Isotherms pore-filling

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... 

These various considerations led Pierce, Wiley and Smith in 1949, and independently, Dubinin, to postulate that in very fine pores the mechanism of adsorption is pore filling rather than surface coverage. Thus the plateau of the Type 1 isotherm represents the filling up of the pores with adsorbate by a process similar to but not identical with capillary condensation, rather than a layer-by-layer building up of a film on the pore walls. 

During the adsorption or occlusion of various molecules, the micropores fill and empty reversibly. Adsorption in zeoHtes is a matter of pore filling, and the usual surface area concepts are not appHcable. The pore volume of a dehydrated zeoHte and other microporous soHds which have type 1 isotherms may be related by the Gurvitch rule, ie, the quantity of material adsorbed is assumed to fill the micropores as a Hquid having its normal density. The total pore volume D is given by... 

Flat Surface Isotherm Equations The classification of isotherm equations into two broad categories for flat surfaces and pore filling reflec ts their origin. It does not restrict equations developed for flat surfaces from being apphed successfully to describe data for porous adsorbents. 

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). 

Figure 9.9 A scheme of distribution of liquid phase (black at the successive stages of slow drying (a), (b), (c), and (d). The insert shows the corresponding points at the desorption branch of isotherm, where U is the degree of pore filling and P/P the partical pressure of solvent vapor [3],...

Figure 12.3 Nitrogen adsorption-desorption isotherms at 77 K showing the pore filling of (a) [Y N(SiHMe2)2 3(THF)2] MCM-412 0 (19) and (h) [Y N(SiHMe2)2 3(THF)2] MCM-41 LP.280 The pore diameters of the parent PMSs are 2.7 (a) and 3.8nm (h). For the former material the isotherm changes from type IV (mesopores) to type I (micropores).

Sorption Properties. Sorption isotherms were determined of n-hexane and 2,3-dimethylbutane on variously pretreated samples of zeolite by a gravimetric method using a Cahn electrobalance. No shape-selective sorption was observed for these sorbates, which bespeaks a pore size greater than about 0.5 nm. The sorption capacity of S2 was appreciably lower than that of zeolite X, Y, or mordenite. Routine sorption capacities were determined by a simple procedure of pore filling with benzene at room temperature after calcination of the samples at various temperatures. 

The fractional pore filling of the micropores of radius r at a given pressure P is given by the Dubinin-Radushkevich (DR) isotherm... 

The surface area S resulting from analyses of these isotherms by BET equation in the p/po range 0.05 to 0.2 and the mesoporous volume Vm, measured at the top of the pore-filling step are reported in Table 1. 

Table 1. As the relative pressure increases, the thickness of adsorbed molecule layers on the pore surfaces increases as well, and then the pore filling process caused by capillary condensation occurs first in the small pores simultaneously with the multilayer adsorption on the larger pores. For specimen III, the value of 4d,max is significantly larger than those values for the other specimens, which is ascribed to the fact that as a result of the pore filling process in the larger macropores the adsorbed volume starts to increase abruptly only near the saturation vapor pressure in the gas adsorption isotherm. From the above results, they suggested that 4d,max / 4d,mm is closely related to rmax, that is, the larger rmax, the wider ranges the length-scale of the fractal regime in value.

The Type V isotherm is initially convex to the p/p° axis and also levels off at high relative pressures. As in the case of the Type III isotherm, this is indicative of weak adsorbent-adsorbate interactions. A Type V isotherm exhibits a hysteresis loop which is associated with the mechanism of pore filling and emptying. Such isotherms are relatively rare. 

The close proximity of the pore walls in the narrowest micropores produces an increased adsorbent-adsorbate interaction energy and this in turn results in the distortion of the initial part of the isotherm. If the pore width w is no more than a few molecular diameters d, the enhanced interactions lead to complete pore filling at very low pip0. In slit-shaped pores, the increased adsorption energy is unlikely to be significant beyond a pore width of about 2d, whereas in cylindrical pores the enhancement may extend up to a pore diameter of 3-4d (see Figure 4.5 Everett and Powl, 1976). 

Truly reversible Type V isotherms are quite rare. It is significant that the example reported by Dubinin (1980) was obtained on a low bum-off (5.7%) carbon, which was certainly ultramicroporous. It was pointed out that with an activated carbon obtained by 20% bum-off, the hysteresis extended over virtually the whole range of pore filling - the water isothenn then having a very similar appearance to that of the Carbosieve isotherm in Figure 9.26. 

The nitrogen isotherm data on non-porous hydroxylated silica in Table 10.1 (Bharabhani et al, 1972) have been used to construct the as-plot in Figure 12.6. Since the initial linear section can be back-extrapolated to the origin, we are reasonably sure that monolayer—multilayer adsorption has occurred on the mesopore walls before the onset of pore filling at / //>° = 0.41 and therefore that there was no detectable primary micropore filling at low / // - Similar results have been obtained by Kruk et al (1997b) and Sayari et al. (1997). 

Somewhat similar differences in isotherm shape have been reported by other investigators (Franke et al., 1993 Rathousky et al., 1994 Ravikovitch et al., 1995 Schmidt et al., 1995 Llewellyn et al., 1996). Very recently (Branton et al., 1997), a 3.4 nm siliceous form of MCM-41 has been found to give a reversible Type IV nitrogen isotherm with a sharp pore-filling step in the range p/p = 0.33-0.37. The values of the BET area and pore volume derived from the nitrogen isotherm are recorded in Table 12.5. Carbon tetrachloride isotherms were determined on the 3.4 nm siliceous MCM-41 at the temperatures of 273, 288, 303 and 323 K. These isotherms were essentially of Type V that at 325 K was completely reversible, while the others had narrow, almost vertical hysteresis loops of Type HI (see Figure 12.8). 

The nitrogen isotherm on the 4 nm sample is of special interest because at first sight it appears to represent an almost ideal case of reversible capillary condensa-tion/evaporation in a narrow distribution of uniform cylindrical pores (cf. Figure 7.S). However, it must be kept in mind that the steep pore-filling riser is located at p)p° 0.42. Because of the pore geometry, there is no detectable interparticle condensation, which often results in a reversible deviation from the standard isotherm at pjp° < 0.42. We may therefore conclude that the condensate has become unstable at the critical chemical potential corresponding to p/p° = 0.42, while leaving the adsorbed multilayer (under the influence of surface forces) on the pore walls. 

A useful indication of the mechanisms of surface coverage and/or pore filling can be obtained by visual inspection of an isotherm. However, it must be kept in mind that the overall shape of an isotherm is governed by the nature of the gas-solid system, the pore structure of the adsorbent and the operational temperature. 

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