It was also found that the iodine value of the solution does not change much with time, after the buffer solution has been added. Moreover, when mercury fulminate is present in mixtures, the addition of a buffer solution also has a favorable effect. Alkaline and acidic compounds are then buffered and the pH is maintained at 4.7 f 1, thus making the procedure more versatile and reliable. It is not practicable to carry out a coulometric titration at high pH values because the hydrolysis of iodine becomes significant under such conditions. At low pH values the oxidation of iodide by oxygen becomes considerable. Maintaining the pH at 4.7 by adding 5 ml of acetate buffer solution to the titration vessel has the additional advantage that the exclusion of oxygen from the generating solution is not necessary. This coulometric procedure was primarily developed for the determination of small amounts of mercury fulminate in mixtures used in explosive trains. Mercury fulminate is used to some extent in commercial blasting caps and military ammunition. When used in blasting caps, mercury fulminate is frequently mixed with potassium chlorate. Therefore, the influence of potassium chlorate was investigated, but it was found not to interfere under these conditions. When applied in primer mixtures, mercury fulminate is often used together
with potassium chlorate and antimony trisulfide. However, the results then tend to be on the low side, with deviations up to 1 % relatively. This is probably due to a reaction like (5): Hg(ONC)z
+ Sb33 + H D
-+
HgS
+ Sbz03 + 2 HCNS
(3)
However, it is often unnecessary to make a correction for this interference. For example, in practice a percussion primer may contain 30 mg of a primer mixture in which the mercury fulminate content may vary between 7 and 9 % or more. When other compounds are present together with mercury fulminate, it is easy to predict whether these will interfere or not, as the coulometric titration is derived from a simple classical iodometric titration of thiosulfate by iodine, for which the interferences are well known. ACKNOWLEDGMENT
The technical assistance of W. R. Urban is gratefully acknowledged. RECEIVED for review July 22, 1968. Accepted September 27, 1968.
Brunauer-Emmett-TellerSpecific Measurement Solids Using Krypton Jan Medema and J. P. W. Houtman Reactor Instituut, De@, NetherIands
IN many fields in which solids are used, the specific surface areas of these substances play an important role. This certainly applies to catalysts and adsorbents for which a large surface area (100 to 1000 m2/gram) is required. It also holds good for pigments and ceramic materials where, generally speaking, small surface areas (0.01-1 m*/gram) are involved. For the measurement of specific surface areas the method developed by Brunauer, Emmett, and Teller ( I ) is of great importance. In this method the adsorption isotherm (see Figure 1) of a weighed sample is measured-Le., the amount of adsorbed gas as a function of pressure at constant temperature. In practice it offers advantages to plot the relative gas pressure-Le., the pressure relative to the saturation pressure (po)at measuring temperature. On the basis of some simplified assumptions, Brunauer er at. derived a formula from which the amount of gas (V,) required for covering the surface with a monomolecular layer can be calculated. If the surface area (A,) occupied by one adsorbed gas molecule is known, the total available surface area of the sample, and thus its specific surface area, can be calculated. In practice, nitrogen is generally used as the measuring gas, though other adsorbates such as argon, krypton, xenon, methane, and butane are also employed. When using nitrogen and the first four mentioned gases, the isotherm is usually determined at -196 "C, the boiling point of nitrogen. Butane offers the special advantage that it can be used at 0 "C.
Various misconceptions seem to exist with respect to the reliability of the results obtained by this method. They are partly due to obscurities in the theory, but also to certain properties of the measuring gases. Objections to the B.E.T. Method. Although the calculation method of Brunauer et al. was rapidly adopted and yielded reasonable results when put to practical tests (2), it was soon recognized ( 3 ) that the B.E.T. formula was not well founded. In fact, with most adsorbents no monomolecular adsorption layer occurs, because, before completion, gas molecules on certain parts of the surface are adsorbed in a second, and sometimes even a third, layer. In fact, a complete monomolecular layer can only be expected if all surface atoms are equivalent and thus are surrounded by other atoms of the solid in the same way. This is the exception rather than the rule (4), certainly for technical powders. Moreover, if the variation in bond strengths between the surface atoms has an effect on the interaction with the gas molecules, it is also to be expected that the way in which the layers of adsorbed atoms are completed will depend on the gas usedLe., on its polarizability. As a result of these varying interactions between surface atoms and adsorbed gas molecules, the assumption of a standard value for A , (the surface of an adsorbed gas molecule) equal to its value in the liquid or solid phase will also be open to question. In the first place, the adsorbed state
(1) S. Brunauer, P. H. Emmett, and E. Teller, J . Amer. Chem. SOC.,60, 309 (1938).
(2) T.N. Rhodin, Adoam Cufal.,5, 85 (1953). (3) P. H. Emmett, ibid., 1, 65 (1948). (4) J. H. de Boer, ibid., 8, 98 (1956). VOL. 41, NO. 1 , JANUARY 1969
209
I
0
L
I COUNTIMIN
I
.
ADSORBED x io-’ ON 14.3mg AL20,
I
I
0.1
0.2
I
I
0.4 RELATIVE PRESSURE
0.3
I
0.5
0.6
Figure 1. Adsorption-desorption isotherm of an A1203sample X = adsorption measurements 0 = desorption measurements
of the gas is not fully comparable to one of the known states (liquid or solid) for which the diameter of the molecule is known. In the second place, variations in A,,, may be expected, depending on the !ype of adsorbent. The value used in practice for A, (16.2 AZ)of nitrogen is derived from the fluid density. For gases such as argon, krypton, xenon, and methane-for which the temperature of measurement lies below the melting point-a value for A , derived from the density of the solid state is sometimes applied. Others use a value derived from the undercooled liquid. Generally, however, an empirical value derived from comparative measurements (5) is used. Moreover, the fact that the temperature of measurement lies below the melting point also affects the choice of the correct saturation pressure (po) ,which plays such an important part in the B.E.T. equation (6, 7). Finally, it should be remembered that in many cases solids do not just have an external surface. The internal surface formed by the pores greatly predominates with catalysts and adsorbents in particular. The size and shape of the pores may show a strong influence in the supply of the measuring gas to the internal surface and also in layer formation on this surface. When examining the various properties of the gases used, there is not a single gas to which at least part of this criticism is not applicable. It is, after all, surprising that the B.E.T. method has yielded such useful results. Where possible, the method has been checked by means of solids with known geometrical forms, whose surface areas could be calculated (2, 3). This has lead to 16.2 A Zas the most useful value for A , in the case of nitrogen. In some instances, however, greatly deviating values (12.9 to 17.7 A2)were also found for this measuring gas (5). Similar checks were also made with krypton. Relatively large variations were then found for A , (between 15.3 and 23.6 A2). RFcently, a “recommended value” of 20.2 A2 (in theory 14.0 A 2 for liquid and 15.2 Az for solid krypton) was obtained by means of a critical analysis of data. The variations found, and the uncertainty as to the ( 5 ) A. L. McClellan and H. F. Harnsberger, J. CoNoid and Interface Sci., 23, 577 (1967). (6) J. M. Haynes, J. Phys. Chem., 66,182 (1962).
( 7 ) P. J. Malden and J. D. F. Marsh, ibid., 63, 1309 (1959).
210
ANALYTICAL CHEMISTRY
correct value of PO (7), have suggested the possibility that krypton could be inferior to nitrogen as a measuring gas. Such a view is usually the result of insufficient knowledge of the many fundamental inaccuracies of the B.E.T. method, which would apply equally to nitrogen as a measuring gas. Instead, it seems preferable to have, in general, some doubt as to the degree of accuracy with which the specific surface can be determined according to Brunauer et al. The measuring gas should be selected with an eye to composition, structure, and texture of the sample, instead of suggesting a particular gas as the standard adsorbate. The use of krypton, for instance, should definitely be recommended instead of nitrogen for a substance whose specific surface area is smaller than 5 m2/gram, in view of the lower value ofp, for krypton. Again, this applies only if the adsorbed amount of gas is obtained from gas-pressure measurements and not by weighing. This latter technique, owing to the fact that it is most time-consuming, is used only for occasional check measurements. In this respect, attention is drawn to a number of existing alternative measuring techniques (8) having the character of a technical analysis. In those instruments, other sources of errornamely, those inherent to the specific measuring technique used-also play a part. The various arguments given above have led us to test the practical usefulness of krypton as a measuring gas for a limited group of samples of different type and origin. Method Using 85Kras a Measuring Gas. A variant of the B.E.T. determination of specific surface area with krypton is that using the radioactive isotope 85Kr (9). The main advantage of this method is that the adsorbed amount of gas can be measured directly, with rapidity and accuracy, using a simple G.M. counter. A measurement based on three points of the reversible part of the adsorption isotherm within the range for pipo between 0.05 and 0.20 is made within 1.5 hours by this method. Also, the measurement of the gas pressure is based on a radiation count, thus obviating the need for accurately calibrated burets and manometers. Krypton-85 as measuring gas has been suggested before by Aylmore and Jepson (10) and by Clarke (11). However, in their apparatus the radioactive counting was used either only for measurement of gas pressure or only for measurement of the amount adsorbed. Therefore, their instruments are still rather complicated. The measuring apparatus as used by us was reduced to the central part of the equipment containing sample holder C in Dewar F [see Figure 1 of (9)]. A supply bottle, A , with a manometer closure, B, at one end of the measuring section and a low-temperature trap, D, with a connection to the vacuum pump at the other end completed the instrument. The apparatus is commercially available from N. V. Philips Gloeilampenfabrieken, Eindhoven, Netherlands. G.M. counter G1, indicating the gas pressure, was calibrated with a McLeod manometer, E. A straight calibration curve (standard deviation less than 1%) can easily be obtained. G.M. counter G2 was originally calibrated by measuring the isotherm for a substance with known surface area as found with nitrogen. In this procedure, po = 2.2 mm Hg-Le., the value for undercooled liquid at -196 “C was used in agreement with Beebe (12). Afterwards, the (8) S. J. Gregg and K. S. W. Sing, “Adsorption, Surface Area and Porosity,” Academic Press, New York, 1967, Chaps. 8 and 2. (9) J. P. W. Houtman and J. Medema, Ber. Bunsen Ges. (2.Elektrochemie), 70,489 (1966). (10) D. W. Aylmore and W. B. Jepson, J. Sci. Instru., 38, 156
(1961). (11) J. T. Clarke, J . Phys. Chem., 68,884 (1964). (12) R. A. Beebe, J. B. Beckwith, and J. M. Honig, J. Amer. Chem. Soc., 67, 1554 (1954).
~~
~~~
Table I. Comparison of B.E.T. Measurements Using Various Adsorbates Surface area m2/gram Type BET. of solid 85Kr C-constant Nz N Pdata measured by TiOz 0.96 (100) 1.5 Delft Technical Universitya Ti Oz 9.2 ( 150) 9.9 Delft Technical University Ti Oz 69.1 ( 150) 69.1 Delft Technical University 175 N. V. Ketjen, Amsterdam AlzOa 174.2 (80) A1zOa-SiOz 608 (50) 608 N. V. Ketjen, Amsterdam Fe 0.43 (300) 0.42 Dutch State Mines, Central Laboratoryb 19.9 (100) 20.5 B.A.S.F. a Fez03 a FeOOH 72.0 (80) 70.6 Gas chromatography (own data) 6.5 (250) 6.2 W. Feitknechtc FeaOc The help of W. de Vleeschauwer is gratefully acknowledged. Kindly provided by T. Scholten. c Obtained from Institut fur Anorganische, Analytische und Physikalische Chemie, Bern University, Switzerland, through J. J. van Loef. Q
Table 11. Comparisons of Results Obtained by Various Methods Surface area m2/gram B.E.T. Geometric surface area Type of solid S6Kr C-constant Geometric measured with AIzO3-SiO2 608 Electron microscope Microscope 0.43 Fe Electron microscope CY Fe203 19.9 Electron microscope a FeOOH 72.0 X-ray diffraction Electron microscope 6.5 Fez04 X-ray diffraction Microscope Human hair 0.04 Electron microscope 77.4 a FezOs 170 Electron microscope FezOs Electron microscope 140 CY FeOOH a Measured by Dutch State Mines. b Measured by W. Feitknecht. (Y
calibration was repeated by means of a series of measurements during which the krypton gas in the lower part of the sample holder was gradually replaced by oil. The two measurements enabled an A , value to be derived for all measured s!mples. The results obtained varied between 19.6 and 214 A2, this being in good agreement with the value for 20.2 A 2 recommended by McClellan, et al. (5).
RESULTS The samples examined by use can be divided into two categories. The first group consisted of a limited number of samples of porous solids whose surface areas measured with 85Kr could be compared with the results obtained with nitrogen. They are given in Table I. The agreement found is excellent. The deviation found for the TiOz sample with a surface area of about 1 m2/gram is probably caused by the inherent inaccuracy in measuring small surface areas with nitrogen, using the normal technique of volume and pressure measurement. Special attention is drawn to the sample from the Dutch State Mines, Central Laboratory. Their figure given for the specific surface area was obtained by means of various measuring gases (N2, CHI). Here the weighing technique was used for nitrogen. The second group of samples consisted of materials with a reasonably-well-known geometry, thus enabling the surface to be calculated from the dimensions. These dimensions were measured with a microscope, an electron-microscope, or by means of X-ray diffraction line broadening. For porous
Roughness factor 1.3 1.4 1.0 1.0 1.4 1.2 1.0 1.3 1.1 1.1 1.2
materials the dimensions of the crystallites were either measured with the X-ray technique or with the electron microscope in combination with an ultrasonic technique of sample preparation leading to disintegration of the porous particles. The results are given in Table 11. We believe the inaccuracies of data obtained in this way to be about 20%. A full comparison of the results is hampered because it is difficult to allow for the natural roughness of the surface. It is only possible to calculate roughness factors from the various data. They are in very good agreement with data found in the literature for similar roughness factors [(2, 8-Chap. 211. CONCLUSIONS
From the above, the conclusion can be drawn that for solid samples examined by us (Al2O,-SiO2, A1203,a! Fe203, TiOs, cy FeOOH, Fe, human hair) there is no fundamental difference between the use of krypton and nitrogen as a measuring gas in the B.E.T. method. This confirms the opinion of Cannon and Gaines (13). Moreover, reliable values for specific surfaces smaller than 5 mz/gram can be more easily found by using krypton. 85Kr has a number of additional, by no means negligible, advantages-such as simple equipment, simple calibration, accurate measurements using smaller samples-so that adjusting times can be reduced considerably. RECEIVED for review February 26, 1968. Accepted September 19, 1968. (13) P. Cannon and G. L. Gaines, Nature, 190,340 (1961). VOL. 41, NO. 1 , JANUARY 1969
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