Experimental determination of adsorption isotherms

The extent of adsorption of gases onto solid surfaces can be determined experimentally using a wide variety of apparatus and techniques, and the literature on this subject is extensive. In general, measurements fall into one of two categories either the volume of the gas adsorbed is determined manometrically, or gravimetric methods are used, where the mass adsorbed on the solid is determined directly. 

In the gravimetric method, the adsorbent (usually in the form of powder) is placed into a bulb, which is mounted on a sensitive balance and the bulb is then evacuated. Next, the weight increase of the adsorbent solid as a function of the absorptive gas pressure is monitored at constant temperature. More recently, the quartz crystal microbalance (QCM) technique has been applied this is very sensitive to mass increases. Quartz is a piezoelectric material and the thin crystal can be excited to oscillate in a traverse shear mode at its resonance frequency when a.c. voltage is applied across the metal (usually gold) electrodes, which are layered on two faces of the crystal. When the mass on the crystal increases upon adsorption, its resonance frequency decreases. The increase in the mass is calculated from the reduction in resonance frequency. On the other hand, adsorption on single flat surfaces can also be measured by ellipsometry, which measures the film thickness of transparent films optically using the difference between light reflection from bare and adsorbed surfaces. 

The total interfacial area, As, must also be known in order to obtain the F2 values in adsorption isotherms. The value of As is generally calculated from the (As = ASpec w) expression, when ASpec is known. Since nearly every solid surface has a roughness and porosity, the evaluation of ASpec is generally difficult and requires special techniques. In most prac- 

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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. 

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. 

J Roles, G Guiochon. Experimental determination of adsorption isotherm data for the study of the surface energy distribution of various solid surfaces by inverse gas-solid chromatography. J Chromatogr 591 233-243, 1992. 

The precise measurement of competitive adsorption isotherms not only of theoretical importance but may help the optimization of chromatographic processes in both analytical and preparative separation modes. The methods applied for the experimental determination of such isotherms have been recently reviewed [90], Frontal analysis using various flow rates can be successfully applied for the determination of competitive adsorption isotherms [91]. 

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. 

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. 

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. 

In adsorption chromatography the relevant functions are the adsorption isotherm parameters. Since there are no theoretical tools available to predict isotherms from physico-chemical data of the solute, solvent and adsorbent, these adsorption isotherm parameters have to be determined experimentally. When measuring the data, it is important to use a broad concentration range, i.e., including both the linear part of the isotherm as well as concentration close to saturation of the stationary phase. Despite the fact that there are several methods available to obtain adsorption isotherm parameters, the experimental determination of the isotherms is still far from being routine work. 

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. 

By the derivation of Eq. (9.8) the ideal model is also useful for nonlinear chromatography as the shape and position of peaks can be reproduced satisfactorily, if a high number of theoretical plates can be assumed. A partly possible analytical solution of the model enables the determination of adsorption isotherms from experimental chromatograms. 

Reviews of experimental methods for determination of adsorption isotherms are given, for example, by Rouquerol et al. [1], Guiochon et al. [2], and Do [3]. Also, there are a number of good review papers that cover some experimental techniques [4-7]. Details about operational procedures can be found in Ref. [1], while Ref. [7] gives a critical review of standard sorption-measuring... 

In diffusional impregnation, the distribution of the solute inside the wet porosity of the pellet is assumed to be governed by two phenomena [24-27] (Figure 4.1a) the diffusion of the solute into the pores of the pellet, described by Pick s law, and the adsorption of the solute onto the support, which depends on the adsorption capacity of the surface and on the adsorption equilibrium constant. These two parameters are experimentally determined from adsorption isotherms, but the final distribution is not fundamentally changed if equilibrium is not reached and adsorption is ruled by kinetics [28]. 

The method of determining adsorption isotherms described above is less accurate than frontal analysis, which is often preferred [133—144] because it ignores all kinetic factors and volume changes of the gas phase caused by adsorption of vapours. However it is considerably faster and simpler, and the adsorption isotherms it yields correspond to those of static methods provided that experimental conditions are so chosen that the errors are minimized [1,126]. Sinailarly, due to the short contact time of adsorbent and adsorbate, GSC allows the determination of adsorption isotherms whenever the injected substance undergoes both adsorption and dissolution in polymer provided that the latter process is slow. 

Equation (2.65) involves only the quantities P and V which are measured directly in the experimental determination of adsorption. Harkins and Jura reported that this simple equation was valid over more than twice the pressure range of any other two-constant adsorption isotherm equation. 

In principle, dynamic aspects of polymer adsorption can be determined with the same methods as one uses to characterize static properties of the adsorbed polymer layer. Fleer et al. [1] have presented an overview of experimental methods for the determination of adsorption isotherms, the adsorbed layer thickness, the bound fraction, and the volume fraction profile. However, in order to determine the dynamics of some property of the adsorbed polymer layer, the characteristic time of the experimental method should be shorter than that of the process investigated. Moreover, flie geometry of the experimental system is often of crucial importance. These factors severely limit the applicability of some experimental methods. In this section we will particularly review those methods which have been successfully applied for characterizing the kinetics of polymer adsorption. 

As stated in the introduction to the previous chapter, adsorption is described phenomenologically in terms of an empirical adsorption function n = f(P, T) where n is the amount adsorbed. As a matter of experimental convenience, one usually determines the adsorption isotherm n = fr(P), in a detailed study, this is done for several temperatures. Figure XVII-1 displays some of the extensive data of Drain and Morrison [1]. It is fairly common in physical adsorption systems for the low-pressure data to suggest that a limiting adsorption is being reached, as in Fig. XVII-la, but for continued further adsorption to occur at pressures approaching the saturation or condensation pressure (which would be close to 1 atm for N2 at 75 K), as in Fig. XVII-Ih. 

Knowing the experimental retention times, the previous equation allows the calculation of experimental concentration on the solid phase. Parameters of adsorption isotherms, can then be determined by fitting experimental and calculated concentrations. 

A. Seidel-Morgenstem, Experimental determination of single solute and competitive adsorption isotherms. J. Chromatogr.A 1037 (2004) 255-272. 

The least resolved measurement is determination of the isothermal rate constant k(T), where T is the isothermal temperature. Although conceptually simple, such measurements are often exceedingly difficult to perform for activated process without experimental artifact (contamination) because they require high pressures to achieve isothermal conditions. For dissociative adsorption, k(T) = kcol (T) [S (Tg = TS = T)), where kcol(T) is simply the collision rate with the surface and is readily obtainable from kinetic theory and Tg and T, are the gas and surface temperatures, respectively [107]. (S ) refers to thermal averaging. A simple Arrhenius treatment gives the effective activation energy Ea for the kinetic rate as... 

It is convenient to divide the extent of adsorption into three categories submonolayer, monolayer, and multilayer. We discuss them in this order. The thermodynamics of adsorption may be developed around experimental isotherms or around calorimetric data. We begin with the definition of adsorption isotherms and how they are determined experimentally (Section 9.2). 

It has been demonstrated previously [28] that phase composition of hexagonal/lamellar mixed phases can be quantitatively determined from gas adsorption data for calcined samples using the following simple procedure. The experimental adsorption isotherm for the calcined HL phase, vHi (p/po)> was fitted with a linear combination of adsorption isotherms for the calcined pure hexagonal phase, vH(p/po), and for the calcined pure lamellar phase, vL(p/p0) ... 

In this paper we have presented a new model for determining the pore size distribution of microporous and mesoporous materials. The model has been tested using the adsorption isotherms on pure as well as mixtures of MCM-41 materials. The experimental data of adsorption of nitrogen at 77.4 has been inverted using regularization technique. The results of PSD by the present model are compared with the pore size obtained from other classical methods, NLDFT [16] as well as the that obtained by X-ray diffraction methods. 

In Tabic 1 and in Fig.2 arc also shown the data of adsorption-structural properties of the produced diamond powders which were determined and calculated by the experimental low-temperature adsorption isotherms. 

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