Physisorption isotherms

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). 

The benefits of the method are appreciated when the textural parameters are compared. Data derived from N2-physisorption isotherms show that Fenton detemplation leads to improved textural parameters, with BET areas around 945 m g for a pore volume of 1.33 cm g , while calcination leads to reduced textural parameters (667m g 0.96cm g ). T-plot analysis, strictly speaking, is not apphcable for these bi-modal materials but it gives a good estimate. It shows that the micropore volume is doubled, which corresponds to an increase in the calculated micropore area from about... 

Aliphatic amines yield surface areas typically around 100 m g (Table 19.1, 1-4). The physisorption isotherms of samples 1-3 are shown in Fig. 19.1. 

Fig. 19.1 Nitrogen physisorption isotherms at 77 K for TiN nanoparticies (the numbers correspond to the sample code in Table 19.1).

TEM investigations support the interpretation of the nitrogen physisorption isotherms (Fig. 19.3). They show particles 5-20 run in diameter, whereas the particle size estimated from the specific surface area, assuming spherical particle morphology, is 7 nm. Indeed, the particle morphology for sample 7 is mostly spherical, but for some crystallites edges are discernible. 

The nitrogen physisorption isotherm and pore size distributions for the synthesized catalysts are shown in Figs. 3 and 4. The Type IV isotherm, typical of mesoporous materials, for each sample exhibits a sharp inflection, characteristic of capillary condensation within the regular mesopores [5, 6], These features indicate that both TS-1/MCM-41-A and TS-l/MCM-41-B possess mesopores and a narrow pore size distribution. 

The majority of physisorption isotherms (Fig. 1.14 Type I-VI) and hysteresis loops (Fig. 1.14 H1-H4) are classified by lUPAC [21]. Reversible Type 1 isotherms are given by microporous (see below) solids having relatively small external surface areas (e.g. activated carbon or zeolites). The sharp and steep initial rise is associated with capillary condensation in micropores which follow a different mechanism compared with mesopores. Reversible Type II isotherms are typical for non-porous or macroporous (see below) materials and represent unrestricted monolayer-multilayer adsorption. Point B indicates the stage at which multilayer adsorption starts and lies at the beginning of the almost linear middle section. Reversible Type III isotherms are not very common. They have an indistinct point B, since the adsorbent-adsorbate interactions are weak. An example for such a system is nitrogen on polyethylene. Type IV isotherms are very common and show characteristic hysteresis loops which arise from different adsorption and desorption mechanisms in mesopores (see below). Type V and Type VI isotherms are uncommon, and their interpretation is difficult. A Type VI isotherm can arise with stepwise multilayer adsorption on a uniform nonporous surface. 

Fig. 1.14 Types of physisorption isotherms (I-VI) and hysteresis loops (H1-H4) according to the lUPAC classifications.

The majority of physisorption isotherms may be grouped into the six types shown in Figure 2. In most cases, at sufficiently low surface coverage the isotherm reduces to a linear form (i.e. na oc p), with is often referred to as the Henry s Law region (On heterogeneous surfaces this linear region may fall below the lowest experimentally measurable pressure). 

In calculations of the mesopore size distribution from physisorption isotherms it is generally assumed (often tacitly) (a) that the pores are rigid and of a regular shape (e.g. cylindrical capillaries or parallel-sided slits), (b) that micropores are absent, and (c) that the size distribution does not extend continuously from the mesopore into the macropore range. Furthermore, to obtain the pore size distribution, which is usually expressed in the graphical form AV /Arp vs. rp, allowance must be made for the effect of multilayer adsorption in progressively reducing the dimensions of the free pore space available for capillary condensation. 

It is evident from the above considerations that the use of the physisorption method for the determination of mesopore size distribution is subject to a number of uncertainties arising from the assumptions made and the complexities of most real pore structures. It should be recognized that derived pore size distribution curves may often give a misleading picture of the pore structure. On the other hand, there are certain features of physisorption isotherms (and hence of the derived pore distribution curves) which are highly characteristic of particular types of pore structures and are therefore especially useful in the study of industrial adsorbents and catalysts. Physisorption is one of the few nondestructive methods available for investigating meso-porosity, and it is to be hoped that future work will lead to refinements in the application of the method -especially through the study of model pore systems and the application of modem computer techniques. 

Catalyst surface areas prior to reaction were determined by application of the BET method to nitrogen physisorption isotherms determined at 77K. 

Indirect Derivation of the Quantities of Adsorption from a Series of Experimental Physisorption Isotherms The Isosteric Method... 

To obtain differential enthalpies of adsorption from physisorption isothermal data, it is advisable to measure a series of adsorption isotherms at different temperatures (see Section 2.8.3). 

The physisorption isotherm on a mesoporous or macroporous adsorbent follows the same monolayer-multilayer path as on the corresponding non-porous surface until the secondary process of capillary condensation occurs. In the case of a macro-porous solid, the deviation from the standard monolayer-multilayer isotherm does not take place until very high relative pressures are attained (with nitrogen adsorption at 77 K, this would be at p)p° > 0.99). 

The main purpose of the present chapter is to introduce the underlying princ which will serve as a basis for the discussion of physisorption isotherms present later chapters. It is not our intention to give a general survey of the theorii physisorption at the gas-solid interface instead, our aim is to provide suffi information to enable the newcomer to surface science to appreciate the advan and limitations of the most widely used procedures for the analysis of experim adsorption isotherms. Our selection of theoretical material is necessarily some arbitrary in view of the vast literature on physisorption. The decision to include t ticular concept or equation is based on either its historical importance or its cu usage. Thus, a few equations were considered worthy of inclusion in this cht although for our purpose they do not merit further discussion or application in si quent chapters. 

A number of different empirical equations have been proposed to allow for the deviations of physisorption isotherms from Henry s law. An approach which is analogous to that used in the treatment of imperfect gases and non-ideal solutions is to adopt a virial treatment. Kiselev and his co-workers (Avgul et al. 1973) favoured the form... 

Although the simple Langmuir equation is more applicable to some forms of chemisorption, the underlying theory is of great historical importance and has provided a starting point for the development of the BET treatment and of other more refined physisorption isotherm equations. It is therefore appropriate to consider briefly die mechanism of gas adsorption originally proposed by Langmuir (1916, 1918). 

According to the IUPAC classification (Everett, 1972 Sing et al., 1985), the upper limit of the internal micropore width is about 2 nm. A characteristic property of microporous adsorbents is that they give Type I physisorption isotherms (see Figure 1.7). As noted previously, the most distinctive feature of a Type I isotherm is the long, almost horizontal plateau, which extends across most, if not all, of the... 

Dubinin was the pioneer of the concept of micropore filling. His approach was based on the early potential theory of Polanyi, in which the physisorption isotherm data were expressed in the form of a temperature-invariant characteristic curve . 

Many different equations have been applied to physisorption isotherms on micro porous adsorbents. The first and best known empirical equation was proposed by Freundlich (1926) in the form... 

There is a growing interest in the presentation of physisorption isotherms in a generalized integral form. This approach was first applied to physisorption in the submonolayer region (Adamson et al., 1961), but much of the current interest is centred on the analysis of micropore filling isotherms. An apparent advantage is that it provides a means of constructing a series of model isotherms by systematically... 

Two stages are involved in the evaluation of the surface area by the BET method from physisorption isotherm data. First, it is necessary to construct the BET plot and from it to derive the value of the monolayer capacity, nm. The second stage is the calculation of the specific surface area, a(BET), from nm, and this requires a knowledge of the average area, a, occupied by each molecule in the completed monolayer (i.e. the molecular cross-sectional area). Questionable assumptions are introduced at each stage and these therefore require careful consideration. 

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