Adsorption molecular theory

Bockris, J. O M., Gileadi, E. and Muller, K. (1967) A molecular theory of the charge dependence of competitive adsorption. Electrochim. Acta, 12, 1301-1321. 

The rate constant for adsorption, A , is also temperature dependent, but the dependence is small compared to that for k r The value and temperature dependence of k, are determined by the rate of gas-solid collisions, which from kinetic molecular theory is given by... 

A number of related non-ideal adsorption isotherms have been proposed in order to fit experimental data of adsorption at electrodes and a review is presented in ref. 107. Recently, a simplified molecular theory of solute adsorption at polarizable electrode interface has been presented by Fawcet and Nobriga [108]. 

Fawcet has recently applied a simple molecular theory of solute adsorption at electrodes to the kinetics of electrode reactions under the effect of SAS [125]. 

There are several theories as to the constitution of the silver subhalides in the latent image. The molecular theory regards the subhalides as definite chemical compounds. The adsorption theory regards them as adsorption-compounds of colloidal silver and subhalides. The molecular theory is advocated by Trivelli,1 who considers the colour-changes to indicate the existence of several silver subhalides, which yield solid solutions with each other and with the silver halides. He also regards the mechanism of reduction with ammonium persulphate as favouring the molecular theory. 

W.A. Steele. The Interaction of Gases with Solid Surfaces, Pergamon Press (1974). (Thermodynamical and statistical theories for gas adsorption, molecular beam scattering from surfaces.)... 

The development of the molecular theory of adsorption should consist of the follov ing aspects ... 

Various complex curves can be satisfactorily approximated by equations of the la and 2 type. However, the second stage in the development of the molecular theory of adsorption concerns the determination of Ki and K2 or Cl and C2, which must depend only on the properties of the system (the structure of the adsorbent and adsorbate molecule) and be independent of the fitting procedure. With the aid of Equation 2, therefore, one can obtain values for Ci and C2 which are practically independent of the number of terms within the series and of the interval of experimental values of a (beginning at a low coverage). Figure 4 shows an example illustrating the determination of Ci. 

The examples cited in this review show that all stages of the development of the molecular theory of adsorption mentioned above have been studied to a limited extent for the adsorbate-zeolite system. The examples also show, however, that in order to determine experimentally the stable constants and to establish their dependence on the details of the zeolite structure and the structure of the adsorbate molecule, more systematic investigations will be needed. 

A. V. Kiselev Zeolites are porous crystals. This means that we can find the molecular field distribution in their channels. The advantage of describing the adsorption on zeolites using the molecular theory consists in obtaining the constants which have a definite physical meaning (for example, the Henry constant and second virial coefficient). Further development of the theory needs a further improvement of the model based on the investigation of the adsorbate-zeolite systems by the use of modern physical methods. 

Again, we do not exhaustively discuss molecular theories of diffusion and adsorption in zeolites but refer to other studies [32-34]. However, we highlight some important results significant to the kinetic analysis we are presenting. 

Nicholson, D. (1975). Molecular theory of adsorption in pore spaces. Part 1. Isotherms for simple lattice models. J. Chem. Soc. FaradayTrans. I, 71, 238-55. Saam, W.F. and Cole, M.W. (1975). Excitations and thermodynamics for liquid-helium films. Phys. Rev. B, 11, 1086-105. 

The Dubinin-Radushkevich (DR) equation was originally devised as an empirical expression of the Polanyi adsorption potential theory, and due to its simplicity it has been widely used to correlate adsorption data in many microporous sohds despite its failure in giving the correct Henry constant at extremely low pressures. This equation is based on the premise that adsorption in micropores follows a mechanism of pore filhng rather than the molecular layering and capillary condensation as proposed for mesoporous sofids. It has the form ... 

The most recent experimental work has involved studies of organic adsorption at the single crystal faces of polarizable solid metal electrodes [57]. These experiments provide details of the role of the metal in organic adsorption. By examining these data within the context of the new molecular descriptions of interfacial adsorption the theory of this important process will be greatly advanced. 

Tompkins (1978) concentrates on the fundamental and experimental aspects of the chemisorption of gases on metals. The book covers techniques for the preparation and maintenance of clean metal surfaces, the basic principles of the adsorption process, thermal accommodation and molecular beam scattering, desorption phenomena, adsorption isotherms, heats of chemisorption, thermodynamics of chemisorption, statistical thermodynamics of adsorption, electronic theory of metals, electronic theory of metal surfaces, perturbation of surface electronic properties by chemisorption, low energy electron diffraction (LEED), infra-red spectroscopy of chemisorbed molecules, field emmission microscopy, field ion microscopy, mobility of species, electron impact auger spectroscopy. X-ray and ultra-violet photoelectron spectroscopy, ion neutralization spectroscopy, electron energy loss spectroscopy, appearance potential spectroscopy, electronic properties of adsorbed layers. 

For many years the relationship between the strength and the molecular structure of the solvent has been considered an important question. Our present interest in this matter is both practical and fundamental. We would like to be able to predict solvent strength when direct experimental data are unavailable, and the fundamental basis of solvent strength is related to the general theory of adsorption. Any theory of solvent... 

In any case there is still a long way until the development of a truly satisfactory molecular theory capable of predicting a priori and quantitatively the adsorption features of any solute. Until that occurs, the two trends mentioned above, together with computer simulations, will co-exist for different scopes The first trend for analyzing experimental data, and for applications to complicated adsorption phenomena as well as to interfacial phenomena affected by adsorption. The second trend along with computer simulations for a better understanding of the molecular nature of the adsorption on electrodes. 

Molecular-based theories are useful for developing rational stabilizer design criteria and investigating the correlation with bulk phase behavior for stabilizers in supercritical fluids. Molecular theories of polymer adsorption, such as the lattice self-consistent field (SCF) theory of Scheutjens and Fleer[69], allow chain structure, adsorption energy, solubility, length, and concentration to be varied independently. Simulation, while more computationally intensive, offers the additional advantages of... 

Having reviewed the properties of single adsorption monolayers, we proceed with the couples of interacting monolayers the thin liquid films. First, we present the thermodynamics of thin films, and then we describe the molecular theory of the surface forces acting in the thin films. We do not restrict ourselves to the conventional DLVO (Deijaguin, Landau, Verwey, Overbeek) forces [2,3], but consider also the variety of the more recently discovered non-DLVO surface forces [4]. The importance of the micelle-micelle interaction for the mechanism of micelle growth is also discussed. 

In this section, we review the molecular theory of surface forces with special attention to the effect of surfactant adsorption and surfactant micelles on the interactions in the thin liquid films and between the particles in dispersions. 

Unfortunately, problems of the adsorption or molecular theory of adhesion are in most instances solved exclusively at the qualitative level and are limited to consideration of a role of the polarity of components in adhesion (the so-called polarity rule high adhesion cannot be achieved between a polar substrate and apolar adhesive, and vice versa). It is very unfortunate that in many books on adhesion the description of adhesion is not given at the molecular level, which is now accessible for the description of intermolecular interactions in liquids and solids. At the same time, it is obvious that from a physical point of view the adsorption theory presents a rather correct concept of interfacial phenomena and agrees with thermodynamics. Within this context, adhesion can be regarded as a particular case of adsorption, inasmuch as the formation of molecular bonds at... 

By combining a number of experimental techniques the role of hydrophobic bonding in surfactant adsorption is better defined. The results can be interpreted with a new molecular theory. 

A continuum description becomes increasingly inaccurate as distances from the interface become comparable to the size of a solute molecule. Another crude concept used in simple continuum models of interfaces for calculating adsorption free energy and electronic spectra involves the use of an effective interfacial dielectric constant. For example, the reduced orientational freedom of interfacial water molecules and their reduced density result in a smaller effective dielectric constant than in the bulk. This is consistent with assigning the water liquid/vapor a polarity value similar to that of CCI4. Finally, we mention that a molecular theory of a local dielectric constant, which reproduces interfacial electric fields, can be developed with the aid of molecular dynamics simulation as described by Shiratori and Morita. ... 

Solvation behavior can be effectively predicted using electronic structure methods coupled with solvation methods, for example, the combination of continuum solvation methods such as COSMO with DFT as implemented in DMoF of Accelrys Materials Studio. An attractive alternative is statistical-mechanical 3D-RISM-KH molecular theory of solvation that predicts, from the first principles, the solvation structure and thermodynamics of solvated macromolecules with full molecular detail at the level of molecular simulation. In particular, this is illustrated here on the adsorption of bitumen fragments on zeolite nanoparticles. Furthermore, we have shown that the self-consistent field combinations of the KS-DFT and the OFE method with 3D-RISM-KH can predict electronic and solvation structure, and properties of various macromolecules in solution in a wide range of solvent composition and thermodynamic conditions. This includes the electronic structure, geometry optimization, reaction modeling with transition states, spectroscopic properties, adsorption strength and arrangement, supramolecular self-assembly,"and other effects for macromolecular systems in pure solvents, solvent mixtures, electrolyte solutions, " ionic liquids, and simple and complex solvents confined in nanoporous materials. Currently, the self-consistent field KS-DFT/3D-RISM-KH multiscale method is available only in the ADF software. 

The following several sections deal with various theories or models for adsorption. It turns out that not only is the adsorption isotherm the most convenient form in which to obtain and plot experimental data, but it is also the form in which theoretical treatments are most easily developed. One of the first demands of a theory for adsorption then, is that it give an experimentally correct adsorption isotherm. Later, it is shown that this test is insufficient and that a more sensitive test of the various models requires a consideration of how the energy and entropy of adsorption vary with the amount adsorbed. Nowadays, a further expectation is that the model not violate the molecular picture revealed by surface diffraction, microscopy, and spectroscopy data, see Chapter VIII and Section XVIII-2 Steele [8] discusses this picture with particular reference to physical adsorption. 

Mention was made in Section XVIII-2E of programmed desorption this technique gives specific information about both the adsorption and the desorption of specific molecular states, at least when applied to single-crystal surfaces. The kinetic theory involved is essentially that used in Section XVI-3A. It will be recalled that the adsorption rate was there taken to be simply the rate at which molecules from the gas phase would strike a site area times the fraction of unoccupied sites. If the adsorption is activated, the fraction of molecules hitting and sticking that can proceed to a chemisorbed state is given by exp(-E /RT). The adsorption rate constant of Eq. XVII-13 becomes... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

In contrast to trace impurity removal, the use of adsorption for bulk separation in the liquid phase on a commercial scale is a relatively recent development. The first commercial operation occurred in 1964 with the advent of the UOP Molex process for recovery of high purity / -paraffins (6—8). Since that time, bulk adsorptive separation of liquids has been used to solve a broad range of problems, including individual isomer separations and class separations. The commercial availability of synthetic molecular sieves and ion-exchange resins and the development of novel process concepts have been the two significant factors in the success of these processes. This article is devoted mainly to the theory and operation of these Hquid-phase bulk adsorptive separation processes. 

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