Capillary condensation distribution measurements

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

Where there is a wide distribution of pore sizes and, possibly, quite separately developed pore systems, a mean size is not a sufficient measure. There are two methods of finding such distributions. In one a porosimeter is used, and in the other the hysteresis branch of an adsorption isotherm is utilised. Both require an understanding of the mechanism of capillary condensation. 

Determination of Pore Size Distributions. The shape and range of a GPC calibration curve are, in part, a reflection of the pore size distribution (PSD) of the column packing material. A consideration of the nature of PSDs for the ULTRASTYRAGEL columns to be used in this work is therefore appropriate. The classical techniques for the measurement of PSDs are mercury porisimetry and capillary condensation. The equipment required to perform these measurements is expensive to own and maintain and the experiments are tedious. In addition, it is not clear that these methods can be effectively applied to swellable gels such as the styrene-divinylbenzene copolymer used in ULTRASTYRAGEL columns. Both of the classical techniques are applied to dry solids, but a significant portion of the pore structure of the gel is collapsed in this state. For this reason, it would be desirable to find a way to determine the PSD from measurements taken on gels in the swollen state in which they are normally used, e.g. a conventional packed GPC column. 

The same equipment as that for measuring surface area can be used to determine the pore size distribution of porous materials with diameters of 20 to 500 A, except that high relative pressures are used to condense N2 in the catalyst pores. The procedure involves measuring the volume adsorbed in either the ascending or the descending branch of the BET plot at relative pressures close to 1. Capillary condensation occurs in the pores in accordance with the Kelvin equation,... 

Before and after experiments the pore sizes of the membranes were measured by permpo-rometry [16], a technique based on blocking of smaller pores by capillary condensation of cyclohexane and the simultaneous measurement of the permeance of oxygen gas through the larger, open pores. The measurements are performed at 20°C on an area of 8.5 10 4 m2. The pore size distribution (Kelvin radii) is determined in the desorption stage using the Kelvin equation. More details on the permporometry technique can be found in [17] and all experimental details of the permporometry apparatus are presented in [16],... 

An excellent material for checking the validity of the corrected Kelvin equation is chrysotile, Mg3(0H)4.Si20s, which consists of hollow needles, the pore volume distribution of which can be measured both by means of calibrated electron microscopy and nitrogen capillary condensation [18]. It appears that capillary... 

Experimental techniques commonly used to measure pore size distribution, such as mercury porosimetry or BET analysis (Gregg and Sing, 1982), yield pore size distribution data that are not uniquely related to the pore space morphology. They are generated by interpreting mercury intrusion-extrusion or sorption hysteresis curves on the basis of an equivalent cylindrical pore assumption. To make direct comparison with digitally reconstructed porous media possible, morphology characterization methods based on simulated mercury porosimetry or simulated capillary condensation (Stepanek et al., 1999) should be used. 

The phenomenon of capillary condensation provides a method for measuring pore-size distribution. Nitrogen vapor at the temperature of liquid nitrogen for which cos(0) = 1 is universally used. To determine the pore size distribution, the variation in the amount of nitrogen inside the porous particle is measured when the pressure is slightly increased or decreased. This variation is divided into two parts one part is due to true adsorption and the other to capillary condensation. The variation due to adsorption is known from adsorption experiments with nonporous substances of known surface area, so the variation due to condensation can be calculated. The volume of this amount of nitrogen is equal to the volume of pores with the size as determined by the Kelvin equation. Once a certain model has been selected for the complicated pore geometry, the size of the pores can be calculated. Usually it is assumed that an array of cylindrical capillaries of uniform but different radii, and randomly oriented represents the porous medium. So the Kelvin equation in the form of Equation 3.9 is used. Since condensation is combined with adsorption, the thickness of the adsorption layer... 

N2 adsorption measurements at 77 K on both the AI2O3 and Novacarb samples show a type IV isotherm with a type A hysteresis loop, indicative of the presence of mesopores with cylindrical pore geometry (Figs. 5a and 5b) [1]. The almost vertical capillary condensation step indicates a relatively narrow distribution of mesopores. Application of the Broekhoff-de Boer (BdB) model leads to a narrow PSD centered around 8 and 15 nm for AI2O3 and carbon, respectively. 

Capillary condensation provides the possibility of blocking pores of a certain size with the liquid condensate simply by adjusting the vapor pressure. A permporometry lest usually begins at a relative pressure of 1, thus all pores filled and no unhindered gas transport. As the pressure is reduced, pores with a size corresponding to the vapor pressure applied become emptied and available for gas transport. The gas flow through the open mesopores is dominated by Knudsen diffusion as will be discussed in Section 4.3.2 under Transport Mechanisms of Porous Membranes. The flow rate of the noncondensable gas is measured as a function of the relative pressure of the vapor. Thus it is possible to express the membrane permeability as a function of the pore radius and construct the size distribution of the active pores. Although the adsorption procedure can be used instead of the above desorption procedure, the equilibrium of the adsorption process is not as easy to attain and therefore is not preferred. 

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.). 

In terms of catalysis, important equilibrium processes include low-temperature gas adsorption (capillary condensation) and nonwetting fluid invasion, both of which are routinely used to characterize pore size distribution. Static diffusion in a Wicke-Kallenbach cell characterizes effective diffusivity. The simultaneous rate processes of diffusion and reaction determine catalyst effectiveness, which is the single most significant measure of practical catalytic reactor performance. 

Specific surface areas and pore size distributions of mesoporous materials are best probed by nitrogen/argon adsorption and capillary condensation which will be outlined in detail below. It should be emphasized that the concept of specific surface area is not applicable when the size of the sorbed molecules approaches the diameter of the pore. Thus, for microporous substances values for specific surface areas have no physical meaning, but are rather characteristic of the volume of gas adsorbed. Nevertheless, these values are frequently used as practical numbers to compare the quality and porosity of microporous materials. The average pore size of microporous materials has to be probed by size exclusion measurements. For this purpose the uptake of a series of sorbates with increasing minimal kinetic diameter on a solid are explored. The drop in the adsorbed amount with increasing size of the sorbate defines the minimum pore diameter of the tested solid. The method will be described in detail below. 

For a chosen value of plpo, Eqs. (8-22) and (8-23) give the pore radius above which all pores will be empty of capillary condensate. Hence, if the amount of desorption is measured for various plpo, the pore volume corresponding to various radii can be evaluated. Differentiation of the curve for cuniulative pore volume ys radius gives the distribution of volume as described in Example 8-6. Descriptions of the method of computation are given by several investigators. As in the mercury-penetration method, errors will result unless each pore is connected to at least one larger pore. 

As a result of the drastic chemical and structural changes of the bulk material, the BET surface area of the amorphous precursor increases from 0.025 to about 60 m2/g depending on the oxidation conditions. Pore-size distribution measurements using nitrogen capillary condensation indicated that the material contained mainly pores of 2-4 nm size besides some larger pores. 

Plachenov (96, 97) estimated the limiting dimensions of the equivalent radii of mesopores. The distribution of the volume of the mesopores calculated from their equivalent radii was compared with capillary condensation measurements. The macroporous and the intermediate mesoporous structure were determined, as were the volume of the micropores and the constant in the equation of the isotherm adsorption theory describing the volume filling of micropores (133, 134). 

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. 

In the above sections, we have amply shown that capillary condensation occurs in the contact zones of elementary particles and the shape of isotherms measured up to a = 1 is determined by existing pore distributions of the porous materials. In addition, it has been shown by sorption methods that porous Vycor glass and Neobead C-5 are ideal porous bodies consisting of spherical elementary particles arranged in characteristic types of packing. Based on these idealized models, we have calculated the effective diffusion coefficients in these porous bodies. 

For the actual catal5dic reaction, the distribution of meso- and micropores is of greater importance. The specific pore volume, pore size, and pore size distribution of microporous materials are determined by gas adsorption measurements at relatively low pressures (low values of p/po = pressure/saturation pressure). The method is based on the pressure dependence of capillary condensation on the diameter of the pores in which this condensation takes place. To calculate the pore size distribution, the desorption isotherm is also determined. Thus a distinction can be made between true adsorption and capillary condensation. The latter is described by the Kelvin equation (Eq. 5-95). 

A pore size distribution (PSD) of a sample is a measure of the cumulative or differential pore volume as a function of pore diameter. PSDs can be calculated from adsorption isotherms based on an analysis which accounts for capillary condensation into pores. This analysis (14.16) uses a model of the pore structure combined with the Kelvin equation (12) to relate the pore size to the value of p/Po at which pore "filling" occurs. Due to limitations in this technique, only pores with diameters from about 3 to 50 nm, called mesopores (14), can be characterized. This pore size range, however, is typical of many porous samples of interest. For samples with pores smaller or larger than this range, alternative techniques, such as mercury intrusion for large pores (14.16), are typically more suitable. 

Individual primary particles could be dense, while agglomerates are most likely porous. Therefore, it is desirable to quantitatively characterize the porosity and pore size and distribution of the agglomerates. For accessible pores, i.e., those that are not completely isolated from the external surface, they can be characterized by using two methods (i) gas adsorption, also known as capillary condensation and (ii) mercury intrusion porosimetry, also called mercury porosimetry for simplicity. The pore size can be diameter, radius, or width. Three types of pores have been classified according to their sizes micropores (<2 nm), mesopores (2-50 nm), and macropores (>50 nm). Generally, gas condensation is applicable to the measurement in mesopores, whereas mercury porosimetry is more suitable to macropores. 

In order to elucidate this problem, Bukhavtsova and Ostrovskii [9] have studied experimentally the reaction kinetics on the catalysts with (and without) capillary condensation. The model catalysts Pt/Si02 with approximately the same characteristics except porous structure (Table 23.4) were used. Two modifications of support Si02 were used KCK-1 with relatively large pores, and KCM-5 with small pores (Figure 23.8). Except pore size distribution, the platinum distribution among the pores with different size was measured by adsorption method [53]. 

In gas adsorption measurements, there is a critical lower value of relative pressure, e.g., / // o 0.4 for nitrogen, below which capillary condensate cannot exist as a separate phase, no matter whether the pore system extends to finer pores or not this is a consequence of the existence of so-called tensile strength limit [6]. As a result of this, a very narrow false maximum may appear on the differential pore size distribution at its fine-pore end, typically between 17 and 20 A in the case of nitrogen. 

The determination of the pore size distribution by application of the Kelvin equation to the capillary condensation part of the Type IV isotherms is almost entirely restricted to the use of nitrogen as the adsorbing gas. This is largely a reflection of the widespread use of nitrogen for surface area measurements so that both surface area and pore size distribution can be obtained from the same isotherm. If the volume of gas adsorbed on the external surface of the solid is... 

The results obtained from the indirect methods are often controversial, because actually it is not a pore system that is examined but rather the processes applied in these methods the results reflect only the pore size distribution response. Any established value of pore diameter has only conventional meaning and may be different than diameters obtained from other methods. The indirect methods more or less influence the object of observation and measurements because the interventions disrupt material structure. Determining of distribution of pore diameters in cement paste is performed by the mercury porosimetry method and the results are partly confirmed by observations and counting the pores by computer image analysis, but mercury intrusion may damage and alter the material microstructure. Furthermore, the intrusion of mercury into a pore is related to the orifice of the pore rather than to its real dimension (Diamond 2000). Other methods, like capillary condensation, give considerably different values. 

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