Adsorption thermodynamic functions

It has long been known that the adsorption of a gas on a solid surface is always accompanied by the evolution of heat. Various attempts have been made to arrive at a satisfactory thermodynamic analysis of heat of adsorption data, and within the past few years broad agreement has been achieved in setting up a general system of adsorption thermodynamics. Here we are not concerned with the derivation of the various thermodynamic functions but only with the more relevant definitions and the principles involved in the thermodynamic analysis of adsorption data. For more detailed treatments, appropriate texts should be consulted. " ... 

Adsorption and Transport of Polyatomic Species in One-dimensional Systems Exact Forms of the Thermodynamic Functions and Chemical Diffusion Coefficient... 

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. 

A Physical Research Technique. It may be used to investigate various parameters of a system, for example, determination of partition coefficients, thermodynamic functions, and adsorption isotherms. 

In analogy to what we did for solutions, we define the change in a thermodynamic function upon adsorption as... 

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 equilibrium thermodynamic functions describing the retention process are essentially related to the net retention volume. For example, the intermolecular adsorption of Gibbs free energy, —AGa, for one mole of solute vapor from a reference gaseous state with the partial pressure, Po, to a reference adsorbed state with the equilibrium spread pressure (or two-dimensional pressure), no, is given as [115]... 

W have previously reported (3, 5) studies of the adsorption of argon at 77° and 90° K on muscovite mica which had been treated to replace the exchangeable surface potassium ions with other cations. The adsorption isotherms and thermodynamic functions evaluated from them showed significant differences among the various ion exchanged forms of mica. We have now obtained data for the adsorption of krypton on these substrates, and wish to discuss the differences in the behavior of the argon-mica and krypton-mica systems. 

Adsorption isotherms for the system BaS04-H20 at three temperatures have been obtained. Thermodynamic study of these data reveals that part of the free energy decrease in the adsorption process involves changes in the partial molal free energy of the adsorbent. From the three isotherms differential and integral heats of adsorption were derived and compared with new calorimetric determinations of the same thermodynamic functions. In both kinds of measurements exactly the same system and exactly the same materials were used. 

Figure 8 shows a result for the simulation of a TPD for typical parameters (96). For a flow rate of 5.0 cm /s, the positions of the response curves are considerably altered in passing from 0.04-cm particles to 0.2-cm particles or for the large particles in passing from a flow rate of 5.0 cm /s to 0.5 cm /s. However, for the low flow rate, the curves are little altered by changing the particle size. In this case, the changes in concentration induced by the flow (qpp/W) are small compared with the rates of diffusion, represented by DJdj. However, this TPD is so slow that the rate of adsorption is similar to the rate of desorption. The gas and surface phases are in quasiequilibrium. This type of TPD has been performed for the desorption of H2 held on Rh/A Os the results are shown in Fig. 9 (98). It is shown that the rate of adsorption is much greater than the net rate of desorption, which permits the use of the data of Fig. 9 to find the thermodynamic functions and A5°(0). A//°(0) decreases from a maximum at low...

We next take up the topic of adsorption of gases on surfaces. This problem is not only of intrinsic interest but also provides valuable pedagogical insight on the systematics that obtain for the many choices for thermodynamic functions of state. These involve new degrees of freedom that are needed to characterize the adsorption process. Accordingly, we consider a system consisting of a very thin layer of atoms held on the surface of a material exposed to a gas phase. The bulk solid or liquid is termed the adsorbent, while the material held on its surface is termed the adsorbate. The process by which material is transferred from the gas to the surface phase is called adsorption. 

The thermodynamic functions for items 1 and 2 are calculated using the standard equations for bulk gases and solids, respectively, so that the focus for adsorption thermodynamics is on item 3. It follows from Equations (5) and (7) that the grand potential (free energy of immersion) for each pure component is... 

Zero Coverage. Inverse gas chromatography has been used successfully In the past decade for studying the surface properties of solids by adsorption of vapour at a gas-solid Interface. Unlike conventional adsorption techniques, IGC allows the measurement of adsorption data down to low vapour concentrations where the surface coverage approaches zero, adsorbate-adsorbate Interactions are negligible, and thermodynamic functions depend on only adsorbate-adsorbent Interactions. 

Quinones et al. [17] measured by frontal analysis multisolute adsorption equilibrium data for the system benzyl alcohol, 2-phenylethanol and 2-methyl benzyl alcohol in a reversed-phase system. Data were acquired for the pure compoimds, for nine binary mixtures (1 3,1 1, and 3 1) and four ternary mixtures (1 1 3,1 3 1, 3 1 1, and 1 1 1). These data exhibited very good thermod5mamic consistency. The thermodynamic functions of adsorption were derived from the single-solute ad-... 

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... 

The features of the theoretical BET isotherm are well-known, but the related features of other thermodynamic functions have been rarely discussed, for instance, the corresponding expression for the isosteric heat of adsorption Qst. ... 

Calculation of thermodynamic functions for adsorption on homogeneous surface... 

Surface phase capacity, i.e., the total amount of substances in the adsorbed phase is the second factor determining the sorption properties of the solid sorbents. This quantity is useful for calculating thermodynamic functions which characterize competitive adsorption at the liquid - solid interface and for determining the specific surface area of the sorbents. 

The analytical forms of the adsorption isotherms and energy distribution functions given by Eqs.(3-6) were presented in our review [1]. By means of these equations there can be obtained the energy distribution function and parameter n which are important characterizations for the experimental adsorption systems. Consequently, by means of the functions F(Ei2) and the parameters n one can obtain quantitative characterization of the adsorbent heterogeneity, sorption properties of the solid, possibility to calculate the surface phase composition and potentiality for calculating the thermodynamic functions which characterize adsorption at the solid - liquid interface. 

The kinetics of the disproportionation of NbClj have been investigated, as have those of the reaction between NbCl3 and NbCls. Thermodynamic functions have been calculated for MX5 (M = Nb or Ta X = Cl or Br)/ The rate-controlling step in the formation of NbClj from Nb and CI2 is the adsorption of CI2 on the metal surface/ In the analogous reaction with Ta, TaC is produced/ ... 

The relationships between CMC and various thermodynamic functions discussed above are also relevant to the adsorption of surfactants at soUd/liquid interfaces and will be discussed later. 

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