Capillary condensation and hysteresis

Capillary Condensation and Hysteresis in Disordered Porous Materials... 

CAPILLARY CONDENSATION AND HYSTERESIS BACKGROUND AND RECENT RESULTS... 

The existing theories for explaining criticalities of capillary condensation and hysteresis can be classified as meniscus theory based on a single idealized pore considering the difference in meniscus shape [1] networking, pore blocking... 

From a theoretical point of view there are of course no new physical principles involved in adsorption on a porous adsorbent. It should therefore be possible to retain the methods discussed in detail above and include capillary condensation and hysteresis within the framework already provided. Thus, it is easy to see that even with hypothetical... 

Mares JW, Weiss SM (2011) Diffusion dynamics of small molecules from mesoporous silicon films by real-time optical interferometry. Appl Opt 50(27) 5329-5337 Naumov S, Khokhlov A, Valiullin R, Karger J, Monson PA (2008a) Understanding capillary condensation and hysteresis in porous silicon network effects within independent pores. Phys Rev E 78(6) 060601-060604... 

On the other hand, these solids are the ideal hosts for a number of active species, comprising enzymes, nanoclusters, etc. [2,3]. Fimctionahzation of the inner surfaces is also possible, which allows grafting of active species, like dyes [4] and metal-containing complexes, e.g., for chiral synthesis [5]. A peculiar feature of these solids is that they provide systems with an a priori known porous structure a side consequence of this has been the rebirth of studies, indeed out of fashion, concerning capillary condensation and hysteresis [6]. 

In practice, the majority of the physisorption isotherms can be divided into six groups (Sing et al, 1985) as shown in Rg. 8.14, each of which has characteristic pore size regimes and pore surface energies. There is a plethora of literature reviews, book chapters and entire books (Do, 1998) dedicated to the understanding of adsorption analysis and as such a full discussion is outside the scope of this chapter. However, the most important isotherms for porous ceramic membrane materials are type I, which corresponds to microporous solids, and types TV and V, which are characteristic of mes-oporous solids (especially ceramics) undergoing capillary condensation and hysteresis during desorption. 

An example of interaction stiffness and force curves for a Si surface with a native oxide at 60% relative humidity (RH) is shown in Fig. 12 [104]. The stiffness and force data show an adhesive interaction between the tip and substrate. The hysteresis on retraction is due to a real change in contact area from surface oxide deformation and is not an experimental artifact. The adhesive force observed during retraction was consistent with capillary condensation and the surface energy measured from the adhesive force was close to that of water. 

Capillary condensation and evaporation do not reversibly take place at the same pressure, which leads to the appearance of hysteresis loops. The hysteresis loop, which is due to the different processes between adsorption into and desorption from the mesopores, is closely related to the pore structure of the mesoporous material.54 86,88 Thus, the pore structures of the mesoporous carbons can be estimated from the shape of the hysteresis loop. 

The saturation of all adsorption sites on the solid surface (6 = 1) is characterized by a plateau in the isotherm. The Langmuir adsorption isotherm is based on the following assumptions the surface is uniform and every adsorption site is equivalent to the others, the substrate surface is saturated when aU adsorption sites are occupied and monolayer formation has occurred, there are no interactions between the adsorbed particles. In general, physisorption isotherms show various shapes. These are, according to the lUPAC classification, types II and III which describe adsorption on nonporous or macroporous adsorbent with strong and weak gas-solid interaction, respectively. Type IV and V are adsorption isotherms which show typically capillary condensation with hysteresis loops and type VI isotherm shows stepwise multilayer adsorption. 

Figure 2.16 Typical nitrogen adsorption-desorption isotherms at 77K for (a) MCM-41 materials templated with alkyltrimethylammonium bromide surfactants with hydrophobic tails of different lengths as indicated (volumes adsorbed for C12, C14, C16 and C18 were incremented by 200, 400, 600 and 800 ml(STP) g, respectively) and (b) nonionic triblock copolymer templated SBA-15 silicas synthesised at different temperatures (volumes adsorbed for 353 K and 373 K were incremented by 200 and 400 ml(STP) respectively). The hysteresis loops observed in this case are typical of the larger mesopores in these materials. Desorption points are represented by closed symbols. Reprinted with permission from Morishige, K. Tateishi, M., Accurate relations between pore size and the pressure of capillary condensation and the evaporation of nitrogen in cylindrical pores, Langmuir, 22, 4165 169. Copyright (2006) American Chemical Society...

In an investigation of the influence of air humidity on adhesion, hysteresis phenomena have been observed [143]. In Fig. IV.IO we show the force of adhesion of spherical glass particles 50 2 /im in diameter as a function of the relative humidity of the air. The lower branch of the hysteresis loop shows the way in which adhesion increases as the air relative humidity is increased the lower branch shows the way in which adhesion drops off as the air humidity is reduced. The failure of the two branches of the adhesion-humidity curve to coincide indicates that the processes of capillary condensation and evaporation of mois-... 

Figure 3.10 (a) Ink-bottle pores associated with hysteresis in capillary condensation, and (b) more practical interconnected pore spaces. 

Consequently, density profiles may be obtained by iteration of Equation 8.16, enabling the calculation of other properties of the fluid such as capillary condensation, adsorption, hysteresis, and phase transition. 

Topic 3.3.3 Capillary condensation and adsorption/desorption hysteresis... 

Porous materials are classified within five types according to the relative positions of their site- and bond- size distributions. This leads to a better understanding of the morphological aspects of the porous medium as well as an assessment of the different mechanisms arising during capillary condensation and evaporation. For each one of these types of materials, relevant characteristics can be recognised in their hysteresis loops. 

The influence of interconnection effects is diagrammatically illustrated on the example of a simple system consisting of one wide capillary of radius pj and two capillaries of radius pj (see Fig. 1). Capillary condensation in cylindrical capillary of radius p occurs at one value of relative pressure x+ (X=P/Ps) and desorption at another value of relative pressure x- The values x+ and X- depend on pore radius p, moreover X-(p)>x+(P) In this inequality the capillary hysteresis on the level of one capillary is displayed. It is conditioned by the difference of the mechanisms of capillary condensation and desorption. Capillary condensation occurs by means of spontaneous filling at the moment of the loss of adsorption film stability on the internal surface of capillary. This process is not reversible. Desorption occurs at the moment of equilibrium meniscus formation on the open end of capillary. 

On this simplest example we see that interconnection effects have essential influence on capillary condensation and desorption processes, and on the shape of hysteresis loop. Ought to remark, that in the literature the main attention was attracted to the blocking effects under desorption, but the effects of capillary condensation s initiation were avoided. Usually the authors assume that the condensation in the network of pores occurs as in the system of unrelated pores (Ref. 1,8). 

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