I N D U S T R I A L A N D ENGINEERING CHEMIXTRY
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Vol. 16. No. 9
Determination of Distribution of Particle Size’ By W. J. Kelly THEGOODYEAR TIRE& RUBBERCo., AKRON,OHIO
I
N STUDYING the
the material settling Past A method is described by which the size of the particles of a suspenProperties of Pigments sion can be easily and accurately determined. The distribution of the entrance of the side and fine Powders it is tube can be calculated. the particle size can also be obtained. The method presupposes the often necessary to know, I n a tube of the type validity of Stokes’ law for the rate of settling. - _ shown in Fig. 2 the differnot only the average size of the individual particles, but ence in level, a, in the two also the percentage of particles of various sizes present in the arms is given by the equation n powder. Several microscopic methods, such as the count a = - h - h (1) d method, have been devised, but these give only the average size and do not permit the determination of the distribution of where his the height of the suspension, D its density, and d the sizes. It is usually more convenient to study the pigments density of the medium or the liquid in the side tube. I n case and powders in liquid suspensions, and hence the most natural of short tubes and dilute suspensions a is very small. If the way of determining the size of particle would be to measure side tube is bent over, the apparent value of a can be inthe rate of”sett1ingin a liquid and by the use of Stokes’ law, creased considerably and measured in terms of the length of so far as it is applicable, calculate the diameter. the liquid column in the horizontal part of the side tube. If this length is I , then PREVIOUS METHODS a = 1 sin b (2) Oden’ has worked out a very ingenious method for weighing where b is the angle which the side tube makes with the the sediment forming a t the bottom of a tube, and from the rate horizontal. at which it formed he was able to calculate the diameter and also I n order to calculate the weight of material which settles the distribution of the Darticles of different diameters. Sved- past the side tube, the density of the suspension, D, has to be berg and Rinde3 improved this method to the extent of adding an automatic weight recorder known in terms of the medium and the specific gravity of the which drew a practically continuous curve. suspended material. Thus
4
’ir
F r o . ~-SEDIY B M A T I O N TUBE (VON HAAN)
Figures are given by Svedberg and Rinde showing the distribution of particle size for gold and mercury hydrosols. The great advantage of this method is t h a t very small amounts of material can be used, However, if large amounts of material are available it is usually more convenient to operate with slightly more concentrated suspensions provided they are still dilute enough so that no flocculation takesplace. A rough method was devised by Wo. Ostwald and von Hahn4for determining the rate of settling, b u t in this method the use of veryconcentrated suspensions, as high as 20 per cent solids, is necessary. The method depends on the fact that a suspension is specifically heavier than the medium, and hence, if the suspension is placed in one arm of a U tube and the suspending medium in the other, the latter will stand a t a higher level. As the solid settles out the suspension becomes specifically lighter and the level difference in the two arms of the tube decreases. From the rate a t which the level difference decreases a rough idea of the rate of settling can be obtained. Von Hahn used a tube such as is shown in Fig. 1. The suspension is placed in the left-hand tube and the medium in the right. A scale is mounted a t the back so that the menisci can be read. The side tube is about 130 cm. long and the whole apparatus about 150 to 160 cm. In order t o get a readable level difference very concentrated suspensions were used. I n these suspensions there was considerable flocculation and as a result the method measured more the rate of flocculation plus settling than that of settling alone.
PRESENT METHOD The method described in this paper is a modification of von Hahn’s, which permits the use of 0.5 to 1 per cent suspensions and by which the actual weight of 1 Presented at the Second National Colloid Symposium, Evanston, Ill., June 18 to 21, 1924. 2 Proc. Roy. SOC.Edinburgh, 86, 219 (1916). * J . A m . Chcm. SOL, 45, 943 (1923). 4 Kolloid-Z., 12, 60 (1923).
D = Vd - vd
+w
(3)
V
where V is the volume of suspension in the large tube above the side tube, v the volume of the pigment and hence also that of the medium displaced, and w is the weight of the solid phase. If S is the specific gravity of the pigment, then
S
W
= -ore,
=
W S
(41
Substituting (4)in (3)
Substituting (5) and (2) in (1) 1 sin b =
hSVd-wd+WS
-
vs
d
--h.
which on simplification gives w =
d VSl sin b
h(S-d)
(6)
I n this equation w and E are the only variables for any given experiment, and as soon as the values of the constants have been determined the equation may be written w = K.I
(7)
in which form it is easily used. The total weight of solid phase in the suspension being known, it is a simple matter to calculate the percentage which settles out in a given time. I n using this method the actual length of the side tube is immaterial, provided it is long enough to take care of the recession due to the settling. The zero point is taken a t the u p per end of the tube and the difference between this point and the position of the meniscus a t any given time is taken as. 2. I n this way the effect of capillarity is eliminated.
PRECISION DISCUSSION I n Equation 6 all values with the exception of 1 and sin b can be determined so accurately that no error inwarisesfromthem. For the values of b obtaining in the determination an error of
September, 1924
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
929
in the capillary is a t the lower end of the horizontal portion. The height of the column in the settling tube is then measured from the entrance of the side tube and also the volume. The stopcock a t the upper end of the side tube is closed and the settling tube emptied. The suspension is then poured in up to the same level where the water stood and the tube placed in the thermostat. The tube is held firmly so that the angle of inclination of the side tube is constant. The stopcock is then opened and readings begun. The first reading is taken 1 minute after setting the tube or a t any other convenient interval. After about five readings have been made they are plotted and extrapolated to zero time in order to get the zero reading on the capillary tube. I n the case of suspensions that settle slowly this is not necessary, as the reading at the end of 1 or even 2 minutes can be taken for the zero without introducing any appreciable error. In order to prevent the water from sticking in the capillary tube, it is recommended that a fairly large capillary (2mm.) be used and also that some protective colloid, such as gum arabic, gelatin, saponin, etc., be added to the water in the capillary to reduce its surface tension and thus render it less liable to give false readings due to imperfections or specks of dirt in the capillary. The tube as shown in Fig. 2 is not applicable in that form, because the water evaporates from both the large tube and the capillary, thus causing the recession to be more rapid than that due to the sedimentation alone. For that purpose a new tube (Fig. 4)has been designed (but not yet built). The large tube, which should be about 2 cm. in diameter, has a ground, jointed cap, in the interior of which a small amount of water can be placed. This water is held a t the same temperature as that in the tube proper, and hence by keeping the FIG. 2 pressure of the water vapor constant below the cap any capillary proceeds this error grows less, and a t 2 cm. has been evaporation which takes place would naturally come from the reduced to 1per cent. I n the example given 18 per cent of the water in the cap, as that is nearer the opening of the tube. material has settled out when the recession attains 2 cm., so The small bulb a t the outer end of the capillary serves the that a t this point the weight of material is known within 1 same purpose. per cent. The dimensions that should work best are given in Fig. 4, For the calculation of the size of the particle it is assumed although the settling tube can be made any convenient length. that Stokes’ law is valid, and hence any error in the calcula- Naturally, the longer the side tube the greater will be the tion will be only that inherent in the law itself. initial level difference and hence the greater the accuracy, for a given suspension. OPERATION
1 per cent in measuring the angle which is about 1 degree 30 minutes will introduce an error of approximately the same magnitude in the percentage of material settling out. The position of the meniscus in the capillary can be read to +0.01 cm., so that a t the start a fairly large error can be introduced from this value. However, as the recession in the
U
The tube and capillary are first cleaned with potassium bichromate-sulfuric acid mixture and then rinsed thoroughly with distilled water. The whole tube is then filled with water to the proper level, which is such that the meniscus
PREPARATION OF THE SAMPLE To get reliable results it is necessary that the sample be perfectly dispersed, or, in other words, all agglomerates must be broken up and only primary particles left. This may be
INDUSTRIAL AND ENGINEERING CHEMISTRY
930
done by moistening a weighed amount, for instance, 1 gram, on a glass plate and rubbing it with a spatula. A few cubic centimeters of a protective colloid solution, such as 5 per cent gum arabic, and a small amount of an electrolyte, such as 1 cc. of a 5 per cent barium chloride solution for barium sulfate or zinc chloride or sodium hydroxide for zinc oxide, etc., is
Vol. 16, No. 9
h is measured from the surface of the liquid to the entrance of the side tube. Hence at any given time all particles of radius calculated from Stokes’ law for this time will have reached the entrance of the side tube. By calculating the radii a t successive time intervals the range of particle size settling between these time intervals is obtained. The figures given in Table I for the size range were calculated in this way. This table gives the distribution of the particle size for the particular sample of barium sulfate used.
Analysis of Dehydrothio-ptoluidine Sulfonic Acid’ By H. R. Lee and D. 0. Jones THENEWPORTCo , M I L W A U K EWrs. ~~,
HE titrimetric diazotization of dehydrothio-p-toluidine sulfonic acid according to the usual method has been found difficult owing to the low solubility of both the sulfonic acid and the diazo compound in acid solution. Numerous trial titrations, made by adding varying quantities of nitrite to an alkaline solution of the amine, then acidifying and completing the titration in the usual manner, gave results ranging from 80 to 90 per cent of theory. This led to the attempt to analyze compounds of this type by adding an excess of nitrite to an alkaline solution of the amine, acidifying, and titrating back the excess of nitrite with a standard solution df a primary amine. The first problem in the development of the back titration method was to find an amine, which would be stable in solution and which would diazotize rapidly and quantitatively at 0 C., to be used as a standard solution for the estimation of excess nitrous acid. p-Nitroaniline and nitrocresidine were found to meet these requirements. The former, being a more common laboratory reagent and having greater solubility in acid solution, was considered more su’itable.
T
FIG.4
added as a peptizing agent and the whole mixture rubbed well with the spatula. The mixture is then diluted gradually until it is fairly thin, washed into a graduate and made up to 100 cc., or whatever volume is desired. In this way a very good dispersion can be made. TABLE I-DISTRIBUTION O F
SIZE I N SULFATE
PARTICLE
Time Minutes 10 20 30 40 50
Radius >7.lu 7.1 to 5 . 0 5 . 0 to 4 . 1 4 . 1 to 3 . 5 3 . 5 to 3 . 2 3.2 to 2.9 2.9 to 2.7 2 . 7 to 2 . 0 2 . 0 to 1.7 1 . 7 to 1 . 2
