Adsorption isotherms, types

In the following discussion we will consider the application of percolation theory to describing desorption of condensate from porous solids. In Sections III,A-III,C we briefly recall types of adsorption isotherms, types of hysteresis loops, and the Kelvin equation. The matter presented in these sections is treated in more detail in any textbook on adsorption [see, e.g., the excellent monographs written by Gregg and Sing (6) and by Lowell and Shields (49) Sections III,D-III,H are directly connected with percolation theory. In particular, general equations interpreting the hysteresis loop are... 

Moisture sorption of microcrystalline cellulose has been studied extensively. Fig. 6A includes the sorption and desorption studies for microcrystalline cellulose. The inserts are plots of moisture content versus time, which approximately represent the kinetics of sorption and desorption at each humidity. The equilibrium adsorption isotherm (Type II) has been fit to the BET equation (C = 16.48, = 0.033 g/g solid) and this curve is... 

A selection of adsorption isotherms types (according to the lUPAC classification of physisorption isotherms) are schematically shown in Figure 1, where the adsorbed amount n is plotted against the relative pressure p/po of the adsorptive gas. Type I isotherms are typical for microporous materials, where the total pore volume of the adsorbent determines the saturation value. Reversible isotherms of type II are obtained for nonporous or macroporous materials, whereas type IV isotherms showing a hysteresis loop are characteristic of mesoporous materials, such as many practical catalytic materials. If the knee at point B of isotherm types II and IV is sufficiently sharp, the uptake at point B can be considered as the monolayer capacity of the material and its specific surface area can then be calculated assuming the formation of a close-packed monolayer of the test gas, provided its molecular area is known. For N2 the standard molecular area is 0.162 nm2. 

Figure 3.3.13. Langmuir adsorption isotherm type behavior for No exchange with a cation exchange resin.

There is a more fundamental classification of adsorption isotherms according to Bmnauer, which divides the adsorption isotherms into five types. Type 1 is the monolayer chemical Langmuir-type adsorption and type II is the multilayer physical BET adsorption isotherm. Type III is for - rather rarely occurring - weak adsorptions and types IV and V are for capillary condensation. There are, however, some adsorption isotherms that do not fit into Bmnauer s classification. 

From the adsorption isotherm type I or for a complete monolayer, when the adsorbent fills all pores, forming a complete monolayer on 1 g of solid, we can calculate the surface area ... 

For dyeing systems based on the Freundlich and Langmuir adsorption isotherm types, similar resnlts are obtained for both CDEP and DDF, further demonstrating that a higher dispersion coefficient leads to a higher dye uptake and a better levelness of dye distribution across the package, though the effect seems to be minor. 

The present discussion is restricted to an introductory demonstration of how, in principle, adsorption data may be employed to determine changes in the solid-gas interfacial free energy. A typical adsorption isotherm (of the physical adsorption type) is shown in Fig. X-1. In this figure, the amount adsorbed per gram of powdered quartz is plotted against P/F, where P is the pressure of the adsorbate vapor and P is the vapor pressure of the pure liquid adsorbate. 

This type of behavior can cause irreversibility in the adsorption isotherm as well as immobility on the surface [106]. 

Adsorption isotherms are by no means all of the Langmuir type as to shape, and Brunauer [34] considered that there are five principal forms, as illustrated in Fig. XVII-7. TVpe I is the Langmuir type, roughly characterized by a monotonic approach to a limiting adsorption at presumably corresponds to a complete monolayer. Type II is very common in the case of physical adsorption... 

Fig. XVII-7. Brunauer s five types of adsorption isotherms. (From Ref. 34.)...

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

Gregg [52] (see also Ref. 48) has surveyed the types of force-area equations obtainable from adsorption isotherms. 

Equation XVII-78 turns out to ht type II adsorption isotherms quite well—generally better than does the BET equation. Furthermore, the exact form of the potential function is not very critical if an inverse square dependence is used, the ht tends to be about as good as with the inverse-cube law, and the equation now resembles that for a condensed him in Table XVII-2. Here again, quite similar equations have resulted from deductions based on rather different models. 

The adsorption isotherms are often Langmuirian in type (under conditions such that multilayer formation is not likely), and in the case of zeolites, both n and b vary with the cation present. At higher pressures, capillary condensation typically occurs, as discussed in the next section. Some N2 isotherms for M41S materials are shown in Fig. XVII-27 they are Langmuirian below P/P of about 0.2. In the case of a microporous carbon (prepared by carbonizing olive pits), the isotherms for He at 4.2 K and for N2 at 77 K were similar and Langmuirlike up to P/P near unity, but were fit to a modified Dubninin-Radushkevich (DR) equation (see Eq. XVII-75) to estimate micropore sizes around 40 A [186]. 

Adsorption isotherms in the micropore region may start off looking like one of the high BET c-value curves of Fig. XVII-10, but will then level off much like a Langmuir isotherm (Fig. XVII-3) as the pores fill and the surface area available for further adsorption greatly diminishes. The BET-type equation for adsorption limited to n layers (Eq. XVII-65) will sometimes fit this type of behavior. Currently, however, more use is made of the Dubinin-Raduschkevich or DR equation. Tliis is Eq. XVII-75, but now put in the form... 

The problem of the theoretical description of biopolymer water adsorption isotherms has drawn the attention of researchers for a long time. In the works [19], [20] a rigorous statistical basis for equations describing the isotherms for the case of homogeneous adsorption surfaces and noninteracting adsorption sites of N different types has been suggested. The general equation is ... 

Fig. I.l The five types of adsorption isotherm, I to V, in the classification of Brunauer, Deming, Deming and Teller (BDDT), together with Type VI, the stepped isotherm.

The effect of these factors on the adsorption isotherm may be elucidated by reference to specific examples. In the case of the isotherm of Fig. 5.17(a), the nonporous silica had not been re-heated after preparation, but had been exposed to near-saturated water vapour to ensure complete hydroxylation. The isotherm is of Type II and is completely reversible. On the sample outgassed at 1000°C (Fig. 5.17(h)) the isotherm is quite different the adsorption branch is very close to Type III, and there is extrensive hysteresis extending over the whole isotherm, with considerable retention of adsorbate on outgassing at 25°C at the end of the run. 

The first stage in the interpretation of a physisorption isotherm is to identify the isotherm type and hence the nature of the adsorption process(es) monolayer-multilayer adsorption, capillary condensation or micropore filling. If the isotherm exhibits low-pressure hysteresis (i.e. at p/p° < 0 4, with nitrogen at 77 K) the technique should be checked to establish the degree of accuracy and reproducibility of the measurements. In certain cases it is possible to relate the hysteresis loop to the morphology of the adsorbent (e.g. a Type B loop can be associated with slit-shaped pores or platey particles). 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

Design criteria for carbon adsorption include type and concentration of contaminant, hydrauhc loading, bed depth, and contact time. Typical ranges are 1.4—6.8 L/s/m for hydrauhc loading, 1.5—9.1 m for bed depth, and 10—50 minutes for contact time (1). The adsorption capacity for a particular compound or mixed waste stream can be deterrnined as an adsorption isotherm and pilot tested. The adsorption isotherm relates the observed effluent concentration to the amount of material adsorbed per mass of carbon. 

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

Figure 1 The five types of physical adsorption isotherms. ...

Scott and Kucera [4] carried out some experiments that were designed to confirm that the two types of solute/stationary phase interaction, sorption and displacement, did, in fact, occur in chromatographic systems. They dispersed about 10 g of silica gel in a solvent mixture made up of 0.35 %w/v of ethyl acetate in n-heptane. It is seen from the adsorption isotherms shown in Figure 8 that at an ethyl acetate concentration of 0.35%w/v more than 95% of the first layer of ethyl acetate has been formed on the silica gel. In addition, at this solvent composition, very little of the second layer was formed. Consequently, this concentration was chosen to ensure that if significant amounts of ethyl acetate were displaced by the solute, it would be derived from the first layer on the silica and not the less strongly held second layer. 

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