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1991 | Buch | 3. Auflage

Introduction Kapitel lesen Erstes Kapitel lesen

Powder Surface Area and Porosity

verfasst von: S. Lowell, Joan E. Shields

Verlag: Springer Netherlands

Buchreihe : Particle Technology Series

Enthalten in: Professional Book Archive

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Über dieses Buch

The rapid growth of interest in powders and their surface properties in many diverse industries prompted the writing of this book for those who have the need to make meaningful measurements without the benefit of years of experience. It is intended as an introduction to some of the elementary theory and experimental methods used to study the surface area, porosity, density, and particle size of powders. It may be found useful by those with little or no training in solid surfaces who have the need to learn quickly the rudiments of surface area, density, pore size, and particle size measurements. S. Lowell J.E. Shields Symbols Use of symbols for purposes other than those indicated in the following table are so defined in the text. Some symbols not shown in the table are also defined in the text. d adsorbate cross-sectional area A area; condensation coefficient; collision frequency C BET constant c concentration D diameter; coefficient of thermal diffusion E adsorption potential permeability aspect factor f F flow rate; force; feed rate g gravitational constant G Gibbs free energy S G free surface energy h heat of immersion per unit area; height H enthalpy heat of immersion Hi heat of adsorption Hsv BET intercept; filament current k thermal conductivity; specific reaction rate K Harkins-Jura constant C length L heat of liquefaction M mass M molecular weight MPa megapascals number of moles n number of molecules; number of particles N N Avogadro's num'ber molecular collisions per square cm per second

Inhaltsverzeichnis

Frontmatter

Theoretical

Frontmatter
1. Introduction
Abstract
There is a convenient mathematical idealization which asserts that a cube of edge length, ℓ cm, possesses a surface area of 6ℓ 2 cm2 and that a sphere of radius r cm exhibits 4πr 2 cm2 of surface. In reality, however, mathematical, perfect or ideal geometric forms are unattainable since under microscopic examinations all real surfaces exhibit flaws. For example, if a super microscope’ were available one would observe surface roughness due not only to the atomic or molecular orbitals at the surface but also due to voids, steps, pores and other surface imperfections. These surface imperfections will always create real surface area greater than the corresponding theoretical area.
S. Lowell, Joan E. Shields
2. Gas adsorption
Abstract
Examination of powdered materials with an electron microscope can generally disclose the presence of surface imperfections and pores. However, those imperfections or irregularities smaller than the microscope’s resolving power will remain hidden. Also hidden is the internal structure of the pores, their inner shape and dimensions, their volume and volume distribution as well as their contribution to the surface area. However, by enveloping each particle of a powder sample in an adsorbed film, the method of gas adsorption can probe the surface irregularities and pore interiors even at the atomic level. In this manner, a very powerful method is available which can generate detailed information about the morphology of surfaces.
S. Lowell, Joan E. Shields
3. Adsorption isotherms
Abstract
Brunauer, Deming, Deming and Teller [5], based upon an extensive literature survey, found that all adsorption isotherms fit into one of the five types shown below in Fig. 3.1.
S. Lowell, Joan E. Shields
4. Langmuir and BET theories (kinetic isotherms)
Abstract
The success of kinetic theories directed toward the measurements of surface areas depends upon their ability to predict the number of adsorbate molecules required exactly to cover the solid with a single molecular layer. Equally important is the cross-sectional area of each molecule or the effective area covered by each adsorbed molecule on the surface. The surface area, then, is the product of the number of molecules in a completed monolayer and the effective cross-sectional area of an adsorbate molecule. The number of molecules required for the completion of a monolayer will be considered in this chapter and the adsorbate cross-sectional area will be discussed in Chapter 6.
S. Lowell, Joan E. Shields
5. The single point BET method [13]
Abstract
The BET theory requires that a plot of 1/W [(P 0/P) — 1] versus P/P 0 be linear with a finite intercept [see equation (4.38) and Fig. 4.1]. By reducing the experimental requirement to only one data point, the single point method offers the advantages of simplicity and speed often with little loss in accuracy.
S. Lowell, Joan E. Shields
6. Adsorbate cross-sectional areas
Abstract
Using the BET equation to determine W m, the monolayer weight, and with reasonable estimates of the adsorbate cross-sectional area, A the total sample surface area, S t, in square meters, can be calculated from equation (4.13).
$${S_t} = \frac{{{W_m}\bar NA}}{{\bar M}} \times {10^{ - 20}}{m^2}$$
(cf.4.13)
with Wm in grams, \(\bar M\) is the adsorbate molecular weight, \(\bar N \) is Avogadro’s number (6.02 × 1023 molecules per mole) and A in square ångströms per molecule. Division by the sample weight converts St to S, the specific surface area.
S. Lowell, Joan E. Shields
7. Other surface area methods
Abstract
Because of its simplicity and straightforward applicability, the BET theory is almost universally employed for surface area measurements. However, other methods and theoretical models have been developed which are briefly outlined in this chapter. No attempt is made to derive and discuss these alternate methods completely but rather to present their essential features and to indicate how they may be used to calculate surface areas.
S. Lowell, Joan E. Shields
8. Pore analysis by adsorption
Abstract
Adsorption studies leading to measurements of pore size and pore size distributions generally make use of the Kelvin equation [45] 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
$$In\frac{P}{{{P_0}}} = - \frac{{2\gamma \bar V}}{{rRT}}\cos \theta$$
(8.1)
where P is the equilibrium vapor pressure of the liquid contained in a narrow pore of radius r and P 0 is the equilibrium pressure of the same liquid exhibiting a plane surface. The terms γ and V̄ are the surface tension and molar volume of the liquid, respectively, and θ is the contact angle with which the liquid meets the pore wall.
S. Lowell, Joan E. Shields
9. Microporosity
Abstract
It is convenient to categorize pores into several size ranges. The largest pore diameters amenable to analysis by the Kelvin equation are about 1000 A which corresponds to relative pressures near 0.99. Pores with diameters greater than this are termed ‘macropores’ . Dubinin [74] calls pores in the Kelvin range, from about 15 to 1000 Å, ‘transitional’ and pores with diameters less than about 15 Å‘micropores’. The failure of V—t plots to pass through the origin has led to the postulation of ‘submicropores’ [75] with diameters less than about 15 Å. According to the IUPAC convention, micropores are characterized by diameters less than 20 Å, mesopores from 20 to 500 Å, and macropores larger than 500 Å.
S. Lowell, Joan E. Shields
10. Theory of wetting and capillarity for mercury porosimetry
Abstract
The experimental method of mercury porosimetry for the determination of the porous properties of solids is dependent on several variables. One of these is the wetting or contact angle between mercury and the surface of the solid.
S. Lowell, Joan E. Shields
11. Interpretation of mercury porosimetry data
Abstract
The experimental method employed in mercury porosimetry, discussed more extensively in Chapter 21, involves the evacuation of all gas from the volume containing the sample. Mercury is then transferred into the sample container while under vacuum. Finally, pressure is applied to force mercury into the interparticle voids and intraparticle pores. A means of monitoring both the applied pressure and the intruded volume are integral parts of all mercury porosimeters.
S. Lowell, Joan E. Shields
12. Hysteresis, entrapment and contact angle
Abstract
Cumulative volume curves generated by intruding mercury into porous samples are not followed as the pressure is lowered and mercury extrudes out of the pores. In all cases, the depressurization curve lies above the pressurization curve and the hysteresis loop does not close even when the pressure is returned to zero, indicating that some mercury is entrapped in the pores. Usually after the sample has been subjected to a first pressurization— depressurization cycle, no additional entrapment occurs during subsequent cycles. In some cases, however, a third or even fourth cycle is required before entrapment ceases.
S. Lowell, Joan E. Shields
13. Particle size
Abstract
The most common technique for measuring the particle size distribution of a fine powder is the monitoring of the change in concentration of a sedimenting suspension.
S. Lowell, Joan E. Shields

Experimental

Frontmatter
14. Adsorption measurements — preliminaries
Abstract
All equipment designed to measure surface area, adsorption—desorption isotherms or pore volume by adsorption actually determines the quantity of gas condensed on a solid surface at some equilibrium vapor pressure. The surface area or pore volumes and pore sizes are then calculated by means of an appropriate theory used to treat the adsorption and/or desorption data. Depending on the apparatus employed, the adsorbed quantity is measured as volume or weight. The accuracy of an adsorption apparatus is, therefore, dependent upon its ability correctly to measure either of these quantities.
S. Lowell, Joan E. Shields
15. Vacuum volumetric measurements
Abstract
Many types of vacuum adsorption apparatus have been developed [121–124] and no doubt every laboratory where serious adsorption measurements are made has equipment with certain unique features. The number of variations are limited only by the need and ingenuity of the users. However, all vacuum adsorption systems have certain essential features, including a vacuum pump, two gas supplies, a sample container, a calibrated volume, manometer and a coolant.
S. Lowell, Joan E. Shields
16. Dynamic methods
Abstract
In 1951 Loebenstein and Deitz [137] described an innovative gas adsorption technique which did not require the use of vacuum. They adsorbed nitrogen out of a mixture of nitrogen and helium which was passed back and forth over the sample between two burettes by raising and lowering attached mercury columns. Equilibrium was established by noting no further change in pressure with additional cycles. The quantity adsorbed was determined by the pressure decrease at constant volume. Successive data points were acquired by adding more nitrogen to the system.
S. Lowell, Joan E. Shields
17. Other flow methods
Abstract
A modification of the Nelson and Eggertsen method was made by Haley [147] who also used helium and nitrogen in a continuous flow system. Haley’s apparatus differs from that described in the previous chapter in that the sample cell can be pressurized while the effluent flows from a pressure regulator through the cell to a flow controller and then to the detector maintained at ambient pressure.
S. Lowell, Joan E. Shields
18. Gravimetric method
Abstract
Balances with adequate sensitivity to measure the small weight changes associated with adsorption can be divided into two categories — electronic beam microbalances and spring balances. Electronic beam balances usually use an electric current to restore the beam to the horizontal position as the weight changes. Their sensitivities are in the order of 1 µg with loadings of approximately one gram. Commercial electronic microbalances are available in vacuum containers with appropriate fittings for vacuum pumps and gauges.
S. Lowell, Joan E. Shields
19. Comparison of experimental adsorption methods
Abstract
The following comparisons of the three most common adsorption techniques (volumetric, continuous flow, and gravimetric) are based on the assumption that routine measurements are to be made. Special requirements may oblige the experimenter to choose one method in preference to another.
S. Lowell, Joan E. Shields
20. Chemisorption
Abstract
The various forces responsible for physical adsorption were discussed in Chapter 2. These include dispersion as well as coulombic forces. Chemical adsorption arises from the inability of surface atoms to interact symmetrically in the absence of a neighbor above the plane of the surface. For this reason, surface atoms often possess electrons or electron pairs which are available for bond formation.
S. Lowell, Joan E. Shields
21. Mercury porosimetry
Abstract
Although many high-pressure mercury porosimeters have been constructed, they all have several essential components, which are perhaps different in their design but nevertheless are common to each apparatus. These components include the following:
(a)
Cell to hold the test sample.
 
(b)
Dilatometer or stem attached to the sample cell in which the mercury level varies with intrusion or extrusion.
 
(c)
Vacuum filling apparatus to remove trapped air from the pores and for transferring mercury into the sample cell.
 
(d)
Pressure generator.
 
(e)
High pressure vessel to contain the sample cell.
 
(f)
Probe to measure the mercury level.
 
(g)
Hydraulic fluid to transmit the pressure to the dilatometer.
 
S. Lowell, Joan E. Shields
22. Density measurement
Abstract
In many areas of powder technology, the need to measure the powder volume or density often arises. For example, powder bed porosities in permeametry, volume specific surface area, sample cell void volumes as well as numerous other calculated values all require accurately measured powder densities or specific volumes. It is appropriate, therefore, to introduce some discussion of powder density measurements.
S. Lowell, Joan E. Shields
23. Particle size analysis
Abstract
The particle size technique described in Chapter 13 combines gravitational sedimentation with the detection of X-ray absorption by a homogeneous suspension of particles. Fig. 23.1 is a schematic diagram of the X-ray sedimentometer shown in Fig. 23.2. The solid concentration is measured at the start of a sedimentation analysis and subsequently, depending upon the analysis parameters, the concentration is measured continuously with time and at various depths, h, below the surface. This is accomplished by scanning the sedimentation vessel with the X-ray beam from the bottom to the top of the sample cell. The hold time near the bottom of the cell and subsequent scan rate are determined by the analysis parameters, for example, maximum and minimum diameters chosen and minimum sedimentation distance.
S. Lowell, Joan E. Shields
Backmatter
Metadaten
Titel
Powder Surface Area and Porosity
verfasst von
S. Lowell
Joan E. Shields
Copyright-Jahr
1991
Verlag
Springer Netherlands
Electronic ISBN
978-94-015-7955-1
Print ISBN
978-90-481-4005-3
DOI
https://doi.org/10.1007/978-94-015-7955-1