Capillary Condensation Theory

The capillary condensation theory was first put forward by Zsigmondy in 1911 to explain the adsorption of gases and vapors by porous solids such as charcoals and silica gel, and to explain the adsorption-desorption hystersic in Type IV isotherms. The theory postulates that, in addition to the formation of layers, the adsorbate gas or vapor condenses in the small capillary pores of the adsorbent as a result of the lowering of vapor pressure brought about by surface tension effects. The cause of this vapor pressure lowering hes in a decrease in free energy of the adsorbate molecules in fine capillary pores. 

As the pressure of the gas or the vapor is inaeased, the thickness of the multimolecular layers in the transitional pores inaeases imtil the layer on the opposite walls combine in the narrowest cross-section of the pore and form a meniscus of condensed adsorbate. This meniscus is concave when the adsorbate wets the surface. The molecules of the adsorbate then condense on the meniscus at a pressure lower than the saturation vapor pressure. The lowering of the eqnihbrium vapor pressure over a concave meniscus, as compared with that over a flat surface at the same temperature, is due to the molecules in a concave surface being held by a large number of neighboring molecules, rather than if they were held on a flat surface. The quantitative relationship between the lowering of vapor pressure and the radius of the capillary, known as the Kelvin equation, was given by Thomson (later Lord Kelvin). The Kelvin equation can be written as 

if a vapor or a gas at pressure p is brought into contact with a porous adsorbent, it should condense as a Uqnid in all pores having a radius less than that calculated from the Kelvin eqnation for that particular value of p, assuming that 6 90°. It is also evident that with inCTeasing relative pressure of the gas or the vapor, wider and wider pores become filled by the condensed adsorbate. Simultaneonsly, with this process of condensation, bnilding up of multimolecular layers continues in pores whose width is snch that the pressure attained is as yet too low for the existing multimolecular layers to permit the formation of a meniscus. At the saturation vapor pressure, the entire pore system is full of the condensate. 

The capillary condensation theory is in conflict with the multiplayer theory of adsorption bnt receives support from certain experimental results. 

It is now firmly believed that adsorption-desorption hysteresis is a direct consequence of capillary condensation in pores of the adsorbent. In fact, Zsigmondy put forward the capillary condensation theory to explain the phenomenon of hysteresis. It has been found that adsorption and desorption curves in certain cases do not meet each other along the whole course of the isotherm so that under a certain pressure the equilibrium amount adsorbed is higher when this pressure is approached from the side of higher pressure (i.e., during desorptio) than when it is approached from the side of lower pressures (i.e., during adsorption). The irreproducibility of this adsorption curve 

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Capillary condensation has been used to evaluate the pore size distribution of mesopores. Various adsorption studies on regular mesoporous silica such as MCM-41 or FSM showed the limitation of the classical capillary condensation theory [1-9]. In the case of the evaluation of the pore size distribution, we assumed that condensates in mesopores are liquid. Recent systematic studies on structures of molecules confined in micropores... 

The adsorption isotherm of N, on FSM-16 at 77 K had an explicit hysteresis. As to the adsorption hysteresis of N-, on regular mesoporous silica, the dependencies of adsorption hysteresis on the pore width and adsorbate were observed the adsorption hysteresis can be observed for pores of w 4.0nm. The reason has been studied by several approaches [5-8]. The adsorption isotherm of acetonitrile on FSM-16 at 303K is shown in Fig. 1. The adsorption isotherm has a clear hysteresis the adsorption and desorption branches close at PIP, = 0.38. The presence of the adsorption hysteresis coincides with the anticipation of the classical capillary condensation theory for the cylindrical pores whose both ends are open. The value of the BET monolayer capacity, nm, for acetonitrile was 3.9 mmol g. By assuming the surface area from the nitrogen isotherm to be available for the adsorption of acetonitrile, the apparent molecular area, am, of adsorbed acetonitrile can be obtained from nm. The value of am for adsorbed acetonitrile (0.35 nnr) was quite different from the value (0.22 nm2) from the liquid density under the assumption of the close packing. Acetonitrile molecules on the mesopore surface are packed more loosely than the close packing. The later IR data will show that acetonitrile molecules are adsorbed on the surface hydroxyls in... 

The capillary condensation theory provides a satisfactory explanation of the phenomenon of adsorption hysteresis, which is frequently observed for porous solids. Adsorption hysteresis is a term which is used when the desorption isotherm curve does not coincide with the adsorption isotherm curve (Figure 5.8). 

Although the routine analytical method of porosity such as BET analysis is established for mesoporous and macroporous solids, nanoporosity evaluation method is not necessarily established. As the term of nanoporosity is not recommended by lUPAC, we need to define the nanoporosity here. The classical capillary condensation theory using the Kelvin relation has a catastrophe for the pores whose pore width w is less than about 4 nm in the N2 adsorption isotherm at 77 K N2 adsorption isotherms even on cylinderical mesopores of w < about 4 nm and open both ends at 77 K disappear, which cannot be described by the classical theory. [6,7] Hence, it is quite convenient to use the nanopores in this articles for the pores whose pore width is less than about 5 nm. 

The calculation methods for pore distribution in the microporous domain are still the subject of numerous disputes with various opposing schools of thought , particularly with regard to the nature of the adsorbed phase in micropores. In fact, the adsorbate-adsorbent interactions in these types of solids are such that the adsorbate no longer has the properties of the liquid phase, particularly in terms of density, rendering the capillary condensation theory and Kelvin s equation inadequate. The micropore domain (0.1 to several nm) corresponds to molecular sizes and is thus especially important for current preoccupations (zeolites, new specialised aluminas). Unfortunately, current routine techniques are insufficient to cover this domain both in terms of the accuracy of measurement (very low pressure and temperature gas-solid isotherms) and their geometrical interpretation (insufficiency of semi-empirical models such as BET, BJH, Horvath-Kawazoe, Dubinin Radushkevich. etc.). 

Although capillary condensation theory has devoted to the determination of pore size distribution of mesopores, adsorption studies on regular mesoporous silica such as MCM-41 [1,2] or FSM [3,4] pointed that classical capillary condensation theory cannot explain the dependence of the adsorption hysteresis on the pore width. Also we have assumed that condensed states in mesopores have the same as bulk liquid. In case of molecules adsorbed in... 

In our efforts to verify deductively our modified capillary condensation theory we found two commercial porous bodies in which spherical elementary particles are arranged in a definite pattern. Therefore, if the radius of the elementary particles and their packing are given, a whole model of pore structure is clearly available for these specimens. By using these specimens as a catalyst or a catalyst carrier a series of investigations was carried out on catalytic activity in relation to the pore structure. 

A NEW CAPILLARY CONDENSATION THEORY AND THE PORE STRUCTURE OF SORBENT... 

During the period 1937-1940 Higuchi proposed a modified capillary condensation theory to explain the isotherms of 18 sorbates on titania gel of the same lot. The new theory proposes that in sorption phenomena vapors may be adsorbed in two ways (a) adsorption due to the surface force of solid sorbents which is usually accomplished by forming a monomolecular film in the relatively low pressure range and (b) capillary condensation of sorbates into pores whose radii are larger than ca. 10 A and covered by an adsorption film. The capillary condensation is undoubtedly due to the vapor pressure depression of the sorbate liquid described by the Thompson equation. 

The new capillary condensation theory, if essentially valid, claims that the shape of isotherms measured up to saturation, that is, x = PjP = 1, is determined by the pore size distribution of porous bodies, and so any theory to explain sorption isotherms by thermodynamic or kinetic mechanisms becomes meaningless except with respect to the formation of monolayer adsorption. Therefore an important problem in sorption is to investigate the pore structure of sorbent specimens, which are easily varied by varying the conditions of their preparation, and to elucidate the pore structure in relation to the material properties. 

This technique can be considered a standard method in the science of porous ceramics and catalysts. It is based on the principle that inside a small pore a gas can condense to a liquid at a relative pressure lower than unity this introduces the capillary condensation theory. The adsorption and desorption isotherms of an inert gas are determined as a function of the relative pressure (prei = pIpQ, i.e., the ratio between the applied pressure and the saturation pressure). N2 is often used as adsorption gas, and the experiments are carried out at the boiling liquid nitrogen temperature (at 1 bar). The adsorption isotherm... 

The modified BET equations for n layers and for type IV and V need some discussion. This is done by comparing the theory of van der Waals adsorption and the capillary condensation theory. The porous solid is assumed to consist of capillaries bounded by two parallel planes, and the spacing between the two layers is denoted as D. This simple configuration is sufficient for our discussion. 

According to the capillary condensation theory (which will be treated in more details in Section 3.9), the pressure at which the condensation will take place in a pore of width D is ... 

The onset of the hysteresis loop indicates the start of the capillary condensation mechanism. The desorption curve (AB C) is always above the adsorption branch (ABC), that is for a given loading adsorbate desorbs from a porous solid at a lower pressure than that required for adsorption. Before proceeding with the analysis of the isotherm, we first start with the basic capillary condensation theory of Lord Kelvin, the former William Thompson. 

This limiting potential, Aq, is independent of adsorbent but is a function of adsorbate. Using the capillary condensation theory, the limiting pore radius r jr corresponding to A r is calculated from ... 

We first consider the capillary condensation. The proposed capillary condensation theory of adsorption assumes that for a given adsorbate, pressure P and temperature T, certain pores of the adsorbent (0 < r < r ) are filled with the... 

According to the Kelvin s capillary condensation theory, the vapour pressure depressed by the curvature of a fluid residing in a cylindrical pore is ... 

Eq. (6.13-16) represents an adsorption isotherm for vapours based on the capillary condensation theory of adsorption. This new isotherm has the correct limits at low pressure as well as when pressure approaches the vapour pressure. 

These sizes can be determined from the aspect of N, adsorption at 77 K, and hence N2 molecules are adsorbed by different mechanisms -multilayer adsorption, capillary condensation, and micropore filling for macropores, mesopores, and micropores, respectively. The critical widths of 50 and 2 nm are chosen from empirical and physical reasons. The pore width of 50 nm corresponds to the relative pressure of 0.96 for the adsorption isotherm. Adsorption experiments above that are considerably difficult and applicability of the capillary condensation theory is not sufficiently examined. The smaller critical width of 2 nm corresponds to the relative pressure of 0.39 through the Kelvin equation, where an unstable... 

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