Adsorption equilibrium, methods

Fig. 5.10 TPR profiles of Fe0x/Zr02 (with 5 wt % of Fe) prepared by the impregnation (left) and by adsorption equilibrium method (right)...

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

The material balance was calculated for EtPy, ethyl lactates (EtLa) and CD by solving the set of differential equation derived form the reaction scheme Adam s method was used for the solution of the set of differential equations. The rate constants for the hydrogenation reactions are of pseudo first order. Their value depends on the intrinsic rate constant of the catalytic reaction, the hydrogen pressure, and the adsorption equilibrium constants of all components involved in the hydrogenation. It was assumed that the hydrogen pressure is constant during... 

Using the methods presented in this chapter, adsorbents for energy applications can be evaluated on the basis of the adsorption equilibrium. The possible... 

Several useful methods are available for extrapolating equilibrium data for a given system to various temperatures and pressures. One convenient method is by use of a reference substance plot. Here, the adsorption equilibrium partial pressure of the adsorbate is plotted against a pure substance vapor pressure, preferably that of the adsorbate. If logarithmic coordinates are used on both axes, lines of constant adsorbent loading, isosteres, are linear for most substances. Therefore, only two datum points are required to establish each isostere. 

An enrichment is defined as a separation process that results in the increase in concentration of one or more species in one product stream and the depletion of the same species in the other product stream. Neither high purity nor high recovery of any components is achieved. Gas enrichment can be accomplished with a wide variety of separation methods including, for example, physical absorption, molecular sieve adsorption, equilibrium adsorption, cryogenic distillation, condensation, and membrane permeation. 

A sharp separation results in two high purity, high recovery product streams. No restrictions are placed on the mole fractions of the components to be separated. A separation is considered to be sharp if the ratio of flow rates of a key component in the two products is >10. The separation methods that can potentially obtain a sharp separation in a single step are physical absorption, molecular sieve adsorption, equilibrium adsorption, and cryogenic distillation. Chemical absorption is often used to achieve sharp separations, but is generally limited to situations in which the components to be removed are present in low concentrations. 

Two preferred methods for preparing clean surfaces consist of generating the surfaces under high vacuum at the beginning. Using remote control manipulators to crush a sample under vacuum exposes fresh surface to an environment in which adsorption equilibrium is very slow. This technique produces a heterogeneous array of crystal faces, however. Far more suitable for the specific and localized examination that diffraction methods offer is crystal cleavage... 

Although UHV is required for LEED measurement, there is considerable interest in applying this technique to surfaces that carry adsorbed species. In view of our discussion of adsorption equilibrium above in the chapter, there is a difficulty here since adsorbed molecules imply an equilibrium gas phase. One way around this problem is to study surfaces at a sufficiently low coverage that the equilibrium gas pressure is compatible with the LEED technique. When higher pressures are desired, the surface is first equilibrated, then the excess gas is pumped out, and the surfaces before and after adsorption are compared through LEED. Chemisorption is better suited for study by this method than physical adsorption because the adsorbed layer remains intact when the equilibrium gas is removed. 

Turning now to adsorption equilibrium, let us apply algebraic methods to a two component 1,2 phase system. From the phase rule there will be two degrees of freedom, but we shall reduce this to one by maintaining the temperature constant. Then for the total system there exists a Gibbs-Duhem equation... 

Ikeda et al. (1984b) plotted Eq. (4.42) by determining the equilibrium concentrations from adsorption isotherms for S(H), S(NH4), and NH4, and using the pH value to determine [H+]. This plot shows good linearity (Fig. 4.11), which confirms that the mechanism hypothesized in Eq. (4.40) is operational. The kv and k- values for Eq. (4.42) can then be calculated from the slope and intercept of Fig. 4.11, and the kinetic Keq can be determined from the ratio kjk x (Table 4.2). It is important to notice that the values calculated kinetically and statically (equilibrium method) are similar, which indicates that the rate constants one calculates from p-jump experiments are chemical kinetics rate constants. These data also verify... 

Fundamental studies on the adsorption of supercritical fluids at the gas-solid interface are rarely cited in the supercritical fluid extraction literature. This is most unfortunate since equilibrium shifts induced by gas phase non-ideality in multiphase systems can rarely be totally attributed to solute solubility in the supercritical fluid phase. The partitioning of an adsorbed specie between the interface and gaseous phase can be governed by a complex array of molecular interactions which depend on the relative intensity of the adsorbate-adsorbent interactions, adsorbate-adsorbate association, the sorption of the supercritical fluid at the solid interface, and the solubility of the sorbate in the critical fluid. As we shall demonstrate, competitive adsorption between the sorbate and the supercritical fluid at the gas-solid interface is a significant mechanism which should be considered in the proper design of adsorption/desorption methods which incorporate dense gases as one of the active phases. 

To determine whether a change in dispersion or in the type of catalytic sites is responsible for these different effects of phosphate, Jian and Prins (59, 75) investigated the kinetics of these hydrogenation and elimination reactions. Unfortunately, no simple chemisorption method has proved capable of determining the dispersion of supported metal sulfides (6). Therefore, an indirect method, involving the determination of rate and adsorption equilibrium constants (the first proportional to the number of sites and the second dependent only on the type of site) had to be used. 

Gas chromatographic (GC) methods also provide possibilities to detect the irreversibly held amounts of a poison (51), although these techniques are less accurate than the gravimetric methods. The number of irreversibly adsorbed molecules can be calculated from the material balance for successively injected pulses of the poison and the eluted amounts. Alternatively, adsorption equilibrium can be attained at low temperature, the adsorbed amount being determined by frontal analysis (51). Desorption may then be carried out at the same temperature and the irreversibly held amount can be calculated either from the difference between adsorbed and desorbed amounts of a first cycle or from the difference of the adsorbed amounts of a first and a second adsorption (52). Desorption temperatures can then be raised stepwise after the first desorption and the dependence of the irreversibly adsorbed amounts on desorption temperature determined from the corresponding desorbed amounts. The accuracy of these GC measurements is limited because of the usually very pronounced tailing of the desorption trace for the systems of interest. 

Roginskif suggested a simplified method of analysis for processes occurring on a nonuniform surface which made it possible to surmount these mathematical difficulties without excessive distortion of the physical model. The method has general applicability to statistical processes however, its application to adsorption equilibrium only will be discussed here. 

The lower concentration limit of the applicability of the foam separation method is determined by the lowest residual concentration and depends on the surface activity of the substances, the rate of establishing of the adsorption equilibrium, foam stability and the apparatus used in the process. During foam accumulation the surfactant is extracted from the solution, thus leading to a decrease in foam stability and expansion ratio. Finally, a concentration is reached at which the foam cannot be withdrawn from the apparatus and the accumulation ratio becomes close to 1. 

---