Hysteresis associated with capillary condensation

In calculations of pore size from the Type IV isotherm by use of the Kelvin equation, the region of the isotherm involved is the hysteresis loop, since it is here that capillary condensation is occurring. Consequently there are two values of relative pressure for a given uptake, and the question presents itself as to what is the significance of each of the two values of r which would result from insertion of the two different values of relative pressure into Equation (3.20). Any answer to this question calls for a discussion of the origin of hysteresis, and this must be based on actual models of pore shape, since a purely thermodynamic approach cannot account for two positions of apparent equilibrium. 

The formation of a liquid phase from the vapour at any pressure below saturation cannot occur in the absence of a solid surface which serves to nucleate the process. Within a pore, the adsorbed film acts as a nucleus upon which condensation can take place when the relative pressure reaches the figure given by the Kelvin equation. In the converse process of evaporation, the problem of nucleation does not arise the liquid phase is already present and evaporation can occur spontaneously from the meniscus as soon as the pressure is low enough. It is because the processes of condensation and evaporation do not necessarily take place as exact reverses of each other that hysteresis can arise. 

The working out of these ideas will be illustrated by reference to a number of simple pore models the cylinder, the parallel-sided slit, the wedge-shape and the cavity between spheres in contact. 

These models, though necessarily idealized, are sufficiently close to the actual systems found in practice to enable useful conclusions to be drawn from a given Type IV isotherm as to the pore structure of a solid adsorbent. To facilitate the discussion, it is convenient to simplify the Kelvin equation by putting yVJRT = K, and on occasion to use the exponential form  

We consider first a cylinder closed at one end, B (Fig. 3.11(a)). Capillary condensation commences at that end to form a hemispherical meniscus r, and are equal to one another and therefore to r , which in turn is equal to r, the radius of the core (cf. Equation (3.7) and Fig. 3.7). Thus capillary condensation, to fill the whole pore, takes place at the relative pressure 

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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. 

Characteristic features of the Type IV isotherm are its hysteresis loop, which is associated with capillary condensation taking place in mesopores, and the limiting uptake over a range of high p/p°. The initial part of the Type IV isotherm is attributed to monolayer-multilayer adsorption since it follows the same path as the corresponding part of a Type II isotherm obtained with the given adsorptive on the same surface area of the adsorbent in a nonporous form. Type IV isotherms are given by many mesoporous industrial adsorbents. 

A closely related problem is the interpretation of physisorption hysteresis, when it appears in the form of an adsorption-desorption loop in association with capillary condensation-evaporation. Until recently, it was generally assumed that some form of hysteresis loop was a distinctive feature of every Type IV isotherm. With some mesoporous adsorbents, the shape of the loop is known to give a useful indication of the type of pore structure (e.g. the uniformity and shape of the pores). 

Hysteresis loops, which appear in the multilayer range of physisoTption isotherms, are generally associated with capillary condensation. It is well known that most mesoporous adsorbents give distinctive and reproducible hysteresis loops (de Boer 1958 Sing era/., 1985). 

The unusual character of the water isotherm on VPI-5 can be seen in Figure 12.16. There are three distinct steps at low p/p°. Step 1 occurs at p/p° <0.001, step 2 at p/p° = 0.013 and step 3 at pjp° = 0.060. Between steps 2 and 3 (here is a narrow hysteresis loop, which in this region of the isotherm cannot be associated with capillary condensation. 

Pores with different sizes show characteristic physical adsorption effects as manifested in the isotherm. The isotherm shows the relationship between the amount of a given gas taken np or released by a solid as a function of the gas pressnre nnder a constant temperature. The type-I isotherm shows a steep increase at very low pressmes and a long satnration platean and is characteristic of microporous materials. The type-IV isotherm exhibits a steep iucrease at high relative pressme and, in many cases, a hysteresis loop, which is associated with capillary condensation in mesopores. 

For water-rinsed and acid-leached rice husks. Fig. 13.11a, b shows lower nitrogen capacity and no apparent desorption hysteresis loop, indicating that the porosity of the two raw materials is relatively lower than that of heat-treated rice husks samples. For carbonized in nitrogen and burned in air atmosphere husk samples. Fig. 13.11c, d shows that the isotherms are of type 1 according lUPAC classification. The hysteresis loops (associated with capillary condensation) found in both samples are of various shapes. According to these observations, BRHA is mainly microporous with narrow pore size distribution while WRHA contains both micro- and mesopores. 

Classification and Modeling. Adsorption isotherms are classified by their shape, which also involves different sorption mechanisms. The isotherm classification of lUPAC (3) has been recently extended by Rouquerol and coworkers (4), subdividing types I, II, and IV (Fig. 4). The deviation of the adsorption and desorption curves (adsorption hysteresis) is associated with capillary condensation in mesopores. The shape of hysteresis loops (Fig. 5) also provides information about the texture of the mesoporous sorbent, including the geometry, size distribution, connectivity, and so on of the pores (3). 

FIGURE 8.11 Temperature dependence of the inverse slope of adsorption step associated with capillary condensation of nitrogen onto MCM-48. Hysteresis and pore critical temperatures, and respectively, are depicted in the plot. Solid lines are guides for the eye. (Adapted from Morishige, K. and Tateishi, M., Langmuir 22 4165, 2003. With permission.)... 

The presence of adsorption hysteresis cannot be reconciled with the laws of classical thermodynamics. It is evident that there are various forms of adsorption hysteresis [7], which require different explanations [7, 39, 40]. In the capillary condensation range, well-defined hysteresis loops are generally associated with delayed condensation or percolation [11] through pore networks or ink bottles [38, 39]. In the case of activated carbons, delayed condensation is likely to be the most important mechanism [11], but we cannot rule out the other effects. 

In general, therefore, there are three processes, prior to the kind of capillary condensation associated with the hysteresis loop of a Type IV isotherm, which may occur in a porous body containing micropores along with mesoporesia primary process taking place in very narrow micropores a secondary, cooperative process, taking place in wider micropores, succeeded by a tertiary process governed by a modified Kelvin equation. 

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). 

Adsorption hysteresis is often associated with porous solids, so we must examine porosity for an understanding of the origin of this effect. As a first approximation, we may imagine a pore to be a cylindrical capillary of radius r. As just noted, r will be very small. The surface of any liquid condensed in this capillary will be described by a radius of curvature related to r. According to the Laplace equation (Equation (6.29)), the pressure difference across a curved interface increases as the radius of curvature decreases. This means that vapor will condense... 

The Type IV isotherm, whose initial region is closely related to the Type II isotherm, tends to level off at high relative pressures. It exhibits a hysteresis loop, the lower branch of which represents measurements obtained by progressive addition of gas of the adsorbent, and the upper branch by progressive withdrawal. The hysteresis loop is usually associated with the filling and emptying of the mesopores by capillary condensation. Type IV isotherms are common but the exact shape of the hysteresis loop varies from one system to another. 

In fact, most mesoporous adsorbents possess complex networks of pores of different size. It is therefore unlikely that the condensation-evaporation processes can occur independently in each pore. The complexity of capillary condensation in porous materials is illustrated by the recent Monte Carlo computer simulation studies of Page and Monson (1996) and Gelb and Gubbins (1998). The well-defined hysteresis loops observed in the simulation results of both studies were attributed to the presence of thermodynamically metastable states and not to kinetic effects. However, it appears that the extent of die hysteresis was associated with the overall heterogeneity of the adsorbent structure and not simply due to capillary condensation within individual pores. 

It is striking that the high compaction pressure, which was sufficient to convert assemblages of spheroidal particles into well-defined mesopore structures (Gregg, 1968), had relatively little effect on the course of the adsorption isotherm. Although the desorption curve was displaced in the multilayer range, the isotherm remained pseudo-Type II (now termed Type lib). We conclude that the resulting hysteresis loop is associated with both the development of a pore network and the delayed capillary condensation on the surface of the platelets. 

Types IV and V are characterized by hysteresis loops and a limiting uptake as p -4 p(sat). Hysteresis Is typical for capillary condensation in mesopores. Type IV, associated with type II, is more common than t3rpe V, which Is associated to type III. Many industrial adsorbents give type IV Isotherms. 

The type II isotherm is associated with solids with no apparent porosity or macropores (pore size > 50 nm). The adsorption phenomenon involved is interpreted in terms of single-layer adsorption up to an inversion point B, followed by a multi-layer type adsorption. The type IV isotherm is characteristic of solids with mesopores (2 nm < pore size < 50 nm). It has a hysteresis loop reflecting a capillary condensation type phenomenon. A phase transition occurs during which, under the eflcct of interactions with the surface of the solid, the gas phase abruptly condenses in the pore, accompanied by the formation of a meniscus at the liquid-gas interface. Modelling of this phenomenon, in the form of semi-empirical equations (BJH, Kelvin), can be used to ascertain the pore size distribution (cf. Paragr. 1.1.3.2). 

Normally, the moisture sorption-desorption profile of the compound is investigated. This can reveal a range of phenomena associated with the solid. For example, on reducing the RH from a high level, hysteresis (separation of the sorption-desorption curves) may be observed. There are two types of hysteresis loops an open hyteresis loop, where the final moisture content is higher than the starting moisture content due to so-called ink-bottle pores, where condensed moisture is trapped in pores with a narrow neck, and the closed hysteresis loop may be closed due to compounds having capillary pore sizes. 

The cooperative structural rearrangement of the network associated with the continuous swelling of the hypercrosslinked sorbent with all the examined organic vapors is indicated by the hysteresis loops always extending throughout the entire range of relative pressures, down to zero (Fig. 10.7). This basically differs from the hysteresis loops caused by capillary condensation in the mesopores of adsorbents with rigid structure in the latter case, the loop closes toward low vapor pressures. 

Adsorption and desorption isotherms for carlxMi aerogels with RIC ratio of 1,500 and different RF mass concentrations are shown in Figure 36.5. The isotherms are type IV, indicating multilayer adsorption on the surfaces of the carbon aerogels. At the front part of the isotherms, the adsorbed volume increases slowly, as described by the BET equation. All isotherms exhibit hysteresis loops, which are associated with the filling and emptying of the mesopores by capillary condensation. As shown in Figure 36.5, the size and shape of the hysteresis loops vary with the RF mass concentration, which is indicative of the different mesopore sizes. 

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