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Comparison of mercury porosimetry, sedimentation and microscopy for determining the grain size distribution of powdered particles
Comparison of Mercury Porosimetry, Sedimentation and Microscopy for Determining the Grain Size Distributionof Powdered Particles M. SVATA AND Z. ZABRANSKY Hp)Torsky
of Polmography,
Insrimze
Czechodorak
AcaMy
of Scrences,
Prague (C&wslorakiiz)
(Received July 14,1%9)
SUMMARY To terifv the validity of the description of the entry offluid into the void spaces of a collection of uniform packed spheres, as suggested by Meyer and Stowe for mercury intrusion measurements, and its applicability to routine work, a series of samples was measured and the results obtained were co.mpared 1% ith those obtained by microscopy and sedimentation. The sampies were selected in a waJ>to give a series offive steps gradually departing from perfect spheres to non-uniform particles encountered in everyday practice. In all cases satis$actory agreement was found between all three methods employed.
INI-RODUCTION
evaluate the results poroosimetry the equation:
To
P=
obtained
by mercury
2ycose r
which was proposed by Washburn’ on the assumption of cylindrical pores, is generally employed. This assumption, however, is often very far from reality, especially in the case of porous bodies prepared by pressing and sintering metal powders. These bodies, when submitted to porosimettic measurements, often exhibit a sudden increase in the volume of voids filled with only a small increase in mercury pressure. This phenomenon cannot be explained by the Washburn model. Frevel and Kressley’ therefore proposed a model and derived expressions for the pressure necesmry for mercury to intrude into a solid composed of a collection of non-porous uniform spheres The treatment defines the pressure necesmry to “break through”, in terms of the largest accessible opening, to the interior of the solid and then relates the size of the opening to the radius of de spheres. The model of Frevel and Posder
Tedzndogy - ELsevim Sequoia S-A., Lausarmc
Kressley is limited to a maximum porosity of 39.54%, which, unfortunately, is too low a limit for real systems, where porosities are often in excess of this value. For this reason a more general&d model was suggested by Meyer and Stowe3 with an upper porosity limit of 47X540/,_ The present paper is meant to contribute to the verification, by experiment, of the theory of Meyer and Stowe by presenting a comparison of the grain size distribution of classified powders as measured by the intrusion of mercury with that obtained by microscopy and sedimentation-
Five samples of differentmaterials were selected to give a series of particle shapes gradually deviating from perfect spheres to non-uniform bodies as obtained by grinding operations. (l)A polymer ofmethylmetacrylic acid, molecular weight 40,000, consisting of perfstly spherical particles (commercially available under the name of Dentacry~anufacturer SPOFA, Prague), was sieved to give a fraction 2040 -m. (2) Carbonyi iron, grain size under 15 m. (3) Carbonyl nickel pre-sintered in an inert medium at a temperature just below the melting point, grain size above 40 m (manufacturer Research Institute of Powder Metallurgy, Sumperk). (4) Glass used for manufacturing fritted glass, ground in a vibrating mill, sized in an air classifierto give several h-actionsfrom which those of 15-20 m and 3040 m were chosen. The above materials were then measured by sedimentation, microscopy and mercury porosimetry. Microscopic examinations were made optically on a laboratory microscope using a calibrated filar micrometer eyepiece. For each evahtation 300 particles were m easured_The frequency curves thus obtained were transformed into a volum~eter
DEERM?NA~ON
OF GRAIN
relationship on the assumption that the particles were spherical (in conformity with the other two methods). For mercury intrusion measurements, the sample was placed in a dilatometer in a glass tube where it was first shaken and then sealed by a piece of glass wool to prevent the reanan gement of particles by the mercury. For evaluation the equations of Meyer and Stowe3 were employed in the form
297
SIZE DISIRIBU-iTON
v r*L ‘1.
m
53
P and y are the pressure and surface tension respectively_ I: and A are given by the expressions
where G is the angle defining the packing arrangement (the acute angle, the sides of which are the edges of the solid figure formed by connecting the centres of a cluster of spheres)_ and 4 and H are further parameters introduced to defme the function E/A. For a given tr and 0 (contact angle) these functions are tabulated3. The values of 140” and 480 dyn/em were employed for the contact angle and the surface tension of mercury. The packing angles, G, were determined individually for each material on the basis of porosities calculated from the values of the true and apparent densities3. Sedimentation analysis was carried out on a Sartorius 4600 type balance from aqueous suspension (1 mg per 1 ml) with the addition of 0.02% surface active agent, with the exception of sample no. 3, where a glycerine-water mixture of viscosity 5 cp had to be employed due to the size and weight of the particles. Evaluation was made by the method of Odenf
SJ-
I
Vrd.
Y. loo CAi?BONYL
NICKEL
i i 50
RBUJa-IS
AND
DISCUSSION
;
results are shown in Figs 1-5. Porosimetric curves are drawn in full, sedimentation curves dashed, and microscope curves shown by dot and dash. As expected, the agreement is best in the eases of samples having a narrow range of particle sires (see
The
i i
J m
Poder
Technor. 3 (1969JlO) 296298
298
M.
0
h_e
x)
a
ZD
SVATA,
=Tpd
4. Ground glass; siere fractron 15-20 pm.
Z.
ZABRANSKY
Porosimetry, on the other hand, measures the voids in a body consisting of particles packed into a container, which means that the mutual interference of individual particles is a part of the method. It was shown by Ksenzhel? that liquid penetrating into a body of intersecting pores of variable radii is nonuniformly distributed throughout the body, because bigger pores inside the body are blocked by smaller pores in the surface layers. Consequently smaller radii are favoured when using mercury porosimetryIt is evident that uniform spheres form a network of nearly uniform voids, and the distribution of liquid will also be nearly uniform. In a body of particles of different sizes, however, the size of the voids can depart widely from a mean value, and the phenomenon described above will, therefore, become apparent and be more noticeable. It was further found (compare Figs. 1 and 5) that deviations from spherical shape do not present difficulties, and that their inlluence is less pronounced than that of differences in size. This, of course, holds only within certain limits. If the particles are irregular to the extent of forming “bridges” when poured into a container (this leads to porosities above 47.a”/& which is the maximum permitted by the theory), the method is no longer applicable.
CONCJXiONS
Fr_e 5. Ground glass. sieve fraction 3D-40 pm.
Fig. 4); in this range the size may be considered as practically uniform. In samples of a wider range of sixes (Fig. 2), deviations become more apparent although even in this case the agreement may be considered satisfactory. As may further be noted from Figs. 2,4 and 5, the porosimetric curves have a tendency to rise more steeply than the other two. This may be explained by the following reasoning. Microscope measurements consider every single particle separately while sedimentation works with diluted suspensions, where there is little or no mutual interference of particles in their downward motion.
In all five cases quoted the agreement between the grain size distribution from the three methods used is satisfactory_ Although it is realised that further investigations will be necesmry, especially with respect to porous bodies prepared by powder metallurgy. the experiments carried out so far suggest that the theory of “breakthrough pressure for penetration between packed spheres- deserves more attention. To workers in powder metallurgy the theory of mercary porosimetry offers a new possibility of analysing the size distribution of class&d powders.
REFERENCES 1 E_ w. w ASHBURX,Proc Narl. Acod Sci. US. 7 (1921) 115 2 L.K FREVEL APD L. 3. I(REssLEy, Anal Chsn.. 35 (1%3) 1492 3 R P. BAND R A. STOWF& J. CoZZord. sci., 20 (1965) 893. 4 S. ODEN, Proc. Roy_ Ser. -gh, 36 (1916) 219. 5 0. S. Ksmmix, ZJL FL Khim.. 37 (1963) 1297.
Powder TechmZ,
3 (1%9/70) 296298
of Polmography,
Insrimze
Czechodorak
AcaMy
of Scrences,
Prague (C&wslorakiiz)
(Received July 14,1%9)
SUMMARY To terifv the validity of the description of the entry offluid into the void spaces of a collection of uniform packed spheres, as suggested by Meyer and Stowe for mercury intrusion measurements, and its applicability to routine work, a series of samples was measured and the results obtained were co.mpared 1% ith those obtained by microscopy and sedimentation. The sampies were selected in a waJ>to give a series offive steps gradually departing from perfect spheres to non-uniform particles encountered in everyday practice. In all cases satis$actory agreement was found between all three methods employed.
INI-RODUCTION
evaluate the results poroosimetry the equation:
To
P=
obtained
by mercury
2ycose r
which was proposed by Washburn’ on the assumption of cylindrical pores, is generally employed. This assumption, however, is often very far from reality, especially in the case of porous bodies prepared by pressing and sintering metal powders. These bodies, when submitted to porosimettic measurements, often exhibit a sudden increase in the volume of voids filled with only a small increase in mercury pressure. This phenomenon cannot be explained by the Washburn model. Frevel and Kressley’ therefore proposed a model and derived expressions for the pressure necesmry for mercury to intrude into a solid composed of a collection of non-porous uniform spheres The treatment defines the pressure necesmry to “break through”, in terms of the largest accessible opening, to the interior of the solid and then relates the size of the opening to the radius of de spheres. The model of Frevel and Posder
Tedzndogy - ELsevim Sequoia S-A., Lausarmc
Kressley is limited to a maximum porosity of 39.54%, which, unfortunately, is too low a limit for real systems, where porosities are often in excess of this value. For this reason a more general&d model was suggested by Meyer and Stowe3 with an upper porosity limit of 47X540/,_ The present paper is meant to contribute to the verification, by experiment, of the theory of Meyer and Stowe by presenting a comparison of the grain size distribution of classified powders as measured by the intrusion of mercury with that obtained by microscopy and sedimentation-
Five samples of differentmaterials were selected to give a series of particle shapes gradually deviating from perfect spheres to non-uniform bodies as obtained by grinding operations. (l)A polymer ofmethylmetacrylic acid, molecular weight 40,000, consisting of perfstly spherical particles (commercially available under the name of Dentacry~anufacturer SPOFA, Prague), was sieved to give a fraction 2040 -m. (2) Carbonyi iron, grain size under 15 m. (3) Carbonyl nickel pre-sintered in an inert medium at a temperature just below the melting point, grain size above 40 m (manufacturer Research Institute of Powder Metallurgy, Sumperk). (4) Glass used for manufacturing fritted glass, ground in a vibrating mill, sized in an air classifierto give several h-actionsfrom which those of 15-20 m and 3040 m were chosen. The above materials were then measured by sedimentation, microscopy and mercury porosimetry. Microscopic examinations were made optically on a laboratory microscope using a calibrated filar micrometer eyepiece. For each evahtation 300 particles were m easured_The frequency curves thus obtained were transformed into a volum~eter
DEERM?NA~ON
OF GRAIN
relationship on the assumption that the particles were spherical (in conformity with the other two methods). For mercury intrusion measurements, the sample was placed in a dilatometer in a glass tube where it was first shaken and then sealed by a piece of glass wool to prevent the reanan gement of particles by the mercury. For evaluation the equations of Meyer and Stowe3 were employed in the form
297
SIZE DISIRIBU-iTON
v r*L ‘1.
m
53
P and y are the pressure and surface tension respectively_ I: and A are given by the expressions
where G is the angle defining the packing arrangement (the acute angle, the sides of which are the edges of the solid figure formed by connecting the centres of a cluster of spheres)_ and 4 and H are further parameters introduced to defme the function E/A. For a given tr and 0 (contact angle) these functions are tabulated3. The values of 140” and 480 dyn/em were employed for the contact angle and the surface tension of mercury. The packing angles, G, were determined individually for each material on the basis of porosities calculated from the values of the true and apparent densities3. Sedimentation analysis was carried out on a Sartorius 4600 type balance from aqueous suspension (1 mg per 1 ml) with the addition of 0.02% surface active agent, with the exception of sample no. 3, where a glycerine-water mixture of viscosity 5 cp had to be employed due to the size and weight of the particles. Evaluation was made by the method of Odenf
SJ-
I
Vrd.
Y. loo CAi?BONYL
NICKEL
i i 50
RBUJa-IS
AND
DISCUSSION
;
results are shown in Figs 1-5. Porosimetric curves are drawn in full, sedimentation curves dashed, and microscope curves shown by dot and dash. As expected, the agreement is best in the eases of samples having a narrow range of particle sires (see
The
i i
J m
Poder
Technor. 3 (1969JlO) 296298
298
M.
0
h_e
x)
a
ZD
SVATA,
=Tpd
4. Ground glass; siere fractron 15-20 pm.
Z.
ZABRANSKY
Porosimetry, on the other hand, measures the voids in a body consisting of particles packed into a container, which means that the mutual interference of individual particles is a part of the method. It was shown by Ksenzhel? that liquid penetrating into a body of intersecting pores of variable radii is nonuniformly distributed throughout the body, because bigger pores inside the body are blocked by smaller pores in the surface layers. Consequently smaller radii are favoured when using mercury porosimetryIt is evident that uniform spheres form a network of nearly uniform voids, and the distribution of liquid will also be nearly uniform. In a body of particles of different sizes, however, the size of the voids can depart widely from a mean value, and the phenomenon described above will, therefore, become apparent and be more noticeable. It was further found (compare Figs. 1 and 5) that deviations from spherical shape do not present difficulties, and that their inlluence is less pronounced than that of differences in size. This, of course, holds only within certain limits. If the particles are irregular to the extent of forming “bridges” when poured into a container (this leads to porosities above 47.a”/& which is the maximum permitted by the theory), the method is no longer applicable.
CONCJXiONS
Fr_e 5. Ground glass. sieve fraction 3D-40 pm.
Fig. 4); in this range the size may be considered as practically uniform. In samples of a wider range of sixes (Fig. 2), deviations become more apparent although even in this case the agreement may be considered satisfactory. As may further be noted from Figs. 2,4 and 5, the porosimetric curves have a tendency to rise more steeply than the other two. This may be explained by the following reasoning. Microscope measurements consider every single particle separately while sedimentation works with diluted suspensions, where there is little or no mutual interference of particles in their downward motion.
In all five cases quoted the agreement between the grain size distribution from the three methods used is satisfactory_ Although it is realised that further investigations will be necesmry, especially with respect to porous bodies prepared by powder metallurgy. the experiments carried out so far suggest that the theory of “breakthrough pressure for penetration between packed spheres- deserves more attention. To workers in powder metallurgy the theory of mercary porosimetry offers a new possibility of analysing the size distribution of class&d powders.
REFERENCES 1 E_ w. w ASHBURX,Proc Narl. Acod Sci. US. 7 (1921) 115 2 L.K FREVEL APD L. 3. I(REssLEy, Anal Chsn.. 35 (1%3) 1492 3 R P. BAND R A. STOWF& J. CoZZord. sci., 20 (1965) 893. 4 S. ODEN, Proc. Roy_ Ser. -gh, 36 (1916) 219. 5 0. S. Ksmmix, ZJL FL Khim.. 37 (1963) 1297.
Powder TechmZ,
3 (1%9/70) 296298