INDUSTRIAL A N D ENGINEERING CHEMISTRY
370
The work on scattering systems was carried out in collaboration with J. Burton Nichols, who supplied many helpful comments on the present development. Many of the measurements repsrted were carried out by 0. H. Graeger, who also worked out t,he details of the method for determining refractive index. LITERATURE CITED
(1) Bailey, E. D., Nichols, J. B . , and Kraemer, E. O., J . Phus. C h m . , 40,1149-55 (1936). ( 2 ) Barnes, M . D., and La Mer, V. K., J . CoZZ. Sci., 1, 79 (1946).
Vol. 18, No. 6
(3) Gamble, D. L., and Barnett, C. E., IND. ENO. CBEM.,ANAL. ED., 9, 310 (1937). (4) Lansing, W. D.,and Kraemer, E. Q.. J . Am. Chem. Soc., 57. 1369 (1935). ( 5 ) Mie, G., Ann. Phyaik, 25, 377 (1908). (6) Pfund, A. H., J.Optical SOC.Am., 24,143 (1934). (7) Rayleigh, Lord (Strutt, J. W.), Phil. Mag.,47,377 (1899). (8) Stratton, J. A., and Houghton, H. G., Phya. Rew., 38, 159 (1931). (9) Svedberg and Pederson, “The Ultracentrifuge”, pp. 338-42. Oxford, Clarendon Press, 1940. PRESENTED before the Division of Industrial and Engineering Chemistry. A M E R i C A N CHEMICAL 8 O C I E T Y , Symposium on Measurement and Creation of Particle Sine, Brooklyn, N . Y., December, 1945. Contribution 208 from the Chemical Department, E. I. du Pont de Nemoura and Company,
Rapid Method for Determining Specific Surface of Fine Particles ALPHONSE PECHUKAS
AND
F. W. GAGE, Pittsburgh Plate Glass Co., Columbia Chemical Division, Barberton, O h i o
The Leo and Nurse method of determining the specific surface of Rne powders using gas permeabilities has been modified for measuring particles whose mean diameters are less than 1.0 micron. The problem of turbulence within the porous wmple plug which accompanies measurements of finely divided pigments has been overcome by using small-bore, highly compressed plugs. Pressure differentials of 1 atmosphere have been substituted for the lower pressures of Lea and Nurse to overcome the resistance to air flow offered by the more highly compressed plugs. The method is rapid and simple in operation and is reproducible, the specific surface values being fairly constant over a range of porosities. A n apparatus suitable for routine work and plant control i s described.
D
URING the past several years the permeability method of determining the specific surface of fine particles has received considerable attention from workers interested in a rapid and accurate meam of measuring the particle size of pigments in the subsieve range. The theory of the permeability method and details of experiments conducted to test its validity have been discussed by Carman (449, who showed that the specific surface of a powder could be expressed by the equation
where So = specific surface of the powder in sq. cm. per cc. K , proportionality constant representing the permeability of the porous medium e = porosity or fractional void of the bed of powder 9
Based on laws of fluid flow, K 1can be expressed by
where
Q, A
= cross-sectional area of the porous medium in sq. cm.
=
rate of flow of the percolating fluid in ml. per second
r)
=
viscosity of the fluid in
L
= thickness of porous m x A ? n cm. AP = pressure difference driving the fluid through the medium
in grama per sq. cm.
Carman has shown that for the same powder a t different porosities the porosity function, e a / ( l e)*, is accurate over a fairly wide range of porosities. Carman worked for the most part with liquids rather than air,
-
being of the opinion that surface area values from air permeabilities tended to be high, owing to incomplete dispersion of the powder in the bed. However, he recognized that not only was it difficult to select a liquid that would give reasonably good dispersion and wetting, but adsorption of the liquid a t the particle surface might tend to decrease the effective porosity, giving a low permeability and therefore a high surface area value. Lea and Nurse (9) have evolved a highly developed gas-permeability method which is appreciably more rapid than the liquidpermeability method and is extremely reproducible. They have shown that gas permeabilities are consistent for different gases and that corresponding values of particle size with gases are more in accord with sedimentation particle size analysis than with liquids. Gooden and Smith (7) have also successfully used air permeabilities for measuring various sized fractions of powdered silica. However, for the more finely divided fractions, agreement was poor between the air permeability particle size and that calculated from microscopic measurements. Blaine (8) has devised an air-permeability apparatus similar to that of Lea and X m e which he found well adapted to comparing the specific surfaces of powdered materials. His procedure was fast and simple and the test results were reproducible. He concluded that the air-permeability apparatus was not only well adapted for testing materials in the range of fineness of portland cement but could be used for testing finer materials. In a more recent article Blaine (9) describes a simplified airpermeability apparatus suitable for rapid comparison of the specific surfaces of portland cements. Not only iE the apparatus simple to construct and operate, but times of less than 3 minutes are required for passing air through the sample bed. Under the auspices of the A.S.T.M. (1) a comparative test of the Lea and Nurse air-permeation method was conducted on eight portland cements. Twenty laboratories participated using twenty different instruments. The agreement between laboratories waa reasonably good, especially when the cements were teated a t average porosities. However, there appeared to be a regular increase in specific surface values with decrease in porosity. It was proposed that a change in the Lea and Nurse formula be made by which the values obtained for specific surface would be more nearly the same regardless of the porosity a t which determined. This change took the form of a constant which could be determined by plotting a function of the surface areas as determined a t different porosities against the porosities a t which they were determined and extrapolating the straight line obtained to zero surface area. The intersection a t the zero surface area line is apparently a constant for each type of material. This constant
ANALYTICAL EDITION
June, 1946 GLASS TEE-
TO VACUUM PUMP
RUBBER TUBING
PREClSlC$B,O,A,E,T~!J PLUG OF RUBBER TUBING
PIGMENT (1.0 ern. in length)
NOTE
- All joints permanent erceDt A and 8.
Nurse formula so t h a t calculated RUBBER TUBING specific s u r f a c e areas are not affected b y t h e porosity at which t h e powder is tested. 25 rnl. PIPET From a theoretical point of view t h e permeability method should be valid within experiFLASK CONTAINING mental errors down WATER t o a particle diameter of 0.1 micron. Figure 1. A i r Permeability However, it has Apparatus been c o n s t a n t l y recognized that the I method has certain limitations which might not permit its being applied t o the measurement of particle size diameters much below 2 microns. Lea and Nurse (9) have stated that the method may be limited t o particles of 10 microns or larger. Work (IO) has found that the porosity function, c 3 / ( l - E)*, is very critical and is not proportional to the permeability over a very wide range in some cases. Thus in making tests of various materials i t is necessary to determine the porosity a t which this function is proportional to the permeability. However, because of its relative simplicity and apparent reproducibility the method definitely merits consideration. X need arose in this laboratory for a rapid, reproducible method for determining the relative particle sizes of pigments in the range of 0.1 to 2.0 microns. Microscopic methods were tedious and only semiquantitative, since with even a dark-field microscope the smaller particles are often overlooked and a true evaluation cannot be made. Adsorption methods are also timeconsuming and often lead t o erroneous results, especially with particles of irregular surfaces. Attention was therefore turned to a n air-permeation method. An investigation of the method detailed by Lea and Nurse (9) demonstrated that some modifications would have to be made before it could be used satisfactorily t o measure the specific surface of pigments having mean diametersless than 1.0 micron. Air flow rates much in excess of 10 ml. per minute were t o be avoided since turbulence resulted, invalidating the equation developed by Carman ( 4 ) for Poiseuille flow. It was also found necessary t o compact the pigment tightly in small-bore tubes in order to avoid channeling, which resulted if only relatively light pressures and large beds were used. These highly compressed pigment beds resisted air fiow to such a n extent that measured rates could be obtained only by using a full atmosphere pressure drop across the bed.
7
1 r
APPARATUS
The essential features of the apparatus first developed for determining the surface area of finely divided pigments are shown in Figure 1. It consists of an Erlenmeyer flask filled with water, a 25-ml. pipet connected to a glass safety reservoir with a permanent heavy rubber connection, and the sample tube, having a n internal diameter of 0.634 cm. and constructed of precision-bore tubing.
371
I n making a determination a lug of pigment of known volume is formed in the sample tube. &his is packed in by hand, using two short cylindrical lengths of metal which fit snugly inside the sample tube and extend beyond i t at each end. The length of the plug is measured with a micrometer which spans the plug and the two metal piecea of known length. To simplify calculations the igment plugs are all formed to a constant length of 1.00 cm. !'his is done by adding or subtracting pigment until the well packed plug is slightly too long and then making a final adjustment by compressing to the exact length. The sample tube is then weighed and placed in the apparatus. The flask of water is drawn to one side, so the pipet tip is no longer immersed in the water, and the vacuum ump started. The stopcock on the vacuum line is then o ened sfowly to avoid sudden a p lication of vacuum to the s a m p i plug. The r w u r e differentiaris noted by means of a mercury gage (not $own in Figure 1) and maintained at approximately 740 mm. of mercury. After permitting the system to come to equilibrium, the rate of flow of air through the sample plug is measured by moving the flask of water back to position and timing accurately the interval re uired to draw 25 ml. of water into the pipet. k i t h the data obtained it was possible to calculate the specific surface of the Sam le. Equations 1 and 2 may be combined and modified to yield t f e following equation:
(3) where
QZ = volume of air in ml. flowing through sample plug in time t or
SO
AtX 0
(4)
where S, = specific surface of the pigment in sq. cm. per gram p = specific gravity of pigment Since p , A , AP, q,,and L are known constants, Equation 4 be put in the following form: S, = K Z where
4- x Qz
-58
(1 -
4 2
K z will, of course, have a unique value for each type of pigment. The porosity may be expressed mathematically as
where
W
=i
weight of pigment in plug in grams
Having measured t , &2, and W , it is a very simple task to combine Equations 5 and 6 to calculate the specific surface, S,
It is clear from the foregoing that the apparatus required and technique are very simple. The method is also rapid, requiring less than a n hour for one determination. If i t is desired, more than one apparatus may be run off the same vacuum manifold. The reproducibility is good, as is indicated in Table I. Small variations in rlp which are experienced because of fluctuations in the barometric pressure have little effect on the specific surface values. Although no attempt is made to use the same weight of pigment for each determination, the porosities are fairly uniform in duplicate determinations with the same pigment. Because of the critical nature of the porosity function, sa/ (1 e)l, the actual values of surface area may not agree too well with those obtained by this method. However, since no known method can be relied upon t o yield infallible surface area measurements, comparisons with other methods, while not precise, serve to indicate whether the method yields results of the right order of magnitude. Harkins and Gans (8)using a:, adsorption method obtained values of 38,000 and 57,300 sq. cm. per gram on two titanium dioxide pigments, which compare very favorably with the results in Table I. Apparently the air-permeation method described here can be relied upon to give values of the correct order of magnitude.
-
372
INDUSTRIAL AND ENGINEERING CHEMISTRY Table
1.
Surface Area of Titanium Dioxide Pigment
Pigment Titanium dioxide 1
Table
Porosity 0.7194 0.7337 0.7286 0.7167
Table 111.
M e a n Particle Diameters of Pigments, Using Rapid Routine Method
Surface Area,
Sq. Cm. per Gram
Pigment
36,600 36,200 35,400 34,900
Titanium dioxide 2
II. Comparison of M e a n Cross-Sectional Diameter Values
(Calculated from specific surface value of a titanium dioxide pigment, assuming various particle shapes. Specific surface area, 36,000 sq. om. per gram) Mean Diameter, Micron Assumed Shaped of Particles 0.42 Spherical 0.37 Rod-shaped, length 1,5times diameter Rod-shaped, length 2 times diameter 0.35 0.33 Rod-shaped, length 3 times diameter 0.31 Rod-shaped, length 4 times diameter
Calcium carbonate 1 Calcium carbonate 2
Table
Weight of Plug Gram 0,6963 0.7376 0.6623 0.6624 0.3424 0.3177 0.3394 0.4432 0.4313 0.4226 0.'4346
AP
Although this method was highly satisfactory as a research tool, it soon became desirable to modify it for routine and more rapid determinations. Therefore, the apparatus was redesigned so that shorter times would be required for making a determination, and calculation of the particle size would be simplified. This modified apparatus, diagrammed in Fi ure 2, consists of a 150-ml. beaker filled with water, an invertef 10-ml. graduated pi et with the tip cut off, a calcium chloride tube, the sample ut,! and a stopcock, which is connected to a source of high vacuum. The sample tube is a stainless steel tube carefully machined and having an internal diameter of 0.579 * 0.0025 cm. All connections are made with heavy, tightly fitting sections of rubber tubing and are all made permanent except those between the calcium chloride tube and the rubber stopper and between the sample tube and the rubber connection. In making a determination the sample tube is weighed and then placed over the bottom plunger of the hand press shown in Figure 3. The sample is transferred to the sample tube by means of a funnel and packed into the tube, using the top section of the hand press. When the plug is reasonably firm the sample tube is reversed, This prevents the tube from coming in contact with either the top or bottom of the hand ress, thus ensuring that the plug length is exactly that between tge two plungers. Sample is added until a firm, solid plug is obtained. Any portion of the
Specific Gravity of Pigment Gram/&.
4.00
2.70 2.70
Volume of Air
Time
da
iU1.
Scc.
Micron
5.0 5.0 7.0 5.0 3.0 3.0 3.0 2.5 2.5 3.0 3.0
151 169 161 116 181 156 195 177 186 218 224
0.74 0.78 0.78 0.78 0.30 0.28 0.28 0.43 9.40 0.38 0.40
IV. Possible Errors in M e a n Diameter Determination
Variable Volume of air, Qn APPARATUS FOR ROUTINE CONTROL WORK
Vol. 18, No. 6
Time, t Length of plug, L Area of plug, A Porosity of plug, e
Maximum % Deviation Accuracy Assumed in dm Due to Error in Measuring Variable in Measuring Variable *O.l ml. hl.0 t25 mm. of mercury t1.7 *l sec. 10.4 10.01cm. 10.3 *2.3 X 10-8 sq. em. t0.5 *2.3 X 10-3 sq. cm. ( A ) -2.0 10.01 cm. (L) t2.0 *0.001 gram ( W ) t0.5 t o .02 gram per ml. ( p ) t1.2
sample which might adhere to the sides of the tube above the surface of the plug is loosened with a sharppointed wire and removed. The tube is again weighed and placed in the apparatus, the two nonpermanent connections being made air-tight. The stopcock is then cautiously opened to the vacuum, held a t less than 5-mm. pressure. About one minute is allowed for the system to come to equilibrium, after which the time for a measured amount of air to pass through the plug is determined. The uantity of air is chosen so that the time required is between 2 a n 1 5 minutes. CALCULATION OF PARTICLE SIZE
For routine control it is convenient to express the specific surface area of the pigment in terms of mean diameter. This is usually done by assuming a spherical shape for each particle. However, whether a spherical shape or a rodlike shape is assumed does not change the order of magnitude of the mean cross-sectional diameter, and in fact does not change the actual value appreciably. This is demonstrated in Table 11, in which. the mean crosssectional diameters of a titanium dioxide pigment calculated on the basis of several assumed particle shapes are presented. Assuming a spherical particle, Equation 4 becomes
RUBBER TUBING
sw
RUBBER STOPPER
=
6 dmp
(7)
where
RUBBER TUBING
= mean cross-sectional diameter in cm. By combining Equations 4 and 7 and expressing d, in microns, the following equation is obtained:
d,
SAMPLE TUBE LGIUM CHIDRIDE TUBE r REMOVABLE TOP
By suitable mathematical expansion Equation 8 becomes
E -l
IO ml. PIPET
,571cm.
Figure 2. Air Permeabi lit'y Apparatus for Routine Work
where
or
K3' - - 1 dmZ-
az
U
Figure 3.
Hand Press
(10)
By employing Equations 9A and 10 the value of d, may be calculated by a simple graphical method. How this can be accomplished is shown in Figure 4.
ANALYTICAL EDITION
June, 1946
373
Figure 4. Chart for Determining Mean Cross-Sectional ,Diameter
Since L, 7 , and A are constants and AP is held within limits, variations within which have only negligible effect on the value of d,, the value of Kat or KaZ,is a function of the ratio of the weight, W , of the sample to its specific gravity, p and a curve is drawn relating these two functions. On the same graph is drawn a family of curves in which K? is plotted versus t / Q z for a series of d, values covering those of the pigments being measured. A few preliminary measurements will determine what range of t / Q 2 and W / p values will be encountered and therefore what ranges must be covered by the graph. To determine the value of d, for any particular pigment, ratios W / p and t/Q2 are calculated. Using the W / p versus K? curve, the Ka2 value corresponding to the W / p value is determined. The intersection of this KS2 value with the t / Q 2 ratio is then found and the value of d, obtained by interpolation. This method is reproducible, as is demonstrated in Table 111. I t was recognized that there would be several sources of error in a measurement of this type. Reference to Table IV will demonstrate, hoyever, that if all errors were cumulative the maximum deviation in the value of d, would be 9.6%, owing to experimental errors. In actual practice the maximum deviation is a p proximately 57, of the value of d,. This does not appear too large in light of the errors accompanying measurements of mean cross-sectional diameters by other methods. SUMMARY
A method for determining the specific surface area of pigments in the range of 0.1 to 1.0 micron has been described. The method is reproducible and is easily modified for rapid control work. Although the specific surface values obtained may not be true values, accurate comparisons of similar pigment types may be made. LITERATURE CITED
(1) Am. SOC.Testing Materials, Working Committee on Fineness, Committee c-1on Cement, Bull. 118,31 (1942).
Blaine, R. L., Ibid., Bull. 108, 17 (1941). Ibid., Bull. 123, 51 (1943). Carman, P. C., J . SOC.Chem. I d . , 57, 225T (1938); 58, 1T (1939). Carman, P. C., Am. SOC.Testing Materials, Symposium on New Methods for Particle Size Determination in the Subsieve Range, p. 24, 1941. Carman, P. C., Trans. Znst. Chem. Engrs. (London), 15, 160 (1937). Gooden, E. L., and Smith, C. M., IND.ENG.CHEM., ANAL.ED., 12,479 (1940). Harkins, W. D., and Gans, D. M., J . Am. Chem. SOC.,53,2804 (1931). Lea, F. M., and Nurse, R. W., J . Soc. Chem. I n d . , 58, 2 R T (1939). Work, L. T., discussion of paper by P..C. Carman, “Shape and Surface of Fine Powders by the Permeability Method”, Am.
SOC.Testing Materials, Symposium on New Methods for Particle Size Determination in the Subsieve Range, p. 24, 1941. PRESENTED before the Division of Industrial and Engineering Chemistry, AMERICAN CHEMICAL SOCIETY. Symposium on Measurement and Creation of Particle Size, Brooklyn, N. Y., December, 1945.
Simultaneous Determination of Hydrogen Sulfide and Carbon Dioxide in a Continuous Gas Stream CLYDE L. BLOHM AND FRED C. RIESENFELD, The Fluor Corp., Ltd., Lor Angeles, Calif. A method i s described for the simultaneous determination of hydrogen sulfide and carbon dioxide in a continuous stream of natural gas. The two acidic gases are absorbed in standardized iodine and barium hydroxide roluticins. O n l y simple laboratory equipment i s required.
I
S T H E course of one of the research projects of this labora-
tory, it was found necessary to analyze a stream of natural gas for hydrogen sulfide and carbon dioxide in such a manner that a large number of analyses could be taken which, at the end of the
operation, could be integrated into a quantitative over-all balance. Various methods are known for determining hydrogen sulfide and carbon dioxide in natural gas. Hydrogen sulfide is most commonly determined by the Tutweiler method (2,4 , 9 ) , or by one of the cadmium sulfide methods (5, 6). The carbon dioxide content of the gas is usually measured by absorption in sodium hydroxide solution in an Orsat (8, 6, 8) or Orsat-type apparatus, or may be determined by absorption in barium hydroxide solution as described by Martin and Green (7). When both hydrogen sulfide and carbon dioxide are present, the total acid gas content
