Particle Size Measurement by a Powder Film Method C. Edward Capes* and Richard D. Coleman National Research Council of Canada, Ottawa, Canada
The mean particle size of fine powders can be determined b y measuring the compressed area of a monoparticulate film of the powder spread on a liquid surface. The application of this technique in determining the thickness of mica flakes in the range 2-30 p and the diameter of sand particles in the range 50-200 p was investigated. A good correlation was found with particle size determined b y other reliable means. It i s concluded that the powder film method can be a useful tool in particle size measurement, particularly in the difficult problem of determining the thickness of very thin flake materials.
I n 1950, Gray pointed out that the mean particle size of fine powders could be determined by measuring the compressed area of a film of the powder spread on a liquid surface (Gray, 1950). The thickness of the film was found to be a definite fraction of the mean particle diameter for a number of po\vders. This technique seems to have been overlooked in the literature of particle size measurement except for some recently published work on a related method (Cartan and Curtis, 1969). The versatility of the powder film method was demonstrated to us when we were faced nith the problem of measuring the thickness of mica flakes in connection with studies of flake-reinforced composite materials. (See, for example, Schreiber and Holden, 1971.) As described below, the powder film method is perhaps the only simple method for determining a representative thickness for such “twodimensional” particles. Its application to measuring the size of more conventional sand particles is also described. Experimental Details
Powder films were formed in a film balance which is well kiiown in the field of surface chemistry (Adamson, 1960; Gray, 1950). This apparatus consists of a shallow tray filled with water, about 3 ft long by 9 in. wide. A movable sweep rod is positioned a t one end and is used to compress the film toward a floating barrier located about one-third of the way from the opposite end. The floating barrier is linked to a torsion wire which may be twisted to maintain the barrier iri the zero or starting position as the film is compressed against it. The amount of twist is indicated and gives a measure of the pressure of the film on the barrier a t each stage of compression. I n operation, the surface of the water was first swept clean of contamination by passing the sweep device over it several times. The floating barrier \vas adjusted to the zero position and the film was spread (see details below). The film was then compressed in small increments and a t each stage the length of the film was recorded, together with the degree of twist on the torsion wire. Two series of particles were used in this work. The first consisted of mica flakes which had been screened t o -140 +ZOO mesh, producing flakes of approximately uniform diameter which were then classified, by water elutriation, into a total of five samples of various flake thicknesses. The second series coiisisted of three sizes of Ottawa sands with the size dibtributions listed in Table I. Gray (1950) listed three obstacles which must be overcome iu order to obtain a moiioparticulate layer oE a powder on 124 Ind. Eng. Chem. Fundom., Vol. 12, No. 1, 1973
water. The first of these is obvious: the powder must float. Since neither mica nor glass floats spontaneously, the particles were first coated with oleic acid to impart the necessary hydrophobic surface. About 2 g of particles was suspended under agitation in reagent grade benzene for approximately 20 min. Five per cent oleic acid based on the weight of particles was then added to the suspension and allowed to mix. The sample was then filtered, dried, and stored until use. The second requirement is that the particles must not be agglomerated in the film. This is likely to be a problem especially with extremely fine powders. Owing t o the relatively large size of our powders, no elaborate deagglomeration procedure was used other than agitation in the presence of oleic acid as noted above. The last obstacle noted by Gray concerns a suitable means to spread the film on the surface, one which avoids loss of particles as dust to the atmosphere or as material sunk in the liquid. I n our experiments, the powder was spread in a draft-free location from a plastic vial employed in the manner of a salt shaker. 4 1/2-in. diameter hole was cut in the cap of the vial and a n 80-mesh screen was positioned to cover the hole. The inverted vial was tapped over the liquid surface and, with gentle blowing on the liquid surface, the particles spread readily. Negligible quantities appeared to sink in the liquid. The weight of particles used was recorded. Results
Typical pressure behavior of both the mica and sand films is shown by the curves in Figure 1. Film pressure, in degrees of twist on the torsion wire required to hold the barrier in its initial position, is plotted against the length of film, that is, the distance between the sweep rod and the barrier. It is necessary to define a point in the compression process a t which a rigid film is produced and reproducible film thickness results. Two points were selected for comparison in this work. The first relies on the film length and pressure data shown in Figure 1, where it is seen that the curves may be approximated by two straight lines, the intersection of which was taken as one point representing a rigid film. The second point chosen occurred a t a greater degree of compression when the film was observed to buckle across the total width of the t’ray,just in front of the sweep rod. If Jl is the weight of particles in the film (in grams), p is the true particle density (in grams per cubic centimeter), A is the area of the rigid film (in square centimeters), and (1 - E ) is the fractional area covered by solids in the film, then it can readily be shown that the thickness of flakes such as
-
~~
Table 1. Size Distribution S a m p l e no.
M e d i a n diameter, p
of Ottawa Sands 90 wt % within range,
49
1 2 3
103
44753 63-150
208
154-282
/J
0 BASED ON VISIBLE FILM BUCKLING
A BASED ON PLOT OF FILM PRESSURE
/
E
e-
o
lor
B 1.0
3.0
IO
20
:
THICKNESS T, microns, microscope method
Figure 2. Thickness parameter from powder film measurements as a function of actual thickness for mica flakes
o BASED ON VISIBLE F I L M BUCKLING
.
A BASED ON PLOT OF FILM PRESSURE
A
FILM LENGTH, cm
Figure 1. Pressure on barrier as a function of area of powder films: A, film composed of 0.16-9 2.4-p mica flakes; 6, film composed of 1.08-9 4 9 - p sand. Arrow indicates point at which buckling was observed
mica and the diameter of (ideally) spherical particles such as sand are given by eq 1 and 2, respectively. 121
thickness = diameter =
~ ( 1 €)A
3 &If 2 p(1 - e)A
-
x x
1 0 4 ~
104
(1)
(2)
I n deriving these equations, it was assumed that a monoparticulate film is formed and that the mica flakes lie flat in the liquid surface. I n practice, the value of (1 - E ) is not known but may be assumed constant for a given material. Accordingly, the experimental results are plotted in Figures 2 and 3, with the quantity M / p A x lo4 or 3/2 M/pA X lo4 shown as a function of particle thickness or diameter, respectively. The thickness of the mica particles was measured with a microscope while the sand particle diameter was measured by screen analysis. Discussion
number of factors such as particle migration and rearrangement, tilting and upturning of anisometric particles, and particle agglomeratioii are involved in determining the characteristics of the compression curves in Figure 1 . Elucidation of these factors, discussed iii some detail by Gray (1950), A\
DIAMETER D, microns, screen onalysls
Figure 3. Diameter parameter from powder film measurements as a function of actual diameter for sand particles
was outside the scope of this investigation. Two points should be noted, however. First, microscopic examination of the films in situ indicated that an essentially monoparticulate layer of particles was obtained and, in the case of mica particles, the flakes were lying flat with their least dimension perpendicular to the liquid surface. Secondly, the intersection of the two straight line portions of the compression curves used as one basis of particle size measurement corresponds approximately to the first point of maximum curvature used by Gray. The data given in Figures 2 and 3 show that there is a good correlation between the parameters measured by the powder film technique and the particle dimensions as determined by other independent methods. The equations of the correlating lines shown in these plots are given in Table I1 and show, as would be espected, that the fraction of the film area covered by solids, (1 - e), is higher a t the point of film buckling than a t the point of intersection of the two straight line portions of the film pressure curves. The fractional area covered by solids is also higher in the case of the mica flakes tlian for the sands. Possible reasons for this include the facts that the essentially two-dimensionai nature of tlie mica particles allows them to tilt and partially overlap their neighbors during compressioii and that the shape of the mica was posInd. Eng. Chem. Fundam., Vol. 12, No. 1, 1973
125
Table II. Correlating Equations for lines in Figures 2 and 3 < colcd from cq 1 or 2
Equation
Sand Particles 3M
i p A+ 104
(i) Based on visible \ , film buckling
=
7 .
u
0.57.
0.43
Conclusion
Mica Flakes A!f -
(i) Based on visible film buckling
PA
x
104
T
114 (ii) Based on plot of film pressure
reliable measurements of particle size using a series of typical samples would normally be required in a given application. Since particle shape and size distribution both affect the packing of the solids in the film, the standards should be similar t o the powders to be measured in both of these properties. With careful attention to film preparation and especially particle deagglomeration, the technique appears to be applicable to particles as small as 1 p or less in diameter (Gray, 1950).
x T
=
0.756
0.25
=
0.57b
0.43
104
a Average coefficient calculated from three measurements (one measurement for each of three particle sizes). * Average coefficient calculated from ten measurements (two measurements for each of five flake thicknesses).
sibly more irregular than that of the sand, allowing a greater degree of interlocking and compacting under pressure. Neasurements of the bulk density of the sands after tapping to minimum volume in a glass tube yielded fractional porosities in the range 0.38-0.46. These values are somewhat less than the 0.43-0.55 range given in Table I1 when the same particles form a film. This is due to the closer packing attainable in a three-dimensional packing compared with the two-dimensional arrangement in a film. Regarding the accuracy of the powder film method, calculations indicate that the size of the sand particles could be predicted with a relative standard deviation of 5-6y0 using the equations given in Table 11. I n measuring the thickness of the mica flakes, higher relative standard deviations of about 15% were found. It is likely that the accuracy could be improved by increasing the amount of data used in the calibration lines. No significant difference in accuracy was found between the correlation developed from the film pressure data and that developed from the visual assessment of film buckling. Due to the inevitably empirical nature of the correlation between film parameters and actual particle dimensions, calibration of the powder film measurements against other
126 Ind. Eng. Chem. Fundom., Vol. 12, No. 1, 1973
The powder film method can be a useful tool in particle size measurement, particularly in routine control work. It does not require elaborate apparatus, uses a relatively large sample to yield a representative average size, is rapid, apart from the time required for sample preparation, and can be applied over a wide range of particle size (Gray, 1950). Use of a mercury surface in place of water to cause the particles to float might be useful in reducing sample preparation time. I n measuring the thickness of flakes such as the mica studied here, other techniques are extremely tedious, inaccurate, or not applicable. For example, microscopic measurement requires that the flakes be mounted by special procedures or held on a glass filament so that their edges are presented for measurement. This is obviously very time consuming and only a few rather unrepresentative measurements can be made on a given sample. Acknowledgment
The authors thank I. E. Puddington, who pointed out the possibilities of the powder film method, J. B. Taylor for help in microscopic measurements, and F. W. Maine of Fiberglas Canada Ltd., who brought our attention to the problem of flake thickness measurements and supplied the mica powders. Nomenclature
A
=
area of rigid powder film, cm2
D
= median diameter of sand particles measured by
M
= weight of particles in film, g
T
=
(1 -
screen analysis, p,
e)
P
average thickness of mica flakes measured by microscope, p = fractional area covered by solids in film = true particle density, g/cma
literature Cited
Adamson, A. .W., “Physical Chemistry of Surfaces,” pp 114118, Intersclence Publishers, Inc., New York, N. Y., 1960. Cartan, F. O., Curtis, G. J., Anal. Chem. 41, 1719 (1969). Gray, V. R., Can. J. Res., Sect. B, 28,277 (1950). Schreiber, H. P., Holden, H. W., Chem. Can. 23 ( 2 ) , 52 (1971). RECEIVED for review November 15, 1971 August 7, 1972 ACCEPTED
Issued
&s
N.R.C.C. No. 12938.
