Surface Area, Density, and Porosity of Powders Apparatus Lea and Nurse (Ref 21) developed the apparatus shown in Fig. 4 to provide permeability measurements. The powder was compacted in the sample cell to a predetermined porosity. Air was permitted to flow through the bed, and the pressure drop (h 1 ) was measured on the first manometer; the air then passed through a capillary flowmeter, across which another pressure drop was measured as h 2 on a second manometer. Fig. 4 Lea and Nurse permeability apparatus with manometer and flowmeter The capillary permitted the system to operate under a constant pressure. The volume rate of flow through the flowmeter, the pressure drop across the bed as measured by the manometer, and the constants associated with the apparatus permitted determination of the specific surface area (surface area per unit volume). Gooden and Smith (Ref 22) added a self-calculating chart to a modified Lea and Nurse apparatus to enable direct readout of the specific surface. The commercial version of their modification is known as the Fisher subsieve sizer (Fig. 5). Fig. 5 Fisher subsieve sizer operation A simplified version of the air permeameter, known as the Blaine permeameter (Fig. 6) (Ref 23), relied on a variable pressure technique (Ref 24). A vacuum was used to displace the oil in a U-tube connected in series with the powder cell. The resultant pressure caused air to flow through the powder bed, and the time required for the displaced oil to fall back to its equilibrium position was measured. This method resulted in a measured specific surface area, which decreased with porosity. Usui (Ref 25) showed that log t and the void fraction exhibited a linear relationship and that a plot of these parameters gave a value for surface area. Fig. 6 Blaine air permeability apparatus. Source Ref 23 References cited in this section 21. F.M. Lea and R.W. Nurse, J. Soc. Chem. Ind., Vol 58, 1939, p 277- 283; Symposium on Particle Size Analysis, Trans. Inst. Chem. Eng., (suppl.), Vol 25, 1947, p 47-56 22. E.L. Gooden and C.M. Smith, Ind. Eng. Chem. Anal. Ed., Vol 12, 1940, p 479-482 23. K. Niesel, External Surface of Powders From Permeability Measurements A Review, Silicates Industrials, 1969, p 69-76 24. R.L. Blaine, ASTM Bull., No. 123, 1943, p 51-55; also see ASTM Bull., No. 108, 1941, p 17-20 25. K. Usui, J. Soc. Mater. Sci. Jpn., Vol 13, 1964, p 828 Surface Area, Density, and Porosity of Powders Limitations For very fine powders, the basic Kozeny-Carman equation is not accurate. This is because the laminar flow assumption on which it is based is no longer valid. Compressed fine particles result in a powder bed with very small channel widths. If these widths are comparable to the mean free path length of the gas molecules, laminar flow conditions are not maintained. Such a situation, involving molecular flow or diffusion conditions, is known as Knudsen flow (Ref 26) and can occur with very fine powders or with coarser particles at low pressures. Figure 7 shows a typical apparatus used to measure find particles under molecular flow conditions (Ref 27, 28). In some powders, both laminar and molecular flow may be significant. This is known as the transitional region. Fig. 7 Modified Pechukas and Gage apparatus for fine powders. Source: Ref 27 Evaluating surface areas with steady-state flow conditions historically excluded noninterconnected blind pores. A method for including blind pores by utilizing transient-state flow measurements is the principle behind the apparatus shown in Fig. 8(a) (Ref 29, 30). A typical flow rate curve, showing extrapolation of the steady-state portion to determine the time lag is given in Fig. 8(b). The basic principle of the permeability analysis has not changed much during the last several years; even so, instruments now use more sophisticated pressure transducer and flowmeter or flow controller. Combined with a computerization of the instrument and an improved data analysis software, the instrument offer a wider variety of analysis tasks and computational methods. Fig. 8(a) Transient flow apparatus Fig. 8(b) Flow rate curve for the transient flow apparatus References cited in this section 26. M. Knudsen, Ann. Physik, Vol 28, 1909, p 75-130 27. A. Pechukas and F.W. Gage, Ind. Chem. Eng. Anal. Ed., Vol 18, 1946, p 37 28. P.C. Carman and P.R. Malherbe, J. Soc. Chem. Ind., Vol 69, 1950, p 134 29. R.M. Barrer and D.M. Grove, Trans. Faraday Soc., Vol 47, 1951, p 826, 837 30. G. Kraus, R.W. Ross, and L.A. Girifalco, J. Phys. Chem., Vol 57, 1953, p 330 Surface Area, Density, and Porosity of Powders Pycnometry Peter J. Heinzer, Imperial Clevite Technology Center Pycnometry is used to determine the true density of P/M materials. Based on the displacement principle, pycnometry is actually a method of determining the volume occupied by a solid of complex shape, such as a powder sample. For commercial pycnometers, typical sample sizes range from 5 to 135 cm 3 (0.30 to 8.24 in. 3 ). A properly prepared specimen can be analyzed in 15 to 20 min. The pycnometric determination of density can be quite useful in P/M applications. In addition to its primary use in measuring the true density of a P/M part or product, it can be used to distinguish among different crystalline phases or grades of material, different alloys, compositions, or prior treatments. Information on the porosity of a material can be obtained from pycnometry if the sample has a uniform geometry, or if the bulk volume is known. Pore volume is the difference between the bulk volume (1/bulk density) and the specific volume (1/true density). Finally, pycnometry can be useful in determining properties that relate to density. Often, P/M materials have no solid counterpart to use for measuring true density, making percentage of theoretical density measurements questionable. Pycnometric measurements of the true density of the powder have provided a good point of reference. Density is one of the most important properties of P/M materials. Critical processing parameters, such as applied force and pressure, and properties of the resulting P/M product, such as strength and hardness, usually depend on the density of the materials being processed. Standard industry practice compares the achieved density of a P/M product with the full, or theoretical, density. Surface Area, Density, and Porosity of Powders Theory and Apparatus Archimedes devised the first method for determining true density by using the displacement principle. Modern pycnometry represents a refinement of the displacement principle and uses either a liquid or gaseous substance as the displaced medium. Absolute densities of solids can be measured by the displacement principle using either liquid or gas pycnometry. In liquid pycnometry, volume displacement is measured directly, as liquids are incompressible. Inability of the liquid to penetrate pores and crevices, chemical reaction or adsorption onto the sample surface, wetting or interfacial tension problems, and evaporation contribute to errors in density measurement. Therefore, gas pycnometry is usually preferred for P/M applications. In gas pycnometry, volume displacement is not measured directly, but determined from the pressure/volume relationship of a gas under controlled conditions. Gas pycnometry requires the use of high-purity, dry, inert, nonadsorbing gases such as argon, neon, dry nitrogen, dry air, or helium. Of these, helium is recommended because it: • Does not adsorb on most materials • Can penetrate pores as small as 0.1 nm (1 ) • Behaves like an ideal gas In commercial pycnometers, the sample is first conditioned or outgassed to remove contaminants that fill or occlude pores and crevices, thus changing surface characteristics. This is accomplished by evacuating the system and heating to elevated temperatures, following by purging with an inert gas such as helium. The helium-filled sample system (Fig. 9) is "zeroed" by allowing it to reach ambient pressure and temperature. At this point, the sample cell and reference volume are isolated from each other and from the balance of the system by valves. Fig. 9 Flow chart for typical pycnometer The state of the system can then be defined by: PV = nRT (Eq 1) for the sample cell and: PV R = n R RT (Eq 2) for the calibrated reference cell. In these equations, P is the ambient pressure, Pa; V is the volume of the sealed empty sample cell, cm 3 ; V R is volume of a carefully calibrated reference cell, cm 3 ; n is moles of gas in the sample cell volume at P; n R is moles of gas in the reference cell volume at P; R is the gas constant; and T is ambient temperature, K. A solid sample of volume (V s ) is then placed in the sample cell: P(V - V s ) = n 1 RT (Eq 3) where n 1 is moles of gas occupying the remaining volume in sample cell at P. The system is then pressurized to P 2 , about 100 kPa (15 psi) above ambient: P 2 (V - V s ) = n 2 RT (Eq 4) where n 2 is moles of gas occupying the remaining volume in the sample cell at P 2 . The valve is then opened the connect the sample cell with the calibrated reference volume, and the pressure drops to a system equilibrium P 3 : P 3 (V - V s ) + P 3 V R = n 2 RT + n R RT (Eq 5) Substituting PV R from Eq 2 for n R RT in Eq 5 and substituting P 2 (V - V s ) from Eq 4 for n 2 RT results in: P 3 (V - V s ) + P 3 V R = P 2 (V - V s ) + PV R (Eq 6) Simplifying: (P 3 - P 2 ) (V - V s ) = (P - P 3 )V R (Eq 7) (Eq 8) V s = V + V R /[1 - (P 2 - P)/(P 3 - P)] (Eq 9) Because P is "zeroed" at ambient before pressurizing, the working equation becomes: V s = V + V R /[1 - (P 2 /P 3 )] (Eq 10) Over the last few years, the gas pycnometer has been further improved by using a more accurate pressure transducer, a better temperature control of the entire system, and by an automation (computerization) of the actual analysis process. Modern pycnometers can now reach an accuracy of 0.01%. Surface Area, Density, and Porosity of Powders Mercury Porosimetry H. Giesche, School of Ceramic Engineering and Sciences, Alfred University Many commercially important processes involve the transport of fluids through porous media and the displacement of one fluid, already in the media, by another. The role played by pore structure is of fundamental importance in understanding of these processes. The quality of powder compacts is also affected by the void size distribution between the constituent particles. For these reasons, mercury porosimetry has long been used as an experimental technique for the characterization of pore and void structure. Gas and mercury porosimetry are complementary techniques with the latter covering a much wider size range from 0.3 mm to 3.5 nm (Fig. 10). Mercury porosimetry consists of the gradual intrusion of mercury into an evacuated porous medium at increasingly higher pressures followed by extrusion as the pressure is lowered. The simplest pore model is based on parallel circular capillaries that empty completely as the pressure is reduced to zero. This model fails to take into account the real nature of more porous media, which consist of a network of interconnecting noncircular pores. The network effects lead to hysteresis and mercury retention during the extrusion cycle. Fig. 10 Pore radii ranges covered by gas and mercury porosimetry Surface Area, Density, and Porosity of Powders General Description Relationship between Pore Radii and Intrusion Pressure. Mercury porosimetry is based on the capillary rise phenomenon whereby an excess pressure is required to cause a nonwetting liquid to enter a narrow capillary. The pressure difference across the interface is given by the equation of Young (Ref 31) and Laplace (Ref 32), and its sign is such that the pressure is less in the liquid than in the gas (or vacuum) phase if the contact angle is greater than 90° or more if is less than 90°. If the capillary is circular in cross section, and not too large in radius, the meniscus will be approximately hemispherical. The curvature of the meniscus can be related to the radius of the capillary, and the Young-Laplace equation reduces to the Washburn equation (Ref 33): (Eq 11) This is the Young-Laplace and Washburn equation where lv is the surface tension of the liquid (e.g., for mercury, 0.485 N/m), r 1 and r 2 are mutually perpendicular radii of a surface segment. The angle is the angle of contact between the liquid and the capillary walls and is always measured within the liquid (Fig. 11). r P is the capillary radius. Fig. 11 Contract angle ( ) of a liquid in a capillary Equipment Fundamentals. The sample is placed into the penetrometer assembly; it is then evacuated to a set vacuum level for a specific time, before the sample cell is filled with mercury. Air is admitted to the low-pressure chamber, and the increasing pressure forces the mercury to penetrate the largest pores of the sample. The amount or volume of mercury penetrating into the sample is recorded at each pressure (or pore size) point; the first reading usually is taken at a pressure of 0.5 psi (0.003 MPa), although readings at a pressure of 0.1 psi (0.7 × 10 -4 MPa) are possible. The pressure is then increased to 1 atm, or in some instruments the pressure is actually increased to a slight overpressure (up to 50 psi in some cases). After the low-pressure run is finished, the penetrometer is then inserted into a high-pressure port and surrounded with a special grade of high-pressure oil; it is special with respect to the dielectric constant and viscosity of the oil under high-pressure conditions. The pressure is increased up to a final pressure of 60 ksi (400 MPa). Commercial instruments work either in an incremental or continuous mode. In the former, the pressure is increased in steps and the system allowed to stabilize at each pressure point before the next step. In the continuous mode, the pressure is increased continuously at a predetermined rate. Schematics of low-pressure and high-pressure systems are shown in Fig. 12 and 13, respectively (Ref 34). Fig. 12 Low-pressure mercury porosimeter. Source: Ref 34 Fig. 13 Micromeritics high-pressure mercury porosimeter References cited in this section 31. T. Young, Miscellaneous Works, Vol 1, Murray 1855, p 418 32. P.S. Laplace, Mecanique Celeste, Suppl. Book 10, 1806 33. E.W. Washburn, Proc. Nat. Acad. Sci. U.S.A., Vol 7, 1921, p 115 34. AutoPore II 9220 Operator's Manual, Micromeritics, 1993 Surface Area, Density, and Porosity of Powders Measurement Techniques Measuring Displacement Volumes (Pore Volume). Mercury volume displacements may be measured by direct visual observation of the mercury level in a glass penetrometer stem (Fig. 14) with graduated markings (Ref 35). However, most (if not all) instruments on the market will measure this volume automatically by one of the following techniques: [...]... For = - 2.66 × 1 0-4 m · P = 200 MPa, the correction term gives an error of 12% [ Table 3 Surface tension of mercury in vacuum Temperature, °C 25 25 20 25 25 16 .5 Surface tension, mN/m 484 ± 1 .5 484 ± 1.8 4 85 ± 1.0 483 .5 ± 1.0 4 85. 1 487.3 Method used Sessile drop Sessile drop Drop pressure Sessile drop Sessile drop Pendant drop corr P = (0.4 85 - 0. 053 ) N/m] 4 85. 4 ± 1.2 484.6 ± 1.3 482 .5 ± 3.0 25 20... (variations) in the particle size distribution, particle shape, and consequently the uniformity of powder blends (a combination of one or more particle sizes of a single powder) and mixes (a combination of one or more types of powders) (Ref 1, 2) References 1 J.H Bytnar, J.O.G Parent, H Henein, and J Iyengar, Macro-Segregation Diagram for Dry Blending Particulate Metal- Matrix Composites, Int J Powder Metall.,... 6 9-7 6 24 R.L Blaine, ASTM Bull., No 123, 1943, p 5 1 -5 5; also see ASTM Bull., No 108, 1941, p 1 7-2 0 25 K Usui, J Soc Mater Sci Jpn., Vol 13, 1964, p 828 26 M Knudsen, Ann Physik, Vol 28, 1909, p 7 5- 1 30 27 A Pechukas and F.W Gage, Ind Chem Eng Anal Ed., Vol 18, 1946, p 37 28 P.C Carman and P.R Malherbe, J Soc Chem Ind., Vol 69, 1 950 , p 134 29 R.M Barrer and D.M Grove, Trans Faraday Soc., Vol 47, 1 951 ,... Vol 45, 1938, p 688 20 P.C Carman, Symposium on New Methods for Particle Size Determination in the Sub-Sieve Range, ASTM, 1941, p 24 21 F.M Lea and R.W Nurse, J Soc Chem Ind., Vol 58 , 1939, p 27 7-2 83; Symposium on Particle Size Analysis, Trans Inst Chem Eng., (suppl.), Vol 25, 1947, p 4 7 -5 6 22 E.L Gooden and C.M Smith, Ind Eng Chem Anal Ed., Vol 12, 1940, p 47 9-4 82 23 K Niesel, External Surface of Powders... and R Rajagopalan, Principles of Colloid and Surface Chemistry, Marcel Dekker, 1997 40 H.M Rootare, A Review of Mercury Porosimetry, Advanced Techniques in Powder Metallurgy, Vol 5, Perspectives in Powder Metallurgy, Plenum Press, 1970 41 M Svata, Powder Technol., Vol 29, 1981, p 1 45 42 J Kloubek, Powder Technolg., Vol 7, 1981, p 63, 162 Surface Area, Density, and Porosity of Powders Restrictions and. .. between the interparticle and intraparticle voids In a packing of nonporous particles there is only an interparticle pore space However, in many applications for example,sorbents the prime concern is in the intraparticle void space In such cases, a judgment must be made as to which part of the measured pore volume belongs to the interparticle voids and which part belongs to the intraparticle porosity... ASTM Standards, Vol 15. 01, ASTM 52 Powder Technol., Vol 29, 1981 Surface Area, Density, and Porosity of Powders References 1 2 3 4 5 6 7 8 S Brunauer, P.H Emmett, and E Teller, J Am Chem Soc., Vol 60, 1938, p 309 I Langmuir, J Am Chem Soc., Vol 38, 1916, p 2221 I Langmuir, J Am Chem Soc., Vol 40, 1918, p 1361 K.S.W Sing and D Swallow, Proc Br Ceram Soc., Vol 39 (No 5) , 19 65 R.T Davis, T.W DeWitt, and. .. and L.A Girifalco, J Phys Chem., Vol 57 , 1 953 , p 330 31 T Young, Miscellaneous Works, Vol 1, Murray 1 855 , p 418 32 P.S Laplace, Mecanique Celeste, Suppl Book 10, 1806 33 E.W Washburn, Proc Nat Acad Sci U.S.A., Vol 7, 1921, p 1 15 34 AutoPore II 9220 Operator's Manual, Micromeritics, 1993 35 Lowell and J.E Shields, Powder Surface Area and Porosity, Chapman & Hall, 1991 36 R.J Good and R.Sh Mikhail, Powder. .. 19 95, p 8 47 G.P Matthews, A.K Moss, and C.J Ridgway, Powder Technol., Vol 83, 19 95, p 61 48 H Giesche, Mater Res Soc Symp Proc., Vol 431, 1996, p 251 49 N.C Wardlow and M McKellar, Powder Technol., Vol 29, 1981, p 127 50 "Pore Volume Distribution of Catalysts by Mercury Intrusion Porosimetry," D 4284, Annual Book of ASTM Standards, Vol 5. 03, ASTM 51 "Bulk Density and Porosity of Granular Refractory... Principles of Colloid and Surface Chemistry, Marcel Dekker, 1997 43 J van Brakel, S Modry, and M Svata, Powder Technol., Vol 29, 1981, p 1 44 B Reich, Chem Ing Tech., Vol 39 (No 22), 1967, p 12 75 49 N.C Wardlow and M McKellar, Powder Technol., Vol 29, 1981, p 127 53 P Webb and C Orr, Analytical Methods in Fine Particle Technology, Norcross, 1997, p 1 65 Surface Area, Density, and Porosity of Powders Surface . Method used 25 484 ± 1 .5 Sessile drop 25 484 ± 1.8 Sessile drop 20 4 85 ± 1.0 Drop pressure 25 483 .5 ± 1.0 Sessile drop 25 4 85. 1 Sessile drop 16 .5 487.3 Pendant drop 25 4 85. 4 ± 1.2 Pendant. F.M. Lea and R.W. Nurse, J. Soc. Chem. Ind., Vol 58 , 1939, p 27 7- 283; Symposium on Particle Size Analysis, Trans. Inst. Chem. Eng., (suppl.), Vol 25, 1947, p 4 7 -5 6 22. E.L. Gooden and C.M Iron oxide 14.3 13.3 Anatase 15. 1 10.3 Graphitized carbon black 15. 7 12.3 Boron nitride 19.6 20.0 Hydroxyapatite 55 .2 55 .0 Carbon black (Spheron-6) 107. 8 110.0 The value of the