capacitative and faradaic currents at low d.c potentials. The imperfect separation results from an increased cell resistance which is in turn due to the low concentration of s u p porting electrolyte. The shift in the position of the base line is a constant a t any particular concentration of supporting electrolyte and therefore can be displaced back to the bottom of the chart by a base line compensation circuit, should it become desirable t o d o so. CONCLUSIONS
of high sensitivity, and therefore can detect the presence of a particular ion well out on the extremities of the peak. The selectivity is excellent as is shown by Figure 9 where two different ions were detected even though they were both eluted at the same time. The fact that oxygen is not reduced reversibly eliminates the necessity for treating the effluent to remove dissolved oxygen before the solution enters the cell. The 15-hour run for the determination of cadmium illustrates the long-term stability or reliability of this system.
The use of square-wave, and by extrapolation, sine-wave polarography provides a n excellent means of monitoring the effluent from an ion-exchange column. The scheme is capable
RECEIVED for review October 20, 1966. Accepted February 24,1967.
Particle Size Distribution Measurement in the 200 to 1200 A Range Ted Lee and C. W. Weber TechnicaI Division, Oak Ridge Gaseous Diffusion Plant, Union Carbide Corp., Nuclear Diaision, Oak Ridge, Tenn.
A relatively inexpensive method for partitle size distribution measurements in the 200 to 1200 A range has been developed for a variety of powders, including clays. The method utilizes 20-kc ultrasonics to deagglomerate and disperse the powder sample in an aqueous medium; a continuous flow centrifuge applying forces up to 60,000 x G to divide the slurry into size fractions, based on Stokes’ limiting diameters: and a gravimetric procedure (or refractive index measurements) to determine the solid content of each fraction. The simple Stairmand calculation i s applied to correct for simultaneous settling of fine particles. The method has been applied to Linde type B alumina polishing powder, and the results have been compared with electron microscopy measurements. Alumina, a major constituent of clays, permitted development with a pure compound of known density. Within the limitations of the equipment, experimental factors which influence accuracy are optimized. Deviations from basic centrifugation theory are discussed.
THISPAPER describes the development of a practical and versatile technique for general application t o particle size distribution measurement. A relatively inexpensive method for measuring the particle size distribution of a variety of powders, .;ncluding clays, was needed for the difficult size range from 200 to 1200 A. Alumina, a major constituent of clays, permitted development with a pure compound of known density. A review of the factors influencing the choice of a method for particle size analysis has been given by Scarlett (1). An exceilent review and bibliography of methods for determining particle size was prepared by a subcommittee of the Society for Analytical Chemistry ( 2 ) . Probably the two best known methods for particle size distribution measurements in the size range of interest are the analytical ultracentrifuge and ;he electron microscope. The analytical ultracentrifuge is expensive, and its use is limited to samples in which the concentration can be determined by optical means. To use the electron microscope, also expensive, requires counting large -- -
(1) B. Scarlett, Chem. Process Eng., 46, 197 (1965). (2) E. Q . Laws, et ui.,Anuiyst. 88, 156 (1963).
620
ANALYTICAL CHEMISTRY
numbers of particles for each sample; this is tedious and impractical for routine applications. A third method for size distribution measurement, also based on centrifugation, is the application of a Sharples supercentrifuge. The supercentrifuge is relatively inexpensive, provides centrifugal force sufficiently strong (up to 60,000 X G) t o settle the small particles of interest, and permits feeding the sample and collecting the size fractions while the machine is operating at sedimentation speeds. The method developed in this report would also be applicable to more refined equipment operating on the same principles, such as the preparative ultracentrifuge with a continuous flow rotor. The supercentrifuge was first applied to particle size distribution measurements by Hauser et of., (3-5). Their method is based on determining the sediment deposited in the centrifuge bowl, and calculating the size distribution from the centrifuge parameters and a calibration factor (6, 7). TO simplify the calculations for routine applications, alignment charts (3, 5, 8) and nomographs (9) were developed and applied. Using the supercentrifuge and the equations developed by Hauser et ui. (3-9, these workers and others (7, 8, 10) obtained usable quantities of sized samples. Sedimentation constants (7) obtained with the supercentrifuge showed good agreement with the more elaborate analytical ultracentrifuge. The size distribution measurement described in this report is based on determining the soiids content in etRuent fractions, rather than in the aeposits. The limiting diameter for each size fraction is calculated by the Svedberg-Nichols equation (3) E. A. Hauser and J. E. Lynn, ind. Eng. Chem., 32,659 (19401. 14) E. A. Hauser and C . E. Reed, J . Phys. Chem.. 40,1169 (1936). (5) E. A. Hauser and H. K. Schachman, Ibid., 44, 584 ( 1940).
(6) R . R. Irani and F. C. Clayton, “Particle Size Measurement, Interpretation and Application,” pp. 85-88. Wiley, New York, 1963. (7) H. K. Schachman, J. Phys. Coiloid Chem., 52, 1034 (1948). (8) S. C. Oliphant: C. R. Houssiere, Jr., and G: H. Fancher, Am. Inst. Mining Mer. Engrs.. Tech. Pub. No. 1530 (1942). (9) E. Saunders, ANAL.CHEM., 20, 379 (i948). (10) F. €3. Norton and S . Speii, J. Am. Cerom. Soc., 21, 367 (1938).
0 0
8 12 16 U L T R A S O N I C S EXPOSURE, hours
20
Figure 1. Ultrasooic deagglomeratioo US. expofllre
time (21); a correction is applied for the settling of fine particles from intermediate levels using a modification of the Stairmand calculation (22). Associated with the correction for fines are dilution errors (23) arising from the radial settling of the particles and the nonlinear centrifugal field. Although no corrections for these errors have been made, their effect on the measured size distribution was evaluated. Determining the solids content of size fractions in the effluent, instead of the sediment, allows retaining the continuous flow feature of the centrifuge, and permits collecting successive size fractions while sedimentation is in progress. This simplifies the collecting and handling of fractions, and eliminates errors (and corrections) for acceleration and deceleration. An important prerequisite t o obtaining size distribution data is the dispersion of the powder sample. For this purpose, 20-kc ultrasonics (14) was evaluated and applied without chemical dispersing agents. The development of the method is described in the procedural order: ultramnic dispersion, centrifugal fractionation, determination of solid content in the size fractions, and calculation of the size distribution. Sources of potential error and techniques for optimization are discussed. Representative results, presented for the size range of interest in Linde B alumina polishing powders, are compared with electron microscopy measureme nts. ULTRASONIC DEAGGLOMERATION AND DISPERSION
A 20-kc ultrasonic cleaning system rated at loo0 watts output (1.6 watts/cm*) is used to disperse the sample without chemical dispersing agents. The sample is prepared for dispersion by adding 16 ml of distilled water to 2 grams of the powder sample, and stirring to form a uniform paste. The paste is transferred to the ultrasonic tank containing sufficient distilled water to provide a depth of 1.5 inches, equivalent to the half wavelength, X/2 (25). The standing wave pattern of X/2, therefore, provides reinforced ultrasonic intensity concentfated in one cwitation level, most effectively dispersing the powder. (11) The. Svedberg and J. B. Nichols, J . Am. Chem. Soc., 45,2910 (1923). (12) C. J. Stairmand, Symposium on Particle Size Analysis, Trans. inst. Chem. Engrs., (.tondon),Suppl. 25, 128 (1947). i13) The. Svedberg and H. Rinde, J. Am. Chem. Soc., 46, 2677 (1924). (14) 1. E. El’piner, “Ultrasound: Physical, and Biological Effects,” pp. 237-9, Consultants Bureau, New York, 1964. (15) Ibid.. pp. 7-9.
An ultrasonic exposure period of 16 hours was established for alumina polishing powder, following a study of relative deagglomeration us. ultrasonic exposure time, as shown in Figure 1. The study involved exposing a series of alumina-inwater suspensions to the ultrasonics for selected periods. After settling 24 hours, the alumina concentration, determined 1 inch below the suspension surface for each ultrasonic exposure period, provided a measure of the relative deagglomeration. The 1-inch level was selected to provide a convenient sampling point with good sensitivity. As shown in Figure 1, the results indicate a rapid rate of dispersion during the initial part of the ultrasonic exposure, followed by relatively little change after 16 hours of exposure. This schedule conveniently permits overnight exposures. The suspension concentration also is important; if it is too high, the powder will settle during the ultrasonic exposure, and the effectiveness of the treatment will be impaired. For Linde B alumina, the sample size was limited to 2 grams in a volume of 2.5 liters. For powders showing less tendency t o settle during the ultrasonic exposure, more concentrated suspensions and smaller volumes can be used. This permits a multiple-sample dispersion technique with which several powder samples can be treated simultaneously in stainless steel beakers placed in the ultrasonic tank. Constant liquid depths of 1.5 inches would be retained for the suspension inside the beakers and the water bath surrounding them. The ultrasonic dispersion action is assumed to be deagglomeration. It is, accordingly, assumed that fracturing to the unit crystal is not occurring, but that the ultrasonic cavitation forces permit breakdown only to the crystalline aggregates. This assumption was confirmed by nitrogen surface area measurements and visual examination of electron micrographs of samples with and without ultrasonics treatment. No difference was obtained in surface area, indicating only deagglomeration by the ultrasonic treatment. Both treated and untreated samples were dried and prepared by spatula dispersion for electron microscopy; the particle size range observed was the same for both. CENTRIFUGATION
Equipment. A Sharples laboratory type Super-centrifuge (3) is used to divide the sample slurry into fractions according to particle size. It is driven with a turbine motor using compressed air. The centrifuge develops centrifugal fields up to h0,OOO X G, and permits continuous feed of the slurry sample and collection of effluent samples while the machine is operated at selected discrete speeds. The system, including slurry flow control, is shown in Figure 2. The centrifuge speed is monitored with an electronic tachometer, and controlled with a pressure regulator in the air line to the turbine. The sample slurry, under pressure, is fed to the centrifuge feed nozzle through a needle valve and a two-float rotameter. The pressure regulator for the air above the slurry supply, and the needle valve in the feed line, provide fine and coarse flow adjustments. Slurry Fractionation. The ultrasonically deagglomerated and dispersed slurry sample is diluted to approximately 5 liters (0.4 mg/ml), and passed through the centrifuge to obtain a series of fractions according t o particle size. Each fraction, approximately 60 ml of effluent, is collected at a discrete flow rate and centrifuge speed, as shown in Table I. The fractions are collected in the order shown, starting with the largest diameter listed. (The limiting diameter represents the smallest size that completely settles in the centrifuge; it is also the largest size which could partially pass through in a fraction.) The speeds are increased and the slurry flows are decreased, as required, without interrupting the continuous operation. Prior to collecting each centrifuge fraction, approximately 200 ml (rotor hold-up volume is 170 ml) is discarded; this represents material exposed to speeds or VOL 39, NO. 6, MAY 1967
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COMPRESSED F I N E FLOW CONTROL SPEED CONTROL
4 Figure 2. Centrifuge system CENTRIFUGE
EED N O Z Z L E S L U R R Y SAMPLE
CONTROL
flows other than those specific for the limiting diameter. In addition to the seven fractions, samples of the original feed slurry are also taken. Centrifuge Parameters and Limiting Diameters. The limiting diameters of successive fractions (see Table I) are in the ratio of 42,required for the Stairmand corrections, t o be discussed later. Combinations of liquid flows and centrifuge speeds were calculated, for the fractionation of alumina, using the appropriate Svedberg-Nichols equation (11):
Table I. Centrifuge Parameters Vis-
cosity, Fraction Temp., No. 1 2 3
poise 9.273 9.273 9.273 9.2;: 8.876 8.154 7.553
23.5 23.5 23.5 23.8 25.4 29.0 32.8
4 5
6 7
Flow,
rnilli-
C
r.p.m. 11.89 X lo3 16.81 >: 103 23.77 x 103 33.51 X lo3 46.51 x 1 0 3 50.00
x
m.oo x
rnl/min
105 100
Limitigg dia., A 1193
loo 100 100 62.7 33.9
IO? 1c3
Table 11. Stairmand Correction for Pines Correcten Fractiori cum. wt. 7 No.
