Adsorbate thermodynamic properties

The bulk properties of celluloses are generally influenced by adsorbed moisture. The effect of the change in bulk solid properties for microcrystalline cellulose has been demonstrated by a tableting operation in a very simplistic manner. Dry microcrystalline cellulose (%MC = 0.07) was compared with material with a moisture content above that associated with completion of the monolayer (%MC = 5.1). A thermodynamic picture of the character of water in these samples can be based on the adsorbate thermodynamic properties A// > 3.5kcal/mole (14.65 kJ/mole),... 

Figure 8.2 summarizes the methods discussed here. The organization of this chapter is as follows. First, methods for calculating the rate constant of an elementary step are described. Then DFT is briefly introduced for estimation of adsorption properties and barriers, followed by an outline of selected statistical Ihermodynantics. Examples of the thermochemistry on Ni(l 11) and Pt(lll) are presented to address thermodynamic consistency of the DFT-predicted adsorption properties. S iempirical methods for predicting adsorbate thermodynamic properties and kinetic parameters are also presented. With this input, microkinetic models can be solved. Finally, analytical tools are described to develop and analyze a nticrokinetic model, with the water-gas shift (WGS) reaction on Pt-based catalysts taken as an example. 

Physica.1 Properties. Carbonyl sulfide [463-58-1] (carbon oxysulfide), COS, is a colorless gas that is odorless when pure however, it has been described as having a foul odor. Physical constants and thermodynamic properties are Hsted ia Table 1 (17,18). The vapor pressure has been fitted to an equation, and a detailed study has been made of the phase equiUbria of the carbonyl sulfide—propane system, which is important ia the purification of propane fuel (19,20). Carbonyl sulfide can be adsorbed on molecular sieves (qv) as a means for removal from propane (21). This approach has been compared to the use of various solvents and reagents (22). 

Finally, in this part of the work we would like to discuss to some extent practical tools to obtain thermodynamic properties of adsorbed fluids. We have mentioned above that the compressibility equation is the only simple recipe, for the moment, to obtain the thermodynamics of partly quenched simple fluids. The reason is that the virial equation is difficult to implement it has not been tested for partly quenched systems. Nevertheless, for the sake of completeness, we present the virial equation in the form [22,25]... 

In order to utilise our colloids as near hard spheres in terms of the thermodynamics we need to account for the presence of the medium and the species it contains. If the ions and molecules intervening between a pair of colloidal particles are small relative to the colloidal species we can treat the medium as a continuum. The role of the molecules and ions can be allowed for by the use of pair potentials between particles. These can be determined so as to include the role of the solution species as an energy of interaction with distance. The limit of the medium forms the boundary of the system and so determines its volume. We can consider the thermodynamic properties of the colloidal system as those in excess of the solvent. The pressure exerted by the colloidal species is now that in excess of the solvent, and is the osmotic pressure II of the colloid. These ideas form the basis of pseudo one-component thermodynamics. This allows us to calculate an elastic rheological property. Let us consider some important thermodynamic quantities for the system. We may apply the first law of thermodynamics to the system. The work done in an osmotic pressure and volume experiment on the colloidal system is related to the excess heat adsorbed d Q and the internal energy change d E ... 

The view that the clay surface perturbs water molecules at distances well in excess of 10 A has been largely based on measurements of thermodynamic properties of the adsorbed water as a function of the water content of the clay-water mixture. There is an extensive literature on this subject which has been summarized by Low (6.). The properties examined are, among others, the apparent specific heat capacity, the partial specific volume, and the apparent specific expansibility (6.). These measurements were made on samples prepared by mixing predetermined amounts of water and smectite to achieve the desired number of adsorbed water layers. The number of water layers adsorbed on the clay is derived from the amount of water added to the clay and the surface area of the clay. 

The value of the thermodynamic property in question is the difference in values for the clay-water sample and the same measurement on an equivalent amount of pure, anhydrous clay (6.). This procedure involves two assumptions 1) the added water is uniformly adsorbed on all clay layers, and 2) the thermodynamic properties of the clay itself do not change when the clay expands and is intercalated by water molecules. 

The assumption that the water is adsorbed in uniform layers on all the clay surfaces for a wide range of mixtures has been criticized (2, 20). The argument is that the individual clay particles in the clay-water mixture do not expand beyond a certain distance regardless of the quantity of water which is added. The clay layers group themselves into tactoids resulting in two populations of water those molecules which are found between the tactoids and those directly perturbed by the clay layers. If true, this would invalidate the procedure used to calculate the thermodynamic properties of the adsorbed water. However, other workers have reported complete delamination of certain smectites (21., 22). It is not clear under what conditions tactoids will form, or not, and this uncertainty is underlined in (21) (see remarks by Nadeau and Fripiat, pages 146-147). 

The validity of the assumption that the various thermodynamic properties of the smectite remain invariant, regardless of the state of hydration, has been addressed in detail by Sposito and Prost (1). They point out that one would, for example, expect hydrolysis of the clay to occur at high water contents, and also, it is likely that the exchangeable cations will change their spatial relationship with the clay layers. Thus, the derived thermodynamic properties of the adsorbed water would not represent correct values. 

Finally, the whole concept of using macroscopic (i.e. thermodynamic) properties to derive a microscopic picture of the adsorbed water is open to question (1, 8.). 

A summary of developments in physical adsorption during the period from 1943 to 1955 has been given recently by Everett 94). The chief difference between the approach used by Brunauer in his book published in 1943 and that in vogue in 1955 is in the great development of the thermodynamic aspects of the subject. Prior to 1943, the main effort was in developing theories to predict the shape of adsorption isotherms. Since then, emphasis has shifted towards the thermodynamic properties of the adsorbed phase, particularly its entropy. 

The perturbation of the surface is automatically included in any measured thermodynamic property. In the presence of such a perturbation the thermodynamic properties of the adsorbed gas alone have no direct physical meaning, although the experimentally measured quantities are still well defined. 

Recent work has shown 103) that for alkali halides the Debye characteristic temperature is not very sensitive to volume changes produced by thermal expansion. This probably indicates that, in general, volume changes of an adsorbent will not markedly affect its bulk thermodynamic properties. 

X, is the molar thermodynamic property of a pure component (adsorbate or adsorbent) and X, is the partial molar property of the component, defined as... 

As stated previously, IGC can also be used to measure the specific surface area of a given powder. The adsorbate gas is not restricted to N2 and Kr rather, the same probes that are used to characterize the surface thermodynamic properties of the powder can be used as probe to measure its specific surface area. Table 13.2 contains a comparison of specific surface area measurements via traditional N2/Kr adsorption vs IGC. 

The transport and adsorption properties of hydrocarbons on microporous zeolites have been of practical interest due to the important properties of zeolites as shape-selective adsorbents and catalysts. The system of benzene adsorbed on synthetic faujasite-type zeolites has been thoroughly studied because benzene is an ideal probe molecule and the related role of aromatics in zeolitic catalysts for alkylation and cracking reactions. For instance, its mobility and thermodynamic properties have been studied by conventional diffusion 1-6) and adsorption 7-9) techniques. Moreover, the adsorbate-zeolite interactions and related motion and location of the adsorbate molecules within the zeolite cavities have been investigated by theoretical calculations 10-15) and by various spectroscopic methods such as UV (16, 17), IR 17-23), neutron 24-27), Raman 28), and NMR 29-39). 

If it were possible to work with monodisperse liquid adsorbent, it would be important and interesting to compare values of thermodynamic properties determined by measurements of different types. Agreement would indicate correctness of the methods and their interpretation. 

It is more important to compare values of thermodynamic properties determined in different ways when solid adsorbents are used. Most adsorption experiments are made with adsorbents consisting of small solid particles of varying sizes and shapes. Complete equilibrium in such systems is not possible, but for many... 

Structural characteristics of adsorbed chains, such as the mean distance of chain ends from the surface and the fraction of segments in each layer, derive from P(i,s). The partition function and thermodynamic properties depend on the eigenvalues of W (Flory, 1969). In the limit n - oo, calculation of thermodynamic functions simplifies because one eigenvalue, denoted by A, dominates the free energy per segment,... 

As a direct consequence of 1), the adsorption enthalpy and other thermodynamic properties are composite quantities, containing at least four terms. Some of these terms may dominate, and this is not necessarily the enthalpy of the adsorptive-adsorbent interaction. As a typical illustration, binding of hydrophobic (parts of) molecules on hydrophobic adsorbents from aqueous solution is mainly driven by their dislike for water and not by their attraction to the surface. 

The water adsorbed on the surface is described by the SPC model [16]. This fast computable model is well suited for very large systems, as it reproduces quite well the thermodynamical properties around ambient temperature, like vapor pressure (0.044 bar against 0.035 bar experimentaly) and enthalpy of vaporization [17]. The extended SPC/E model [18] is not adapted to study adsorption properties since the polarization correction that it introduces cannot be well defined in the highly inhomogeneous environment of a molecule adsorbed on a surface. Furthermore, the predicted vapor pressure is only half the experimental value [19]. 

Gas flow processes through microporous materials are important to many industrial applications involving membrane gas separations. Permeability measurements through mesoporous media have been published exhibiting a maximum at some relative pressure, a fact that has been attributed to the occurrence of capillary condensation and the menisci formed at the gas-liquid interface [1,2]. Although, similar results, implying a transition in the adsorbed phase, have been reported for microporous media [3] and several theoretical studies [4-6] have been carried out, a comprehensive explanation of the static and dynamic behavior of fluids in micropores is yet to be given, especially when supercritical conditions are considered. Supercritical fluids attract, nowadays, both industrial and scientific interest, due to their unique thermodynamic properties at the vicinity of the critical point. For example supercritical CO2 is widely used in industry as an extraction solvent as well as for chemical... 

There are several reports in the literature that measure binary adsorption equilibria using gas chromatography [4,S,6]. In GC techniques the adsorbent is equilibrated with a continuous flow of carrier gas (gas 1). Then a pulse of gas 2 is injected at the column inlet. A peak of the gas 2 is eluted at the exit of the column after some time. Net retention time (or volume) is calculated from the first moment of the peak after correcting for void volume (by measuring the retention time of a non-adsorbing species). If the carrier gas is inert (i.e. helium) the net retention time is related to the pure component Henry s constant. Typical binary measurements reported so r use a mixture of the two gases as carrier and introduce a small perturbation in composition. The net retention volume is related to the thermodynamic properties by [4]... 

As a useful thermodynamic property, the isosteric heat of adsorption has been generally applied to characterize the adsorbent surface. The isosteric heat of adsorption is evaluated simply by applying the Clausius-Clapeyron equation if one has a good set of adsorption equilibrium ta obtained at several temperatures. 

Z = 0, m = 0 Z = 1, m = 0, m = dzl and Z = 2, m = 0. Since the rotational constants of the isotopic hydrogens are large, these four states are, to a good approximation, adequate for the description of the thermodynamic properties of the adsorbed state over a considerable temperature range. 

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