Pores mesopore filling

Adsorbents such as some silica gels and types of carbons and zeolites have pores of the order of molecular dimensions, that is, from several up to 10-15 A in diameter. Adsorption in such pores is not readily treated as a capillary condensation phenomenon—in fact, there is typically no hysteresis loop. What happens physically is that as multilayer adsorption develops, the pore becomes filled by a meeting of the adsorbed films from opposing walls. Pores showing this type of adsorption behavior have come to be called micropores—a conventional definition is that micropore diameters are of width not exceeding 20 A (larger pores are called mesopores), see Ref. 221a. 

At 9 hours of immersion, instead, isotherms do not show the pore filling associated with mesopores, which in turn appears again between 25 and 26 hours. After 28 hours of soaking, no mesopore filling is observed (figure 3). The DFT pore size distributions also confirm the presence of mesopores (around 2.2 nm) only at 2 hours of immersion and between 25 and 26 hours. The peak at around 5 nm is probably due to the textural interparticles porosity (figure 3 inset). 

As discussed in Section 1.4.2.1, the critical condensation pressure in mesopores as a function of pore radius is described by the Kelvin equation. Capillary condensation always follows after multilayer adsorption, and is therefore responsible for the second upwards trend in the S-shaped Type II or IV isotherms (Fig. 1.14). If it can be completed, i.e. all pores are filled below a relative pressure of 1, the isotherm reaches a plateau as in Type IV (mesoporous polymer support). Incomplete filling occurs with macroporous materials containing even larger pores, resulting in a Type II isotherm (macroporous polymer support), usually accompanied by a H3 hysteresis loop. Thus, the upper limit of pore size where capillary condensation can occur is determined by the vapor pressure of the adsorptive. Above this pressure, complete bulk condensation would occur. Pores greater than about 50-100 nm in diameter (macropores) cannot be measured by nitrogen adsorption. 

Adsoiptive molecules transport through macropores to the mesopores and finally enter the micropores. The micropores usually constitute the largest portion of the internal surface and contribute the most to the total pore volume. The attractive forces are stronger and the pores are filled at low relative pressures in the microporosity, and therefore, most of the adsorption of gaseous adsoiptives occurs within that region. Thus, the total pore volume and the pore size distribution determine the adsorption capacity. 

We turn now to the question of validity of the Kelvin equation. Although the thermodynamic basis of the Kelvin equation is well established (Defay and Prigogine 1966), its reliability for pore size analysis is questionable. In this context, there are three related questions (1) What is the exact relation between the meniscus curvature and the pore size and shape (2) Is the Kelvin equation applicable in the range of narrow mesopores (say >vp < 5 nm) (3) Does the surface tension vary with pore width The answers to these questions are still elusive, but recent theoretical work has improved our understanding of mesopore filling and the nature of the condensate. 

A third possibility is a Type I isotherm with a short plateau, which terminates at p/p°< 1. An upward deviation, as indicated in Figure 8.1c, occurs at high p/p° when the microporous adsorbent also contains some wide mesopores or narrow macropores. Since the wall area of such relatively wide pores is likely to be much smaller than the micropore area, the scale of multilayer development or mesopore filling may be quite small. 

Values of the total specific mesopore volume wp(mes) in Table 12.4 have been obtained from the amounts adsorbed at p/p° = 0.95, by making the usual assumption that the pores were filled with the condensed liquid adsorptive (i.e. assuming the validity of the Gurvich law). The fairly good agreement between the three values of vp(mes) is consistent with the assumption that the capillary condensed state of argon is the supercooled liquid rather than the solid. 

The view is generally held that capillary condensation is responsible for mesopore and macropore filling (i.e. in pores of width 2 nm). Since the filling of macropores (to > 50 nm) occurs at very high pjp°, we are essentially concerned with mesopore filling. Capillary condensation can be regarded as a secondary process, which is always preceded by adsorption on the pore walls. 

To convert the micropore capacity into the micropore volume, it is usually assumed that the pores are filled with liquid adsorptive - as in the case of mesopore filling. This procedure does not allow for the dependency of molecular packing on both pore size and pore shape. For this reason, we recommend that the term apparent micropore volume should be adopted and that the gas and temperature should always be specified. 

The adsorption isotherm starts at a low relative pressure. At a certcdn minimum pressure, the smallest pores will be filled with liquid nitrogen. As the pressure is increased still further, larger pores will be filled and near the saturation pressure, all the pores are filled. The total pore volume is determined by the quantity of gas adsorbed near the saturation pressure. Desorption occurs when the pressure is decreased from the saturation pressure. The majority of physisorption isotherms may be grouped into six types [9]. Due to capillary condensation, many mesoporous systems exhibit a distinct adsorption-desorption behaviour which leads to characteristic hysteresis loops (Type IV and V isotherms) whose shape is related to pore shape. Type I isotherms, characterised by a plateau at high partial pressure, are characteristic of microporous samples. A typical isotherm, representative of a mesoporous sample is given in Fig. 4.6, with a schematic representation of the adsorption steps. 

Many adsorbents are porous, and porosity increases the surface area and provides spaces where adsorbate molecules may condense. However, the presence of porosity makes the treatment of the adsorption process more complex, because adsorption in small pores is preferred over that on plane surfaces. The reason is capillary condensation, which we have seen in Sections 4.7 and 4.8, whereby the pores are filled with the liquid at pressures less than P°2 due to the strong attraction between condensed molecules. Pores having a width of less than 2 nm are classified as micropores, 2-50 nm as mesopores, and greater than 50 nm as macropores. It is generally realized that the adsorption isotherm is not coincident with the desorption isotherm, and this phenomenon is called adsorption hysteresis. 

Low temperature N2 adsorption isotherm gives a reliable information on the mesoporous texture of solids. The adsorption-desorption plot follow the type IV isotherm with hysterisis in the mesopore filling region, the pore size distribution obtained by BJH analysis of nitrogen adsorbed is shown in Fig.3. The pore size distribution is narrow and the maximum is centered around 30 A for all the samples indicating a uniform pore texture of the samples... 

Types IVand V Capillary condensation in mesopores. Initially, a multilayer is adsorbed on the capilla walls. When the pressure is further increased, liquids droplets form preferentially at sites where the curvature fulfills the Kelvin equation. When two opposing droplets touch, the pore is filled. On desorption, pores whose radius is smaller than the Kelvin radius are emptied. The adsorption branch indicates the extent ofthe pores, and the desorption branch the size ofthe pore openings [Evertt 1976]. 

It is assumed that the surface tension and the molar volume are independent of the radius of curvature associated with the porosity. Corrections or adjustments can be made to the above Kelvin equation because in an adsorption process, at the stage when mesopore filling occurs, already the walls of the pore contain adsorbed material such that the effective diameter of the pore is reduced and /"p = tk + (where t is the thickness of the adsorbed layer). Another correction is where the pore shape is not cylindrical but is perhaps slit-shaped when the meniscus is hemi-cylindrical and the effective pore width Wp = + 2t. However,... 

---