Porous solids pore size distribution, determination

A Type II isotherm indicates that the solid is non-porous, whilst the Type IV isotherm is characteristic of a mesoporous solid. From both types of isotherm it is possible, provided certain complications are absent, to calculate the specific surface of the solid, as is explained in Chapter 2. Indeed, the method most widely used at the present time for the determination of the surface area of finely divided solids is based on the adsorption of nitrogen at its boiling point. From the Type IV isotherm the pore size distribution may also be evaluated, using procedures outlined in Chapter 3. 

In writing the present book our aim has been to give a critical exposition of the use of adsorption data for the evaluation of the surface area and the pore size distribution of finely divided and porous solids. The major part of the book is devoted to the Brunauer-Emmett-Teller (BET) method for the determination of specific surface, and the use of the Kelvin equation for the calculation of pore size distribution but due attention has also been given to other well known methods for the estimation of surface area from adsorption measurements, viz. those based on adsorption from solution, on heat of immersion, on chemisorption, and on the application of the Gibbs adsorption equation to gaseous adsorption. 

Although a number of methods are available to characterize the interstitial voids of a solid, the most useful of these is mercury intrusion porosimetry [52], This method is widely used to determine the pore-size distribution of a porous material, and the void size of tablets and compacts. The method is based on the capillary rise phenomenon, in which excess pressure is required to force a nonwetting liquid into a narrow volume. 

ISEC, which was introduced by Halasz and Martin in 1978 [119], represents a simple and fast method for the determination of the pore volnme, the pore size distribution profile, and the spe-cihc snrface area of porous solids. Generally, ISEC is based on the principle of SEC. SEC, also referred to as gel permeation or gel filtration chromatography, is a noninteractive chromatographic method that separates analytes according to their size by employing a stationary phase that exhibits a well-dehned pore distribution. 

The pore-size distribution is the distribution of pore volume with respect to pore size (Figure 3.66). It is an important factor controlling the diffusion of reactants and products in the porous solid and thus an essential property for its characterization. The computation of pore size distribution involves a number of assumptions, and therefore reporting of the data should always be accompanied by an indication of the method used for its determination. 

To achieve a significant adsorptive capacity an adsorbent must have a high specific area, which implies a highly porous structure with very small micropores. Such microporous solids can be produced in several different ways. Adsorbents such as silica gel and activated alumina are made by precipitation of colloidal particles, followed by dehydration. Carbon adsorbents are prepared by controlled burn-out of carbonaceous materials such as coal, lignite, and coconut shells. The crystalline adsorbents (zeolite and zeolite analogues are different in that the dimensions of the micropores are determined by the crystal structure and there is therefore virtually no distribution of micropore size. Although structurally very different from the crystalline adsorbents, carbon molecular sieves also have a very narrow distribution of pore size. The adsorptive properties depend on the pore size and the pore size distribution as well as on the nature of the solid surface. 

Early studies involving NMR include the work by Hanus and Gill is [6] in which spin-lattice relaxation decay constants were studied as a function of available surface area of colloidal silica suspended in water. Senturia and Robinson [7] and Loren and Robinson [8] used NMR to qualitatively correlate mean pore sizes and observed spin-lattice relaxation times. Schmidt, et. al. [9] have qualitatively measured pore size distributions in sandstones by assuming the value of the surface relaxation time. Brown, et. al. [10] obtained pore size distributions for silica, alumina, and sandstone samples by shifting the T, distribution until the best match was obtained between distributions obtained from porosimetry and NMR. More recently, low field (20 MHz) NMR spin-lattice relaxation measurements were successfully demonstrated by Gallegos and coworkers [11] as a method for quantitatively determining pore size distributions using porous media for which the "actual" pore size distribution is known apriori. Davis and co-workers have modified this approach to rapidly determine specific surface areas [12] of powders and porous solids. 

Stoeckli and Kraehenbuehl [1984] have proposed a relationship between the heat of immersion and the micropoious volume of a porous solid, applicable to materials having a wide range of external surface areas. This allows a rapid determination of the pore size distribution below 0.8 to 1 nm. The technique, however, requires a non-porous standard material of surface composition similar to the membrane material. 

The measurement of the heat of immersion of a "dry" material in different liquids can permit a rapid and accurate determination of the surface area and pore size distribution below 10 A. The enthalpy change is related to the extent of the solid surface, to the presence of micropores and to the chemical and structural nature of the surface. The technique has been mainly applied to carbons [64]. The immersion liquid is usually water for hydrophilic oxides like mineral oxides, or an organic liquid (benzene, n-hexane) for hydrophobic solids like carbons. One of the limitations of this technique is that the specific enthalpy of immersion of the open surface must be determined with a non-porous standard material of surface composition similar to the porous solid studied. The non-microporous part of the surface area can be determined by prefilling the micropores with an absorbate prior to immersion. Information on the size of micropores can be obtained from the kinetics and enthalpy of immersion into a set of liquids with increasing molecular size [5]. 

J. P. Olivier, W.B. Conklin and M.V. Szombathely, Determination of pore size distribution from density functional theory a comparison of nitrogen and argon results, in J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.), Characterization of Porous Solids III, Studies in Surface Science and Catalysis Vol. 87, Proc. of the lUPAC Symposium (COPS III), Marseille, France, May 1993, Elsevier Amsterdam, 1994, pp. 81-90. 

Thermoporometry. This method is based on the observation that the equilibrium conditions of solid, liquid and gaseous phases of a highly dispersed pure substance are determined by the curvature of the interface (s) (10,17). In the case of a liquid (in this work, pure water) contained in a porous material (the membrane), the solid-liquid interface curvature depends closely on the size of the pores. The solidification temperature therefore is different in each pore of the material. The solidification thermogram can be translated into a pore size distribution of the membrane with the help of the equations derived by Brun (17). For cylindrical pores, with water inside the pores, it leads to the following equations ... 

The pore size distribution function is an important characteristic of a porous solid. Given a pore size distribution J H) and a set of local isotherms pip, H) determined by any methods presented in Sections 11.3—11.5, the overall amount adsorbed is given by... 

Physical-adsorption studies are valuable in determining the physical properties of solid catalysts. Thus the questions of surface area and pore-size distribution in porous catalysts can be answered from physical-adsorption measurements. These aspects of physical adsorption are considered in Secs. 8-5 and 8-7. 

Thermoporimetry [10,11] can reliably be used to obtain the pore-size distribution of porous particles suspended in water. The basis of the technique is that the surface area of the ice-liquid water interface increases when the ice penetrates narrow pores. As the diameter of a pore is smaller, the increase in interfacial area is larger. To freeze the water in narrower pores thus requires lower temperatures. The temperature at which the heat of solidification of water is set free thus indicates the width of the pores, and the amount of heat released indicates the pore volume. Measurement by DSC (differential scanning calorimetry) can provide the data for determination of the pore-size distribution of porous particles suspended in pure water. It has been observed that the first layer of water molecules present on the surface of oxides cannot be frozen apparently the interaction with the surface of the oxides is so high that the layer is already frozen without attaining the structure of ice. Thermoporimetry can, therefore, also provide data about the interaction of water with the surfaces of solids. Thermoporimetry with other liquids, e. g. benzene, can provide information about the interaction of surfaces with, e. g., apolar liquids. 

The morphologic characterization of the immobilized enzyme is important to correlate the biocatalyst performance with porous structure parameters. BET analysis, which is usually based on N2 isothermal adsorption at 77 K, allows determining the solid-specific surface area, total pore volume, pore size distribution, and mean pore diameter. It is not recommended for solids with a low specific surface area (<5 m g ). Table 2 shows the specific smface area, mean pore diameter, and total pore volume determined by BET for the pure sol-gel silica matrix having TEOS as the precursor and the same matrix with the encapsulated CGTase. 

Pore systems of solids may vary substantially both in size and shape. Therefore, it is somewhat difficult to determine the pore width and, more precisely, the pore size distribution of a solid. Most methods for obtaining pore size distributions make the assumption that the pores are nonintersecting cylinders or slit-Uke pores, while often porous solids actually contain networks of interconnected pores. To determine pore size distributions, several methods are available, based on thermodynamics (34), geometrical considerations (35-37), or statistical thermodynamic approaches (34,38,39). For cylindrical pores, one of the most commonly applied methods is the one described in 1951 by Barrett, Joyner, and Halenda (the BJH model Reference 40), adapted from... 

A general problem of the MIP technology—as it had been established during the last decades—is linked to the simultaneous—and widely random—formation of the imprinted receptor sites and the polymer matrix. A certain amount of matrix material is required to host and stabilize the receptor sites. This polymer can form a nonporous or a porous structure in the first case receptor sites on the solid surface determine MIP performance, in the latter case pore size and pore size distribution as well as pore connectivity play an additional role. Random distribution and uneven accessibility of imprinted receptor sites in the (three-dimensional) volume of an MIP material—typically particles—are characteristic for the state of the art. 

The parameter Bq is the viscous flow parameter and is a function of solid structure only. Since a porous solid usually exhibits a pore size distribution, this parameter must be determined experimentally. 

Olivier J P, Conklin W B, Vonszombathely M (1994) Determination of Pore-Size Distribution from Density-Functional Theory - a Comparison of Nitrogen and Argon Results. Characterization of Porous Solids III 87 81-89... 

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