(14.7 parts per thousand). It appears, then, that the precision of the titration is improved by carbonic anhydrase. The enzyme naturally does not enhance the sharpness of the end point, only the rate a t which it is attained, but this faster rate is very helpful in titrating labile solutions. The quantity of protein introduced in these experiments did not add a detectable blank to the titration. The effect of carbonic anhydrase qpon the titration of carbonate with hydrochloric acid to both the phenolpbthalein and the methyl orange end points was also investigated. We were able to perceive no advantage gained by using the enzyme over titrations performed with reasonable care in its absence. Like other protein enzymes, carbonic anhydrase may be inactivated under
certain conditions. For example, it is destroy::: by 30 minutes’ heating a t 65” C., and it is unstable dt pH values above 13 and h e l o w 3 (4,6,8).The pH a t whicll carbonic anhydrase exhibits maximal catalytic activity is not clearly stated in the literature, but fortunately the activity is high in the pH region of importance in the carbon dioxide titration. Certain substances act as inhibitors of carbonic anhydrase; among these are copper, silver, gold, mercury, zinc, and vanadium salts, as well as sulfides, cyanides, thiocyanates, and azides (4,6,8). LITERATURE CITED
(1) Keilin, D., Mann, T., Biochem. J . 34,
1163 (1940).
(2) Kern, D. M., J . Chem. Educ. 37,
14 (1960). (3) Kolthoff, I. M., Stenger, V. A,, “Volumetric Analysis,” 2nd Ed., Vol.
11, p. 131, Interscience, New York,
1947. (4) Meldrum, N. U., Roughton, F. J. W., J . Physiol. 80, 113 (1933). (5) Roughton, F. J. W., Booth, V. H., Biochem. J. 32, 2049 (1938). (6) . . Roughton. F. J. W.. Clark. A. SI..
in Sumner,‘J. B., Myrback, K.,Eds.; “The Enzymes: Chemistry and Mechanism of Action,” Vol. I, Part 2, p. 1250, Academic Press, New York, 1951. ( 7 ) Roughton, F. J. W., Meldrum, N. U., Brit. Patent 403,096,p. 6, clauses 60 to 100, (Dec. 1, 1933). (8) Vallee, B. L., in Anson, M. L., Bailey, K., Edsal, J. T., Eds., “Advances in Protein Chemistry,” Vol. X, p. 333, Academic Press, New York, 1955. (9) Waygood, E. R. in Collqwick, S. P., Kaplan, N. O., Eds., Methods of Enzymology,” Vol. 11, p. 836, Academic Press, New York, 1955. (10) W.ilbur, K. M., Anderson, N. G., J . Bzol. Chem. 176, 147 (1948).
RECEIVED for review Kovember 21, 1960. Accepted March 6, 1961.
Particle Size Measurements with an Improved Contin uo us1y- Recording Sed imenta t ion A pparatus EMlL S. PALIK Chemical Products Plant, lamp Metals and Components Department, General Nectric Co., Cleveland, Ohio
b An improved continuously-recording sedimentation apparatus has been developed and its performance characteristics compared with other methods of particle size analysis. A comparison of the apparatus with two sedimentation methods shows acceptable agreement for a fluorescent powder whereas comparison with a method utilizing changes in electrolytic resistivity shows a significant difference. The apparatus has been found useful in the particle size analyses of fluorescent powders and may be used to analyze other powders with a size distribution in the range of 2 to 60 microns.
S
SEDIMENTATION balances for the measurement of particle size have been reported in the literature. The earliest form of this a p paratus was described by Oden ( I S ) who employed an analytical balance for weighing particles settling out of suspension, The Oden balance was modified by Coutts and Crowther (6) into a continuously-recording instrument by incorporating electromagnetic weighing and control with the original method of adding small weights a t the requisite times. Later, Bostock (6) substituted a torsion wire for the conventional beam balance to detect the weight of particles settled, but his design did not provide for automatic continuous weighEVERAL
956
ANALYTICAL CHEMISTRY
ing of the particles. More recently, emphasis has been placed on developing automatic recording balances utilizing a variety of transducers (1, 3, 8, 12) with which to convert weight changes into an electrical signal suitable for amplification and recording. The present paper describes a sedimentation apparatus, referred to hereafter as the sedimeter, in which the sensitive springoptical arrangement of Rabatin and Gale (1’7)has been modified by the use of a torsion balance. The convenient feature of the optical transducer has been retained in the present design. Similar applications of the torsion balance principle have been described by Rabatin and Card (16)and also by Avgustinik and Dzhansis (2) to detect weight changes in thermogravimetric analyses and surface area measurements. The above modification together with additional changes in design resulted in a recording sedimentation apparatus having improved performance over the original spring design. This paper reports the first known application of the torsion-optical principle to the measurement of the settling rate of fine powders. APPARATUS
Construction. A diagrammatic sketch of the sedimeter is illustrated in Figure 1. The light source, 1, consists of a 6.3-volt tungsten filamentlamp
operating from a constant voltage transformer mounted in the housing directly behind the instrument panel, 3. The light originating a t 1 passes through a fixed slit, 2. The collimating lens, 4, is a double convex lens with a 15-cm. focal length. The torsion balance, 5, is of standard design except that it has been modified by employing more sensitive torsion elements. These elements (Sandsteel Mainsprings No. 2125, Watch-Motor Mainspring Co., Inc., N. Y.) have a 1.10 111111. width and 0.17 mm. thickness. The balance is mounted on a platform, 6, and shielded from stray light and air currents. Attached to the left extremity of the balance is an adjustable counter - weight, 7, with which to counterbalance the pan. A stainless steel pan, 8, 6.50 em. in diameter and soldered to a stainless steel stem 20 cm. in length, is attached to the right arm of the balance through an opening in the platform. These dimensions provide for an initial particle settling distance of 11.7 cm. The pan is immersed in an unsilvered, flat-bottomed Dewar settling vessel, 9, having a Lucite cover into which is cemented a thermometer, 10. During sedimentation the thermometer is immersed to a depth of about 2 cm. in the suspension. Although no temperature control is used, the temperature during sedimentation remains a t 25” i 1” C. To the left arm of the balance there is attached a rigid opaque metal shield, 11, 2.5 cm. X 5.5 cm., which intercepts the collimated beam emerging from the fixed slit, 12. The transmitted
Figure I . sedimeter
Schematic
diagram
of
light passes through an adjustable exit slit, 13, used to adjust the zero and h a 1 recorder position. A millimeter scale located a t the operator side of the adjustable slit is partially illuminated by the light beam. The shadow of the shield falls on this scale and determines the total upward displacement of the shield. Finally, the light strikes a General Electric Type PV-1 barrierlayer photovoltaic cell, 14. The voltage drop across the photocell can be adjusted by a 10-turn 10,000 ohm potentiometer, 15, located on the instrument panel. The current reaching the recorder can be conveniently 'interrupted by a photocell switch, 16, connected in series between the potentiometer and the recorder. A timer switch.> 17. --, mounted on the instrument panel permits automatic on-off operation of the apparatus. Also mounted on the panel are main power, light source, recorder, and chart drive switches. The sedimeter is housed in an aluminum case and mounted on four shock absorbing leveling screws, 18. The sedimeter with a General Electric Type H F strip chart recorder equipped with a multispeed chart drive unit is shown in Figure 2. The front cover of the top housing of the sedimeter has been removed to display the torsion balauceoptical arrangement. Operation. After sedimentation has hegun the operation of the sedimeter is entirely automatic. Exactly 600 ml. of previously dispersed suspension are used in the settling vessel, this volume including both sample and dispersant volume. The sample size varies from 4 to 6 grams depending on the density of the powder and the sensitivity settings of the instrument. The instrument is first adjusted by use of a blank consisting of 600 ml. of the proper dispersing medium in the settling vessel. This adjustment involves opening the exit slit to a distance of 6.0 mm. and varying the resistance across the photocell to obtain a recorder reading of 9.5 mv. The shadow position produced hy the shield must then be adjusted upwards to intercept approximately 0.5 mm. of the light beam and give a base line recorder reading of 9.0 mv. This adjustment is carried out by means of the moveable counterweight located a t the left extremity of the ~~
~~~
~~
~~
~
~~~~~
balance. The sample weights are so chosen that upon complete settling of the particles the recorder reading will decrease to a value of about 1.0 mv. While the hlank is in position, the distance from the pan to the meniscus is noted (11.7 em.) together with tbe shadow position on the millimeter scale. The blank is now replaced by the sample suspension which is vigorously shaken by drawing the pan upward and downward several times. The vessel is then quickly placed in position, the pan attached to the balance, and the photocell switch turned on. This action requires less than 5 seconds and produces no significant error with samples of density less than 5 grams per cubic centimeter. The recorder equipped with a multispeed chart drive unit affords the operator a wide selection of sensitivities in the measurement of the particle settling rate, particularly during the initial stages of sedimentation when settling is very rapid. Thus, the settling rate may necessitate a fast chart drive initially and, then, by a quick manual gear shift a slower speed can be utilized durine later staees of settline. The tfmpmitiirr of t h e sus~iennsimis riotrd at tt.r bi.ginning snil vomplt.tion of the run along nith t l i c final ahadow position on the millimeter scale. The difference between the initial and find shadow positions represents the distance through which the pan has been displaced. This value which averages approximately 5 mm. is subsequently used in the calculations. I
-
The sedimentation data were converted to particle size distributions by the method outlined by Oden (14) and modified by Gaudin et al. (7). The latter form is.given by Equation 1.
where
W
and the geometric standard deviation, ro, were determined directly from the plots of weight per cent greater than diameter, D, us. log D, employing log-probability coordinates, as described by Om and DallaValle (15).
.I
TREATMENT OF THE DATA
P
Figure 2. C o n t i n u o u s l y - r e c o r d i n g redimeter
= weight per cent of particles settled a t time t, sec. = weight per cent greater than
diameter, D, cm. falling through height, h, cm. as given by Stokes' expression shown in Equation 2.
where viscosity in poise of the settling medium PI = density in grams/cc. of the Darticles, determined hv fluid displacement p2 = density in grams/cc. of the settling medium g = acceleration due to gravity
'1 =
Since a log normal distribution was observed for the powders investigated, the use of only two parameters to represent the distribution is justified. The geometric mean diameter, M , (p),
RESULTS AND DISCUSSION
In all of the following measurements m wiiic~i cric sedimeter is evaluated, three fluorescent powders were used: a lamp phosphor (calcium halophosphate type) and two electronic phosphors (zinc cadmium sulfide and zinc sulfide-zinc cadmium sulfide types). A light microscope examination revealed that the shapes of these particles approximate spheres, thus justifying the use of Stokes' equation. It was experimentally determined that the recorder reading obtained from the torsion balance-optical arrangement is linearly proportional to the weight of particles settled over the range used in the sedimentation measurements. Hence, the recorder data can be converted directly to weight per cent settled data and applied in the particle size calculations. The sensitivity of the sedimeter was determined to be 0.006 em. of pan d i e placement per division of recorder paper having 100 divisions full scale. This figure corresponds to 0.029 gram (air weight) of powder per division of chart paper. By varying the adjustable slit width and sample size, the sensitivity may be increased if necessam. A discussion of errors in connection with this apparatus includes sample dispersion, sample volume, and disturbance around the pan. Dispersion is achieved by a vigorous mechanical stirring of the powder in a suitable disnersine medium such as dilute ammonium hydroxide or potassium silicate solution. Previously, it was determined that powders settling in these media yield lower sedimentation volumes than in other available media. The sample volumes were not allowed to exceed 0.3% of the suspending volume, :~~
~
VOL. 33, NO. 7, JUNE 1961
957
-.\
'm
Table 1. Repeatability of Sedimeter with Zinc Cadmium Sulfide in o.3Y0 Potassium Silicate Solution
111"(P)
00
12 0 12.0 12.2 12 0 12.0 12.2 Av.12.1 70 Std. dev. & 0 . 9 2
5 10 20 WEIGHT
5 0 70 90 98 % GREATER THAN
Figure 3. Particle size distribution of zinc cadmium sulfide in 0.3% potassium silicate solution 0 Sedimeter Pipet A Sedimentation balance
thus minimizing hindered fall of particles (18). The error due to disturbance around the pan during the course of a determination can be significant as shown by Coutts and Crowther (6). This error arises from a n inevitable flow of liquid after sedimentation has begun from the lower density volume immediately below the pan upward through the settling volume above the pan, causing interference with the free vertical fall of the particles. The effect of the error varies mith particle size and tends to displace the distribution curve tomards the coarse sizes. In the sedimeter the disturbance was minimized by suspending the pan as near as possible to the flat base of the settling vessel. The error is small for the particular samples studied as shown in Figure 3 by the close agreement nith the Bureau of Standards pipet method, described by Jackson and Saeger (IO). Jacobsen and Sullivan (11) and Gaudin et al. ( 7 ) have also discussed the pan error and described modifications to minimize it in their sedimentation measurements. The repeatability of a typical particle size measurement using the sedimeter is shown in Table I. The precision of the sedimeter is shown in Table 11. A fine fraction and a coarse fraction of calcium halophosphate powder were analyzed individually by the apparatus together Rith a third sample consisting of a 50-50 mixture of the two fractions. The observed results of the mixture are compared with the calculated values which were obtained by averaging the results of the fine and coarse fractions. It m-as of considerable interest t o compare the performance of the sedimeter with other sedimentation methods of particle size measurement. Figure 3 gives the cumulative distribution curves for a zinc cadmium sulfide in potassium silicate solution. The sedimentation 958
1.61 1.65 1.61 1 64 1.64 1 60 1.63 i l . 3
ANALYTICAL CHEMISTRY
balance referred to in the figure is the spring balance of Rabatin and Gale ( 1 7 ) . As shown in Figure 3, the sedinieter permits measurements to be extended to sizes coarser than that allowed by the original spring balance. In addition, the results of the sedimeter compare more closely with the independent pipet method than do the results of the sedimentation balance. The sedimeter was also compared with the Coulter counter, described by Berg (4), which employs a novel principle of particle size analysis involving changes in liquid resistor volume. It was found n-ith Coulter counter measurements on calcium halophosphate employing a 0.1% NH40HlY0 NaCl suspending medium that the weight distribution curves are shifted towards the coarser size by 1 to 2 microns compared with the sedimeter. Figure 4 compares the sedimeter with the Coulter counter using a calcium halophosphate sample suspended in 0.1% NH40H-1% KaC1. Also shown is the distribution curve obtained with the sedimeter in which the 1% NaCl mas omitted from the suspending medium. These results suggest that the higher ionic strength media recommended for the optimum operation of the counter may in some instances promote flocculation. K i t h other substances, such as a zinc cadmium sulfide phosphor in which a lower ionic strength media
Table II.
(0.3% potassium silicate) was employed, the observed discrepancy between instruments \\ as not as serious. Figure 4 suggests that a second factor, in addition to ionic strength effects, may be involved in the observed difference betneen the trio methods. Additional comparison data between the Coulter counter and a scdimentation method have been rcportpd by Irani (9). Finally, it was of interest to compare the sedimeter against standard sieves to determine its accuracy in the coarse range. Table 111 gives the resuits using a zinc sulfide-zinc cadmium sulfide po-ivder n-ith four screen sizes. The close agreement between the sedimeter and sieves in this table indicates that the sedimeter is capable of measuring coarse particles up to 60 microns in size. Thus, the turbulence occurrifig in the initial period of sedimentation has a negligible effect on the measurement of coarse particles. The turbulence produced 'by the pan action in miving the suspension dampens out within a fely seconds. I t is probable hon-ever, that measurcnients on sizes
2 5 IO 20
50 7 0
90
98
WEIGHT % GREATER THAN
Figure 4. Particle size distribution of calcium halophosphate
A Sedimeter in 0.1% NHdOH
+
1% NaCl Coulter counter in 0.1% NH4OH 4- 1% NaCl 0 Sedimeter in 0.1% NH40H only
Precision of Sedimeter with Calcium Halophosphate in 0.1% Ammonium Hydroxide Weight Per Cent in Range
Range, P
Fine
Coarse
Mixture observed
Mixture calculated
0-5 5-10 10-15 15-20 2&25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 >60
17.5 55.0 24.0 3.5 2.5 0 0 0
0 5.0 19.0 20.0 13.0 10.0 7.5 5.5 4.5 3.5 3.0 2.5 6.5
8.0 29.0 21.0 13.0 8.0 5.5 3.5 3.0 2.0 2.0 1.5 1.0 3.0
8.8 30.0 21.5 11.8 7.8 5.0 3.8 2.8 2.3 1.8 1.5 1.3 3.3
0
0 0 0 0
larger than 60 microns would be in error for this reason.
Table 111.
Comparison of Sedimeter with Sieves
ACKNOWLEDGMENT
Mesh Screen
Size, p
The author acknowledges the helpful suggestions given to him by Jacob G. Rabatin.
1000 500 400 325 230
22 25 37 44 62
LITERATURE CITED
(1) Arnes, D. P., Irani, R. R., Callis, C. F., J . Phys. Chem. 63, 531 (1959). (2) Avgustinilc, A. I., Dzhansis, V. D., J . . l p p l . Chem. (U.S.S.R.) 24, 433-8 (1951). (3) Bachmann, D., Gerstenberg, H., Chem-1ng.-Tech. 29, 589-94 (1957). ( 4 ) Berg, R. H., Am. SOC.Testzng Materzals Spec. Tech. Publ. iVo. 234, 245 (1958). (5) Bostock, K., J . Scz. I n s t r . 29, 209 (1952). (6) Coutte, R. H., Crowther, E bI., Trans. Faraday SOC.21, 374 (1925). (7) Gaudin, A. hI., Schuhmaiin, R., Schlechten, A . W., J . Phys. Chem. 46, 903 (1942). (8) Hayakawa, T., Tomotsu, T., Takagi,
R . , Makishima, S., KBgy6 Kagaku
Zasshi 60, 1249-52 (1957). (9) Irani, R. R., ANAL.CHEM.32, 1162 (1960). (10) Jackson, C. E., Saeger, C. M., J . Research Natl. Bur. Standards, R. P. 757, 14, 59 (1935). (11) Jacobsen, A. E., Sullivan, W. F., IND.ENG. CHEM.,ANAL.ED. 19, 855 (1947). (12) Lincoln, K. A , Rev. Sci. Instr. 31, 537-9 i 1960). (13) Oden, S.; Intern. Mitt. Boden 5 , 257-311 (1915). (14) Oden, S.,PTOC. Roy. SOC.Edinburgh
Wt. yo Greater than Stated Size Sieve Sedimeter 18.0 14.7 10.8 5.7 0
):1(
19 .c 15.9 8.0 4.5 0
36, 219 (1916). Orr, C., Jr., DallaValle, J. M.,
Fine Particle Measurement,” Chap.
2, Macmillan, Kew York, 1959. (16) Rabatin, J. G., Card, C. S., ANAL. CHEJI.31, 1689 (1959). (17) Rabatin, J. G., Gale, R. H., Ihid., 28, 1314 (1956). (18) Stairmand, C. J., Symposium on Par-
ticle Size Analysis, Supplement to
Trans. rnst. Chem. Engrs. 25, 128, (1947).
RECEIVED for review October 27, 1960. Accepted January 18, 1961.
A Simple and Rapid Method for Fluoride Ion Determination SIR: I n the course of studying the mechanism of chemically etching singlecrystal silicon (4, 5 ) in solutions of nitric and hydrofluoric acids, a n interesting effect was observed which may prove useful in developing a simple and rapid method for fluoride ion determination. When a n n-type silicoii electrode (single-crystal, transistor-grade Si) is made the anode of a n electrolytic cell, shielded from room light and in a solution which does not chemically etch silicon, the current is limited to a f m microamperes per square centimeter of anode area. Brattain and Garrett ( I ) and Flynn ( 2 ) have found that the anodic dissolution of semiconductors requires positive electron holes, but only a relatively small number are available in the surface region of n-type silicon in a nonetching solution. In a n etching solution, such as HF and H S O s acid mixtures, the over-all reaction a t the surface of the silicon includes the formation of excess electron holes (4) and these can increase the anodic limiting current by several orders of magnitude. The number of excess electron holes produced is directly proportional to the chemical etch rate and the etch rate is directly proportional to the amount of HF in nitric acid (up to about
10 neight % HF). Therefore the anodic limiting current of a n n-type silicon electrode in HF and HSOs solutions should be directly proportional to the amount of HF in the chemical etch. This has been verified experimentally (5) The effect just described suggests that the experiment may be useful in developing a general method for fluoride ion determination. The technique involves adding the sample, preferably condensed in volume, to a known volume of concentrated (70%) nitric acid. The mixture chemically etches silicon, and the anodic limiting current density of the electrode should be
APIEZON W WAX
_ _ _ _ ~ F-
I N CONC. H N O ~
Figure 1. Experimental arrangement for fluoride ion determination
proportional to the amount of fluoride ion in the original sample. The experimental arrangement is simple, as illustrated in Figure 1. An ordinary 1.56-volt dry cell is a n adequate power source, as indicated by anode potential-current density curves for n-type silicon in HNO,-HF solutions ( 5 ) . The cathode material should be insoluble in fluoride and H N 0 3mixtures; platinum meets this requirement. Current through the cell is determined by the anodic limiting current density at the silicon electrode. It is measured nith a standard ammeter. The shape of the single-crystal silicon electrode is not important. The bar form is usually the easiest to obtain. The resistivity of the n-type silicon should be about 1 ohm-em. or less to avoid a n excessive I R drop in the electrode. .In ohmic contact is made to one end by abradinq the surface with No. 600 mesh S i c , depositing electroless nickel ( S ) , and soft-soldering it to a copper wire. To protect the solder joint and copper wire from fumes of nitric acid, a region above and below the contact is coated with a suitable masking material, such as Apiezon W wax dissolved in toluene, which can be painted on. The exposed surface area of the silicon electrode must be known with reasonable accuracy, since the total limiting current is dependent upon surface VOL. 33, NO.
7,JUNE 1961
959
