the understanding of surface heterogeneity (in the energetic sense). In principle such information can also be obtained by isotherm analysis, see sec. 1.7. 

W. Rudzinski, Lee Shyi-Long, T. Panczyk, Yan Ching-Cher, A fractal approach to adsorption on heterogeneous solids surfaces. II. Thermodynamic analysis of experimental adsorption data . Journal of Physical Chemistry B, 105 10857-10866 (2001). 

This book is the first volume of a Treatise on Thermodynamics based on the methods of Gibbs and De Donder. It deals with the following topics fundamental theorems, homogeneous systems, heterogeneous systems, stability and moderation, equilibrium displacements and equilibrium transformations, solutions, azeotropy, and indifferent states. The second volume deals with surface tension and adsorption while the third and last will be concerned with irreversible phenomena. 

The calorimetric studies of the surface heterogeneity of oxides were initiated half a century ago, and experimental findings as well as their theoretical interpretation have been recently reviewed by Rudzinski and Everett [2]. The last two decades have brought a true Renaissance of adsorption calorimetry. A new generation of fully automatized and computerized microcalorimeters has been developed, far more accurate and easy to manipulate. This was stimulated by the still better recognized fact that calorimetric data are much more sensitive to the nature of an adsorption system than adsorption isotherm for instance. It is related to the fact that calorimetric effects are related to temperature derivatives of appropriate thermodynamic functions, and tempearture appears generally... 

Riccardo and coworkers [50, 51] reported the results of a statistical thermodynamic approach to study linear adsorbates on heterogeneous surfaces based on Eqns (3.33)—(3.35). In the first paper, they dealt with low dimensional systems (e.g., carbon nanotubes, pores of molecular dimensions, comers in steps found on flat surfaces). In the second paper, they presented an improved solution for multilayer adsorption they compared their results with the standard BET formalism and found that monolayer capacities could be up to 1.5 times larger than the one from the BET model. They argued that their model is simple and easy to apply in practice and leads to new values of surface area and adsorption heats. These advantages are a consequence of correctly assessing the configurational entropy of the adsorbed phase. Rzysko et al. [52] presented a theoretical description of adsorption in a templated porous material. Their method of solution uses expansions of size-dependent correlation functions into Fourier series. They tested... 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

MSL models present the correct Henry s law limit and obey the requirement of thermodynamic consistency. This model is often used to account for the effect of the size difference in the study of multicomponent adsorption equilibria [29,30]. The MSL model can be extended to include effects such as lateral interactions in the adsorbed phase as well as surface heterogeneity [80]. 

An advantage of the potential theory is that its fiill version draws a direct connection between the properties of a bulk phase with those of an adsorbed phase. To do so, the adsorbate should be considered as a segregated mixture in the potential field emitted by the surface. The description of the adsorbed mixture is purely thermodynamic, with application of the same equations of state, which have been used for the bulk phase. The properties of the adsorbent and, in particular, the surface heterogeneity are expressed by the form of the surface potentials. This makes it possible to evaluate adsorption of rather nontrivial mixtures under complex thermodynamic conditions, provided that thermodynamic models for the corresponding bulk phases are available. 

Moreover, the use of heat-flow calorimetry in heterogeneous catalysis research is not limited to the measurement of differential heats of adsorption. Surface interactions between adsorbed species or between gases and adsorbed species, similar to the interactions which either constitute some of the steps of the reaction mechanisms or produce, during the catalytic reaction, the inhibition of the catalyst, may also be studied by this experimental technique. The calorimetric results, compared to thermodynamic data in thermochemical cycles, yield, in the favorable cases, useful information concerning the most probable reaction mechanisms or the fraction of the energy spectrum of surface sites which is really active during the catalytic reaction. Some of the conclusions of these investigations may be controlled directly by the calorimetric studies of the catalytic reaction itself. 

In the last two sections the formal theory of surface thermodynamics is used to describe material characteristics. The effect of interfaces on some important heterogeneous phase equilibria is summarized in Section 6.2. Here the focus is on the effect of the curvature of the interface. In Section 6.3 adsorption is covered. Physical and chemical adsorption and the effect of interface or surface energies on the segregation of chemical species in the interfacial region are covered. Of special importance again are solid-gas or liquid-gas interfaces and adsorption isotherms, and the thermodynamics of physically adsorbed species is here the main focus. 

In heterogeneous metal catalysis alkanes, alkenes, and aromatics adsorbed on the metal surface rapidly exchange hydrogen and deuterium. The multiple adsorption of reactants and intermediates lowers the barriers for such exchange processes. Hydrogenation of unsaturated aliphatics and isomerisation can be accomplished under mild conditions. Catalytic dehydrogenation of alkanes to alkenes requires temperatures >200 °C, but this is because of the thermodynamics of this reaction. 

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