Porous solids adsorption isotherms

Recently, Terzyk et al. [35] have proposed a hybrid model that describes adsorption on porous solids and which takes into account the possibility of adsorption in pores and on external surfaces that are characterized by different fractal dimensions. The resulting adsorption isotherm is the sum of two terms, each involving the relevant fractal exponent. The first term describes the pore filling and the second term accounts for the adsorption on external surfaces. Nonetheless, to the best of our knowledge, the hybrid isotherm of Terzyk et al. [35] has not yet been applied to describe experimental data. 

Recent progress in the theory of adsorption on porous solids, in general, and in the adsorption methods of pore structure characterization, in particular, has been related, to a large extent, to the application of the density functional theory (DFT) of Inhomogeneous fluids [1]. DFT has helped qualitatively describe and classify the specifics of adsorption and capillary condensation in pores of different geometries [2-4]. Moreover, it has been shown that the non-local density functional theory (NLDFT) with suitably chosen parameters of fluid-fluid and fluid-solid interactions quantitatively predicts the positions of capillary condensation and desorption transitions of argon and nitrogen in cylindrical pores of ordered mesoporous molecular sieves of MCM-41 and SBA-15 types [5,6]. NLDFT methods have been already commercialized by the producers of adsorption equipment for the interpretation of experimental data and the calculation of pore size distributions from adsorption isotherms [7-9]. 

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]. 

As a general rule, adsorbates above their critical temperatures do not give multilayer type isotherms. In such a situation, a porous absorbent behaves like any other, unless the pores are of molecular size, and at this point the distinction between adsorption and absorption dims. Below the critical temperature, multilayer formation is possible and capillary condensation can occur. These two aspects of the behavior of porous solids are discussed briefly in this section. Some lUPAC (International Union of Pure and Applied Chemistry) recommendations for the characterization of porous solids are given in Ref. 178. 

The adsorption branch of isotherms for porous solids has been variously modeled. Again, the DR equation (Eq. XVII-75) and related forms have been used [186,194]. With respect to desorption, the variety of shapes of loops of the closed variety that may be observed in practice is illustrated in Fig. XVII-29 (see also Refs. 195 and 197). 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

If the region FGH of the isotherm represents the filling of all the pores with liquid adsorbate, then the amount adsorbed along to plateau FGH, when expressed as a volume of liquid (by use of the normal liquid density) should be the same for all adsorptives on a given porous solid. This prediction is embodied in a generalization put forward many years ago by Gurvitsch and usually known as the Gurvitsch rule. 

Fig. 3.2 Adsorption isotherms for argon and nitrogen at 78 K and for n-butane at 273 K on porous glass No. 3. Open symbols, adsorption solid symbols, desorption (courtesy Emmett and Cines). The uptake at saturation (calculate as volume of liquid) was as follows argon at 78 K, 00452 nitrogen at 78 K, 00455 butane at 273 K, 00434cm g .

It follows therefore that the specific surface of a mesoporous solid can be determined by the BET method (or from Point B) in just the same way as that of a non-porous solid. It is interesting, though not really surprising, that monolayer formation occurs by the same mechanism whether the surface is wholly external (Type II isotherm) or is largely located on the walls of mesopores (Type IV isotherm). Since the adsorption field falls off fairly rapidly with distance from the surface, the building up of the monolayer should not be affected by the presence of a neighbouring surface which, as in a mesopore, is situated at a distance large compared with the size of a molecule. 

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... 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

The advantage of equation 17.14 is that it may be fitted to all known shapes of adsorption isotherm. In 1938, a classification of isotherms was proposed which consisted of the five shapes shown in Figure 17.5 which is taken from the work of Brunauer et alSu Only gas-solid systems provide examples of all the shapes, and not all occur frequently. It is not possible to predict the shape of an isotherm for a given system, although it has been observed that some shapes are often associated with a particular adsorbent or adsorbate properties. Charcoal, with pores just a few molecules in diameter, almost always gives a Type I isotherm. A non-porous solid is likely to give a Type II isotherm. If the cohesive forces between adsorbate molecules are greater than the adhesive forces between adsorbate and adsorbent, a Type V isotherm is likely to be obtained for a porous adsorbent and a Type III isotherm for a non-porous one. 

Emmett, P. H. Advances in Colloid Science 1 (1942) 1. The measurement of the surface areas of finely divided or porous solids by low temperature adsorption isotherms. 

Typical adsorption isotherms that obey Eqs. (5) and (7) are shown in Figs. 2.1 and 2.2, respectively. It should be noted that a linear Langmuir plot can be obtained by plotting l/[nA]s against 1/P where the slope is 1/k and the intercept is l/[ng] as seen after rearrangement of Eq. (7). The adsorption isotherms are utilized primarily to determine the surface area of porous solids and the heats of adsorption. The isotherms yield the amount of gas adsorbed. By multiplying with the area occupied per molecule... 

It must be remembered, in interpreting adsorption isotherms on coal, that coal expands sizably when temperature is increased, and coal swells appreciably during adsorption. These factors are relatively unimportant for porous inorganic solids. On heating from —195°C. to room temperature the volume of coal expands about 10%, and at least more or less consistent with this, pore openings at —195°C. seem to be 4A. while at room temperature they are about 5A. Further, on adsorption of water or methanol the volume of coal increases 10-20%, and with some exceptional polar adsorbates coal eventually dissolves. 

Any solid is capable of adsorbing a certain amount of gas, the extent of adsorption at equilibrium depending on temperature, the pressure of the gas and the effective surface area of the solid. The most notable adsorbents are, therefore, highly porous solids, such as charcoal and silica gel (which have large internal surface areas - up to c. 1000 m2 g-1) and finely divided powders. The relationship at a given temperature between the equilibrium amount of gas adsorbed and the pressure of the gas is known as the adsorption isotherm (Figures 5.1, 5.5-5.6, 5.8, 5.11, 5.13). 

Type II isotherms (e.g. nitrogen on silica gel at 77 K) are frequently encountered, and represent multilayer physical adsorption on non-porous solids. They are often referred to as sigmoid isotherms. For such solids, point B represents the formation of an adsorbed monolayer. Physical adsorption on microporous solids can also result in type II isotherms. In this case, point B represents both monolayer adsorption on the surface as a whole and condensation in the fine pores. The remainder of the curve represents multilayer adsorption as for non-porous solids. 

Condensation can, therefore, take place in narrow capillaries at pressures which are lower than the normal saturation vapour pressure. Zsigmondy (1911) suggested that this phenomenon might also apply to porous solids. Capillary rise in the pores of a solid will usually be so large that the pores will tend to be either completely full of capillary condensed liquid or completely empty. Ideally, at a certain pressure below the normal condensation pressure all the pores of a certain size and below will be filled with liquid and the rest will be empty. It is probably more realistic to assume that an adsorbed monomolecular film exists on the pore walls before capillary condensation takes place. By a corresponding modification of the pore diameter, an estimate of pore size distribution (which will only be of statistical significance because of the complex shape of the pores) can be obtained from the adsorption isotherm. 

The capillary condensation theory provides a satisfactory explanation of the phenomenon of adsorption hysteresis, which is frequently observed for porous solids. Adsorption hysteresis is a term which is used when the desorption isotherm curve does not coincide with the adsorption isotherm curve (Figure 5.8). 

Although the BET equation is open to a great deal of criticism, because of the simplified adsorption model upon which it is based, it nevertheless fits many experimental multilayer adsorption isotherms particularly well at pressures between about 0.05 p0 and 0.35 pQ (within which range the monolayer capacity is usually reached). However, with porous solids (for which adsorption hysteresis is characteristic), or when point B on the isotherm (Figure 5.5) is not very well defined, the validity of values of Vm calculated using the BET equation is doubtful. 

Figure 7.42 Types of gas sorption isotherm - microporous solids are characterised by a type I isotherm. Type II corresponds to macroporous materials with point B being the point at which monolayer coverage is complete. Type III is similar to type II but with adsorbate-adsorbate interactions playing an important role. Type IV corresponds to mesoporous industrial materials with the hysteresis arising from capillary condensation. The limiting adsorption at high P/P0 is a characteristic feature. Type V is uncommon. It is related to type III with weak adsorbent-adsorbate interactions. Type VI represents multilayer adsorption onto a uniform, non-porous surface with each step size representing the layer capacity (reproduced by permission of IUPAC).

According to the IUPAC,79 the hysteresis loops are classified into four types from Type HI to Type H4. The Type HI loop in Figure 3 is characteristic of the mesoporous materials consisting of the pores with cylindrical pore geometry or the pores with high degree of pore size uniformity.88,89 Hence, the appearance of the HI loop on the adsorption isotherms for the porous solids generally indicates facile pore connectivity and relative narrow PSD. 

Physical adsorption of gases and vapors is a powerful tool for characterizing the porosity of carbon materials. Each system (adsorbate-adsorbent temperature) gives one unique isotherm, which reflects the porous texture of the adsorbent. Many different theories have been developed for obtaining information about the solid under study (pore volume, surface area, adsorbent-adsorbate interaction energy, PSD, etc.) from the adsorption isotherms. When these theories and methods are applied, it is necessary to know their fundamentals, assumptions, and applicability range in order to obtain the correct information. For example, the BET method was developed for type II isotherms therefore, if the BET equation is applied to other types of isotherms, it will not report the surface area but the apparent surface area. 

The Adsorption isotherm . The relation between the amount adsorbed and the pressure in the gas, the adsorption isotherm is a complicated one, and depends on the nature of the solid surface, on its homogeneity or otherwise (and few, if any, solid surfaces are homogeneous), and of course on the forces between gas molecules and solid, which depend on the chemical nature of the gas. For many porous, and some other, solids, a first approximation is given by Freundlich s well-known equation if x is the amount of gas adsorbed, and p the pressure of the gas,... 

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