Determination of Chemical Yield. After the gammaactivity measurements had been completed, the samples were diluted t o 100 ml with water. About 1.2 ml of each solution was sealed in a polyethylene ampoule and irradiated for 3 hours together with aliquots of the carrier solution treated in a similar way. After 2 days’ delay the induced activity of 5 0 in each solution was measured as described above. In the case of Sulfide ore-I, which had the highest 5lCr activity, it was necessary to correct for the remaining activity from the first irradiation by gamma-counting 1.00 ml of the diluted sample and subtracting. For the other samples this correction was unnecessary. RESULTS AND DISCUSSION The mean values listed in Table I for the chromium content of the standard rock are for two determinations per sample. As an approximate measure of the precision of the method, the mean relative standard deviation has been calculated to be The present value 114 i 3 ppm for W-1 is in excellent agreement with the previous neutron activation results, 113 ppm by Turekian and Carr (2) and 116.3 ppm by Das and Pendharkar (5). The agreement with the 120-ppm value recommended in the review report by Ahrens and Fleischer (6) is also satisfactory.
*3z.
(5) M. S. Das and M. S. Pendharkar, unpublished work (1964), cited in M. Fleischer, Geochim. Cosrnochim. Acta, 29,1263 (1965). (6) L. H. Ahrens and M. Fleischer, U. S. Geol. Surc. Bull., 1113, 83 (1960).
Most errors of importance in the present method, errors due to neutron flux gradients in the irradiation container and counting errors, are random errors, and will be included in the observed spread of duplicate determinations. Possible systematic errors are most likely to occur from neutron shielding effects or from interfering nuclear reactions. Because a dilute solution was used as standard, and none of the major elements in the standard rocks are strong neutron absorbers, the shielding effects were negligible. The only r , its consignificant interfering reaction is j4Fe (n, ~ r ) ~ l Cbut tribution is only of the order 0.1-0.2z and no correction was therefore deemed necessary. The mean values presented, on the basis of the preceding discussion, are probably accurate to is%. If an additional precipitation step had been added in the chemical procedure, the size of the final sample would have allowed the counting to be performed in the well of the NaI crystal. This would increase the sensitivity of the method by about a factor of 10. Such a step would mean a considerable increase in the amount of work. As the observed precision was satisfactory and the content of chromium in most minerals and rocks is above 1 ppm, no such additional step was introduced. The method in its present form should be satisfactory for the determination of C r in most geochemical samples.
RECEIVED for review October 31, 1966. Accepted February 17, 1967. The work was carried out while A. 0. Brunfelt held a research fellowship granted by the Norwegian Research Council for Science and Humanities.
Specific Surface Area by Low-Pressure Permeametry Clyde Orr, Jr. Georgia Institute of Technology, Atlanta, Go.
PERMEAMETRY IS A WELL KNOWN TECHNIQUE (1-3) for evaluating the relative size parameters of powders. A gas, usually air, is made to flow laminarly through a chamber containing the granular material a t essentially atmospheric pressure, while the flow rate and accompanying pressure drop across the chamber are measured. The results agree approximately with microscopic or screening analyses when the particles are relatively coarse and spherical; they may be misleading when the particles are irregular and fine. That this should be so is apparent from an examination of the flow pattern. A gas near atmospheric pressure under a low driving force moves in viscous flow through a channel when the diameter of the space is much greater than the mean free path of the gas molecules. The velocity is actually zero at the boundary. most of the flow occurring along the center of the open spaces among the particles. Roughness on a microscopic scale thus has little effect on the resistance to flow. Knudsen flow prevails when the mean free path of the gas molecules is approximately 10 times the diameter of the passageway (4). In this case the flow is governed not by the (1) P. C . Carrnan, J . SOC.Chem. Ind. (London). 57, 825-34 (1938). (2) li. D. Cadle, “Particle Size.“ Reinhold, New k’orb, 196-,
gas viscosity but by collisions of the gas molecules with the confining surfaces. The present work describes a flow apparatus and a technique of operation a t progressively lower pressures; the technique achieves specific surface area results that are in remarkably close agreement with low temperature gas adsorption (BET) values for the same material. The analysis ( 5 ) is based on the equation
derived ( 6 ) in part by applying a statistical treatment to describe the motion of a free molecule passing through a random pore space. Nomenclature is defined at the end of the article. EXPERIMENTAL A schematic diagram of the apparatus is given in Figure 1. It consists of a sample holder, a 0- to 20-mm Hg differential pressure gauge, a micrometer flow-regulating valve, a pressureindicating manometer, a flow-rate indicator, a mechanical
pp. 132-4.
C. Orr, Jr., and J. M DallaValie, “Fine Particle ‘Measuremen’ ” Macrnillan, New York, 1Y59, pp. 134-63. (4, G. N. Patterson, “Molecular Flow of CJases.” Wiie;,. New
(31
Yorh, 1956, pp. 1.59-6:.
( 5 ) B. V. Deryagin, N. N. Zakhavaeva, M. V. Talaev, B. N. Parfanovich. and E. V. Makarova, “Research in Surface Forces,” Conlultants Bureau, New York, 1964, pp. 155-60. (6) H. V . Deryagin, Akad. Nuuh SSSR,53, 623-6 (1946).
Ftow-Rate
Pressure Regulator
I
Helium Cylinder
20 m n'i
E
0
r
a
y
'
0.8
TO Vacuum
-
Pump
%
Figure 1. Diagram of apparatus
8
pressure regulator, a v;icuum pump, and a cylinder of helium. The powder bed is fo-med within a metal cylinder having a porous bottom, the bottom first being covered with a filter paper. The powder is added incrementally and pressed by means of a loose-fitting plunger after each addition in order to secure as much uniformity as possible. The flow-rate indicator, made of glass, contains a light liquid. When its stopcock is open, gas flows directly through with the liquid remaining a t equal levels in each leg. The level in the right leg begins to fall as soon as the stopcock is closed and gas in the system is expelled, The flow rate is established from the volume rate of liquid displacement. T o prepare for a test, the powder was first dried. Then the powder bed was 8-stablished and its length and weight were recorded. If thi: density of the powder was known, the bed porosity was immediately calculated; if not, the powder density was carefully determined and then the porosity was calculated. The ked was next fitted into the permeameter system and the entire apparatus was flushed thoroughly with helium The micrometer valve was then closed and the portion of the a p p a r a x s downstream, including the sample, was evacuated. From time t o time the valve was opened to allow helium to flow i.hrough the bed in order to carry out desorbed atmospheric vapors and gases. Finally, the valve was closed and the bed was evacuated until the differential pressure gauge indicated no degassing. This required from a few minutes to seven1 hours depending upon the nature of the powder. A test was made b,y opening the micrometer valve until approximately the desired pressure difference was indicated by the differential gauge. Initially, this was most often 10 to 15 m m Hg. After allowing a few minutes for the system to come to equilibrium, the stopcock of the flow indicator was closed and the timi: for a given volume of gas t o pass was recorded. The stopcc'ck was then opened. Also recorded a t this time were the pressure drop across the powder bed, the pressure upstream 3f the valve, and the ambient temperature. The downstrearn pressure was essentially zero, a s the vacuum pump was always allowed t o operate. The resistances of the filter paper and the porous holder bottom were small compared t o the resistance of the powder; their combined resistance as established previously was subtracted, nevertheless, in order to arrive at the true powder resistance. The micrometer needle valve was next partially closed, and, after equilibrium was again established, the procedure was repeated. This was continued until several sets of data were collected a t progressively lower differential pressures. Table I presents the data from a typical test. RESULTS
Equation 1 , rearranged in terms of directly measurable quantities with provision included for variations in ambient temperature and upstream pressure, becomes
c,
z
0 1481
At -- -
Dqt'~(273
I. 0
E 0.9
lnclicotor
-
+
. ~ ~ r r : 6 0( 2 7 3 r9-i -- x 173 i) t P -
i
2)
0.7
0.6
0.5
[
0,
Tungsten
0.4
0.3
0
Cell Area = 1.290 crn' 9 0.635 cm'
Cell Area
a2
? Ressure Drop, mm Hg
Figure 2. Representative experimental results
Table I. Experimental Data for Tungsten Powdera Time for 1 cc of heliumb to pass through bed, seconds Pressure drop, mrn Hg 18.45 91.9 18.23 103.6 13.12 162.4 10.18 218.2 9.43 231.4 8.62 263.1 4.83 539 Density = 19.3 gram/cc; bed length = 0.56 cm; bed diameter = 0.635 crn; sample weight = 1.267 grams. At a temperature of 25.0" C and an absolute pressure of 782 mrn Hg. f1
Table 11. Comparison cif Results Specific surface area, ________ ___meter-*/gram Material Gas adsorption Knudsen flow 0.49 0.47, 0.48 Tungsten 0 91 0.85 Tungsten carbide 6.1 6.3 Zinc oxide Cupric oxide 3.4 3.1 Carborundum grit 0.098 0.076 1.10 1.08 Salt 2.07 2.10 Cement Zinc 1.59 1.55 Titanium dioxide 2.16 1.92 ~~
As the pressure drop across the bed (as well as thr: actual
pressure within the bed) diminishes, the mean free path of the gas molecules becomes greater, and Knudsen flow is established in more and more of the void spaces. The indicated specific surface increases, as shown in Figure 2. Within the accuracy of the data, the relationship between the pressure ioss and the .specific: surfrice i ? wnilogarithmic. The results extrapoiated io L e x ) :>ressai.e . ~ w Q . where Knudsen flow can occur throughout the ired. shouid hr \he true specific surface area of he powder. 01. :9
YO
7,
brvE 1967
Y
835
This behavior is borne out by the comparison of data presented in Table 11. Tests with powders having extensive internal pores resulted in specific surface values lower than indicated by gas adsorption. NOMENCLATURE
A
=
L M
= = =
P Q q
= =
Cross-sectional area of bed, cmz Length of bed, cm Molecular weight of gas, gram/mole G a s pressure upstream of valve, mm Hg Gas flow rate, mole/cm2 second G a s flow rate, cm3/second
R = Gas constant, 8.31 X IO7 dyne cm/mole OK S, = Specific surface area of powder, m*/gram
se = Specific surface area of powder, cm2/gram T = Absolute temperature, OK t = Temperature, "C AP = Pressure loss across powder bed, dyne/cm2 Ap = Pressure loss across powder bed, mm Hg E = Bed porosity [ = (apparent volumeabsolute volume)/apparent volume] = Absolute powder density, gram/cm3 p RECEIVED for review November 7, 1966. Accepted March 14, 1967.
Polarographic Determination of Aminocaproic Acid in Nylon Polymer Thomas A. Robinson' Fibers Division, Allied Chemical' Corp., Petersburg, Va.
DURING THE POLMERIZATION Of E-CaprOlaCtam to nylon-6, c-aminocaproic acid is formed by the hydrolysis of the amide group of the monomer and remains in the final polymerization product in low concentrations. In a study of the kinetics of the polymerization of caprolactam by Hermans, Heikens, and Van Velden, the concentration of aminocaproic acid in equilibrium polymer ranged from 0.0008 to 0.005 millimole per gram of polymer (1). This low concentration presents a problem in the quantitative determination of aminocaproic acid in nylon. In their study, Hermans and coworkers used paper chromatography to analyze for the aminocaproic acid. The experimental polymers were extracted with methyl alcohol t o remove the amino acid, along with caprolactam and oligomeric material. The extract solutions were concentrated and spotted on paper. .By use of the proper eluant, the aminocaproic acid was separated from the other components. After using ninhydrin to develop the spots, these were visually evaluated by several observers against known aminocaproic acid standards (2). I n our evaluation of Hermans' method, it was found that the spot size and color intensity varied too much for it to be useful. Attempts were made t o correlate spot area to concentration, but again reproducibility was lacking. Turian, Tyurin, and Zhantalai have reported a polarographic procedure for the analysis of caprolactam (3). The monomer was first hydrolyzed in 1 N sulfuric acid and converted to aminocaproic acid. After neutralization and the addition of sufficient base to make the solution 0.2N in sodium hydroxide, the aminocaproic acid was reacted with a large 1 Present address, Agricultural Division, Mobil Chemical Co., Richmond, Va.
Hermans, D Heikens, and P. F. Van Velden, J . Polymer Sci., 30, 81-104 (1958). (2) Ibid., 16, 451-7 (1955). (3) Ya. I. Turian, Yu.M. Tyurin, and B. P. Zhantalai, Z / I .Analit. Khim., 16, No. 3, 352-8 (1961).
(1) P. H.
836
e
ANALYTICAL CWEMISTR7
excess o formaldehyde to form quantitatively the Schiff base as shown below: NHz(CH2)COOCHzO + CH,N(CHz),COOH,O (Schiff base) Although it is possible to carry out the polarographic reduction of the Schiff base in a n alkaline medium, the authors reported that the limiting current is increased 5-8 times when the solution is buffered to a pH of 6-8 or the solution is acidic, pH 1-2. It was also recommended that the formaldehyde concentration not exceed 4-5 % in the final solution, as contaminants might interfere. Turian and coworkers indicated that the aminocaproic acid could be determined in the range of 0.038-35.0 millimoles per liter. Therefore, this procedure had very good possibilities for the analysis of aminocaproic acid in nylon polymer.
+
+
EXPERIMENTAL
Apparatus. I n this study, a k e d & Northrup ElectroChemograph was used. The electrode system was a dropping mercury electrode us. a saturated calomel electrode (Sargent No. S-29405). The instrumental settings and variables were: current span, 1-2 Fa; damping, 3 (maximum); DME drop time, 4-5 seconds; voltage span, -0.70 to -1.40 volts; nitrogen purge, 20 minutes before each sample and 30-45 seconds between each scan; and number of scans, 3-4 per sample. Reagents. Reagent grade chemicals were used whenever possible. The aminocaproic acid was recrystallized twice from water. The caprolactam was commercial grade. Sample Preparation. Twenty grams of nylon polymer were ground t o 20 mesh and water was extracted by boiling reflux for 12 hours. The hot solution was filtered and concentrated by evaporation t o approximately 5 ml. Some oligomeric material precipitated and was removed by filtration. The filtrate was placed in a 50-ml volumetric flask and to it were added 5.0 ml of formaldehyde, 15.0 ml of citric acid-sodium hydrogen phosphate buffer, p H 8.0, and 2.0 ml of 2N potassium chloride. The sample solution was diluted to volume with distilled water. Standard solutions were prepared in a similar manner, using aliquots of a known aminocaproic acid solution.
