Mobile adsorption entropy

Using the mobile adsorption entropy (Eq. 9) A//ads can be evaluated from at least a pair of experiments at two different isothermal temperatures under otherwise identical experimental conditions. 

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. 

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

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. 

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). 

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. 

Hence, for example, Dollimore etal have considered thermodynamic aspects of the adsorption of organic vapours on graphites and carbon blacks. Heats of adsorption and entropies of adsorbed vapours were determined, and the authors came to the conclusion that mobile adsorption appeared to be very important in the systems. In some ways the observation that C2-C4 hydrocarbons were adsorbed flat on a graphite surface tends to support this conclusion, although Hoory and Praunitz prefer to explain their results in terms of double bond interaction with the graphite.Jonas et al. find... 

When evaluating the entropy change in the mobile adsorption it is assumed that the rotational, vibrational and electronic degrees of freedom of the molecules are preserved. It allows considering only the translational entropy of the surface gas and the entropy of vibrations of its molecules perpendicular to the surface. These oscillations are induced by the characteristic vibration frequency of the adsorbent... 

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... 

The formula 5.32 for the standard entropy of the adsorbate in the mobile adsorption model can be rewritten as ... 

The determination of the adsorption entropy from the isotherms 38) has unexpectedly established that benzene adsorption on porous glass is of a mobile type, with the properties of a two-dimensional ideal gas. Only at low coverages (less than 1 X 10 mole-gm ) the freedom of motion is decreased, and the molecules may be held on definite sites, which is also reflected by an increase in the adsorption energy. 

The adsorption entropy and enthalpy of naphthalene (80 J/molK and 13 kJ/mol, respectively) were higher than the entropy and enthalpy of tetralin (60 J/molK and 5 kJ/mol) or hydrogen (64 J/molK and 5 kJ/mol). The higher enthalpy of naphthalene is indicative of the stronger adsorption of naphthalene, which was also qualitatively observed (see 3.3 Naphthalene and Tetralin Conversion). However, these adsorption parameters indicate that the adsorbed compounds, which are active for the hydrogenation, are fairly mobile on the surface and their adsorption is energetically weak. 

Experimental observations of these empirical correlations clearly prove the postulated proportionality. These correlations suggest a similarity between the bond (with lower coordination) of the adsorbed particles to the modified surface and the bond to the surface of the pure macroscopic phase of the compound, which is relevant for the desublimation process. The adsorption behavior of atoms and compounds for most of the experiments used in the described correlations were evaluated using differently dehned standard adsorption entropies [65-70]. Adsorption data from more recent experimental results were evaluated applying the model of mobile adsorption [4]. Hence, data from previous experiments were re-evaluated using the latter model. These correlations based on estimated standard sublimation enthalpies allow predictions of adsorption enthalpies for selected compounds for the case of zero surface coverage. These results are only valid for experimental conditions using the same reactive gases, and thus, similarly modified stationary surfaces. 

Fig. 7.10 Change of the molar adsorbate entropy as a function of the adsorbed amount for localized and mobile adsorption process. S° is the standard molar entropy of the adsorptive in the gas, liquid or solid state...

The standard entropy of adsorption AS2 of benzene on a certain surface was found to be -25.2 EU at 323.1 K the standard states being the vapor at 1 atm and the film at an area of 22.5 x T per molecule. Discuss, with appropriate calculations, what the state of the adsorbed film might be, particularly as to whether it is mobile or localized. Take the molecular area of benzene to be 22 A. ... 

In general, it seems more reasonable to suppose that in chemisorption specific sites are involved and that therefore definite potential barriers to lateral motion should be present. The adsorption should therefore obey the statistical thermodynamics of a localized state. On the other hand, the kinetics of adsorption and of catalytic processes will depend greatly on the frequency and nature of such surface jumps as do occur. A film can be fairly mobile in this kinetic sense and yet not be expected to show any significant deviation from the configurational entropy of a localized state. 

One notes in Table 1.2 a uniform increase in the adsorption energies of the alkanes when the microspore size decreases (compare 12-ring-channel zeohte MOR with 10-ring-channel TON). However, at the temperature of hydroisomerization the equilibrium constant for adsorption is less in the narrow-pore zeohte than in the wide-pore system. This difference is due to the more limited mobility of the hydrocarbon in the narrow-pore material. This can be used to compute Eq. (1.22b) with the result that the overall hydroisomerization rate in the narrow-pore material is lower than that in the wide-pore material. This entropy-difference-dominated effect is reflected in a substantially decreased hydrocarbon concentration in the narrow-pore material. 

Hence, according to the transition state theory, adsorption becomes more likely if the molecule in the mobile physisorbed precursor state retains its freedom to rotate and vibrate as it did in the gas phase. Of course, this situation corresponds to minimal entropy loss in the adsorption process. In general, the transition from the gas phase into confinement in two dimensions will always be associated with a loss in entropy and the sticking coefficient is normally smaller than unity. 

Clearly, the sticking coefficient for the direct adsorption process is small since a considerable amount of entropy is lost when the molecule is frozen in on an adsorption site. In fact, adsorption of most molecules occurs via a mobile precursor state. Nevertheless, direct adsorption does occur, but it is usually coupled with the activated dissociation of a highly stable molecule. An example is the dissociative adsorption of CH4, with sticking coefScients of the order 10 -10 . In this case the sticking coefficient not only contains the partition functions but also an exponential... 

Transition metal colloids can also be prevented from agglomeration by polymers or oligomers [27,30,42,43]. The adsorption of these molecules at the surface of the particles provides a protective layer. In the interparticle space, the mobility of adsorbed molecules should be reduced decreasing the entropy and thus increasing the free energy (Fig. 2). 

An example illustrates the usefulness of Table II. Suppose a certain adsorption reaction is 0.5 order, and it is concluded that dissociation accompanies adsorption that is. Step 2 applies. Suppose also that L has been found by a nonkinetic method to be 10 sites cm, and that according to TST L is calculated to be 10 sites cm . To decrease the calculated value of L by a factor of 100 means that AS (a negative quantity) as calculated from the model is 18.4 e.u. (that is, 2 x 9.2 e.u.) too low. Thus, in this example the gas did not lose as much entropy upon adsorption as had been supposed. Such a result could indicate that the dissociated fragments are mobile, not limited to fixed sites. 

The inner structure of polyelectrolyte multilayer films has been studied by neutron and X-ray reflectivity experiments by intercalating deuterated PSS into a nondeut-erated PSS/PAH assembly [94, 99]. An important lesson from these experiments is that polyelectrolytes in PEMs do not present well-defined layers but are rather interpenetrated or fussy systems. As a consequence, polyelectrolyte chains deposited in an adsorption step are intertwined with those deposited in the three or four previous adsorption cycles. When polyelectrolyte mobility is increased by immersion in NaCl 0.8 M, the interpenetration increases with time as the system evolves towards a fully mixed state in order to maximize its entropy ]100]. From the point of view of redox PEMs, polyelectrolyte interpenetration is advantageous in the sense that two layers of a redox polyelectrolyte can be in electrochemical contact even if they are separated by one or more layers of an electroinactive poly ion. For example, electrical connectivity between a layer of a redox polymer and the electrode is maintained even when separated by up to 2.5 insulating bUayers [67, 101-103]. 

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