Determination of Adsorption Isotherms

Both volumetric and gravimetric techniques have been used for the determination of adsorption isotherms of gases on solids. The volumetric technique is one of the widely used methods for the adsorption isotherm determination and is based on the measurement of the pressure-volume relation to determine the 

Typical gravimetric units for both sub-atmosphere and high pressure measurements of equilibrium adsorption isotherms are shown schematically in Fig. 3.5 [1,15]. The all-glass sub-atmosphere unit is housed in an insulated constant temperature box free from any kind of disturbance, either mechanical or thermal. The unit contains a Cahn 2000 electrobalance with sensitivity of 10 g for 

The volumetric unit shown in Fig. 3.6 is typically used for the determination of the BET surface area. The major parts of the unit are shown in the figure. Detailed description of the operation of the volumetric unit can be found in Lippens et al. [16]. 

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The determination of adsorption isotherms at liquid-solid interfaces involves a mass balance on the amount of polymer added to the dispersion, which requires the separation of the liquid phase from the particle phase. Centrifugation is often used for this separation, under the assumption that the adsorption-desorption equilibrium does not change during this process. Serum replacement (6) allows the separation of the liquid phase without assumptions as to the configuration of the adsorbed polymer molecules. This method has been used to determine the adsorption isotherms of anionic and nonionic emulsifiers on various types of latex particles (7,8). This paper describes the adsorption of fully and partially hydrolyzed PVA on different-size PS latex particles. PS latex was chosen over polyvinyl acetate (PVAc) latex because of its well-characterized surface PVAc latexes will be studied later. 

The determination of adsorption isotherms offers the possibility to study the atmospheric corrosion process when the metal is covered by a corrosion products layer. 

The application of the volumetric method for the determination of adsorption isotherms can be performed as follows. First, the adsorbate gas is introduced into the manifold volume, V and the quantity dosed is measured, usually in cubic centimeters at STP, that, is, standard temperature and pressure, specifically 273.15 K and 1.01325 x 10 Pa... 

The determination of adsorption isotherms is less tedious than is often considered, and in some case, a simple first approximation based on a few experimental results enables us to immediately acquire interesting first process designs. 

The increased concentration of the inhibitor in the surface layer relative to the bulk solution is caused by adsorption. The adsorption may be at a kink, step, or terrace site and be effective in influencing the step velocity. Unfortunately, the experimental determination of adsorption isotherms of inhibitors is rare and the approach in the past has been to try and obtain information indirectly from the analysis of crystal growth data. 

Reactions, the determination of adsorption isotherms and the calibration of the humidity sensor were performed in a batch reaction system of a total volume of 168 ml or 178 ml depending on the size of the enzyme reactor (Figure... 

The first step is devoted to the determination of adsorption isotherms. Several adsorption isotherm determination methods have been described [13], and we developed a laboratory apparatus allowing to determine very precise adsorption isotherms in supercritical fluids. 

We may divide the experimental techniques available for the study of adsorption from solution into three main categories (a) for the determination of adsorption isotherms, (b) for the measurement of the energies involved, and (c) for the provision of extra information on the properties of the adsorbed layer. 

The presence of surface OH groups or H2 O molecules can play a primary role in adsorption. For example, a microcalorimetric study of the adsorption of stearic acid, from heptane solution, on ferric oxide (Husbands et al., 1971) revealed that preadsorbed water enhanced adsorption of stearic acid. When adsorption takes place from a dry organic liquid, residual surface water may act as special agent. This was shown for the adsorption of a silane coupling agent (y-amino-propyl-triethoxysilane) on silica covered with water molecules for 6 < 1 (Trens and Denoyel, 1996). By the simultaneous determination of adsorption isotherms and the enthalpies of displacement (of heptane by various silanes) it was demonstrated that the amine function was able to displace some of the surface water and make it available for the hydrolysis of the silane into trisilanol, whereas the residual water was able to promote the formation of siloxane bonds between the trisilanol molecules and the surface. 

The aim of this chapter is to highlight current developments in these various fields of preparative HPLC, with particular emphasis on applications that have been developed at Chemical Analytical Development at Novartis Pharma AG. Drug substance purifications from biological and synthetic sources are presented, along with the separation of chiral and/or achiral molecules on chiral stationary phases and typical isolations of by-products. Special attention is given to the determination of adsorption isotherms and their interplay with respect to the layout of chromatographic processes as well as the choice of... 

Figure 21-6. Experimental setup of ECP (a), MDM (b), and ADM (c) method for the determination of adsorption isotherms. The concentration-time relation of the dispersed taU in the ECP approach (a) is completely defined by the course of the adsorption isotherm, as can be visuahzed by the injection of increasing samples amounts. Solvent injections at defined concentrations will result in pulses in the MDM approach (b) which are linked to the adsorption isotherms. Although very precise during application of the ADM method, the data points of the adsorption isotherms (c) have to be measnred individually.

Several methods allowing the determination of adsorption isotherms exist. The most economical one is the use of saturated salt solutions, generating known water partial pressures, followed by the measurement of the silica weight uptake. However, the time needed to obtain a suitable adsorption isotherm is excessively long (several weeks), and experimental precautions need to be taken to achieve meaningful results. Specialized equipments, quite expensive ones, have been developed for the water adsorption isotherm determination, based on highly sensitive microbalances. 

A major advantage of the determination of adsorption isotherms by IGC is the fact that the first derivative of the isotherm is readily calculable by application of the following relationship ... 

The essential parts of a volumetric apparatus are a closed system of known volume, a source of adsorbate and a pressure measuring device. This type of apparatus is more commonly used for the determination of adsorption isotherms, but kinetics can be measured provided that the adsorbent surface is large and the response of the pressure measuring device is much faster than the rate of adsorption. These criteria are usually only satisfied by powders or films which show activated adsorptions. Bond has discussed the phenomenon of activated adsorption. Although the results may often be ascribed to contamination or incorporation into the bulk of the material, in other instances a genuine activated chemisorption is found. 

Figure 4 Determination of adsorption isotherms. Left - perturbation data and corresponding fit by isotherm model (lines). Right - overloading experiments (points, injeetion volume 0.13...5ml) and simulations (lines).

In this section a short overview is given of preparative chromatography and the determination of adsorption isotherm parameters - single and competitive - to be used for computer-assisted optimization of separations. 

The dynamic methods are based on direct chromatography and are popular because they are faster and easier to automate. Four direct chromatographic methods that are available for determination of adsorption isotherms are frontal analysis (FA) [13, 109] frontal analysis by characteristic points (FACP) [109], elution by characteristic points (ECP) [109] and the perturbation peak (PP) method [118-121], The FACP and ECP methods have... 

There are, so far, only two reports on the determination of isotherm data from mixtures containing more than two components. In both cases, the FA method was used for ternary mixtures [135, 136], There are no reports on the experimental determination of adsorption isotherms for quaternary mixtures using any chromatographic method. The competitive quaternary adsorption isotherm parameters could be very valuable for the separations of the four isomers of a compound with two chiral centers, or for the preparative separation of two compounds in the presence of one or two impurities. 

In contrast to the well-developed thermodynamic methods for determining gas/ liquid equilibriums the theoretical determination of adsorption isotherms is not yet feasible. Only approaches to determining multi-component isotherms from experimentally determined single-component isotherms are known. Such approaches are explained in more detail in Section 2.5.2.3. Careful experimental determination of the adsorption isotherm is therefore absolutely necessary. The different approaches for isotherm determination are discussed in Chapter 6.5.7. 

The most studies of adsorption from solution have been concerned with the adsorption from two-component mixture, for example [1,2], Practical use of adsorption however deals with the adsorption from multicomponent systems. In liquid chromatography in a many cases for the separation of mixture of solutes the multicomponent eluents are used. The most difficulties in the investigation of adsorption from multicomponent systems arise at the determination of some component concentration at once in equilibrium solution over the adsorbent. Moreover for the determination of adsorption isotherm in this case large experimental data are needed. 

The thermodynamic characteristic of adsorption from solutions can be determined from the dependence of adsorption on temperature. But the determination of adsorption isotherms from solution at different temperatures is the rather complicate problems. Liquid chromatography may be very useful method for the determination of thermodynamic characteristics of adsorption at small coverage [11] because of the measurement of retention volume (the Henry constant) at different temperatures of the chromatographic columns makes it possible to calculate the heats of adsorption and the differential standard change entropy of adsorption from ... 

For the determination of adsorption isotherms a constant mass of adsorbent (3g granular activated carbon and natural zeolite for Zinc and 5 g granular activated carbon and natural zeolite for Cd) and 0.2 dm3 of solution with known initial concentration were mixed at 500 rpm at a constant temperature of 25°C. The equilibriums were established for 2-11 days for each heavy metal-adsorbent system. Aqueous samples were taken for heavy metals concentration measurements using AERL 3520 Atomic Absorption Spectrophotometer. 

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