Equilibrium of adsorption

Equilibrium of Adsorption, (a) The Soap Films. The isotherms of adsorption of the organic cations of the soaps are reproduced on the Figure 2. Classical methods (20) are used to obtain the surface densities of the soaps I and IV. 

The kinetics and the equilibrium of adsorption of anions PoCl62" by ionized monolayers of cationic soaps have been studied and both phenomena are analogous to those observed with the polymer ion exchangers... 

From simple measurements of the rate of a photocatalytic reaction as a function of the concentration of a given reactant or product, valuable information can be derived. For example, these measurements should allow one to know whether the active species of an adsorbed reactant are dissociated or not (22), whether the various reactants are adsorbed on the same surface sites or on different sites (23), and whether a given product inhibits the reaction by adsorbing on the same sites as those of the reactants. Referring to kinetic models is therefore necessary. The Langmuir-Hinshelwood model, which indicates that the reaction takes place between both reactants at their equilibrium of adsorption, has often been used to interpret kinetic results of photocatalytic reactions in gaseous or liquid phase. A contribution of the Eley-Rideal mechanism (the reaction between one nonadsorbed reactant and one adsorbed reactant) has sometimes been proposed. 

When an outgassed solid (the adsorbent) is confined to a closed space and exposed to a gas or vapor (the adsorptive) at a given pressure and temperature, an adsorption process takes place. The adsorptive molecules are transferred to, and accumulate in, the interfacial layer, as a consequence of an attractive force between the surface of the solid and the adsorptive (the adsorptive actually adsorbed by the adsorbent is named adsorbate). After some time, the pressure becomes constant and the thermodynamic equilibrium of adsorption is achieved. 

The quantitative difference in adsorption behavior of linear polymers between alkaline and acidic conditions can be verified from surface plasmon resonance (SPR) results [111]. As seen in Fig. 6, the adsorption kinetics change along any profile of rapid saturation, gradual increase after rapid increase or gradual increase, depending on the type of linear polymers. The equilibrium of adsorption is reached faster for NaPGA and NaHA than for DNA. However, the film at equilibrium is thicker at acidic condition than at alkaline condition. The quantitative estimation of adsorption of DNA on dendrimer SAMs can be also carried out from the intensity increase of a UV-vis absorption band at 258.8 nm [110]. 

The primary requirement for an economic separation process is an adsorbent with high selectivity and capacity. The selectivity may depend upon differences in either kinetics or thermodynamic equilibrium of adsorption. Differences in diffusion rates between molecules, due to steric effects, can be large enough to provide transient selectivity. The separation factor is the ratio between the diffusion coefficients of the molecules. 

In Chap. 8 heterogeneous catalysis was explained by postulating a three-step process (1) chemisorption of at least one reactant on the solid, (2) surface reaction of the chemisorbed substance, and (3) desorption of the product from the catalytic surface. Now our objective is to formulate rate and equilibrium equations for these steps. We shall consider the kinetics and equilibrium of adsorption and then examine rate equations for the overall reaction. 

For data obtained at equilibrium of adsorption on faces, thermodynamic analysis is possible and is more valid than for polycrystalline electrodes because the distribution of the charge density is controled (uniform) at the electrode surface (see Sections V.l and V.2). 

Equilibria. Equilibrium of adsorption on solids is usually represented by an adsorption isotherm, which shows the concentration of the respective species on or in the solid as a function of its concentration in the contacting fluid at constant temperature (see Section 2.6 for details). 

Equilibrium of adsorption on a solid is characterized by an adsorption isotherm, which shows the concentration on the solid as a function of the concentration in the contacting fluid. A quantitative measure of uptake of a gaseous species by a liquid is the distribution coefficient, defined as the ratio of the concentration on the solid to that in the contacting fluid. If concentration-independent, the coefficient is also called Henry coefficient. Diffusion of a species in a porous solid is expressed in terms of an effective diffusion coefficient, whose value accounts for the retardation by the solid matrix. Mass transfer to or from a solid is expressed in terms of a mass-transfer coefficient, the flux being the product of that coefficient and a concentration difference as "driving force."... 

The software of the PAT1 allows the programming of a complete sequence of experiments, such as transient and harmonic relaxations after the equilibrium of adsorption has been established. The oscillations were usually performed at various frequencies, so that sufficient data for the dilational rheology were available. A typical result, as an example, is shown for / -LG in Figure 5, where... 

Stationary hanging mercury drop electrodes (h.m.d.e.) are suitable for evaluating a slow equilibrium of adsorption and subsequent reduction. Solid metal or graphite electrodes are used mainly for oxidation. From the molecular biophysical point of view such measurements are performed for characterization of structural and conformational transitions caused by physical and electrochemical influences, such as heat, light, electrical fields, solvents, ions, and other ligands. In all cases, one can distinguish between reversible (allosteric and conformational modifications) and irreversible (denaturation, strand break, enzyme reactions) processes. Besides these investigations, biochemical analysis, clinical tests, and electrochemical synthesis are fruitful applications. 

Under the natural conditions. Coal-bed methane in coal is in the dynamic equilibrium of adsorption and resolution. The change of coal body temperature depends on the adsorption heat and... 

The Langmuir s isotherm is one of the most common models used to represent equilibrium behavior in the adsorption process. Its main concept proposes the uniformity in terms of surface adsorption sites with adsorption monolayers. Also considered independent interactions of neighboring sites and possibilities of dynamic equilibrium of adsorption and desorption (Fogler, 2002 Ruthven, 1984). 

Lao, M.Z., and Ye, Z.H., Phase equilibrium of adsorption separation of xylene isomers with type-Y zeolites. Chem. Eng. Commun., 35(1). 89-100 (1985). 

If the interaction of one of the enantiomers is only small, it will not be adsorbed and, in extreme cases, can be eluted within the void time. However, in most cases both enantiomers show some retention, requiring an equilibrium of adsorption and desorption. In some cases, one might observe that one or both of the enantiomers are strongly adsorbed and are not eluted during the run time of the... 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

As also noted in the preceding chapter, it is customary to divide adsorption into two broad classes, namely, physical adsorption and chemisorption. Physical adsorption equilibrium is very rapid in attainment (except when limited by mass transport rates in the gas phase or within a porous adsorbent) and is reversible, the adsorbate being removable without change by lowering the pressure (there may be hysteresis in the case of a porous solid). It is supposed that this type of adsorption occurs as a result of the same type of relatively nonspecific intermolecular forces that are responsible for the condensation of a vapor to a liquid, and in physical adsorption the heat of adsorption should be in the range of heats of condensation. Physical adsorption is usually important only for gases below their critical temperature, that is, for vapors. 

As is made evident in the next section, there is no sharp dividing line between these two types of adsorption, although the extremes are easily distinguishable. It is true that most of the experimental work has tended to cluster at these extremes, but this is more a reflection of practical interests and of human nature than of anything else. At any rate, although this chapter is ostensibly devoted to physical adsorption, much of the material can be applied to chemisorption as well. For the moment, we do assume that the adsorption process is reversible in the sense that equilibrium is reached and that on desorption the adsorbate is recovered unchanged. 

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

The quantity 2 has been called (by Hill) the equilibrium heat of adsorption. It follows from the foregoing definitions that... 

A(liquid adsorbate at 7 ) = (adsorbed, in equilibrium with pressure P, at T) for 6 values of 0.1 and 1.5. Calculate also the entropies of adsorption for the same... 

Detailed derivations of the isothemi can be found in many textbooks and exploit either statistical themio-dynaniic methods [1] or independently consider the kinetics of adsorption and desorption in each layer and set these equal to define the equilibrium coverage as a function of pressure [14]. The most conmion fomi of BET isothemi is written as a linear equation and given by ... 

The term heat of adsorption has been defined in a number of different ways. Unfortunately, the initial and final states of the adsorption system and the conditions under which the exchange of heat takes place have not always been adequately defined. As in all applications of thermodynamics, it is essential that the experimental data refer to a system which has reached equilibrium. 

The BET treatment is based on a kinetic model of the adsorption process put forward more than sixty years ago by Langmuir, in which the surface of the solid was regarded as an array of adsorption sites. A state of dynamic equilibrium was postulated in which the rate at which molecules arriving from the gas phrase and condensing on to bare sites is equal to the rate at which molecules evaporate from occupied sites. 

Picture the transfer, under equilibrium conditions, of dn mole of adsorptive from the bulk liquid where its chemical potential is /i , to a... 

H2O/100 kg of adsorbent. At equilibrium and at a given adsorbed water content, the dew point that can be obtained in the treated fluid is a function only of the adsorbent temperature. The slopes of the isosteres indicate that the capacity of molecular sieves is less temperature sensitive than that of siUca gel or activated alumina. In another type of isostere plot, the natural logarithm of the vapor pressure of water in equiUbrium with the desiccant is plotted against the reciprocal of absolute temperature. The slopes of these isosteres are proportional to the isosteric heats of adsorption of water on the desiccant (see... 

---