Table 111. Transition Temperatures and Energies of Some Nonideal Crystals Sample Heptachlor Aldrin Heptachlor epoxide Dieldrin Sample 1 Sample 2 l:lmixofland2
- - - -
sz, sz L, s1 SZ,sz L , Temp. Temp. AH, AH, "C "C cal/mole cal/mole 83 93 5490 450 61 99 3870 330 119 166 5140 720
SI
124 130
175 180
.]:%
175
177
3850 4400 2080/ 2130
550 690 590
s1 + L,
AH,
cal/mole 5940 4200 5860 4400 5090 4800
and holding it a t that temperature. The subsequent run showed peaks a t 114, 123, 170, and 174 "C, with transition energies equivalent to those observed in the initial determination. The two resulting forms were present in approximately equal amounts. Methyl mercuric chloride (compound 60) posed several problems. Its high toxicity and volatility necessitated the use of cysteine solution traps on the exit line. MeHgCl reacts with aluminum, but the rate was unknown, so a n initial analysis was done in a sealed aluminum pan. At 100 "C, a large exotherm occurred, and material escaped from the pan. Subsequent analyses were done in gold pans, which contributed a problem of their own as they d o not seal as well as the aluminum, and a significant amount of material was sometimes lost by sublimation. However, three sets of data were obtained at 2 X 2.5 "C and the means are given in Table I. The formation of a layer of gold amalgam made the heat of fusion values questionable, even through they were selfconsistent. A check determination a t 10 "C/min, however, gave the same value, Either the film was formed after fusion, or it represented such a small part of the sample that the results were not conspicuously affected. Because there was a possibility of bromide and/or iodide contamination, we attempted to determine whether DSC could detect these contaminants, MeHgCl (calculated purity 99.8 %) was mixed
with 2.5 mole MeHgBr and melted. After solidification, the purity of the mixture was calculated as 99.3 mole Z, clearly showing that the bromide does not depress the melting point of the chloride significantly. Capillary melting points of mixtures confirm the lack of depression. A check analysis, usually GLC, is done routinely to verify the purity value obtained. The check analyses for compounds 2, 5, 6, 15,25,29, 34,42,45,46,47, 49, 52,60, and 63 of Table I have not yet been completed. The data for a number of chemicals which carried the notation "decomposes" in the first paper are now included. The samples analyzed earlier a t 0.625 "C/min did decompose, but these chemicals are not inherently thermally unstable ; purification gave samples which did not decompose o n melting, although a few still required analysis a t 2.5 "C/min. With a few exceptions, the values represent the average from three or more replicates.
SUMMARY Some minor improvements in the earlier method of purity determination by DSC have been presented: a n initial determination using a fast heating rate, the employment of a faster heating rate for unstable chemicals, and a correction in AT. The reliability of the method has been computed: the standard deviation is less than 4% in the value of the heat of fusion. This 4% would affect the purity value as 4% of the impurity measured (i.e., 99.5 0.02).
*
ACKNOWLEDGMENT The author thanks Pasquale Lombard0 for the purification and preparation of some of the samples, for consultation concerning this work, and assistance with the preparation of this manuscript. Augustus R. Glasgow, Jr., checked the calculations. The author is also grateful to the listed manufacturers who supplied most of the pure samples and much valuable information about them. RECEIVED for review January 12, 1972. Accepted March 30,1972.
Permeametry in the Knudsen-Flow Regime John F. Brock' and Clyde Orr, Jr. School of Chemical Engineering, Georgia Institute of Technology, AtLanta, Ga. LOW-PRESSURE (Knudsen region) permeametry has been investigated (1-4) on a number of occasions in recent years as a means for determining the specific surface area of fine powders. Satisfactory agreement of results with those of low temperature gas adsorption (BET) is obtained in many instances, but in other cases the permeametry results are low, Present address, Procter and Gamble Co., Cincinnati, Ohio. (1) G. Kraus and J. W. Ross, J. Plzys. Clzern., 57, 334-6 (1953). (2) B. V. Deryagin, N. N. Zakhavalva, M. V. Talaev, B. N. Parfanovich, and E. V. Makareva, "Research in Surface Forces," Consultants Bureau: New York, 1964, pp 155-60. (3) C. Orr, Jr., ANAL.CHEM., 39, 834-6 (1967). (4) N. G. Stanley-Wood, "Surface Area Measurement by a Simple
Diffusion Apparatus," Presented at the Second Particle Size Analysis Conference, Bradford, England, Sept. 1970. 1534
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8,JULY 1972
sometimes very greatly so. Gas adsorption techniques are generally conceded to give as reliable a value of total surface area-/.e., external plus that of cracks, crevices, pores, and fissures, as can presently be obtained. This has led to the suggestion (3) that agreement between the two techniques results when the powders are nonporous and that permeameter values less than BET ones indicate the presence of pores. Fortunately, the area associated with pore walls can be independently evaluated by a mercury pressure-intrusion technique. If Knudsen-flow permeameter values are indeed representative of external area, these values added to mercury-intrusion areas should equal the total area and coincide with BET values. That this is so within measurement limitation for at least 16 different materials is the basis for this report.
THEORETICAL
Pressure
Micrometer
Permeametry. Of the several equations relating the surface areas S,, of a unit mass of powder to the pressure loss AP of a gas flowing at reduced pressure and the rate Q through length L and cross-sectional area A of a bed of powder of density p packed to the porosity e, the most satisfactory relationship ( 5 ) for a non-adsorbing gas is 9AAP (1 - E)PLQ(MRT)I‘~
“[F
t2Ar p,[M(273
+
OS4’’
L
x
(273 + 273
“1
=
0.000952
e2(273
+
f)li2
APbr
PbL
--2a cos 0 P
(4)
By measuring the volume of mercury penetrating a porous substance as a function of applied pressure, a pore volume distribution may thus be obtained. Assuming right cylinder pores of length h, the pore area S,, is 2 iv-rhand pore volume Vis iv-r2h,giving S,,
=
2 Vjr
=
- zpAv ~
u
cos 0
=
0.0225 ZPAV
( 5 ) B. V. Deryagin, Akad. Nauk SSSR, 53, 633-6 (1946).
I-----
Cupric carbonate-A
,
Cupric carbonate4
v)
v)
0.1 I
0
I
I
4
8
12
I
16
Pressure (mm Hg)
Figure 2. Specific surface area
US.
pressure
Low Temperature Gas Adsorption. Information about the BET technique (6) is so readily available (7-11) that it suffices here to note that total surface area by gas adsorption S,, is basically calculated from V,AN
swQ =
v
(7)
where V , is the volume of gas required to form a layer one molecule thick on the surface of a mass of 1 gram, A the area occupied by one adsorbed molecule, N the Avogadro constant, and V the gas molar volume, both volumes being reduced to standard temperature and pressure. EXPERIMENTAL
Permeametric measurements were made with a KnudsenFlow Permeameter, Model 1401, of the Micromeritics Instru-
(5)
Then combining Equations 4 and 5 and introducing appropriate values for the surface tension (474 dyne/cm) and contact angle (130”), the pore area can be calculated from pressure-volume increment data by the realtionship
,s,
--
n
(3)
where APb is the pressure loss due to the packed powder bed only; its value is actually the pressure immediately upstream of the packed bed less the loss due to downstream parts of the system at the same flow rate, the correction being established from calibration data obtained without powder. Experimentally, S,, is found to increase somewhat as AP, decreases. These data plot a straight line on a log-arithmetic grid and extrapolate (3) to the proper S,, at APb = 0. Mercury Intrusion. If a pore space is assumed circular in cross section, the force tending to drive pressurized mercury into the pore is iv-r2P,where r is the pore radius and P the pressure applied to the mercury. The resisting force for a non-wetting liquid like mercury is -2 iv-r u cos 6, where u is the mercury surface tension and 6 the contact angle (greater than go”, hence the negative sign). The opposing forces are equal at equilibrium, hence the pore radius and applied pressure are related by p ==
Helium
Figure 1. Diagram of altered perrnearneter
(2)
with 7 the time in seconds for the flow of 1 cm3 (STP) of gas, pb the packed bed bulk density, P the actual pressure in Torr where the 1 cm3 of flowing gas is measured, and t the temperature in degrees centigrade. For the particular apparatus of this study, the area A was held constant at 1.42 cm, P was fixed at 1000 Torr, and helium gas was employed. Hence, Equation 2 reduces to S,,
1
Vacuum
where also M is the molecular weight of the gas, R the gas constant, and T the absolute temperature. When gas flow is produced by a vacuum pump giving a downstream pressure of essentially zero, Equation 1 may be rearranged to
(6) S. Brunauer, P. H. Emmett, and E. Teller, J. Amer. Chem. Soc., 60, 309-19 (1938). (7) S. J. Gregg and K. S. W. Sing, “Adsorption, Surface Area and Porosity,” Academic Press, New York, N.Y., 1967. (8) C. Orr, Jr., and J. M. Dalla Valle, “Fine Particle Measurement,”
Macmillan, New York, N.Y., 1959. (9) D. M. Young and A. D. Crowell, “Physical Absorption of Gases,” Butterworths, London, 1962. (10) S. Ross and J. P. Olivier, “On Physical Adsorption,” Interscience, New York, N.Y., 1964. (11) “The Solid-Gas Interface,” Vols. 1 and 2, E. A. Flood, Ed., Dekker, New York, N.Y., 1967. ANALYTICAL CHEMISTRY, VOL. 44, NO. 8 , JULY 1972
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Table I. Typical Measured and CalculatedPermeameter Data Time for Measured flow of 1 cc Corrected Calculated pressure at 1000 mm pressure surface loss, Torr loss, Torr Hg, sec area, m2/g Iron blue; density, 1.70 g/cc; sample weight, 0.2476 g; bed length, 0.304 cm; ambient temperature, 24 "C; porosity, 0.663 123.05 13.89 70.6 14.70 172.11 10.15 10.85 72.2 6.20 312.20 5.63 73.3 Extrapolation 74.1 Boron nitride-A; density, 2.25 g/cc; sample weight, 0.4357 g; bed length, 0.306 cm; ambient temperature, 24 "C; porosity, 0.555 13.52 68.71 12.50 14.18 10.25 93.90 9.36 14.51 161.95 5.85 6.55 15.61 3.62 324.45 3.07 16.42 Extrapolation 17.2 Polyvinyl chloride-A; density, 1.52 g/cc; sample weight, 0.7410 g; bed length, 0.730 cm; ambient temperature, 24 "C; porosity, 0.529 14.10 2.36 5.30 0.110 3.24 3.90 0.113 10.90 7.80 4.98 2.60 0.114 10.20 1.28 0.126 4.50 Extrapolation 0.13 Cupric carbonate-A; density, 3.95 g/cc; sample weight, 0.6869 g; bed length, 0.354 cm; ambient temperature, 24 "C; porosity, 0.654 12.39 3.72 14.40 20.70 62.50 4.33 3.94 5.40 2.44 4.12 3.25 116.91 Extrapolation 4 . 2 Table 11. Experimental Surface Areas PermePorosGas ametry imetry Combined adsorption external internal area, S,, area, S,,, area, S,,, Description of S,, area, Swo, material m2/g m2/g m2/g m2/g 0 74.1 Iron blue pigment 74.1 70.0 0 57.0 57.0 54.1 Titanium dioxide 0 17.2 18.4 17.2 Boron nitride-A 0 14.0 14.0 14.4" Carbon black-A 8.0 7.5a 8.0 0 Carbon black-B 0 0.48 0.48 0.52 Tungsten 0 0.13 0.13 0.15 Polyvinyl chloride-A 0.94 1.11 0.17 1.10 Polyvinyl chloride-B 1.12 1.31 1.27 0.19 Polyvinyl chloride-C 0.75 1.05 1.28 0.30 Polyvinyl chloride-D 22.2 26.4 26.8 4.2 Cupric carbonate-A 19.1 19.1 3.6 15.5 Cupric carbonate-B 4.82 4.98 0.27 4.55 Boron nitride-B 4.48 5.98 5.70 1.50 Iron oxide-A 9.79 9.50 1.77 8.02 Iron oxide-B 7.21 5.62 2.10 5.11 Iron oxide-C Determined by electron microscopy.
+
5
ment Corporation, Norcross, Ga., which was altered t o give increased sensitivity and rapidity of operation. The absolute pressure gauge of the commercial instrument was replaced with a 0-20 Torr pressure transducer Model P/N 41GB of the Consolidated Controls Corporation, Bethel, Conn., and a microammeter readout ; this reduced equilibration times from a n average value of approximately 30 min to 2 min. The flexible bellows system that feeds the 1 cm3 of gas was replaced with a more flexible bellows, and temperature control was added. The new bellows system was mounted 1536
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
Table 111. Graphical Integration for Iron Oxide-A Pressure range, psia P X AV 90-130 0.22 130-180 1.24 180-220 1.40 220-270 2.20 270-350 6.80 350-480 19.50 480-600 30.80 600-760 59.10 760-810 12.52 8 10-900 9.42 900- 1050 10.72 1050- 1400 14.69 1400-1900 13.20 1900-2400 8.60 2400-3000 5.40 3000-4000 3.50 5000-50,000 0.00 199.31 Area = 0.0225 x 199.31 = 4.48 m2/g. Table IV. Description of Powder Materials Total specific surface Density, area, Material g/cm3 m2/g Data source Iron blue 1.70 70.0" Mic. Inst. Corp. Titanium dioxide 54.1" Mic. Inst. Corp. 4.17 19.3 0 . 52h Mic. Inst. Corp. Tungsten 1.52 Polyvinyl chloride 1 .28h Mic. Inst. Corp. Polyvinyl chloride 1 , 27h Mic. Inst. Corp. 1.57 Mic. Inst. Corp. Polyvinyl chloride 1 .l o b 1.60 0. ljb Mic. Inst. Corp. 1.52 Polyvinyl chloride 26.8a Mic. Inst. Corp. 3.95 Cupric carbonate-A 19.l a Mic. Inst. Corp. 3.95 Cupric carbonate-B 5.70" Mic. Inst. Corp. 5.25 Iron oxide-A Mic. Inst. Corp. Iron oxide-B 9.50" 5.25 5.6P Mic. Inst. Corp. 5.25 Iron oxide-C 18.4a R. A. Pierotti, 2.25 Boron nitride-A Georgia Tech R. A. Pierotti, 2.25 4.98a Boron nitride-B Georgia Tech 14.4c B. W. Davis, 1.87 Carbon black-A Georgia Tech 7.5c B. W. Davis, 1.89 Carbon black-B Georgia Tech 0 N2 adsorption surface area determination using BET method. Kr adsorption surface area determination using BET method. Surface area determined by electron microscopy (particles spherical).
on a foam rubber pad, connected to other parts of the system with vacuum rubber hose, and a permanent magnet-eddy current stabilizer was added to minimize vibrational effects. A schematic diagram of the modified instrument is included as Figure 1. The instrument was operated according to standard procedure. Typical experimental data obtained using Equation 3 are given in Table I ; Figure 2 shows some of the characteristic linear plots of results; while column two of Table I1 presents the final S,, values. Mercury intrusion data were obtained with a Micromeritics Instrument Corporation Mercury Penetration Porosimeter, Model 905-1, a typical plot of penetrating mercury volume ES. pressure being shown in Figure 3. To the first plateau on such a curve, the mercury has been utilized in filling void spaces among the particles, but between the plateaus the mercury fills the pore spaces within the particles. The
100
071
10
Pore Diameter lmlcrons) 10 01
Total, or gas absorption, surface areas S,, were not determined as a part of this work; this information was obtained from the source of the powder as was the other pertinent information listed in Table IV. It may be noted that carbon black surface areas were calculated from size data taken from electron micrographs rather than obtained by gas adsorption. These particles were essentially spherical and quite uniform in size. Specific surface areas determined from gas absorption and from particle size data under this circumstance have been shown previously to be in essential agreement (12).
0 01
I
0.4
CONCLUSION 0.0 1
10
102 1o3 Pressure (psia)
104
105
Figure 3. Penetration volume us. pore diameter for iron oxide-A latter represents the data of interest in calculating pore surface area Swm.This area was determined by considering the volume axis to be divided into a number of small volume increments and obtaining the mean pressure corresponding to each incremental volume. These two values were multiplied together, and the sum of all values was obtained in accordance with Equation 6. Table I11 represents a typical calculation and the third column of Table I1 summarizes the results. Whileo the data of Table I11 indicate a smallest pore radius of 221 A according to Equation 4, other materials, notably the cupric c$rbonates, were found to have pore radii down to 18.4 A or near the minimum attainable at the instrument limit of 50,000 psia.
The particle materials of this study were chosen for no particular reason other than that they were available, that some of the needed information about them was already known, and that they appeared to have widely differing pore and surface properties. The results in Table 11, particularly the correspondence evident in the right two columns, reveals that, at least for the 16 powders tested, it is possible to arrive at the total surface area from a summation of external and internal measures. The results support the idea that Knudsen-flow measurements relate to the surface exclusive of micropores. Finally, the results lend confidence to each type of measurement despite the assumptions utilized in arriving at it. RECEIVED for review January 28, 1972. Accepted March 30, 1972. (12) J. C. Arne11 and G. 0. Henneberry, Can. J. Research, 26A, 29-38 (1948).
Low Level Calibration Mixtures for Gaseous Pollutants Robert C. Paule National Bureau of Standards, Washington, D.C.20234 IN AIR POLLUTION MEASUREMENTS, there has developed a considerable need for instrument calibration standards in the analysis of gaseous materials at the ppm and ppb level. One response to this need has been the development (1) and certification (2) of SOs permeation tubes. These tubes, under constant temperature conditions, effuse SOs at a given rate and by controlling the gas flow over the tubes, one can produce low level calibration standards. The tubes have an advantage, through continuous flow, of overpowering any adsorption-desorption effects occurring within the inlet and measurement systems. The permeation rates, however, are sufficiently temperature sensitive so as to require thermostating, and a period of several hours is needed for the establishment of steady state flow conditions. Furthermore, permeation tubes have been limited in practical usage to the easily condensable gases since, for reasonable lifetimes, the tubes must hold an appreciable quantity of liquified gas. Presented herein is an alternate technique for the production of low level calibration mixtures for gaseous pollutants. The (1) A. E. O’Keefe and G. C. Ortman, ANAL.CHEM., 38,760 (1966). (2) SO2 permeation tubes, SRM 1625, may be purchased from the Office of Standard Reference Materials, National Bureau of Standards, Washington, D.C. 20234.
technique consists of encapsulating, measuring, and storing a very small quantity of pure pollutant gas as a microbubble and then at the time of analysis, of mixing the pollutant gas with a known large quantity of “clean” diluent gas. The mixing operation is done in a separate, passivated dilution cylinder. Pollution standards are frequently needed in a range from 10 ppb to 100 ppm, and with a usable volume of about 1000 cm3. For a volume of 1000 cm3, and considering the ppb and ppm levels to be on a volume per volume basis, this means that the volume of pure pollutant will vary from 10-5 to 10-l cm3. Such volumes are conveniently contained and measured in capillary tubing. If larger volumes of calibrated gas mixtures are needed, the required volumes can be produced by using larger “capillary” tubing and dilution cylinders. Higher pressures in the dilution cylinder may also be used. Precision bore, glass capillary tubing can be used as a convenient “volumetric flask” for the measurement of the bubble volume and as a readily inspectable storage container for the bubble. Experience has shown that the bubble remains as a stable slug of gas so long as one end of the capillary tube is sealed; it will not float upward when the capillary is held in a vertical position. ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
1537
