1168
ANALYTICAL CHEMISTRY
60% Isopropyl Alcohol Solution. Dilute 60 ml. of reagent grade isopropyl alcohol to 100 ml. with distilled water. PROCEDURE
Pipet a 10-ml. sample of colorless anesthetic solution, which should contain about 20 mg. of sodium bisulfite and not more than 0.5 mg. of epinephrine, into a comparison tube, and add 0.1 ml. of the ferrous sulfate-citrate reagent, followed by 1.0 ml. of the buffer reagent. hlix the solution, allow it to stand 10 minutes, and examine it in the spectrophotometer a t a wave length of 530 millimicrons. The color quickly reaches its maximum intensity and remains essentially constant for some hours. The concentration of epinephrine is read directly from a calibration curve. The calibration curve is prepared in the usual fashion by plotting optical density against epinephrine. The density readings are obtained after the instrument has been set to read 0.0 when the comparison tube contains distilled water. Boric acid, which is sometimes present in tablet preparations, will interfere with the determination of epinephrine by the regular procedure. A modified procedure has been found suitable for such products. Dissolve a number of tablets in a sufficient volume of 0.2% sodium bisulfite solution or distilled water to provide a suitable concentration of epinephrine and bisulfite. To 5 ml. of this epinephrine solution add 4 ml. of the 15% mannitol solution, followed by 0.1 ml. of the ferrous sulfate-citrate reagent and 2 ml. of the b d e r reagent. The calibration curve for the regular procedure and for this modified procedure is identical if the 5 ml. of solution employed for the analysis contain not more than 60 mg. of boric acid. A straight line is obtained n-hen optical density is plotted against concentration of epinephrine,
These methods may be used on many local anesthetic products without performing any preliminary separations. I n the case of the usual procaine hydrochloride solution, no turbidity results from the addition of the buffer. Solutions of tetracaine hydrochloride, metycaine hydrochloride, and some other products become cloudy or milky \Then the buffer reagent is added. I n an instance of this nature, a 5-ml. sample of the anesthetic solution is added to 5 ml. of 60% isopropyl alcohol and the color is then developed 11-ith the usual reagents. ACKNOWLEDGMENT
The author wishes to acknowledge the technical aid of Genevieve Stein, Veronica Flood, and Janet Edwards who assisted with much of the experimental work in this study. LITERATURE CITED
(1) Barker, J. H., Eastland, C. J., and Evers, N., Biochem. J . , 26,
2129-43 (1932). (2) Glasstone, S.,Analyst, 50,49-53(1925). (3) Mitchell, C.A,, Ibid., 48,2-15 (1923). Ibid., 49,361-6(1924). (4) Price, P.H., (5) Vogeler, G., Arch. ezptl. Path. Pharmakol., 194,281-3 (1940). (6) Yoe, J. H., and Jones, A. L., IND.ENG.CHEM.,ANAL. ED., 16, 111-15 (1944). RECEIVED May 13, 1948. Presented before the Division of Analytical and SOCIETY, Micro Chemistry a t the 113th Meeting of the .-1MERIcAx CHEMICAL Chicago, Ill.
AGRICULTURAL DUSTS Preparation of Dusts of Uniform Particle Size by Fractional Sedimentation H. P. BURCHFIELD, DELORA K. GULLSTROM, AND G. L. MCNEW' Naugatuck Chemical Dicision, United States Rubber Company, Naugatuck, Conn. A method based on fractional sedimentation is described for the isolation of particle size fractions from agricultural dusts. Mathematical procedures are developed by which it is possible to estimate the type and number of sedimentations required, as well as the mean radius, particle size distribution, and amount of each fraction that will be obtained. The isolation of fractions of definitely known distribution aids in the evaluation of those biological and physicochemical properties which are modified by changes in particle size.
T
HE protective value of a fungicidal dust depends on particle
size as d l as innate toxicity of the chemical to the organism. This Tyas clearly demonstrated by the J-vorlr of Kilcoxon and McCallan on sulfur (10) and Heuberger and Rorsfall on cuprous oxide ( 5 ) . In glass slide tests against Xacrosporzum sarcinaejorine Cae ., the latter authors showed that the percentage of spores not germinated increased from 53.0 to 98.3% when the mean particle size of the cuprous oxide was reduced from 2.57to 1.65-micron diameter at a constant deposition of 100 X 10-4 mg. of copper per square centimeter. I n addition to its effect on fungi toxicity, particle size may also be a factor in the stability of spray suspensions, the flowability and rate of settling of dusts, and the tenacity and chemical stability of spray or dust deposits on weathering. In the evaluation of new protectants it is frequently desirable to study these effects on a laboratory scale, using samples with narrow and clearly defined particle size ranges, in order to determine the optimum state of subdivision for the material. Samples ground in a laboratory hammer mill usually have a wide range o f 1
Present address, Department of Botany, Iowa State College, .4mes, Iowa.
particle size distribution; hence biological and physical tests carried out on them, reflect only the average properties of the materials without focusing attention on the size class that possesses the most desirable characteristics. Methods have been described for fractionating dusts by elutriation by water ( 1 ) and air ( 6 ) , but the apparatus is complicated and not readily available. The need for a rapid simple method for separating size fractions for biological assay led to the development of the sedimentation procedure described in this paper. EXPERI AI ENTA L
Separations were carried out on the organic fungicides Phygon (2,3-dichloro-l,4-naphthoquinone, 9) and Spergon (tetrachloro-pbenzoquinone, 8). Technical grade Phygon was purified by sublimation followed by recrystallization from benzene. The melting point was 190" C. and the specific gravity 1.645 a t 25'/ 25' C. The sample of Spergon was obtained by recrystallization of the crude product from acetic acid. I t had a melting point of 290 O C. and a specific gravity of 1.948 a t 25 O /25' C. The crystalline compounds were ground by two passes through a laboratory model Raymond pulverizer equipped with a 0.25mm. (0.01-inch) herringbone screen, The particle size distribu-
V O L U M E 2 0 , NO. 1 2 , D E C E M B E R 1 9 4 8
,
1169 I
0.09-
Table I. Schedule for Purification of 2,3-Dichloro-1,4naphthoquinone Size Fractions by Resedimentation
0.08-
Total s o . of
0.07-
Range. llicrons
He-edinieiitations
0.06-
0.5- 1.0 1.0- 3 . 0 3.0- 5 . 0
3 2
'1'1% ke-Off Poi r i t b " , Microns
Yc within Range (Theory)
0 . 8 (3) 2 ( I ) , 3 (1) 4 ( 2 ) , 5 (2) 5,0-10,0 7 (2). 8 (11, 9 (2) 10.0-20.0 4 15 (21, 18 (2) G 35 ( 6 ) 20.0-35.0 Surnbers in parentheses indicate number of resedimentation level
0.05dr
.?
95.0 97.9 94.3 97.5 93.9 93.1 a t each size
0.04003-
0.02
-
0.01
'0
4
0
I2
I6
20
24
2
The upper fraction \vas then tranzferred to a 2000-nd. cylinder and the sediment resuspended by stirring. After a sufficient length of time had elapsed for all particles of radius greater than 3 microns to pass the halfway point, the upper portion of the suspension was withdrawn as described above. These operations resulted in the separation of the original suspension into fractions containing particles in the 0- to 3-, 0- to 5-, arid 0- to m-mlcron ranges. (The symbols 0 and m ai'e u 4 t u describe the practical loner and upper limits of the distribution 1,arher than in their usual sense.)
Additional separations carried out in an aiinlogoue manner, but tvith varying heights and times of sedinicntation ultimately rwultrd in the isolation of fractions containing 0- to 1-, 0- to 3-, 0- to 5,0- to lo-, 0- to 20-, and 0- to 35-micron particle. rll % ( r ) is negative and the expression has no physical meaning. By analogous reasoning, the bottom section of the column initially contains material with a partial frequency distribution equal to j(r)s:so, and during sedimentation more material is added with a distribution equivalent to Equation 10. The @ function for the material in the bottom of the column at the end of the qrdimentation period is therefore (12) for r 5 T I . As the length of the column is finite, the quotient r z / r ? must be set equal to unity for values of r > rl. Subsequent operations are conducted in a similar manner. Thus if the original top fraction is resedimented and cut a t an equivalent radius of rl microns a t a point s1 cm. from the bottom of the new column, the lower fraction that is obtained will have a 9 function equal to
and on substituting the value for % ( r ) from Equation 11 in Equation 13, the partial distribution function for the new sample 1s
For the general case it is easily demonstrated that the @ function for any final fraction is equal to the product of the initial distribution function, and a series of terms describing the separation and purification operations, or @(r)
=
f ( r ) [ A l ] [ i l ? l . . . .[AnI[&IIB~l. . . .[Bkl
(15)
where
and
On substituting numerical values for r , and plotting @ ( r ) against r, a curve describing the particle size distribution within the range is obtained. The area under the curve is proportional to the total volume of material in the fraction, or
where W is the weight of the initial sample, d is the density of the material, and ro is the upper limit of the size fraction. On dividing @ ( r ) d rby the volume of a single particle, a number distribution curve is obtained, which upon integration yields an expression for the number of particles in the fraction. (17) The mean particle radius is defined as r =
[4s]”3
Therefore, on substitution of Equations 16 and 17 in Equation 18 an expression for the theoretical mean radius is obtained in terms of the initial particle size distribution curve, and the
r=
(19)
The integrals in Equaiioil 19 call be readily evaluated by plotting the weight and number distribution curves and determining the areas under them by graphical or mechanical integration. 9 s an example of these calculations, the derivation of the distribution curves and the calculation of the mean radius for a 3- to 5-micron fraction will be briefly considered. Several of the steps included in the experimental procedure are eliminated to shorten the treatment, but the calculations are entirely analogous to those actually used.
T a b l e 111. Calculation of D i s t r i b u t i o n Curves for Typical 3- to 5-hficron F r a c t i o n Radius, Microns
-j(r)
‘4
B
2.0 2.5 3.0 3.5 4.0 4.3 4.5 4.7 4.9 5.0
0.084 0.084 0.083 0,080 0.077 0.074 0.072 0.071 0.069 0.068
0 84 0.75 0.64 0.51 0.36 0.26 0.19 0.12 0.04 0
0.33 0.45 0.61 0.79 1 1
Rd 0.011 0.042 0.135 0.388
1
-Q(r! x 10 0.39 1.32 3.57 7.91 13.77 9.62 6.87 4.09 1.38 0
-S(r)
x
108
11.7 20. I 31.6
40.6
01.4 28.9 18.03 9.4 2 8 0
The hypothetical experimental condition> arc defiued as folloTvs :
h sample of ground Phyyon i i suspended in a wetting agent solution in a 50-em. cylinder and cut a t a point 25 cm. from the bottom, a t the 5-micron level. The upper fraction] containingoto 5-micron material, is resedimented in a 50-cm. cylinder and cut 5 cm. from the bottom of the column a t the 4-micron level. This operation is repeated four times in order to separate out material in the 0- to 3-micron range. After values for s and SO are substituted] the expected m i g h t distribution curve for the sample assumes the form
and the number distribution curve the form
Values forf(r) (Table 111)are calculated by substituting values for i-, taken a t suitable intervals in the range from 2 to 5 microns, in Equation 7. For the material used in these experiments m = 1.47,and c = 2.91. Values for
and
B =
[0.1 + 0.9 161
are calculated for the values of T used in the calculation of f(r). For values of r > 4, B is set equal to unity. Values for the product + ( T ) are computed (Table 111) and plotted against r on suitable coordinates. This is the weight distribution curve (Figure 3). @ ( r ) is then multiplied by 3 / 4 m 8 to obtain N ( r ) , which when
ANALYTICAL CHEMISTRY
1172 plotted against 7 gives the number distribution curve (Figure 4). T h e greas under the curves from 7' = TO to 7 = 5 are measured graphically and substituted in Equation 19. The mean radius calculated in this manner is 3.57 microns. The purity of the sample (percentage of material expected within the 3- to 5-micron range) is given by
0
2
.
4
RADIUS- MIICRONS
F i g u r e 4. Numben Distribution Curve of Typical 3- to 5-MiororL Fraotion and the total weight of the sample expected from 200 grams of the ground dust is 200 J6a(r)dr
RADIUS
=
3.5 grams
Expressions for the number of particles per gram and the specific surface of the size fractions can he derived as follows.
- MICRONS
Figure 3. Weight Distribution Curve of Typical 3- to S-Micron Fraction
4
LLFigure 5.
(23)
2
3
5
6
Photomierngraphs of 2,3-Diehloro-1,4-naphtho~uinoneSize Fractions (125 X) 4. %Ion 1. 0.5-l.Op 1-3r 3. 3-5" 2.
5.
10-20p
6. 20-3511
V O L U M E 20, NO. 1 2 , D E C E M B E R 1 9 4 8
The number of particles, d S , in an infinitesimal segment of the distribution is given by the differential form of Equation 17 On multiplication by 47ri.2 and integration, a n expression for the total surface is obtained. Division by Equation 2 3 gives the specific surface.
Analytic solutions for the integrals described in this section would be very complex and not worth while considering the transitory use to which they would be put. The graphical integrations are relatively simple, and the results accurate to within the limits of error of the experimental data. DISCUSSION
Experimental and theoretical values for the mean radii of dichloronaphthoquinone and tetrachlorobenzoquinone size fractions prepared by fractional sedimentation are shoTn in Table IV. The correlation b e t w e n observed and calculated values is unexpectedly good. Stokes’ law in its usual form is based on the assumption of spherical particles. The data presented indicate that deviations from the lan-, caused by irregularly shaped particles, muyt be relatively unimportant in the case of ground powders. These experiments ~vercdesigned primarily to obtain samples for biological assay, rather than a5 a measure of adherence to the sedimentation law; hence it is probablc that a more refined technique would yield an even closer correlation. Experiments with irregularly shaped crystalline materials might provide information on the magnitude of the deviations, and serve as a direct experimental check on the modified equations which have been developed describing their Sedimentation rates ( 3 ) .
Table IV.
Range, Microns 0.5-1.0 1.0-3.0 3.0-5.0 5.0-10.0 10.0-20.0 20.0-35.0
1173 1 ielda oi rlic &e fractions are from 1 t o 5 grams on a 200-gram -ample. Larger quantities can be obtained by carrying out wxessive sedimentations on the same fraction and combining rhe upper portions of the columns. The distribution curves within the intervals are changed by this procedure and the calculations must be revised. The sedimentation procedures described here are illustrative only, and can be varied to meet individual requirements by changing the positions and breadths of the intervals or the order in rvhich the separations are made. The schedule described in Figure 2 was arrived at chiefly from a consideration of time requirements. By separating the 0- to 5-micron fraction first, the larger fractions can be separated and purified while the slower settling fine materials are undergoing their initial separations. The time required for the preparation of a complete series of samples does not exceed 3 days for a material of density greater than 1.5. The method is generally applicable to insoluble materials with densities sufficiently greater than that of the dispersion medium. When the density differential is small, sedimentation of the finer particles may be too slow to afford a practical separation. The theoretical limiting value is that a t which Brownian movement displacements are of the same order of magnitude as the vertical displacement due to sedimentation. Density differences between unlike materials do not affect the distribution curves of the size fractions if the sedimentation times are adjusted to equivalent radii by use of Stokes’ law. Equation 15 is dependent only on the initial distribution and the radii a t which the separations are made; hence fractions obtained on different materials will be identical except for deviations caused by departures from sphericity. The usefulness of the sedimentation procedure depends largely on the possibility of calculating in advance the conditions for the separations and the properties of the resulting fractions. The upper limit of a fraction is determined by Stokes’ law. By setting up a tentative distribution equation for the interval desired, it is possible to arrive a t conditions a t which the frequency below the interval is negligible in comparison with the frequency near the mid-point. The distribution curves that are obtained completely define the properties of the sample. If the particle size distribution of the initial sample cannot be described by a logistic or Gaussian function, a frequency curve obtained by taking tangents to the cumulative curve can be used. Errors introduced by this procedure will be small, as the final distribution of the sample is determined primarily by the method of separation.
Comparison of Experimental and Theoretical Mean Radii for Particle Size Fractions Theoretical TetrachloroMean Microns benzoStandard Radius, Dichloronaphthoquinone, quinonea, Deviation, Microns Run A Run B Microns Micron 0.62 0.66 0.65 0.65 0.03 1.64 1.48 1.39 1.64 0.04 3.57 3.62 3.55 3.48 0.05 7.47 7.33 7.11 7.73 0.15 13.3 13.8 15.1 14.7 0.23 27.1 28.4 29.9 1.0
ACKNOWLEDGMENT
The authors wish to thank H. S . Campbell, General Laboratories, United States Rubber Company, for the photomicrographs that appear with the text.
...
4
Obtained from initial distribution equivalent to t h a t of dichloronaphthoquinone.
LITERATURE CITED (1) Andreasen, A. H. M., and Lundberg, J. J. V.,KoZEoid Z.,49, 48-51 (1929). ._ ~~.-.,. (2) Berkson, J., J . Am. Statistical Assoc., 39, 357-66 (1944). (3) Boselli, J., Compt. rend., 152, 133-6 (1911). (4) Gullstrom, D. K., and Burchfield, H. P., ANAL.CHEM.,40, 1174 (1948). ( 5 ) Heuberger, J. W., and Horsfall, J. G., Phytopathology, 29, 303-21 (1939). (6) Roller, P. S., ISD. ENG.CHEM., ANAL.ED.,3, 212-16 (1931). (7) Stokes, C. G., P h i l . M a g . , 29, 60-2 (1846). (8) Ter Horst, TT. P., U. S. Patent 2,349,771 (1944). (9) Ibid.. 2.349.772 (1944). (10) Wilcoxon, F., and McCCallm, S. E. A., Contrib. Boyce Thompson Inst., 3, 509-29 (1931). ~
Theoretical calculations indicate that between 93.1 and 97.9% by weight of the size fractions should lie within the desired intervals (Table I). The degree of homogeneity attained is illustrated by the photomicrographs made a t 125 diameters on a series of dichloronaphthoquinone size fractions (Figure 5 ) . I n general, the number of particles which appear t o lie outside the desired size ranges is small. The series of photographs provides a good illustration of the improvement in coverage of foliage surface which would be expected in going from the larger particle size material to the smaller.
RECEIVED May 12. 1948. Presented before the Division of Agricultural and Food Chemistry a t the 113th Meeting of the AMERICAN C m m c A L SOCIETY, Chicago, Ill.
