Like all other spectrophotometric methods for beryllium, this new procedure is not as sensitive as that based on the fluorescence of the morin complex. The latter has been said to lack precision (9) and to be susceptible to the effects of varying the concentration of indifferent electrolytes (6), but more recent work (6, 7) has apparently eliminated these troubles. The method based on Fast Sulphon Black F is, when used in the presence of EDTA and cyanide ion, more selective than previously described methods (6, 8) based on sulfosalicylic acid (ultraviolet method; Ce, Zr, Cu, Fe, NOS-, PO,-* interfere), quinizarin-2-sulfonic acid (Zn, Ca, Cu, Mn, Al, F-, NOS- interfere) p-nitrophenylazo-orcinol (E = 2000, Mg, Zn, Cu interfere), quinalizarin (Fe, Ti, Zr, Co, Ni, etc., interfere), and 8hydroxyquinaldine (most heavy metals interfere). It compares most closely perhaps with the acetylacetone method, which is dependent, however, on an extraction and ultraviolet measurement. Although the molar absorptivity for this last method (E = 31,600) (3) is twice that of the Fast Sulphon Black F method, citrate, acetate, ammonia, and moderate amounts of aluminum interfere. The stability of the Fast Sulphon Black F reagent and its beryllium complex is excellent and considerably better than that of some of the above reagents. Many of the lake-formation methods (Aluminon, Eriochrome Cyanin, etc.) require the presence of gelatin for stabilization and are subject to a wide
range of interferences, though many of them could probably be made much more selective in the presence of cyanide or EDTA. CONCLUSIONS
The proposed method for beryllium offers the advantages of high selectivity and good sensitivity without necessitating the use of extraction, ultraviolet equipment, or a fluorometer. The calibration curve is very reproducible and all the solutions are stable. The pH range requires careful control and consequently the ammonia medium used in these experiments may be profitably replaced with a pH 11 to 11.2 buffer to allow more latitude in experimental manipulation. A buffer based on sodium hydroxide and glycine proved to be entirely satisfactory for work in pure beryllium solution and could presumably be used in the presence of a large number of other ions. A piperidinebased buffer similar to that used by Sill and his coworkers (6, ‘7) in their improved morin procedure would probably be yet more satisfactory and the EDTA and KCN could be incorporated in it in a similar manner. Color development with the glycine buffer was slower than in an ammonia medium and slightly lower absorbances were obtained than when NHa was used, but the system was well established within the recommended 3-hour period. Elwell and Scholes (4) have observed that the time of color development may
be greatly reduced by heating the solution after addition of the reagents. ACKNOWLEDGMENT
We are grateful to the Spanish High Council for Scientific Research for the provision of a research grant to one of us (A.M.C.), and to F. Burriel Marti for granting leave of absence from the University of Madrid to allow the scholarship to be taken up. We also acknowledge our debt to R. Belcher for helpful discussions and thank W. T. Elwell and I. R. Scholes of I.C.I. (Metals Division), Ltd., for independently verifying the recommended procedure. LITERATURE CITED
(1) Belcher, R., Cabrers, A. M., W a t , T. S., Anales Real. SOC. Espaii. Pis. y Qubm., in press. (2) Belcher, R.,Close, R. A., West, T. S., Chem. and Ind. (London)1957, 1647.
(3) Charlot, G.,“Dosages ColorimBtriques des Elements Min&aux,” 2nd ed., p. 168, Masson et Cie., Paris, 1961. (4) . . Elwell, W. T., Scholes, I. R., private communication.’ (5) Sandell, E. B.,NColcrimetric Methods for the Determination of Traces of Metals,” pp. 304-24, Interscience, New York, 1959. (6) Sill, C. W., Willis, c. P., ANAL. CHEM.31,598 (1959). (7)Sill, C. W., Willis, C. P., Flygare, J. K., Ibid., 33,1671 (1961). (8) Snell, F. D., Snell, C. T., Snell, C. A., “Colorimetric Methods of Analyais,” Vol. I I A , pp. 188-200, Van Nostrand, New York, 1959. RECEIVED for review September 21, 1962. Accepted December 10,1962.
Characterization of Granular Solids by Quantitative Attrition DAVID E. KRAMM and IRVING C. STONE Washington Research Center, W. R. Grace & Co., Clarksville, Md.
b A new method for the characterization of granular solids has been developed. The method involves quantitative attrition and the usefulness is illustrated by some studies with silicaalumina catalysts.
A
SOLID composed of fine particles bonded together to form a cohesive intact body may be called a granular solid. If such a solid is of uniform composition, possessing uniform strength, then repeated physical impacts will gradually break away surface particles, decreasing the mass of the intact solid. This process, termed attrition, has been studied for granular solids.
Granular solids can be formed from free flowing loose powders by compaction or pelleting. Such diverse materials as a graphite electrde, a cube of sugar, or an aspirin tablet are examples of granular solids. Technologies such as powder metallurgy obviously depend on granular solids. Many workers have studied the physical properties of granular solids. In particular, physical strength has often been important. The methods used to measure physical strength have been largely empirical. For example, Sheinhartz and McCullough (3) determined a friability index by tumbling granular solids and then doing a sieve analysis. Other empirical methods fre-
quently employed have measured crushing strength (2) or resistance to highvelocity air jets (1). In our work with silica-alumina catalysts we have developed a fundamental method for studying granular solids. Specifically, a quantitative attrition method for characterizing granular solids has been developed. EXPERIMENTAL
Equipment. A Model 3A Wig-L Bug, manufactured by the Crescent Dental Co., was used in this work. The Wig-L-Bug was equipped with a small metal sample chamber 1 inch long and 0.5 inch in diameter. A Veeder-Root clutch speed counter, VOL. 35, NO. 3, MARCH 1963
313
weighed, and the attrited fines are discarded. The intact core weight is calculated as a percentage of the initial weight, TY, to obtain the per cent intact. This process is repeated until the intact core is reduced t o 20 or 30% of the initial weight, W. The data generated, a series of times and weights, characterize the granular solid.
70 Graphite
50
0.
00
'E f ._
0'0
50
L
8 An
After heating 7'0 K = 2.24 x 10-3
THEORY
) Amorphous Carbon
8 20
10
200
100 ATTRITION TIME
Figure 1. Attrition curves for ideal granular solids
manufactured bv Veeder-Root Inc., Hartford, Conn., mas used. This device counts shaft revolutions. Procedure. The Wig-L-Bug imparts a rapid reciprocating motion to the small metal chamber. One revolution oi the Wig-L-Bug motor shaft gives rise to one complete back and forth motion of the reciprocating chamber. The motor operates at 3200 to 3300 r.p.m. A small piece, 0.1 to 0.2 gram, of the granular solid is placed in the metal chamber and briefly shaken. If the initial shape is not spherical, it rapidly becomes so. When the sample becomes approximately spherical, it is removed and accurately weighed to the nearest tenth of a milligram. This is the initial weight, TV. The weighed sample is again placed in the chamber and shaken for an accurately timed interval such as 15 seconds. The sample is removed, the intact core is accurately
dw -
dt a w
Letting K equal the constant of proportionality and assigning it a negative sign, since w decreases as t increaseq, gives :
dw
Separating the variables and integrating
lnw = - K t + C 1 (4) where C1 is the constant of integration. Since w = TV at time t = 0: In E' = C1 (5) Substituting C,into (4) and rearranging gives :
(G)
= -
~
t
Accordingly, if the logarithm of the quantity (lOOw/W) is plotted against the attrition time, a straight line should result. The constant K , representing the slope of this line, will be called the attrition constant. RESULTS
002
006
ATTRITION TIME
010
(Seconds)
Figure 2. Attrition of Domino cane sugar, an ideal granular solid
314
Figures 1 and 2 show attrition curves for three granular solids: graphite, amorphous carbon, and a cube of sugar. As expected, straight lines were obtained when log (lOOw/W) was plotted against the attrition time. This experimentally confirms the attrition law dwldt = -Kw. The slopes of the attrition curves, represented by K in Equation 2, may be used to characterize the granular solid. As K increases, a granular solid becomes more friable; as K decreases, the solid becomes harder and more attrition-resistant. I n the case of the sugar cube, an attrition constant of 4950 X was obtained. This represents a solid over 1000 times less attrition-resistant than graphite, which has an attrition constant of 4.35 X 10-3. The time
IANALYTICAL CHEMISTRY
(Seconds)
-k'w
dt
In
ATTRITION TIME
Figure 3. Attrition of silica-alumina catalyst; strengthened interparticle bonds
intervals required for the sugar measurement mere too short to obtain with a stopwatch. Instead, motor shaft revolutions were counted with the VeederRoot clutch speed counter. Revolutions are readily calculated as time since the speed of the Rig-L-Bug motor (r.p.m.) is known. Having established the validity of the method, it was nest applied t o problems involving silica-alumina catalysts. Some of these will be illustrated briefly. A single pellet from a batch of pelletized silica-alumina catalyst was subjected t o attrition until the weight loss reached 30%. The pellet n-as then removed from the Wig-L-Bug and heattreated 1.5 hours at 740" C. After weighing, attrition \%-as continued.
100i;\Before 90
80
8 20
\
Let W equal the weight of the intact granular solid after any attrition time, t. The attrition rate is then given by dwjdt. For spherical solids of uniform strength, the attrition rate should be proportional t o the weight of the body1.e. :
300
(Seconds)
loss on heating
?-Weight
lo>
