Pore Size distribution: relation measurement

Pores are holes, cavities and/or channels communicating with the silica surface. Pores can be regarded as cylinders with a diameter, p, usually measured in nm, sometimes in A (=0.1 nm). Their total volume is the pore volume, Vp, measured in cmVg or mL/g of material. The pore size distribution is measured by the mercury intrusion method [1,4]. A good chromatographic silica packing should have a narrow pore size distribution. In such case, pore volume, pore diameter and specific surface area can be linked by the approximative relation ... 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Another property of importance is the pore volume. It can be measured indirectly from the adsorption and/or desorption isotherms of equilibrium quantities of gas absorbed or desorbed over a range of relative pressures. Pore volume can also be measured by mercury intrusion techniques, whereby a hydrostatic pressure is used to force mercury into the pores to generate a plot of penetration volume versus pres- sure. Since the size of the pore openings is related to the pressure, mercury intrusion techniques provide information on the pore size distribution and the total pore volume. 

Most size exclusion chromatography (SEC) practitioners select their columns primarily to cover the molar mass area of interest and to ensure compatibility with the mobile phase(s) applied. A further parameter to judge is the column efficiency expressed, e.g., by the theoretical plate count or related values, which are measured by appropriate low molar mass probes. It follows the apparent linearity of the calibration dependence and the attainable selectivity of separation the latter parameter is in turn connected with the width of the molar mass range covered by the column and depends on both the pore size distribution and the pore volume of the packing material. Other important column parameters are the column production repeatability, availability, and price. Unfortunately, the interactive properties of SEC columns are often overlooked. 

Thermoporometry [107] has also been used in evaluating resin porosity [108] and in effect gives information on the solvent wetted state of resins. The technique exploits the phenomenon that the freezing point of a liquid is depressed when it is confined in pores of small radius. Calorimetric measurements on solvent imbibed resins at increasingly reduced temperatures allows a distribution curve to be generated. This in turn can be related to a pore size distribution. The technique is not routine nor widely practiced and more information is available in reference [17]. 

Adsorption studies leading to measurements of pore size and pore-size distributions generally make use of the Kelvin equation which relates the equilibrium vapor pressure of a curved surface, such as that of a liquid in a capillary or pore, to the equilibrium pressure of the same liquid on a plane surface. Equation (8.1) is a convenient form of the Kelvin equation ... 

The performance of a catalyst in industrial usage is likely to be determined by its pore structure, that is to say, by its total pore volume and its pore size distribution. In cases where the active phase is mounted on a porous support, its pore characteristics may affect the accessibility of the active phase to the reactants, as well as other features of the catalyst s performance. For these and other reasons it is important to have agreed and reliable procedures for the measurement of these and related quantities progress in this direction is surveyed in Section 11.1.4.7. 

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 applied pressure is related to the desired pore size via the Washburn Equation [1] which implies a cylindrical pore shape assumption. Mercury porosimetry is widely applied for catalyst characterization in both QC and research applications for several reasons including rapid reproducible analysis, a wide pore size range ( 2 nm to >100 / m, depending on the pressure range of the instrument), and the ability to obtain specific surface area and pore size distribution information from the same measurement. Accuracy of the method suffers from several factors including contact angle and surface tension uncertainty, pore shape effects, and sample compression. However, the largest discrepancy between a mercury porosimetry-derived pore size distribution (PSD) and the actual PSD usually... 

Nitrogen adsorption/condensation measurements were performed using an Autosorb-1 analyzer to calculate sample surface area and pore size distribution. BET analysis at 77 K was applied for extracting the monolayer capacity from the adsorption isotherm and a N molecular cross-sectional area of 0.162 nm2 was used to relate tne monolayer capacity to surface area. PSD s were calculated from the desorption branches of the isotherms using a modified form of the BJH method [18]. Mercury intrusion measurements were performed using an Autoscan-33 continuous scanning mercury porosimeter (12-33000 psia) and a contact angle of 140°. 

The measured true density of clinker is typically 3150-3200 kg m the value calculated from the X-ray densities and typical proportions of the individual phases is about 3200kgm" The difference is probably due mainly to the presence of pores inaccessible to the fluids used in the experimental determination. Using mercury porosimetry. Butt et al. (B35) determined pore size distributions and discussed their relations with burning and cooling conditions and grindability. 

Now, an important question is How, those parameters Sp, Vp, (Dmax/2c), c, and x are affected by the gradual narrowing of pores due to some kind of surface functionalization A second question is which of, and how, the parameters t, c and (Dmax/2o) are interrelated. The question becomes more interesting, and perhaps intriguing, since all the above quantities are calculated just from one kind of measurement, namely the N2 adsorption/desorption data. A partly answer to the above question was attempted in a previous work [10] in which sixteen mesoporous vanado-phoshoro-aluminates solids were tested and some relationships between c and (Dmax/2o) were established. A first target of this paper is to extend the search for such possible inter-relations to a class of mesoporous silicas, with a random pore size distribution whose porosity has been systematically and gradually modified by surface fiinctionalization... 

Pore Size Distribution. The pore size distribution is a measure of the average size of the pores and the variability of pore sizes. It is usually determined by mercury porosimetry. This technique is based on a simple conceptual model of the pores that treats the pores as capillary tubes. The pressure required to force mercury into a pore (assuming that the pore behaves like a circular capillary) can be related to the radius of the pore by... 

Shalliker, R.A. Douglas, G.K. Rintoul, L. Comino, P.R. Kavanagh, P.E. The measurement of pore size distributions, surface areas, and pore volumes of zirconia and zirconia-silica mixed oxide stationary phases using size exclusion chromatography. J. Liq. Chromatogr. Relat. Technol. 1997, 20 (10), 1471-1488. 

The objective of this chapter is to present the fundamental theories of adsorption followed by the description and discussion of experimental techniques for the measurements of adsorption isotherms and for the determination of surface area and pore size distribution. The adsorption of gases on microporous membranes and the inter-relation between adsorption and permeation are then discussed. The adsorption in liquid phase is briefly presented. The chapter concludes with a brief summary. 

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]. 

The modelling of gas permeation has been applied by several authors in the qualitative characterisation of porous structures of ceramic membranes [132-138]. Concerning the difficult case of gas transport analysis in microporous membranes, we have to notice the extensive works of A.B. Shelekhin et al. on glass membranes [139,14] as well as those more recent of R.S.A. de Lange et al. on sol-gel derived molecular sieve membranes [137,138]. The influence of errors in measured variables on the reliability of membrane structural parameters have been discussed in [136]. The accuracy of experimental data and the mutual relation between the resistance to gas flow of the separation layer and of the support are the limitations for the application of the permeation method. The interpretation of flux data must be further considered in heterogeneous media due to the effects of pore size distribution and pore connectivity. This can be conveniently done in terms of structure factors [5]. Furthermore the adsorption of gas is often considered as negligible in simple kinetic theories. Application of flow methods should always be critically examined with this in mind. 

The pore-size distribution of porous media is inherently important, as it is directly related to such characteristics as fluid flow and storage, and multiphase fluid distribution and displacement. The methods used to measure the pore-size distribution include image... 

Some authors (7, ) have used measured parameters of solute and solvent transport for calculation of membrane pore size distributions. Difficulties associated with this approach are of both experimental and theoretical nature. The experiments need to be carried out under conditions that minimize or eliminate effects of boundary phenomena (polarization) and of solute adsorption (fouling) on the measured coefficients. This is rarely done. An even more serious obstacle in this approach is the absence of quantitative and valid relations between measured transport parameters and the size parameters of a "representative pore."... 

Microfiltration membranes are characterized by bubble point and pore size distribution whereas the UF membranes are typically described by their molecular weight cutoff (MWCO) value. The bubble point pressure relates to the largest pore opening in the membrane layer. This is measured with the help of a bubble point apparatus.t Jt l The average pore diameter of a MF membrane is determined by measuring the pressure at which a steady stream of bubbles is observed. For MF membranes, bubble point pressures vary depending on the pore diameter and nature of membrane material (e.g., hydrophobic or hydrophilic). For example, bubble point values for 0.1 to 0.8 pm pore diameter membranes are reported to vary from 1 bar (equals about... 

Size can refer to volume, area, or length, and therefore pore-size distribution may be defined in terms of any one of these properties. In practice, the definition of size adopted is highly dependent upon the method of measurement. For example, the area size distribution of pores is often measured by image analysis of soil thin sections, while water retention data are usually interpreted in terms of the distribution of pore diameters (Bullock Thomasson, 1979). For consistency with the definition of the Peclet number, we have chosen to define size in terms of length, L. Dullien (1991) has proposed the following interrelationships between the different definitions of size L = VIS in three-dimensions or L=AJP in two-dimensions, where V is volume, S is surface area, A is cross-sectional area and P is perimeter. These relations can be used to compare pore-size distributions measured using different methods. 

Since carbon molecular sieves are amorphous materials, the dimensions of their pore structures must be measured phenomenologically by the adsorption of small probe molecules with different critical dimensions. There is insufficient long range order to utilize standard x-Ray diffraction methods for characterization. The earliest reports of molecular sieving carbons dealt primarily with coals and charcoals. Sorption of helium, water, methanol, n-hexane, and benzene was measured and related to the porosity of the carbon. Pore-sizes were estimated to be two to six angstroms (3-6). In a classic paper P.H. Emmett described methods for tailoring the adsorptive properties and pore size distributions of carbon Whetlerites. 

Measurement of the porosity of plasma-sprayed ceramic coatings can be accomplished by a wide variety of methods that can be divided into those yielding as a result a simple number, the porosity or pore volume related to the total volume of the coating in cm3 g-1, and those that yield a pore size distribution function. In many cases, the former methods are sufficient to characterise the porosity of a coating. 

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