Adsorption entropy functions

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 ... 

Heat and Entropy Functions. Both differential and integral heats and entropies of adsorption were evaluated from the data for argon adsorption on muscovite (3). The variations in these functions with coverage for the potassium and barium muscovite were discussed in terms of localized adsorption on the various kinds of geometrical sites on the mica surface. On the cesium mica, however, the heat of adsorption of argon was higher and more uniform than on the potassium and barium micas, and the entropy functions showed a monotonic decrease with coverage. 

We may assume that both argon and krypton adsorbed on mica are essentially two-dimensional liquids at the completion of the first monolayer (2, 4). The rise in the entropy functions for argon adsorption on potassium and barium mica as the monolayer point is approached may then reflect the transition from substantially localized adsorption at lower coverages to a mobile film. No such phenomenon is observed with krypton, suggesting that there is no change in the behavior of the adsorbed phase during formation of most of the first monolayer. 

It has been shown recently that the adsorption equilibrium function (/) can be used to obtain information on the thermodynamics of chemisorption processes as they occur during a catalytic reaction 2). Thus, the free energy, enthalpy, and entropy of oxygen chemisorption on nickel, platinum, and silver surfaces were determined while these surfaces were being used for the catalytic decomposition of water. 

The work of adsorption is determined from Eq. (1) by using the Hnear section of the surface pressure curve as a function of the bulk concentration of the surfactant (the surface pressure does not exceed 3mN/M). The values obtained for the work of adsorption are usually compared with the values obtained for certain fractional surface coverages. Thus, it becomes possible to estimate the change in the free energy as a function of the molecular interaction in the monolayer. (The relation between the values of the work of adsorption determined from different isotherms is discussed in Refs. [37-39]). The adsorption entropy and enthalpy are determined from the temperature dependence of the work of adsorption [36-39]. 

The set of curves of adsorption entropy are represented in Fig. 38d. The change in comparison to perfect mixtures is clearly indicated by the appearance of a shoulder in the intermediate region of the function. 

FIGURE 3.5 Coverage of species A plotted as a function of pressure at three different values of adsorption enthalpy, A//. The temperature is 300 K and the standard adsorption entropy is... 

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

We again assume that the pre-exponential factor and the entropy contributions do not depend on temperature. This assumption is not strictly correct but, as we shall see in Chapter 3, the latter dependence is much weaker than that of the energy in the exponential terms. The normalized activation energy is also shown in Fig. 2.11 as a function of mole fraction. Notice that the activation energy is not just that of the rate-limiting step. It also depends on the adsorption enthalpies of the steps prior to the rate-limiting step and the coverages. 

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... 

We assumed earlier that both the concentrations and the entropies of adsorption are similar for the two gases. Then the partition functions are about the same and Eq. (49) can be simplified ... 

The differential molar entropies can be plotted as a function of the coverage. Adsorption is always exothermic and takes place with a decrease in both free energy (AG < 0) and entropy (AS < 0). With respect to the adsorbate, the gas-solid interaction results in a decrease in entropy of the system. The cooperative orientation of surface-adsorbate bonds provides a further entropy decrease. The integral molar entropy of adsorption 5 and the differential molar entropy are related by the formula = d(n S )ldn for the particular adsorbed amount n. The quantity can be calculated from... 

The thermodynamic functions of fc-mers adsorbed in a simple model of quasi-one-dimensional nanotubes s adsorption potential are exactly evaluated. The adsorption sites are assumed to lie in a regular one-dimensional space, and calculations are carried out in the lattice-gas approximation. The coverage and temperature dependance of the free energy, chemical potential and entropy are given. The collective relaxation of density fluctuations is addressed the dependence of chemical diffusion coefficient on coverage and adsorbate size is calculated rigorously and related to features of the configurational entropy. 

Here, AH(A-B) is the partial molar net adsorption enthalpy associated with the transformation of 1 mol of the pure metal A in its standard state into the state of zero coverage on the surface of the electrode material B, ASVjbr is the difference in the vibrational entropies in the above states, n is the number of electrons involved in the electrode process, F the Faraday constant, and Am the surface of 1 mol of A as a mono layer on the electrode metal B [70]. For the calculation of the thermodynamic functions in (12), a number of models were used in [70] and calculations were performed for Ni-, Cu-, Pd-, Ag-, Pt-, and Au-electrodes and the micro components Hg, Tl, Pb, Bi, and Po, confirming the decisive influence of the choice of the electrode material on the deposition potential. For Pd and Pt, particularly large, positive values of E5o% were calculated, larger than the standard electrode potentials tabulated for these elements. This makes these electrode materials the prime choice for practical applications. An application of the same model to the superheavy elements still needs to be done, but one can anticipate that the preference for Pd and Pt will persist. The latter are metals in which, due to the formation of the metallic bond, almost or completely filled d orbitals are broken up, such that these metals tend in an extreme way towards the formation of intermetallic compounds with sp-metals. The perspective is to make use of the Pd or Pt in form of a tape on which the tracer activities are electrodeposited and the deposition zone is subsequently stepped between pairs of Si detectors for a-spectroscopy and SF measurements. 

The integral heats and entropies of adsorption for water on fused quartz powder have been obtained as a function of particle size. In the light of previous studies, this is indicative of identical surface structure for all samples studied. The results further indicate that many crystalline quartz powders are amorphous in their surface layers. 

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