Adsorption Entropies

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

The accepted explanation for the minimum is that it represents the point of complete coverage of the surface by a monolayer according to Eq. XVII-37, Sconfig should go to minus infinity at this point, but in real systems an onset of multilayer adsorption occurs, and this provides a countering positive contribution. Some further discussion of the behavior of adsorption entropies in the case of heterogeneous adsorbents is given in Section XVII-14. 

Neither the thermodynamic nor the rheological description of surface mobility has been very useful in the case of chemisorbed films. From the experimental point of view, the first is complicated by the many factors that can affect adsorption entropies and the latter by the lack of any methodology. 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

Let us consider that Ed corresponding to a peak on the desorption curve is coverage dependent, while kd (and thus the adsorption entropy) remains constant. (For the variability of kd see Section II.A.) When seeking the required function Ed (6) we refer to Eq. (8) in which the term exp (— Edf RT) exhibits the greatest variability. A set of experimental curves of the desorption rate with different initial populations n,B must be available. When plotting ln(— dn,/dt) — x ln(n ) vs 1/T, we obtain the function Ed(ne) from the slope, for the selected n, as has been dealt with in Section V. In the first approximation which is reasonable for a number of actual cases, let us take a simple linear variation of Ed with n ... 

The entropy factor should also be considered since cyclization results in a more ordered structure. The C5 cyclization of n-hexane involves an entropy decrease of about 15-17 entropy units (e.u.). The corresponding values for cyclohexane and benzene formation are about 25 and 38-45 e.u., respectively. These values are comparable with calculated values of adsorption entropy (29). Thus, adsorption of a molecule to be cyclized may supply a considerable part of the entropy change in other words, adsorption should take place in a geometry favorable for cyclization. This is one of the main roles of the catalyst. 

The free translation has a very high entropy, while the entropy of a vibration is moderate. For this reason the adsorption entropy is usually negative. At a given pressure the equilibrium between gas and adsorbate will shift towards desorption when the temperature is increased. 

Finally, a classification of catalysts by Matsuura [212] may be mentioned, in which the relation of adsorption entropy to heat of adsorption of butene-1 appears, surprisingly, to be linear. The conclusion can be drawn that moderate heats of adsorption (about 40—50 kcal mol 1) characterize suitable catalysts. Only here is the right combination of surface mobility and adsorption intensity found. Apparently, the oxygen is then tempered sufficiently to make a selective oxidation possible. Otherwise, the oxides are non-active (e.g. low heat of adsorption in FeP04 and low mobility) or active but non-selective because of high mobility coupled to a large heat of adsorption (e.g. Fe304). 

Whilst hydrogen enters into a chemisorptive bond with charcoal at very low temperatures, oxygen remains physically adsorbed unless relatively high temperatures are reached. At liquid-air temperatures the adsorption entropy of oxygens shows that the adsorbed molecules are completely free to move and rotate over the surface 168). 

Measurements of deviation of the standard adsorption entropy at graphitized carbon black have been carried out for thietane and other heterocyclic molecules. The theoretical standard entropy for the thietane molecule shows a greater deviation from the experimental value in comparison to others, which seems to indicate that for thietane a simple model of an adsorbed molecule with 2° of freedom is not accurate <1997ZP1333>. 

The two contrasting approaches, the macroscopic viewpoint which describes the bulk concentration behavior (last chapter) versus the microscopic viewpoint dealing with molecular statistics (this chapter), are not unique to chromatography. Both approaches offer their own special insights in the study of reaction rates, diffusion (Brownian motion), adsorption, entropy, and other physicochemical phenomena [2]. 

Elements 108 - 116 are homologues of Os through Po and are expected to be partially very noble metals. Thus it is obvious that their electrochemical deposition could be an attractive method for their separation from aqueous solutions. It is known that the potential associated with the electrochemical deposition of radionuclides in metallic form from solutions of extremely small concentration is strongly influenced by the electrode material. This is reproduced in a macroscopic model [70], in which the interaction between the microcomponent A and the electrode material B is described by the partial molar adsorption enthalpy and adsorption entropy. By combination with the thermodynamic description of the electrode process, a potential is calculated that characterizes the process at 50% deposition ... 

The entropy of a mobile adsorption process can be determined from the model given in [4], It is based on the assumption that during the adsorption process a species in the gas phase, where it has three degrees of freedom (translation), is transferred into the adsorbed state with two translational degrees of freedom parallel to the surface and one vibration degree of freedom vertical to the surface. From statistical thermodynamics the following equation for the calculation of the adsorption entropy is derived ... 

The adsorption behavior of atoms and compounds for most of the experiments used in the described correlations were evaluated using differently defined standard adsorption entropies [28,52-57], Adsorption data from more recent experimental results were evaluated applying the model of mobile adsorption [4], In addition, data from previous experiments were reevaluated using this model. 

Yet, the Information that can be obtained from an entropy calculation is at least as interesting as a knowledge of the heat of adsorption. It is possible in principle to decide whether the adsorbed layer is mobile or localized, hi favorable cases the adsorption entropy will also reveal whether a molecule is rotating freely or not in the adsorbed state. 

For further discussion of the measurement of adsorption entropies, see F. Rouquerol. J. Rouquerol, G. Della Gatta and C. Letoquart, Thermochim. Acta 39 (1980) 151. 

The isotherm fields measured could be described with sufficient accuracy by using a modified Langmuir isotherm model, considering the dependence of adsorption enthalpy and adsorption entropy on ACC loading [4]. 

Adsorption entropies may be determined from calorimetric experiments provided that care is taken to ensure reversibility of the heat exchange. 

The numerous values obtained in [6,9-11] would deserve more analysis, discussion and comparison with later data. There are some unexpected trends and deviations in the Aads H values possibly, they originate from ambiguous chemical states of the particular elements. The experimental data on Aac S.S are also of fundamental interest. As will be seen later in this chapter, evaluation of the experiments with TAEs is based on calculation of the adsorption entropy from the first principles. The studies [6,9-11] reported observation of a correlation between the experimental... 

The above equations, especially Eq. 5.54 (and so the mobile adsorption model) obtained wide use in radiochemistry of TAEs. The adsorption entropy was calculated from Eq. 5.33 accepting A/V = 1. Several authors proposed approximate... 

Adsorption Entropy on Heterogeneous Surfaces with Surface Diffusion... 

Pursuing more realistic formulae for calculation of the adsorption enthalpy, we will incorporate the mixed adsorption entropy S /R. From Eqs. 5.42 and 5.70 it follows that the entropy change for the each partial adsorption isotherm is ... 

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