66100-2 - X ADSORPTION AND VACUUM TECHNIQUE PAUL A. FAETH THEUNIVUR STYyOF MWf!GAN E[i GIN [E RII t\V'G LIBRARY IG October 1962 Sve~t a! Scweze aWNd THE UNIVERSITY OF MICHIGAN Ann Arbor, Michigan

NOTICE Final Disposition. After this document has served its purpose, it may be destroyed. Please do not return it to the Institute of Science and Technology.

Institute of Science and Technology The University of Michigan PREFACE In recent years surface chemistry and adsorption have taken on new interest for industry. Their growing importance is illustrated by their use in the purification of petroleum by chromatographic techniques, syntheses depending on contact catalysis, sugar refining, hydrogenation of oils, clay treatment of gasolines, and compounding of rubber articles. More recently they have come to be used in the study of thin films, semiconductors, semiconductor devices, and the development of the catalytic muffler. Within the last few years a tremendous effort has been made to apply the theories of semiconductors in linking the properties of solids to the heretofore classical fields of adsorption and surface chemistry. For the sake of better understanding of the processes mentioned above, the surface properties of the adsorbent must be studied. The investigation of surface areas, pore volume distributions, total pore volumes, densities, and surface activities, along with kinetic experiments and such measurements as resistivity, thermoelectric power, magnetic susceptibility, nuclear magnetic resonance, and others, all lead to a better understanding of adsorbents and adsorption phenomena. In 1955 C. B. Willingham and the author wrote "The Assembly, Calibration, and Operation of a Gas Adsorption Apparatus for the Measurement of Surface Area, Pore Volume Distribution, and Density of Finely Divided Solids."' Since that time many requests for copies have been received. Because of the continual interest in this subject, it was suggested that the original adsorption bulletin be revised. It was decided to revise the original work,which was concerned only with volumetric techniques, and to extend the discussion to a gravimetric technique. The purpose of this report is to describe in some detail the assembly, calibration, and operation of a volumetric and a gravimetric gas-adsorption apparatus in such a way that this report may be used as a manual by those beginning adsorption studies, and also by others whose techniques and procedures may benefit from this presentation. Published by Mellon Institute of Industrial Research, Pittsburgh, Pa.

Institute of Science and Technology The University of Michigan ACKNOWLEDGMENTS The author is indebted to many who have helped to bring this manuscript to completion. Among them are E. V. Ballou, G. Parravano, and J. T. Sommerfeld, whose criticisms of the text for content and style were most helpful. The author is obliged to A. W. Czanderna for his comments and for his permission to reproduce data and figures from his thesis. Special thanks are due C. B. Willingham for his criticisms of the text and for his encouragement during the writing. In addition, the author wishes to acknowledge the directors of the Mellon Institute for their permission to reproduce certain drawings from the original adsorption bulletin that are contained in the volumetric section. The author is indebted to J. T. Wilson of the Institute of Science and Technology at The University of Michigan for permission to publish this manuscript through the Institute. He further acknowledges the financial support of the Institute of Science and Technology during this work, which was performed during a postdoctoral fellowship. iv

Institute of Science and Technology The University of Michigan CONTENTS Notices............................. ii Preface.................................. iii Acknowledgments....................... iv List of Figures.............v............... vi List of Tables.......................... vii Abstract.1...................... 1 1. Volumetric Apparatus for the Measurement of Surface Area, Pore Volume Distribution, and Density of Finely Divided Solids........... 1 1.1. Introduction 1 1.2. Surface Area and the B.E.T. Equation 2 1.3. Assembly of the Adsorption Apparatus 4 1.4. Calibrations and Bulb Factors 12 1.5. Determination of Surface Areas from Nitrogen Adsorption 15 1.6. Determination of Surface Areas from Krypton Adsorption 21 1.7. Measurement of Pore Volume Distribution 28 1.8. Determination of the Density of Solid Materials by Helium Displacement 31 2. Gravimetric Apparatus for the Measurement of the Sorption of Gases in and on Solids 34 2.1. Introduction 34 2.2. Construction of the Balance System 35 2.3. Assembly of the Balance 37 2.4. Construction of the Furnace Thermocouples 39 2.5. Operation of the Balance 40 2.6. Calibration of the Balance 42 2.7. Measurement of an Isotherm 45 2.8. Other Measurements 48 2.9. Summary 53 Appendix: Cross-Sectional Areas of Adsorbed Molecules.......... 53 References................................... 56 Bibliography.................................. 58 V

Institute of Science and Technology The University of Michigan FIGURES 1. Schematic Diagram of the Gas-Adsorption Apparatus............. 5 2. Typical Sample Tubes............................... 7 3. Details of Mercury Seal and Electrical Contacts for the Manometers..... 8 4. Gas-Purification Train......................... 9 5. Dewar Flask for Use As a Liquid-Nitrogen Bath................ 11 6. Device for Controlling Liquid Level of Nitrogen Bath............. 12 7. Detailed Drawing of the Heating Unit...................... 13 8. The Correction Factor, /, for the Nonideality of Nitrogen at Liquid-Nitrogen Temperatures.............................. 20 9. Plot of B.E.T. Variables from Data in Table IV................. 21 10. Vapor Pressure of Liquid Nitrogen, Liquid Krypton, and Solid Krypton As a Function of Temperature......................... 25 11. Plot of B.E.T. Variables for Data in Table VI.................. 27 12. Typical Nitrogen Isotherm for Use in Calculating Pore Volume Distribution. 29 13. Volume of Pores of Radius Equal to or Larger Than r, Plotted with Respect to Pore Radius................................ 30 14. Plot of the Pore Volume Distribution As a Function of the Pore Radius... 30 15. The Quartz Beam Microbalance......................... 35 16. Scale Drawing of the Microbalance....................... 36 17. The Microbalance Assembly........................38 18. The Auxiliary Vacuum System..........................39 19. The Magnetic Compensation Solenoid......................40 20. Standard Null Position..............................41 21. The Microbalance Electrical Circuit.....................41 22. Stardard Resistor......................42 23. Microbalance Calibration Curves..................... 44 24. The TMF Effect............................... 46 25. Raw Data of a Typical Pr-O Isotherm..................... 46 26. A Typical (Calculated) Pr-O Isotherm..................... 48 27. Rate of Oxidation of Pr203........................... 2A p oi e R a7.23. sri f...............50 28. Adsorption of Nitrogen on Rutile at 78~K...................... 51 vi

Institute of Science and Technology The University of Michigan TABLES I. Bulb Factors................................. 14 II. Size of Sample and Quantity of Nitrogen Used, Based on an Estimated Specific Surface............................... 16 III. Data for Nitrogen Adsorption.......................... 19 IV. Work Sheet for Calculating B.E.T. Variables.................. 19 V. Data for Krypton Adsorption........................... 24 VI. Work Sheet for Calculating B.E.T. Variables from Data in Table V...... 26 VII. Data for Density Determinations of Solids................... 33 VIII. Work Sheet for Density Determinations of Solids................ 33 IX. Furnace Thermocouple Calibration....................... 41 X. Microbalance Calibration Data....................... 43 XI. Surface Area Data for the Adsorption of Nitrogen on Rutile at 78 K...... 51 XII. Cross-Sectional Areas of Adsorbed Molecules.................. 54 vii

ADSORPTION AND VACUUM TECHNIQUE ABSTRACT A volumetric adsorption apparatus and a gravimetric one are described. The discussion of the volumetric method includes a detailed description of the construction and calibration of the basic apparatus, typical sample tubes, a special dewar, a heater, and special control devices. The procedures and methods of calculating specific surface area by the B.E.T. method using both nitrogen and krypton, and of calculating true density, are presented step by step. The measurement of pore volume distribution is also discussed. The gravimetric technique uses a quartz beam microbalance. The construction, manipulation, and calibration of the balance are described, along with procedures and calculations for typical measurements based on mass increases. These techniques include the measurement of sorption equilibrium, surface area, sorption kinetics, and magnetic susceptibility. VOLUMETRIC APPARATUS FOR.THE MEASUREMENT OF SURFACE AREA, PORE VOLUME DISTRIBUTION, AND DENSITY OF FINELY DIVIDED SOLIDS 1.1. INTRODUCTION This report describes the gas-adsorption apparatus used by the author in the work of the Department of Research in Physical Chemistry at the Mellon Institute for studies of the surface area, pore volume distribution, and density of a variety of finely divided and porous solids. A schematic diagram of the completed apparatus is shown, as are detailed drawings of several types of sample tubes, a manometer, a purification train, a special dewar, a constant level device, and a heater. The assembly, calibration, and testing of the gas-measuring system, the nitrogen thermometer, and the auxiliary systems for gas purification and transfer are discussed. The operation of the apparatus is explained, and the calculations and corrections for making typical measurements by use of nitrogen and krypton gases are given. A table listing values for the cross-sectional area per adsorbed particle of various adsorbates is included in an appendix. The determination of true density is discussed, and an illustrative example provided. The adsorption apparatus and technique have been automated by Ballou and Doolen (Reference 1). This adaptation is excellent for the surface-area measurement of large numbers of samples having somewhat similar properties. 1

Institute of Science and Technology The University of Michigan 1.2. SURFACE AREA AND THE B.E.T. EQUATION Adsorption is said to occur when a-fluid (i.e., a gas or a liquid) comes into contact with a solid and some of the fluid tends to adhere in the form of layers of fluid molecules. This process is called physical adsorption when adhesion is caused by relatively weak forces such as van der Walls forces. It is called chemisorption when the forces at the solid-fluid boundary (i.e., the interface) are strong enough to promote chemical reaction (Reference 2, page 4). The magnitude of these forces, of course, varies from system to system, and there is no sharp dividing line between the energies of physical and chemical adsorption. It is physical adsorption which permits the calculation of surface area and pore volume distribution. If the number of adsorbed molecules of a fluid which covers the adsorbent with a monomrnolecular layer could be determined, and if the area occupied by a single adsorbed molecule were known, the surface area available to the adsorbate molecules could be calculated. Since a method of calculating the area of an adsorbed particle has been described (Reference 3), the problem that remains is to calculate the number of molecules in a physically adsorbed monolayer. Several treatments lend themselves to a theoretical explanation of specific adsorption data (References 4, 5, and 6), but until 1938 no really general treatment had been proposed. In that year Brunauer, Emmett, and Teller (B.E.T.) (Reference 7) proposed a theory of multimolecular adsorption from which a value for the monolayer could be calculated. From the B.E.T. theory, the adsorption of a gas on a solid may be represented by the equation: V Cx n n+1 V m - (n + 1)x + nx n+ V- 1+ (C- 1)x -Cxn+1j( where x is the relative pressure, P/P0, P is the equilibrium pressure and P0 is the saturation pressure; V is the volume of gas adsorbed at equilibrium; Vm is the volume adsorbed in a monolayer; n is the number of layers; and C is a constant related exponentially to the heat of liquefaction and the heat of adsorption (Reference 2, page 154). When n = 1, Equation 1 reduces to Equation 2, the Langmuir equation: V kP V kP (2) V l + kP m where k is equal to C/P0. When n is infinite, P 1 (C - 1) P + (3) V(PO- P) - VmC VCPO 2

Institute of Science and Technology The University of Michigan A plot of P/V (P0 - P) with respect to P/P0 is usually linear over the range of relative pressures from 0.05 to 0.35 where the slope, S, is (C - 1)/VmC and the intercept, I, is 1/VmC. Since 1 C-i 1 S+I= + = V C V C V m m m then V = (S + I)1 (4) m The specific surface may be calculated from the following relationship. V K specific surface m (5) sample weight in grams where K is a constant for each adsorbate and is calculated from Equation 6. NA K M (6) V v where N is Avogadro's number, A is the area occupied by one adsorbate molecule, usually in the liquid state, and M is the gram molecular volume. For nitrogen and krypton at liquid-nitrogen temperatures, K is 4.38 and 5.28, respectively, when the specific surface is expressed in square meters per gram. Several authors (References 8 through 13) have endeavored to improve the theory of adsorption (and catalysis), with some success. It must be noted, however, that the equations derived from the B. E.T. theory still remain general enough to apply to most of the experimental data encountered. As a consequence, many experimenters use the B.E.T. method qualitatively as well as quantitatively to describe changes on the surface of the sorbent. The volumetric adsorption apparatus is used not only to obtain data to compute a surface area, but also to obtain data necessary to calculate pore volume distributions, densities, and adsorption rates. 1.2.1. PORE VOLUME DISTRIBUTION. Reference 14 describes a technique by which the pore volume distribution in porous solids may be determined from adsorption data. Suitably corrected, the Kelvin equation (Equation 7) can be used to describe the pore volume distribution of a porous solid over a range of pore radii from 5 A to 300 A. P -2aV cos 0 (7) P 0 rRT where P and P0 are as before, ax is the surface tension of the adsorbate, V is the molal volume of the liquid adsorbate, 0 is the contact angle, r is the capillary radius, T is the absolute tem3

Institute of Science and Technology The University of Michigan perature, and R is the gas constant. Since the experimental techniques applied in this measurement differ only slightly from those used to determine surface areas, some mention of the method will be made later. 1.2.2. DENSITIES. True densities of adsorbents may be obtained very easily withthe gasmeasuring system of the adsorption apparatus (Reference 15). Since helium is chemically inert and is not adsorbed at the operating temperature, it is an ideal displacing fluid. The densities calculated by use of helium are usually higher than values obtained by other techniques, because the dimensions of the helium atom permit it to penetrate into pores too small to be accessible to many commonly used displacing liquids such as benzene or toluene. 1.2.3. KINETIC MEASUREMENTS. The apparatus that will be described below is very versatile and may be used for other studies and purposes with only slight modification. Kinetic studies of the rate of uptake of a gas by a solid may be made if the rate of uptake is not too rapid. The apparatus, then, is used as a constant-volume system. To use it as a constant-pressure apparatus, one must provide a manostat arrangement (Reference 16) or change the volume of the system. Frequently this is difficult to do. 1.3. ASSEMBLY OF THE ADSORPTION APPARATUS The complete apparatus is diagramed in Figure 1. It consists of a system of four interconnected units: the sample tube, burettes, manometer, and mercury reservoirs; the gas-purification train and the gas storage reservoirs; the nitrogen thermometer and its manometer; and a high vacuum source (not shown) that consists of a mechanical pump, a diffusion pump, and a cold trap. Each of these units can be isolated from the others. The apparatus was arranged foreasy access to all of its parts, particularly the most frequently used stopcocks. It was mounted on a frame equipped with service lines for gas, water, air pressure, and electricity. The individual pieces of the apparatus (other than stopcocks) in Figure 1 are lettered. The letters have the following significance. A Sample tube B, B' Gas burettes, calibrated, for measuring the working volumes of gas C Manometer used to measure the gas pressure over the sample and in the gas burettes D Mercury reservoirs for the manometer and the burettes E Fine pressure control for manometer C (Reference 17, page 261) 4

Institute of Science and Technology The University of Michigan F - 0 M2 13( - 15 171 1 FIGURE 1. SCHEMATIC DIAGRAM OF THE GAS-ADSORPTION APPARATUS F Gas reservoirs, 3-liter capacity, for storage of purified gases G Calibrated doser for measuring quantities of (krypton) gas H Uncalibrated gas holder, used to compress gas enough to produce liquid-vapor equilibrium in the nitrogen thermometer bulb at liquid-nitrogen operating temperatures I Manometer of gas thermometer system J Drying tube filled with anhydrous calcium sulfate (Drierite) K Calibrated McLeod gauge for krypton system and general usage L Gas thermometer bulb M To mechanical oil pump N To source of air pressure, about 15 psig O To traps and purification train P To high vacuum source The stopcocks shown in Figure 1 were equipped to operate under pressure or vacuum. They are identified in the figure and in the text by numbers which have the following significance. 5

Institute of Science and Technology The University of Michigan 1 10-mm straight-bore stopcock; connects high vacuum source and gas-adsorption apparatus 2 4-mm oblique-bore three-way stopcock; used to equalize pressure on the legs of manometer (C); also used in producing Torricellian vacuum required in the right leg of the monometer 3 2-mm oblique-bore capillary stopcock; connects gas-measuring system to vacuum 4 2-mm oblique-bore capillary stopcock; used to introduce gas from the reservoirs into the gas-measuring system 4a 2-mm oblique-bore stopcock; isolates krypton system from gas reservoirs 5 4-mm oblique-bore stopcock; for evacuating reservoirs, F, and gas-purification train 6, 6a 2-mm oblique-bore three-way capillary stopcocks; connect sample tube to the gasmeasuring systems (see text) 7, 7a 2-mm oblique-bore three-way capillary stopcocks of the krypton doser, G 8 4-mm oblique-bore stopcock used to isolate McLeod gauge 9 4-mm oblique-bore stopcocks of gas reservoirs, F 10 2-mm oblique-bore capillary stopcock to the vacuum leg of manometer I 11 4-mm oblique-bore stopcock; used to evacuate the thermometer system and to fill this system with gas 12 4-mm oblique-bore three-way stopcock; diverts gas flow from either of the cold traps in the purification train into a single line connected to the gas reservoirs 13, 14, 2-mm oblique-bore capillary stopcocks used as fine controls of the flow of mercury 15 between the mercury reservoirs and the burettes 16, 17, 2-mm oblique-bore three-way capillary stopcocks; pressure-vacuum controls for 18, 19 the mercury reservoirs 20, 20a 4-mm oblique-bore stopcocks; outlet to atmospheric pressure through drying tube J Only stopcocks specially ground for high vacuum should be used; these should be held by some means to permit the use of pressure as well as vacuum.2 All connecting lines are 10-mm o.d. (outside diameter) tubing, except as indicated in Figure 1. The burettes, reservoirs, and manometers are custom made, and can be readily constructed from stock items of Pyrex glassware if adequate glass blowing facilities are available. The components of the high-vacuum system, including traps, oil- or mercury-vapor diffusion pumps, vacuum gauges, and mechanical fore pumps, are available from laboratory supply houses. 1.3.1. SAMPLE TUBES. Various types of sample tubes may be used with the adsorption apparatus. The surface area and density of the sample material dictate the size and shape of the 2Excellent precision-ground stopcocks may be purchased from Eck and Krebs Co., Long Island City, N. Y.; a universal stopcock adaptor, supplied by the Emil Greiner Co., N. Y., permits safe pressure and vacuum operation of stopcocks. 6

Institute of Science and Technology The University of Michigan 20 cm FIGURE 2. TYPICAL SAMPLE TUBES sample tube to be used. Four typical sample tubes, drawn to scale, are shown in Figure 2. In tubes (a) and (b), the sample is introduced through the open side arm into the bulb and the side arm sealed; after the tube is filled with finely divided materials and the side arm is sealed, a glass-wool plug is placed in the capillary shank. Tube (b) is similar to (a) except that it provides for evacuation on two sides of a sample plug. Tube (c) eliminates glass working by the operator. First it is filled with the sample; then a glass-wool plug is set in place, and the excess volume in the connecting tube is filled with a close-fitting rod. Tube (d), designed to surround the gas thermometer bulb, is used primarily for density determinations. It may also be used for surface-area estimations of low-area materials, in which nitrogen is used as the adsorbate. All tubes shown are provided with a connection to a 10/30 standard taper joint or joints adaptable to 10/30 and are constructed from Pyrex or Vycor glass. 1.3.2. BURETTES. The measuring burettes are similar to those described by Joyner (Ref - erence 17, page 261). Burette B has a total volume of 250 ml (10-, 15-, 25-, 50-, and 150-ml 7

Institute of Science and Technology The University of Michigan bulb volumes). Burette B' is optional; it has a total volume of 50 ml, and bulb volumes of 5, 5, 10, 10, and 20 ml, respectively. Distilling flasks provide a convenient source of bulbs suitable for the construction of burettes. Calibration lines are etched between bulbs and at the ends of each bulb train. Before the burette is mounted, the volume of each bulb is determined by weighing, at constant temperature, the volume of mercury between appropriate lines etched on the bulbs. Weighings to five significant figures are sufficient. The burettes are mounted securely before they are sealed into the system. A constant-temperature bath should be connected to the burettes if room temperature varies more than ~ 1~C during the operating period. 1.3.3. BURETTE -SYSTEM MONOMETER. The tungsten-through-glass electrical contacts of the burette monometer (C in Figure 1) are drawn in detail in Figure 3. The upper wire is 70 mm I FIGURE 3. DETAILS OF MERCURY SEAL AND ELECTRICAL CONTACTS FOR THE MANOMETERS bent at right angles, and the vertical portion is centered in the tube. This tungsten contact is made pointed by grinding or by chemical treatment while hot with sodium nitrite. The contacts, I, should be cleaned by electrolysis in dilute alkali solution before the manometer is permanently mounted. The manometer is mounted on a wooden support which has a flush-mounted, millimeter-scaled mirror. The position of the mirror is adjusted, by means of machined screws at the bottom of the mount (Figure 1), so that an appropriate scale division coincides with the up8

Institute of Science and Technology The University of Michigan per tungsten pointer. Provision is made for a small 1/25-watt neon indicator lamp (NE-51) in the vicinity of the upper tungsten contact. The 115-volt a-c electrical circuit consists of the neon lamp, a 200,000-ohm 1-watt resistor, and the electrodes connected in series. The lamp can be made to flicker by gently tapping the manometer when the Hg inside it is almost touching the upper tungsten contact. An "electric eye" vacuum-tube circuit (Reference 17, page 276) is often used as an alternative. An S-shaped capillary tube is placed at the top of the right arm of the manometer, as illustrated in Figure 3 (Reference 18). This device is used to set the vacuum leg of the manometers, and eliminates the necessity of constant pumping of the vacuum leg. To set the manometer, mercury is forced up the leg through the capillary S-tube and the stopcock. This stopcock is then closed, and the mercury is allowed to return to the manometer reservoir. Tapping the S-tube gently as the mercury begins to recede causes the mercury thread to separate in the S and form a seal. Conveniently, leaks through the stopcock can be detected as a change in the mercury levels in the S-tube. 1.3.4. PURIFICATION TRAIN. Gases used for all measurements should have at least 99.99% purity. This may be achieved by use of the simple gas-purification train illustrated in Figure 4. Gas enters at A and is directed to flow through either trap or both in series, as desired. (a) Top View A 1 0 cm Trap 1 Trap 2 (b) Side View FIGURE 4. GAS-PURIFICATION TRAIN In use, trap 1 is filled with 3/16-inch glass beads and trap 2 with adsorbent-grade coconut charcoal, 18 to 28 mesh. When the trap has cooled to liquid-nitrogen temperature, water and other condensable impurities are removed from the helium and nitrogen before they are stored in the reservoirs (F in Figure 1). The glass beads are used for nitrogen purification, and the 9

Institute of Science and Technology The University of Michigan charcoal for helium purification. Other purifying agents (Reference 17, page 272, and References 19 and 20) may replace or supplement those mentioned to eliminate specific impurities from the adsorbate. 1.3.5. MERCURY RESERVOIRS. The mercury reservoirs shown as D in Figure 1 are constructed from 500-ml round-bottom flasks. Tubes are fashioned at the side and bottom to facilitate changing the mercury. Each reservoir is supported by a plaster-of-Paris mold in a brass dish. A 1/2-inch o.d. brass rod is attached to the dish and clamped to the frame with standard clamp holders. When filled, the reservoirs are used to supply mercury to the burettes and manometer. This is done by applying air pressure or vacuum to the mercury surface in the reservoir through stopcocks 16-19. Before the mercury reservoirs are operated, they should be wrapped with masking tape or an electrical insulating tape, to prevent injury to the operator in case the reservoir breaks. 1.3.6. GAS RESERVOIRS. The four gas reservoirs, F in Figure 1, are constructed from 3-liter round-bottom flasks. One reservoir is used for helium and the other three for adsorbate gases, nitrogen, oxygen, etc. Before the reservoir is charged, it is connected through stopcocks 9 and 11 to manometer I, and evacuated through 5. Then, with stopcock 5 closed, gas enters through 12 from the purification train, 0. When a pressure of about 900 mm is obtained on manometer I, stopcock 9 is closed and the excess gas in the train is then pumped off. By keeping the pressure in the reservoirs above atmospheric pressure, contamination of the adsorbate gases with air is minimized. For safety, each reservoir should be wrapped with masking tape and spray-coated with a tough plastic film (Krylon). Krypton is supplied in 1-liter Pyrex flasks that can be sealed directly to the system between stopcocks 4 and 7. 1.3.7. THE DEWAR FLASK. A dewar flask convenient for use with liquid nitrogen is shown in Figure 5. Its capacity is approximately 1.5 liters. The neck of the flask is narrowed as shown to prevent rapid loss of the refrigerant. In the figure, A is 1/2-inch Transite, B is 1/6-inch aluminum, G is Pyrex glass, and H is a sealing wax (Apiezon-W). The dewar is wrapped with 1inch masking tape and sprayed with a plastic as a safety measure. In order to prevent the condensation of atmospheric oxygen in the dewar when using liquid nitrogen, and to maintain a relatively stable bath temperature, the mouth of the dewar is covered and pure dry nitrogen is bubbled through the liquid-nitrogen bath at a rate of about 25 bubbles per minute. This procedure also minimizes density inversions within the bath, which sometimes cause large and unexpected changes in the value of P0. 10

Institute of Science and Technology The University of Michigan 2 1/8 1 1/2 liter Capacity O-G 4 —-B A FIGURE 5. DEWAR FLASK FOR USE AS A LIQUID-NITROGEN BATH 1.3.8. CONSTANT-LEVEL DEVICE. A modificationof a device described by Feld and Klein (Reference 21) is used to maintain a constant level in the liquid-nitrogen bath. It is shown diagrammatically in Figure 6,where the letters have the following significance. A Liquid-nitrogen reservoir B Transfer tube with silvered and evacuated jacket C Level-sensing bulb, air-filled D Mercury manostat E Dewar with level of liquid nitrogen controlled As used here, the manometer shown replaces the somewhat more complex valve system used by Feld and Klein. With a 4-liter reservoir, this system can maintain the level in the liquidnitrogen bath within 5 mm for 36 hours. Thus a complete isotherm determination lasting two days, can be carried out with no danger that the sample will warm to above the bath temperature while unattended overnight. 1.3.9. THE HEATER. A heating unit suitable for degassing samples at elevated temperatures is constructed by winding Nichrome resistance wire around an Alundum tube and applying proper insulation. A scale drawing of the heater, showing the details and materials of construc11

Institute of Science and Technology The University of Michigan A FIGURE 6. DEVICE FOR CONTROLLING LIQUID LEVEL OF NITROGEN BATH tion, is shown in Figure 7, where A is 1/2-inch Transite, B is 1/16-inch aluminum, C is an appropriate insulating material, D is a 3/8-inch grooved Alundum tube, E is a porcelain electrical insulator, and F is the insulated leads of the resistance heater unit (B and S No. 22 Nichrome wire). A mercury-in-glass thermometer or a thermocouple, placed in the heater near the sample tube during an evacuation, is used to determine the bake-out temperature. 1.4. CALIBRATIONS AND BULB FACTORS Before any measurements are attempted with the apparatus, it must be proven to be vacuum tight. Upon completion of the glass working, the ground joints are sealed with a lubricant such as Apiezon N.3 All atmospheric exits are closed, and the apparatus is evacuated by the mechanical vacuum pump. A high-frequency vacuum tester is used to check the entire system for imperfections in the sealed glassware. If no "pinholes" are found, the system is pumped under high vacuum (diffusion pump) for several days to remove water and adsorbed gases. Flame 3Product of Metropolitan-Vickers Electrical Co., Ltd., available through James G. Biddle Co., Philadelphia 7, Pa. 12

Institute of Science and Technology The University of Michigan (a) Top View 7 1/2" A FF (b) Side View FIGURE 7. DETAILED DRAWING OF THE HEATING UNIT brushing of the connecting lines with an air-gas flame aids in this process. After the water is removed, all stopcocks are closed and the apparatus is allowed to equilibrate for 24 hours. Leaks caused by faulty greasing of ground joints are found by noticing changes in manometer C when the various units are connected. Faulty stopcocks can be quickly isolated and regreased. If pinholes or faulty ground joints are found, the above procedure is repeated after the necessary repairs. The mercury reservoirs are then filled with triple distilled mercury. The quantity of mercury added is approximately 1 1/2 times that needed to fill the piece of apparatus served by the reservoir. The section of capillary connecting stopcock 6 to burettes B and B' and to the top of the upper tungsten contact of manometer C is the zero bulb volume. Since it is a part of the working system, its volume must be calibrated. Gas calibration according to simple pressure-volume relationships is recommended. Stopcocks 3, 4, and 6 are closed. The mercury in each burette is set at the top etched line (zero bulb volume). Helium is introduced through stopcock 4 until the manometer registers a pressure of about 500 mm. No. 4 is closed and the manometer is zeroed at the upper tungsten contact by use of the fine adjustment and the indicator lamp. The pressure of an unknown quantity of gas of volume X is read and recorded as P1. The mercury is lowered to the second etched line (bulb volume 1B), the manometer is zeroed again, and the pressure P2 corresponding to a new volume is recorded. 13

Institute of Science and Technology The University of Michigan At constant temperature the following relationship is valid: P1X = P2(X + Y) or X = P2Y/(P1 - P2) (8) Y is the volume of the first bulb as determined by weighing with Hg. The zero bulb volume may be checked by determining the pressure at another bulb volume such as 2B. An alternative method of determining the zero bulb volume is discussed by Joyner (Reference 17). To facilitate computations of volumes of gases at standard conditions, a table of conversion factors for both burettes, such as Table I, is prepared for each bulb setting and for each combination of bulbs. A volume of gas measured under one set of conditions can easily be converted to its volume at standard conditions by use of Equation 9: PIV1 P2V2 T T or P1V1 T2 P1 V. = - F (9) 2 T1 P2 T 1 TABLE I. BULB FACTORS* Nitrogen Bulb Zero 1B' 2B' 3B' 4B' 5B' Zero 2.991 4.551 6.041 9.244 12.581 19.252 1B 6.594 8.154 9.644 12.847 16.184 22.252 2B 11.886 13.446 14.936 18.139 21.476 28.147 3B 20.853 22.413 23.903 27.106 30.443 37.114 4B 38.167 39.727 41.217 44.420 47.757 54.428 5B 90.075 91.635 93.125 96.328 99.665 106.336 Krypton McLeod system 58.71 Upper doser tube 0.2583 Lower doser tube 0.6372 *These sets of factors, applicable only to the apparatus used at the Mellon Institute Laboratory, are used in the illustrative examples which follow. 14

Institute of Science and Technology The University of Michigan where subscripts 2 and 1 denote standard and operating conditions respectively F is the bulb factor, defined as V ~T2 D25 F =V 2 25 (10) v 1 P DO V1 is the accumulative volume of the bulbs T2 is 273.160K P2 is 760 mm Hg Do is the density of mercury at 0~C D is the density of mercury at 250C, or more correctly, 25 the operating temperature of the bulbs A table of factors may then be constructed by substituting the appropriate values in Equation 10. Three tables of factors may be constructed that use density values of mercury at 200C, 250C, and 300C. In practice one uses the table most nearly corresponding to the operating bulb temperatures. The nitrogen adsorption system is now completely calibrated and ready for adsorption measurements. 1.5. DETERMINATION OF SURFACE AREAS FROM NITROGEN ADSORPTION Before the surface area can be determined from nitrogen adsorption isotherms, three preliminary operations must be performed. These include selecting the sample, outgassing the sample, and determining the dead space. 1.5.1. SELECTING THE SAMPLE. It is advantageous to know the approximate area of the material in question in order to determine the quantity of sample needed for a determination. If the surface area cannot be estimated, it is recommended that a 0.5-gram sample4 beused with an initial charge of 30 cc of nitrogen. For the burette system described, these quantities will be sufficient for a determination of areas between 10 and 500 m2/gram, or at least will serve in a trial run for estimating the adsorption capacity of the sample. With nitrogen as the adsorbate, equilibrium pressures in the range 40 to 280 mm Hg will be needed for a determination. Table II serves as a rough guide to the amount of sample to be taken. In a burette system having a total operating volume of about 300 cc, it is convenient to use a nitrogen volume of approximately 30 to 40 cc at standard conditions. The sample needed for a measurement of surface area using 4 Sampling techniques are available which provide means of obtaining representative samples (Reference 22). 15

Institute of Science and Technology The University of Michigan TABLE II. SIZE OF SAMPLE AND QUANTITY OF NITROGEN USED, BASED ON AN ESTIMATED SPECIFIC SURFACE Estimated Volume of N2 Specific Surface Sample Size at S.T.P. (m /gram) (grams) (cc) 1 3-4 30 10 2-3 30 100 0.5-1.0 30 500 0.2-0.3 30 700 0.1-0.2 30-40 1000 0.1 40-50 nitrogen increases rapidly as the specific surface decreases to below 1 m /gram. It is advisable, as will be explained later, to use other gases, such as krypton, methane, ethane, etc., as the adsorbate gas for areas much less than 1 m /gram. 1.5.2. REMOVAL OF ADSORBED WATER AND CONDENSABLE VAPORS. Before an adsorption isotherm can be taken, adsorbed vapors must be removed from the surface of the sample, usually by evacuation at high temperature. Typically, the sample is heated under continuous evacuation at 2000C for two hours. No specific conditions will cover all materials. If the material is unstable toward heat or the adsorbed vapors desorb slowly, the conditions of temperature and time must be altered to clear the surface without changing the area. With hydrated and temperature-sensitive, highly porous materials, special temperatures and evacuation periods must be used; otherwise the areas will be changed by decomposition of the hydrate or sintering of the porous material. 1.5.3. DETERMINATION OF THE DEAD SPACE WITH HELIUM. The volume of gas present in the free space of the sample tube at standard conditions, and not adsorbed by the sample at equilibrium, is used in calculating the volume of gas adsorbed. This volume must be measured at the adsorption temperature. Helium is used to determine this volume, because it is chemically inert and does not adsorb appreciably even at liquid-nitrogen temperature (Reference 23). The procedure for measuring the dead space is the same for most gases and adsorbents. With a sample attached to the apparatus and properly baked out and under vacuum, the sample tube is isolated from the burette system by closing stopcock 6. Approximately 30 cc of helium is admitted to the burette system (4B bulb, 230 mm Hg pressure) through stopcock 4. The volume of gas taken is determined by noting the pressure in the burettes at two different bulb volumes, such as 4B and 3B, and using Equation 9. An appropriate cold bath is then placed 16

Institute of Science and Technology The University of Michigan around the sample tube. Stopcock 6 is opened, and the helium is allowed to expand into the sample tube. When thermal equilibrium is established, the pressure is read and the volume of helium (S.T.P.) remaining in the burette system is calculated. The volume of helium present in the sample tube is the difference between the total helium and the quantity remaining in the burette system at the equilibrium pressure. The ratio of the volume of helium in the sample tube divided by Pc is a constant. P is the equilibrium pressure, corrected to 0~C by multiplying the C c observed pressure by the ratio of the density of mercury at 0~C to its density at TB. The constancy of this ratio, the dead-space factor Fs, can be checked by changing the volumes in the burettes and obtaining different equilibrium pressures. The magnitude of the dead-space factor is preferably of the order of 0. 001 to 0.01 cc/mm; it varies as the volume of the dead space surrounding the sample. Before proceeding with the area measurement, the helium gas must be removed from the adsorption system. 1.5.4. MEASUREMENT OF THE ISOTHERM. When the sample has been prepared for nitrogen adsorption, the dead-space factor determined, and the sample tube and burette system evacuated, stopcocks 6, 4, and 3 are closed; an appropriate volume of nitrogen (see Table II) is admitted to the burette system through stopcock 4, which is then closed. The mercury is adjusted in manometer C, and the pressure is read and recorded. The burette temperature is also recorded. A check determination of the volume is made by adjusting the mercury in the burette to a different level and recording the new pressure. The pressures and temperatures are used in Equation 9 to determine the initial charge of nitrogen at standard conditions. With the liquidnitrogen bath in place around the sample tube, stopcock 6 is slowly opened. The pressure will decrease as the nitrogen expands into the evacuated sample tube and adsorption begins. The mercury in the burettes is adjusted to produce a pressure near 100 mm Hg, and the system is allowed to equilibrate. When equilibrium is reached, no further decrease in the pressure is observed; the pressure, P, the burette bulb used, the burette temperature, TB, and the vapor pressure of nitrogen,P0 (I in Figure 1), at the liquid-nitrogen bath temperature are recorded. In operation, the gas thermometer system (H, I, and L in Figure 1) is filled with the particular adsorbate being used, if the condensed adsorbate has a vapor pressure greater than 10 mm Hg at the operating bath temperature. (An alternative method of determining PO, described in Section 1.1.6, may be used if the vapor pressure of the condensed adsorbate is below 10 mm Hg.) To fill the gas thermometer system with nitrogen, a few milliliters of mercury are first run into H through stopcock 13. The gas thermometer system is then evacuated through stopcocks 10 and 11. When evacuation is complete, stopcock 10 is closed. Nitrogen is admitted from reservoir F 17

Institute of Science and Technology The University of Michigan through stopcock 11 until a pressure difference of 500 mm Hg is reached in manometer I; then stopcock 11 is closed and the excess nitrogen pumped off through stopcock 5. The vacuum leg of manometer I is set by a procedure similar to that for setting manometer C. To determine P0 for nitrogen, a liquid-nitrogen bath is placed around the thermometer bulb L, and H is filled with mercury until nitrogen begins to condense in bulb L. Condensation takes place between 750 and 850 mm Hg, according to the temperature of the liquid-nitrogen bath. P0 is then determined as the difference in the heights of the mercury in manometer I. The volume in the burettes is then reduced by changing the mercury level so that a bulb combination occurs which causes the pressure in the system to increase by about 30 to 40 mm Hg. When equilibrium is again established, another set of data, i.e., pressures, burette volume, and burette temperature, is recorded. The above procedure is repeated until three sets of data in the desired range (P/P0 = 0.05 to 0.35) are obtained. If a complete isotherm is desired, data must be taken at intervals until the value of P/P0 is approximately 1.0. A plot in which the volume adsorbed per gram is taken as ordinate and the relative pressure (P/P0) is taken as abscissa shows characteristics which are specific for certain materials. Characteristic isotherms are given by Reis (Reference 24). Also, from such a plot the specific surface may be determined by the point B method described by Emmett et. al. (Reference 25). By this technique the quantity Vm may be directly determined by extrapolating the linear portions of the isotherm to zero relative pressure. However, this method is not applicable for all adsorbent-sorbate combinations and consequently is employed only when the B.E.T. plot over the specific range of relative pressures is nonlinear. 1.5.5. TABULATION OF DATA AND CALCULATIONS. The following is an example of the recorded data and the calculations used in determining the quantity of gas adsorbed in a monolayer, Vm. Tables III and IV are offered as convenient guides for recording data and calculations for the determination of Vm of a typical adsorbent. Table IV represents, line for line, values calculated from the data of Table III. The columns in Table III are arranged as follows: B Gas employed C Position of stopcock 6 D Burette bulb in use E Equilibrium pressure F Equilibrium pressure corrected to 0 C G Temperature of the burette system H Pressure reading of the nitrogen (gas) thermometer 18

Institute of Science and Technology The University of Michigan TABLE III. DATA FOR NITROGEN ADSORPTION* A B C D E F G H Stopcock Burette Observed Corrected Temperature Nitrogen Vapor Line Gas 6 Bulb Pressure, P Pressure, Pc TB Pressure, P0 (mm Hg) (mm Hg) (o C) (mm Hg) (Dead-Space Determination) 1 He closed 4B 171.3 22.2 2 He closed 3B 313.8 22.2 3 He open 3B 251.8 250.6 22.4 4 He open 4B 151.0 150.3 22.4 (Adsorption Measurement) 5 N2 closed 4B 225.1 22.6 6 N2 closed 5B 95.2 22.6 7 N2 open 4B+5B' 107.9 107.4 22.8 846.0 8 N2 open 4B 144.0 143.3 22.8 848.3 9 N2 open 3B+3B' 187.2 186.3 22.8 843.3 *Sample weight = 0.5976 grams. TABLE IV. WORK SHEET FOR CALCULATING B.E.T. VARIABLES A B C D E F G H J Line Vt Vb Vs Va P/P0 1-P/P0 Va(l - p/p0 P/Va(P - P) 1 22.14 2 22.15 F = Column D 0.0176 cc/mm s P 3 22.15 17.77 4.38c 4 22.15 19.50 2.65 5 29.05 6 28.99 7 29.02 19.84 1.90 7.28 0.1275 0.8725 6.35 0.02008 8 29.02 18.57 2.55 7.90 0.1698 0.8302 6.56 0.02588 9 29.02 17.15 3.32 8.55 0.2220 0.7780 6.65 0.03338 19

Institute of Science and Technology The University of Michigan In Table IV, Columns B and C represent Vt, the total volume of gas taken, and Vb, the volume of gas remaining in the burettes at the equilibrium pressure. These volumes are calculated from Equation 9. Column D records Vs, the volume of gas present in the sample tube and not adsorbed. Vs is calculated from Equation 11. Vs = (Pc) (Fs) ( 3) (11) P is the equilibrium pressure corrected to 0 C, F is the free-space factor, and P is a correcc s tion for the nonideality of nitrogen (Reference 26) (Figure 8). Column E records Va, the volume of gas adsorbed. It is obtained by subtracting the values in Columns C and D from those in Column B, i.e., Va= Vt - Vb - Vs (12) Column F records P/Po, the relative pressure, and is obtained by dividing the value in Column E of Table III by that in Column H. Columns G, H, and J then follow directly. If P/P0 is plotted against V (p - P) (Figure 9), a straight line which has an intercept I Va(O and a slope S is obtained. From the values of the slope and intercept, V is calculated from m Equation 4. The area is then computed from Equation 5. For the example given in Table III, Table IV, and Figure 9, V is found to have a value of 7.02 cc. If this value is substituted into Equation 5, a value for the specific surface of 51.5 m /g is obtained. 1.07 1.06r- 1.05 1.04 F 1.03 c 1.02 8 1.01 1.00, I, 0 500 1000 PRESSURE (mm Hg) FIGURE 8. THE CORRECTION FACTOR, /, FOR THE NONIDEALITY OF NITROGEN AT LIQUID-NITROGEN TEMPERATURES 20

Institute of Science and Technology The University of Michigan 0.030 - 0.020 - 0.010 Intercept = 0.0021 Slope = 0.1403 Nitrogen Adsorption C I I 0 0.10 0.20 P P0 FIGURE 9. PLOT OF B.E.T. VARIABLES FOR DATA IN TABLE IV 1.6. DETERMINATION OF SURFACE AREAS FROM KRYPTON ADSORPTION The use of nitrogen as the adsorbate in determining specific surface area is practical when the samples have specific surface areas in the range of 1 to 2000 m /g. But if the specific area of the material is less than 1 m2/g, considerable error results. The reason is that the volume of gas adsorbed, Va, is small in comparison to the volume of gas in the sample tube at the relative pressures needed in the calculations. It is impossible to reduce the free space in the sample tube beyond some minimum value. It remains then to reduce the quantity of gas not adsorbed by the sample so that Va is relatively large compared to the amount of gas remaining in the sample tube and not adsorbed at the desired relative pressure. The first set of equilibrium data is usually taken at a relative pressure of 0.1. In order to reduce the quantity of gas not adsorbed, the pressure P must be reduced; but then the ratio of P/P0 = 0.1 decreases unless the value of P0 diminishes accordingly. Vapors such as water, propyl alcohol, heptane (Reference 27), ethane, ethylene (Reference 28), and others (Reference 29) have been suggested as possible adsorbates in the low-area region, and have been used. However, their use involves various techniques not readily available 21

Institute of Science and Technology The University of Michigan to many laboratories. Krypton, suggested by Beebe et al. (References 30and 31) as a satisfactory adsorbate, has been found suitable for specific surface measurements because the correction for unadsorbed gas is kept low by the low saturation pressure of liquid krypton at liquidnitrogen temperatures. The technique of making pressure measurements, though more refined than that used for nitrogen, need not be so refined as the techniques applied by Wooten and Brown (Reference 28). Modification of the nitrogen apparatus to use krypton is slight, and the gas is convenient to handle at room temperature. Also, measurements can be made with relatively small quantities of material. The technique is especially adapted to measure materials of low specific surface; it may also be applied to small research quantities (20 mg or less) of fairly high-area materials. Therefore, a single volumetric adsorption apparatus may be designed to operate effectively over the region from very-low to very-high areas (200 cm2/g to 2000 m /g). 1.6.1. MODIFICATION OF THE APPARATUS FOR KRYPTON ADSORPTION. In order to use krypton as well as nitrogen for adsorption measurements, a McLeod gauge, K in Figure 1, and a doser, G, must be included in the apparatus. The McLeod gauge,6 designed to operate in the desired pressure range (0.1 to 1.5 mm Hg), is calibrated by standard procedures (Reference 32) before it is mounted in the system. The doser is constructed and used in conjunction with manometer C for measuring quantities of krypton added. The doser consists of two 3-way oblique-bore stopcocks connected by a 10-mm o.d. tube and a 2-mm capillary of such length as to produce volumes between stopcocks of approximately 1.8 and 0.6 cc respectively. The volumes of the two tubes are accurately determined by weighing the mercury in the tubes at constant temperature. The precedure is similar to that used in calibrating the nitrogen-system burettes. Doser factors for the two tubes are then calculated from Equation 10. A final check of the vacuum "tightness" of the glassware should be made before measurements are attempted (Section 1.4). One other volume must be known before the apparatus is ready for use. This is the volume of the McLeod gauge, the lines to stopcock 6a, and the line through stopcock 7a to stopcock 7. This volume is measured by applying the simple P, V relationship described above (Equation 8). First the nitrogen and krypton systems are evacuated by use of the diffusion pump. Stopcocks 3, 4, 4a, 6a, and 7a are then closed. Helium is introduced into burette B (4B level) through stopcock 4 until manometer C registers a pressure of about 500 mm Hg. Stopcock 7 is then closed. At this point the doser contains a quantity of helium at a known pressure and volume. Stopcock-7a is then opened, and the gas is permitted to expand into the McLeod gauge. The 6An excellent McLeod gauge is produced by the Todd Scientific Co., Cedars, Pa. 22

Institute of Science and Technology The University of Michigan pressure of the new volume is then determined with the McLeod gauge, and the volume of the McLeod system is calculated. This procedure may be repeated and an average value computed from which a "bulb" factor is calculated. All parts of the krypton system are now calibrated, and the system is ready to operate. 1.6.2. SELECTION OF THE SAMPLE SIZE. The choice of sample size is more difficult withkrypton adsorption than with nitrogen adsorption because of the rather small quantities of gas adsorbed and the small value of P0. For materials having an estimated specific surface of less than 1 m2/g, samples of approximately 3 to 5 grams should be used with initial doses of krypton of approximately 0.03 cc S.T.P. in a system having a total operating volume of about 175 cc. 1.6.3. REMOVAL OF ADSORBED VAPORS AND THE DEAD-SPACE FACTOR. The conditions governing bake-out, described in Section 1.5.2, apply to materials suitable for krypton adsorption. The dead-space factor is determined in the same way as for nitrogen areas (Section 1.5.3). In fact, the procedure for using krypton to determine area is identical with the nitrogen procedure up to the point of actual adsorption. 1.6.4. MEASUREMENT OF THE ISOTHERM. Assume that a reasonable amount of sample has been chosen and degassed, the dead-space factor is known, and the system is under high vacuum. Since the adsorption capacity of the sample in question is unknown, several additions of krypton may be needed before equilibrium pressures in the desired range are attained. Before each addition, thekrypton already in the doser must be known. At very low pressures (0.05 mm or less) this correction need not be made. At the beginning of a measurement, stopcocks 7a, 6a, 4a, and 3 are closed. The mercury in burette B is adjusted to the 3B level. Krypton is admitted to the doser and burette system through 4a until a pressure reading of about 50 mm has been established on manometer C. The doser now contains a quantity of gas of known volume at pressure P, as read on the manometer C. Next stopcock 7 is closed, stopcock 7a is opened, and the gas is expanded into the McLeod gauge unit. A pressure reading is recorded, and the quantity of gas that was taken is easily verified by using Equation 9. With the liquid-nitrogen bath in place around the sample tube, stopcock 6a is opened to the McLeod gauge and adsorption begins. Assume further that the correct amount of krypton has been added and that an equilibrium pressure of about 0.2 mm is established. The reading on McLeod gauge is recorded. The tem23

Institute of Science and Technology The University of Michigan perature of the doser and McLeod gauge (TB) and the vapor pressure (P0) of the nitrogen in the nitrogen thermometer are recorded. The McLeod gauge is set at its cut-off point, stopcock 7a is closed, and stopcock 7 is opened. The mercury in the burettes is lowered so that manometer C registers a pressure of 10 to 20 mm. This pressure is recorded, along with the temperature of the doser. Stopcock 7 is closed, 7a is opened, and the krypton is allowed to reach a new adsorption equilibrium pressure. When equilibrium is again established, the pressure P, the temperature TB, and the pressure P0 of the nitrogen thermometer are again recorded. This procedure is repeated until the desired number of sets of data have been obtained. Data for a typical determination are tabulated in Table V. Only the free-space-factor data are given, since the calculations for the free-space factor are similar to those already described. 1.6.5. THE CALCULATIONS. Basically the calculations for determining areas by krypton adsorption are similar to the calculations for nitrogen. They do, however, differ in several respects. First, the total volume of krypton, Vt, at any equilibrium pressure is the sum of all the krypton additions made previously. The volume adsorbed, Va, is obtained by subtracting the TABLE V. DATA FOR KRYPTON ADSORPTION* A B C D E F G H J K L Burette Stopcocks or Manometer C McLeod P TB N2 P Line Gas McLeod 6 7a 7 Pressure P - ___ —-- _ - (mm Hg) (mm Hg) (mm Hg) (oC) (mm Hg) 1 He 3B closed 184.5 23.3 2 He 2B closed 324.3 23.3 3 He 2B open 240.8 239.7 23.4 4 He 3B open 154.0 153.3 23.4 5 Kr cut-off closed closed open 27.9 23.3 6 Kr closed open closed 0.300 23.3 7 Kr open open closed 0.170 0.169 24.2 809.5 8 Kr cut-off open closed open 16.3 24.2 9 Kr open open closed 0.300 0.299 24.3 809.5 10 Kr cut-off open closed open 16.1 24.3 11 Kr open open closed 0.435 0.433 24.4 809.5 *Sample weight = 2.5145 grams. 24

Institute of Science and Technology The University of Michigan volume of gas in the McLeod system, Vmc, and the volume of gas Vs in the free space surrounding the sample and not adsorbed, Vs, from the total volume of krypton present. Va=Vt- Vmc- Vs (13) a t mc s Vt and Vmc are calculated from Equation 9, and Vs is calculated from Vs = (Pc) (F ) (14) The correction for the deviation of krypton from ideality is omitted, since small quantities and low pressures are being employed. Second, the value of P0 for krypton is obtained indirectly. Figure 10 shows an extrapolated plot of log P of liquid Kr versus 1/T (References 33 and 34), superimposed on a plot of log P -,100_ 0 0 H:10 Liquid Kr -104 o ga1.0 10 3 _C ~ = F \XSlid Kr \ O 0! 0.1, 102 10 11 12 13 14 15 1/T x 103 FIGURE 10. VAPOR PRESSURE OF LIQUID NITROGEN, LIQUID KRYPTON, AND SOLID KRYPTON AS A FUNCTION OF TEMPERATURE of nitrogen versus 1/T (Reference 35) over the temperature range 70~K to 850K. To determine the P0 for liquid krypton, the value of 1/T for P0 nitrogen is determined, and a vertical is then drawn to intersect the log P versus 1/T curve for liquid krypton. The intersection represents the P0 of liquid krypton at the operating temperatures. If the krypton apparatus alone has been constructed, the value for P0 can be determined by noting the vapor pressure of solid krypton. This is done at the end of the surface area measure25

Institute of Science and Technology The University of Michigan ment by admitting an excess of krypton gas to the sample and measuring the equilibrium vapor pressure of the solid with the McLeod gauge. From this, the value of the vapor pressure of the supercooled liquid is graphically obtained from Figure 10. Some error is introduced by this technique, since changes in P0 due to bath temperature changes during a determination must be absorbed in the final measured P0 of the solid. However, the error is small. The lines in Column A of Table V are listed as in Column A of Table VI. The other columns in Table V are as follows. B Gas C Burette bulb, or position of McLeod gauge D, E, F Positions of stopcocks G Pressure reading at manometer C when krypton is being added to doser H Pressure at adsorption equilibrium J Correct pressure K Temperature of bulbs L Pressure reading at manometer I Here again the lines (Column A) of the data of Table V correspond to the lines (Column A) of the calculations in Table VI. The gas being used is represented in Column B of Table V, the burette bulb being used, or the position of the McLeod gauge, in Column C; the positions of the primary stopcocks are represented in Columns D, E, and F, the pressure of manometer C when making krypton additions to doser, G, in Column G, the pressure at adsorption equilibrium in Column H, and the corrected pressure in Column J. In Column K the temperature of the bulbs is recorded and the pressure reading of manometer I in Column L. TABLE VI. WORK SHEET FOR CALCULATING B.E.T. VARIABLES FROM DATA IN TABLE V A B C D E F G H J K L Gas in Krypton Line Doser Vt Vmc vs a P1 - P/P0 1-P/P0 Va(-P/PP/ 0 P) (cc) (cc) (cc) (cc) (cc) (mm Hg) Free space factor calculated as before = 0.0140 cc/mm. 5 0.0600 0.0600 7 0.0004 0.0600 0.0336 0.0024 0.0240 2.79 0.0609 0.9391 0.0226 2.70 8 0.0349 0.0945 9 0.0006 0.0945 0.0592 0.0042 0.0311 2.79 0.1075 0.8925 0.0278 3.87 10 0.0345 0.1284 11 0.1284 0.0858 0.0061 0.0365 2.79 0.1559 0.8441 0.0308 5.06 26

Institute of Science and Technology The University of Michigan Column B of Table VI represents various quantities of krypton in the doser under different conditions. Since the adsorption apparatus is evacuated at the beginning of a determination, no correction for the gas remaining in the doser is needed before the first addition of krypton. However, correction is needed for successive additions. Line 5 (Table V and Table VI) represents the data and calculations for the first addition. However, the second addition, as represented in lines 7 and 8 of both tables, needs correction. Line 7, Column B, of Table VI gives the volume of krypton in the doser under the conditions of line 7, Table V, i.e., at the first equilibrium pressure; and line 8, Column B of Table VI gives the volume of krypton in the doser under the conditions of line 8 of Table V, i.e., after the second addition of krypton. The actual volume of krypton added to the krypton system, then, is line 8, Column B of Table VI, minus line 7, Column B of Table VI. Adding this volume to that given in line 5, Column C of Table VI, gives the true total volume of krypton present in the system at the end of the second addition. This procedure is repeated for other additions. Columns D, E, and F are as before; Column G has already been described; Column H is calculated by dividing Column H of Table V by Column G of Table VI. Here again, the values in Column L of Table VI versus those in Column H of Table VI can be plotted linearly. From the slope and intercept of the plot, V can be calculated. The area is computed from Equation 5. The B.E.T. variables, as determined from the data and calculations of Tables V and VI, are plotted in Figure 11. Vm, calculated from Equation 4, is 0.0385 cc; the area computed from this figure is 807 cm /gram. 6.04.0 2.0 Intercept (I) = 1.19 Slope (S) = 24.81 Krypton Adsorption 0 0.04 0.08 0.12 0.16 0.20 P P0 FIGURE 11. PLOT OF B.E.T. VARIABLES FOR DATA IN TABLE VI 27

Institute of Science and Technology The University of Michigan 1.6.6. ALTERNATIVE METHOD. An alternative method of determining the data has been described by Beebe et al. (Reference 30) and by Bloecher (Reference 31). This technique uses the fact that the McLeod gauge can serve as a burette. Consequently, various known quantities of krypton can be removed in order to determine V. This is a desorption process. 1.7. MEASUREMENT OF PORE VOLUME DISTRIBUTION The quantity of gas adsorbed by a finely divided solid is essentially the sum of the gas held on the geometric surface of the particle and the gas as condensate within the pores of the sorbent. (With many solid adsorbents this latter contribution to adsorption is very large.) For many purposes, the change in surface area is used to determine the effect of various treatments on the structure of solid adsorbents. However, a more informative result can be obtained by noting a change in the pore volume distribution of a porous solid. The measurement of pore volume distribution from nitrogen isotherms has been described by Barrett et al. (Reference 14). Barrett's method is useful with materials having pore radii within the range 5 A to 300 A. Above 300 A the mercury porosimeter technique described by Ritter and Drake (Reference 36) is applicable. These two techniques have been found to augment each other (Reference 37). The calculation of pore volume distribution requires data from a nitrogen isotherm, which can be collected by use of the gas adsorption apparatus. The technique is not basically different from that used to determine Vm from nitrogen adsorption isotherms. An example of the calculations is given by Barrett; however, the data taken and their general use will be briefly explained here. Three points on the nitrogen isotherm were used to determine Vm; as many as twenty or thirty points will be needed to construct the complete isotherm necessary for computing pore volume distribution. Table III may be used to record the data, and Table IV, excluding Columns F, G, H, and J, may be used as a work sheet. The adsorption branch and the desorption branch of a nitrogen isotherm are constructed by determining the volume of nitrogen adsorbed per gram of adsorbent (Va/gram) at various relative pressures from 0.05 to near 1.0 and then from 1.0 to 0.05. A typical isotherm is shown in Figure 12. From the Kelvin equation (Equation 7), a master work sheet may be set up giving calculated values of the relative pressure for given values of pore radius. From the desorption branch of the isotherm in Figure 12, one can tabulate the volume of nitrogen adsorbed per gram at the calculated relative pressures corresponding to a particular pore radius. These volumes of gas are then converted to liquid volumes. Some idea of the probable pore volume distribution can be obtained by constructing a plot of the difference 28

Institute of Science and Technology The University of Michigan 100 E 90 0: 80;E D70' 60 3 AdDesorption 0 40 cf) 30 Adsorption 20 FOR USE IN CALCULATING PORE VOLUME DISTRIBUTION between the liquid volumes, AV1, divided by the pore radius increment chosen, Ar, versus the average pore radius of the increment, r. Barrett incorporated a correction for a change in pore volume over a given increment in pore radius. This correction, discussed in detail in Reference 14, provides a method whereby AV1 is modified to take into account the differences in pore radius caused by physically adsorbed gas and pore condensate. Upon completion of the correction for the liquid volume in the pores, several informative plots may be constructed. From the data thus calculated a plot of pore radius, r, versus the total pore volume in pores of radius equal to or larger than r can be made. An example is shown in Figure 13. From the smoothed curve, approximate pore volume maxima can be found by noting the portions of the curve where the slope is changing most rapidly. Plotting the derivative of the curve in Figure 13 versus the average pore radius gives a distribution curve describing the relative contributions of the various pore sizes to the total pore volume. The derivative is obtained by dividing the value of EVp at F (from Figure 13) by the particular pore radius increment that determined i, i.e., (,V /Ar), and plotting this against F. Such a plot, illustrated in Figure 14, shows changes in the pore radius which account for large changes in pore volume. 29

Institute of Science and Technology The University of Michigan 0E0i 0.05 - OE~ I I I 1 0 100 200 300 PORE RADIUS r(A) FIGURE 13. VOLUME OF PORES OF RADIUS EQUAL TO OR LARGER THAN r, PLOTTED WITH RESPECT TO PORE RADIUS 20 15 i0 0 5 0 100 180 PORE RADIUS (Ai) FIGURE 14. PLOT OF THE PORE VOLUME DISTRIBUTION AS A FUNCTION OF THE PORE RADIUS 30

Institute of Science and Technology The University of Michigan 1.8. DETERMINATION OF THE DENSITY OF SOLID MATERIALS BY HELIUM DISPLACEMENT The helium displacement technique may be used to determine the densities of finely divided solids. These are true densities if vapor pockets are assumed absent. Helium has several properties which make it ideal for density measurements: it is chemically inert; it does not adsorb on most materials at room temperature; it can penetrate into pores not accessible to other displacing fluids such as toluene or benzene; and it is virtually ideal in its behavior as a gas. 1.8.1. CHOICE OF SAMPLE SIZE AND SAMPLE TUBE. A sample tube large enough to accomodate 50 cc of the sample is recommended. When smaller volumes are used there is risk of losing significant figures in the calculations. Sample tube D, shown in Figure 2, has been found convenient for the measurement. The standard joint must be modified slightly for materials of fairly large particle size; a standard taper adaptor is then used. 1.8.2. SAMPLE TUBE CALIBRATION. The density system consists of the sample tube, the line to each of the burettes at the desired bulb volume, and the line to the zero marker of the manometer. First the volume of the empty sample tube is determined; four or five separate determinations are enough. The average value obtained, when used in the calculations, reduces the errors caused by different methods of seating the standard taper joints. The system is first evacuated with a diffusion pump. After degassing, the sample tube is immersed in a 600-ml beaker of water at room tempetature, or a constant-temperature bath. Stopcock 6 is closed. Helium is introduced into the burette system through stopcock 4 until there is a pressure difference of about 150 mm Hg at 4B bulb level. The pressure P1 and temperature are recorded. Stopcock 6 is then opened and a few minutes are allowed for equilibrium to be established. The manometer is again adjusted to the zero marker, and the new pressure, P2) is recorded. The volume of the sample tube is determined from Equation 15, which is similar to Equation 8. PlV1 = P2V2 = P2(V1 + Vc) or Vc =V1(P1 - PP2) (15) Where subscripts 1 and 2 denote stopcock 6 closed and open, respectively; V1 is the total calibrated volume of the burette system up to stopcock 6; and Vc is the calibrated volume of the empty sample tube. This procedure may be repeated and the average value taken as the correct calibrated volume. 31

Institute of Science and Technology The University of Michigan 1.8. 3. PREPARATION OF SAMPLE. A sample is introduced into the sample tube, thetube is seated into the 10/30 standard taper joint, and the sample is degassed, with the precautions previously mentioned. (A separate high-vacuum degassing unit with suitable traps should be provided if organic materials are present that are volatile at 200 C.) Then the oven is removed, and the sample and tube are cooled and immersed in a liquid at constant temperature. 1.8.4. DENSITY DETERMINATION. The procedure is similar to that used in the calibration. Stopcock 6 is closed and helium is introduced into the burette system through stopcock 4 until a pressure of 200 mm Hg is reached at 4B bulb level. The system is equilibrated thermally and the pressure, P1, recorded. Stopcock 6 is then opened, the system is again permitted to attain equilibrium, and the new pressure is recorded. A development of the density relationship follows. Constant temperature is again assumed. It follows from Equation 15 that when stopcock 6 is closed, then opened, P1V1 = P3V3 = P3 [V1 + (Vc -Vsd)] (16) where P1, V1, and V are as before; Vsd is the volume of the solid present in the sample tube; and P3 is the pressure with stopcock 6 open and a sample present. Solving for Vsd, P 3Vsd = P3V1 + P3V - PV1 Vsd= V1 + Vc V(P1/P3) Vsd K - k(P1/P3) (17) where K = V1 + V and k = V1. K and k are constants only when pressures measured at the same bulb volume are compared. The density is calculated by dividing the weight of sample taken by Vsd' i.e., D = Sample Wt/Vsd (18) Several checks of Vsd can be made by taking the pressure reading of various bulb volumes before and after stopcogk 6 has been opened. By correlating these pressures according to bulb number, several checks can be made with one sample of helium. 1.8.5. CALCULATIONS. Tables VII and VIII represent data and calculations for a typical density determination. The columns in Table VII are arranged as follows. B Position of the mercury in the burettes C Position of stopcock 6 32

Institute of Science and Technology The University of Michigan TABLE VII. DATA FOR DENSITY DETERMINATIONS OF SOLIDS* A B C D E F G Line Bulb Stopcock Sample __ __ 6 obs Temperature 1(k) K (mm Hg) ( C) (cc) (cc) (Calibration) 1 4B closed 178.5 25.0 106.57 2 3B closed 327.3 25.0 58.17 3 2B closed 575.8 25.0 33.09 4 2B open 225.8 25.1 5 3B open 173.5 25.1 6 4B open 120.3 25.1 (density) 7 4B closed 241.3 23.0 106.57 158.13 8 3B closed 442.5 23.0 58.17 109.73 9 2B closed 778.5 23.0 33.09 84.65 10 2B open 390.1 23.0 11 3B open 282.5 23.0 12 4B open 184.3 23.0 * Sample weight = 77.052 grams. TABLE VIII. WORK SHEET FOR DENSITY DETERMINATIONS OF SOLIDS ( Calibration-Equation 15) lines 1 and 6 V = 106.57(178.5 - 120.3) 51.56 cc c 120.3 lines 2 and 5 58.17(327.3 - 173.5) 51.57 cc c 173.7 lines 3 and 4 V = 33.09(575.8 - 225.1) 51.55 cc c 225.1 Average value of V is 51.56 cc. (Density- Equation 18) lines 7 and 12 D = 158.13 - 10657(2413/1843) = 4.143 g/cc 77.052 lines 8 and 11 D 77.052 109.73 - 58.17(442.5/282.5) = 4.140 g/cc 77.052 lines 9 and 10 D = 77.052 84.65 - 33.09(778.5/390.1) = 4.138 g/cc Average value of D is 4.140 g/cc. 33

Institute of Science and Technology The University of Michigan D Observed equilibrium pressure E Sample temperature F Accumulative bulb volume corresponding specifically to the burette bulb being used G Accumulative bulb volume plus the volume of the calibrated empty sample tube corresponding to the particular burette bulb in use Table VII shows the calculations for an empty-tube calibration and a density determination. It is estimated that the density values are reproducible to within ~2 units in the second decimal place. 2 GRAVIMETRIC APPARATUS FOR THE MEASUREMENT OF THE SORPTION OF GASES IN AND ON SOLIDS 2.1. INTRODUCTION Although the adsorption apparatus described in Section 1 is versatile, it cannot be applied to all types of adsorption experiments. To supplement the measurements of a volumetric adsorption system, it is advantageous to have access to a gravimetric adsorption system. A particularly important advantage of a gravimetric apparatus is that one can make continuous measurements of extremely small changes in a chemical system. But as happens with all refinements, the increased sensitivity of the measurement is accompanied by many problems not encountered in the volumetric system. The use of some balances at times becomes very tedious and the time required for perfecting the operation of the balance for different techniques can be relatively long. Several types of "balances" are used in gravimetric work. The quartz-spring type used by some authors (Reference 38) depends on the fact that the elongation of a quartz helix is proportional to the mass acting on the spring. Thus the quantity of gas adsorbed, for example, can be weighed. Automation of this type of balance is discussed by Klevens et al. (Reference 39). The torsion balance, which was used by Donau (References 40 and 41) among others, is a beam balance with fixed supports. Here the mass rotates the beam over a stationary quartz rod; the deflection of a reference needle is a measure of the mass change. Another design is the cantilever balance (Reference 42). This design operates on the principle that a horizontally fixed, fused silica rod will bend along its length in proportion to a force applied some distance along the rod.6 6Variations of the above-mentioned balances may be purchased from the Microchemical Specialties Co. of Berkeley, California. 34

Institute of Science and Technology The University of Michigan A fourth type of balance, which will be discussed here, is the quartz beam microbalance. It is the balance discussed by Czanderna and Honig (References 43, 44, and 45) and has been used by the author (Reference 46). This balance has several advantages, which will be summarized later. The design was automated by Cochran (Reference 47); refinements of his automation scheme have also been described (Reference 48). Rhodin (Reference 49) gives an excellent general discussion of balances, and Gulbransen (Reference 50) discusses their application. 2.2. CONSTRUCTION OF THE BALANCE SYSTEM 2.2.1. THE MICROBALANCE. The balance illustrated in Figure 15 consists of a symmetrical beam (A), constructed from fused silica rod one millimeter in diameter; a carriage (B) designed to support the beam is constructed from fused silica rod two millimeters in diameter. Fused silica was chosen because of its strength, chemical inertness, and small temperature coefficient of expansion. A scale drawing of the balance is shown in Figure 16. The balance beam is supported on two pivot points made of tungsten wire 0.005 inch in diameter. Before being installed on the beam, the wires are electropolished to a point by being dipped into and out of a 20% sodium hydroxide solution while passing an alternating current of 6 to 10 volts (higher voltages cause imperfect polishing). Special care should be taken to avoid annealing the hard-drawn wires, for annealed tungsten points become blunted after several months of operation and must be replaced. Once properly prepared, the wires are cemented to the beam with fused silver chloride. A variation of this method may also be used to prepare the tips. Unpolished tungsten wires are cemented in place on the beam, and then the beam is placed in a horizontal position with the wires dipping into the basic solution. As the tips become polished they are reduced to the same length. In the first method the tips are dipped into and out of the solution by a rotating cam device; in the second the beam may be rocked by hand. Whichever method is used, the tips are inspected through a low-power microscope and those found imperfect or split are discarded or repolished. FIGURE 15. THE QUARTZ BEAM MICROBALANCE 35

Institute of Science and Technology The University of Michigan (a) Top View Of Beam (b) Side View Of Beam (c) Side View Of Frame 10 mm l l (d) Top View Of Frame FIGURE 16. SCALE DRAWING OF THE MICROBALANCE The pivot support wires of the beam rest in cups resembling parabolic cones and located in the ends of vertical silica rods attached to the carriage. The cups are prepared by the use of a simple glassblowing technique that has been described by Johnson and Nash (Reference 51). One indicator hook (C) is attached to the beam and one to the carriage. These hooks are located in the same vertical plane and are observed by means of a Gaertner 38X cathetometer telescope when the balance is in use. They are fashioned from quartz fiber. The null system was recently modified (Reference 52) to use two horizontally opposed tungsten wires (3-mil) instead of quartz hooks. The wires are pointed, and aligned so that they almost touch. The use of tungsten wires minimizes interfering light reflections; if the points are properly aligned at null position, the necessity of an expensive traveling microscope is eliminated. Y branches (D) are located in a horizontal plane at the ends of the beam. Across the branches of each Y, a tungsten wire two mils in diameter is cemented with fused silver chloride. A slight depression is made in the center of each wire. These cross members can also be formed from fused quartz (Reference 48). 36

Institute of Science and Technology The University of Michigan 2.2.2. THE SUPPORT FIBERS. Thin fibers are used to suspend objects from the balance beam at the Y branches mentioned above. They are drawn from fused silica rods, and hooks are fashioned at their ends. It is important that they be as thin and uniform as possible (Reference 53). If they are not uniform in diameter, they will bend when they cool. They can be straightened by suspending a platinum weight from the lower hook on the fiber and carefully annealing the entire length of the fiber with the flame of a microtorch. 2.2.3. THE SAMPLE CONTAINER. Spherical sample bulbs, approximately 10 mm in diameter, are constructed from fused silica (or Pyrex). A hook is fashioned from the surface of the bulb, and the strain is relieved in the manner described in the preceding paragraph. A tiny hole (0.5 to 3 mm diameter) is formed in the top of the bulb so that the bulb can be filled with a powdered sample (up to 1 gram) and gases can be admitted. 2.2.4. THE ALNICO WIRE NEEDLE. An Alnico wire needle employed for magnetic compensation (see below) is encased in a Pyrex tube, and a hook is fashioned at each end. It is important that the needle remain motionless within the glass, that the unit be as light as possible, and that the encasement be vacuum tight. The needle is approximately three inches long and about 1/16 inch in diameter. It is magnetized by brushing a small horseshoe magnet (always in the same direction) two or three times over its length. 2.3. ASSEMBLY OF THE BALANCE In operation, the balance beam and the support frame are aligned and enclosed in a Pyrex envelope, as shown in Figure 17. For best operation the tungsten points should be in the same horizontal plane and the beam should be horizontal at the null position. The carriage is held in place with a drop of Apiezon-W black wax applied inside the housing to two legs of the frame. Fused silica fibers (C) are suspended from the Y branch supports; the platinum weights (A), Alnico needle (B), sample bulb (D), and its counterbalance (E) are suspended on other fibers. The curvature of each fiber hook in the train should contain a well defined minimum. A fused silica tube (25-mm o.d.) is mounted around each fiber train via a 29/42 standard taper groundglass joint. The flat-ground end-caps of the balance housing and the fused silica legs are cemented with Apiezon-W wax. One housing cap is designed to be attached to the auxiliary vacuum rack. Two Hevi Duty7 type 70 tube furnaces are used to heat the sample and the counterweight. The balance must be installed with extreme care to assure that the parabolic cups and the tungsten tips are free from grease and small pieces of grit. The entire balance and the housing 7 Manufactured by the Hevi Duty Electric Company, Milwaukee, Wis, 37

Institute of Science and Technology The University of Michigan FIGURE 17. THE MICROBALANCE ASSEMBLY must first be cleaned with soap and water, rinsed with acetone, allowed to dry, and gently flamed with a microtorch. 2.3.1. THE AUXILIARY VACUUM LINE. The basic components of the vacuum line, such as fore pump, diffusion pump, traps, gas storage vessels, manometers, etc., were discussed in Section 1.3. (The usual precautions should be taken.) Figure 18 shows the auxiliary system used with this particular balance. It is recommended that stopcocks be equal in quality to the E & K precision-grade, bulb types. Most of the stopcocks used were either 2- or 4-mm oblique-bore units. 2.3.2. GENERATION OF GASES. The acquisition of the gases to be used in the experiments is extremely important. In the volumetric experiments, pure gases are obtained by removing impurities from gases available commercially in tank cylinders. It is also convenient to obtain small amounts of high-purity gases by the thermal decomposition of appropriate solid compounds. For example, oxygen and nitrogen may be obtained from the thermal decomposition of KMnO4 and NaN3, respectively. To accomplish this in the laboratory, a 500-ml round-bottom flask (Figure 18) is half filled with either KMnO4 (for oxygen generation) or about 10 grams of NaN3 (for nitrogen generation), and sealed into a purification train. A Glasscol heating mantle is attached to each flask, and a copper gauze tube lined with asbestos paper is fitted around the as38

Institute of Science and Technology The University of Michigan Nr N2 1 1 02 ) ( 02 ) IIIIIH 75 To Balance FIGURE 18. THE AUXILIARY VACUUM SYSTEM sembly. The solid can then be heated in vacuo from room temperature. KMnO4 can be heated to 2000C, and NaN3 to about 3000C, before significant decomposition occurs. The decomposition rate is moderate if a heating rate of about 1 0C per minute is maintained. The quantity of NaN3 used must be calculated so that the nitrogen generated is compatible with the absolute volume of the gas reservoirs at a pressure between700 and 900 mm Hg. This precaution is not necessary with KMnO4 since the decomposition of this material is easier to control. Extreme caution should be exercised during the decompositions, especially with the NaN3. The first few millimeters pressure of each gas should be discarded. As the gases are generated, each passes through a trap filled with 4-mm glass beads and cooled with dry ice. If needed, a desiccant such as P205 or BaO should be used. The dried gases are collected in threeliter storage flasks; each flask is wrapped with masking tape as a safety measure and is equipped with an open-end mercury manometer which serves to detect leaks and to indicate the quantity of gas in the storage system; closed-end manometers may also be used. 2.4. CONSTRUCTION OF THE FURNACE THERMOCOUPLES The thermocouples used to measure the temperature of the sample are fashioned from No. 18 Chromel and Alumel wires. The thermocouple junctions are made by use of a medium temperature oxygen-natural gas flame and a sodium borate flux. The lead wires are threaded into a two-hole ceramic rod and cemented with Sauereisen cement into the wall of a type 70 Hevi 39

Institute of Science and Technology The University of Michigan Duty tube furnace. Each wire of the Chromel-Alumel junction is silver soldered to copper lead wires; these are the cold junctions which are kept at 0~C during an experiment. 2.4.1. CALIBRATION. Since it is desirable to calibrate the thermocouples in the position in which they are to be used, the following procedure is adopted. A second thermocouple is constructed in the manner described above. The furnace couples are compared with this master couple by means of an experimental arrangement similar to that used for the microbalance assembly. A sample-tube furnace is set aside and the quartz tube of the balance is clamped in position. A quartz thimble filled with a calibration solid is inserted inside the leg. The tip of the master thermocouple is inserted into a 10-mm o.d. quartz sleeve, and the assembly is inserted into the thimble; the position of the tip is adjusted in the furnace to correspond to the sample position on the microbalance. The temperature of the furnace is increased at intervals and the e.m.f. of the master thermocouple is compared to the furnace thermocouples. A primary calibration of the master thermocouple (in situ) is obtained from the freezing points of the various calibration solids used (Pb, Sn, Zn, Sb, Ag, and NaCl). The furnace thermocouples register higher temperatures than the master couple; this is to be expected, because of radiation losses through the ends of the tube furnace. In an identical experiment using the counterpoise furnace, the results obtained duplicated the results of the sample thermocouple calibration. Therefore, the data of the sample furnace calibration may be used to describe both furnace thermocouples. The data for a typical calibration are given in Table IX. Sample temperatures can be calculated by use of a plot of the data in Table IX and a Leeds and Northrup conversion table. 2.5. OPERATION OF THE BALANCE The microbalance is used as a null-indicating instrument. A small D-type solenoid (Figure 19) is fitted around the balance leg containing the Alnico needle so that one end of the needle FIGURE 19. THE MAGNETIC COMPENSATION SOLENOID 40

Institute of Science and Technology The University of Michigan TABLE IX. FURNACE THERMOCOUPLE CALIBRATION Furnace Master Thermocouple Thermocouple Temperature (mv) (mv) (oC) 0 0 0 11.77 11.11 269 12.70 12.05 293 20.50 19.20 464 21.30 20.19 487 23.00 21.80 525 24.70 23.20 557 27.30 25.80 619 27.91 26.08 625 30.89 29.20 698 31.30 29.20 698 34.55 32.40 772 38.05 35.71 853 39.31 37.10 890 42.16 39.82 960 44.00 41.65 1009 is suspended in the center of the solenoid and the other end is out of the solenoid. Each D is wound with 55 turns of No. 22 insulated copper wire. A small current passing through the magnetic compensation solenoid is used to maintain the balance in null position (Figure 20). The current is provided by three 6-volt lead storage batteries connected in parallel; it is controlled by a resistance box (Helipots, 2-watt; Figure 21). The Alnico needle is permanently magnetized (Section 2.2.4) so that it can be attracted into or repulsed by the field of the solenoid. The change in compensating current through the solenoid is proportional to the change in mass of the sample, as measured with a type-B Rubicon potentiometer by observing the change in voltage across a standard Manganin resistor (Figure 22). It is important that the solenoid remain in place after the balance has been calibrated; otherwise recalibration is necessary. I I I A 00 A 00 A.000 A Solenoi d To Resistor te/ntiomet ef Selector DPDT..it. TT FIGURE 20. STANDARD FIGURE 21. THE MICROBALANCE ELECTRINULL POSITION CAL CIRCUIT 41

Institute of Science and Technology The University of Michigan FIGURE 22. STANDARD RESISTOR 2.6. CALIBRATION OF THE BALANCE 2.6.1. ABSOLUTE METHOD. A primary method based on Archimedes' principle is best for calibrating the microbalance. If a mass of volume V is suspended from the microbalance, and the (nitrogen) gas pressure surrounding the mass is varied, the compensation voltage will vary linearly with the pressure at room temperature (but see Section 2.7.2). A plot of these variables will have a slope Sn that depends on the volume of the mass being measured. If two samples with identical masses and different volumes are chosen, the following relation may be employed to calculate the sensitivity of the balance. (V1 - V2)M ~ 106 S= (S1 -S2) ZPV (19) where S is the balance sensitivity micrograms/microvolt); M is the molecular weight of the gas (nitrogen, 28.016 grams/mole); V1 is the volume of a sealed Pyrex bulb (milliliters), and V2 is the volume of an equivalent mass of platinum wire. S1 and S2 are the calculated slopes (microvolts/millimeter) of the curves obtained from a plot of compensation voltage versus (nitrogen) gas pressure for each volume; P is 760 mm; V is 22,400 ml, and Z is a constant (equal to 1.0915 at room temperature) which is used to correct the PV product for the nonideality of nitrogen. In practice, a sealed Pyrex bulb approximately 1 cm in diameter is used for V1. A hook is fashioned from the surface of the bulb. The volume of the bulb may be determined in several ways. The easiest method is to weigh the bulb first in air and then in distilled water. Since it will float in water, an appropriate weight of Pt must be added to submerge it. Care should be taken to avoid trapping bubbles on the bulb and the Pt weights. The difference in mass between the two weighings is equal to the mass of water displaced by the bulb. The volume of water displaced is calculated by dividing the difference in mass by the density of water at the temperature 42

Institute of Science and Technology The University of Michigan of the weighing. The bulb is then attached to the fiber train at A (Figure 17), and pressurecompensation voltage data are recorded. V2 is much easier to obtain. A mass (in air) of Pt wire equal to the mass of the bulb (V1) must be procured. The volume of the Pt wire is obtained by dividing the mass of the wire by the density of Pt (21.45 grams/ml). The Pt wire is then attached to the fiber train in place of the buoyancy bulb, and a set of pressure-compensation voltage data is recorded. It is important that no change in the suspension fibers or counterweights be made other than to remove the Pyrex bulb and replace it with the platinum weight. The masses for V1 and V2 should not be different by more than one milligram. Typical data are given in Table X and represented graphically in Figure 23. The sensitivity of the balance is calculated from Equation 19. TABLE X. MICROBALANCE CALIBRATION DATA Volume V * Volume V2** 1 2 Nitrogen Compensation Nitrogen Compensation Pressure e.m.f. Pressure e.m.f. (mm Hg) (mv) (mm Hg) (mv) 6.9 19.866 4.2 20.874 28.7 19.455 72.8 20.720 74.9 18.598 117.0 20.614 105.1 18.050 176.7 20.485 149.7 17.237 253.4 20.320 181.1 16.648 317.3 20.194 219.3 15.941 263.1 15.142 297.6 14.497 337.4 13.764 336.6 13.742 296.7 14.481 194.8 16.384 97.4 18.192 4.3 19.916 *Vl = 0.5453 ml. **V2 = 0.0112 ml. 2.6.2. INTERNAL METHOD. A second method of calculating the sensitivity of the balance is to use an internal standard. By measuring known mass changes as e.m.f. changes, the sensitivity factor can be calculated. This procedure is satisfactory and convenient. The reference 43

Institute of Science and Technology The University of Michigan * Increasing Pressure * Decreasing Pressure 15 - 16Z 1718Z o 19U V 2 20 0 100 200 300 PRESSURE (mm Hg) FIGURE 23. MICROBALANCE CALIBRATION CURVES masses used for this purpose are, for example, PrO1.50 and PrO1.83 prepared under standardized conditions (Reference 54). A sample (60 mg) of commercial grade Pr6 1 lis suspended from the balance and converted to PrO by heating to 940~C in vacuo for 15 hours. The sam1.50 ple is then cooled to room temperature while being continuously pumped. The compensation voltage of the balance at room temperature under these conditions is recorded as the PrO1.50 reference mass. Oxygen is admitted to the balance housing up to a pressure of 150 mm, the temperature is slowly increased to 9400C, and the system is allowed to equilibrate for one hour. The temperature is then reduced to room temperature over a period of about six hours. At room temperature the balance housing is again evacuated to constant mass, and a balance reading is recorded as the PrO1.83 reference mass. This procedure is used to obtain mass readings under identical conditions of temperature and pressure. The difference between the two readings is considered to be due to the difference in the theoretical mass between these two compositions. Equations 20 and 21 (Section 2.7.4) are used to calculate the sensitivity. This method must be used with care; the change in the stoichiometry of the decomposition material must be exact and known. For example, if KMnO4 is substituted as a calibration solid, one must be sure that oxygen alone is the final decomposition product in the gas phase, and not a mixture of desorbed H2o and 02. 44

Institute of Science and Technology The University of Michigan 2.7. MEASUREMENT OF AN ISOTHERM An adsorption isotherm is calculated in three steps, the collection of the raw data, the collection of data to be used to correct for buoyancy effects, and the analysis of the data. These three stages are discussed below for a typical Pr-O isotherm. Other techniques have also been described (Reference 45). 2.7.1. COLLECTION OF THE DATA. The process of collecting raw data is similar for every experiment performed on the microbalance. The mass change, which is observed as a change in the voltage across the standard resistor, is monitored as a function of either gas pressure, sample temperature, or time. Some slight modifications in procedure must be made, however, for each kind of experiment. These points will be discussed separately below. The calculations and data obtained for several different types of experiments will be presented. 2.7.2. GAS PRESSURE-BUOYANCE IRREGULARITIES. All experiments performed on the microbalance show that at low pressures and high temperatures the apparent mass change of a noninteracting gas and solid with pressure is not linear. This effect, which results from the TMF (thermomolecular flow) of gases along the suspension fibers, occurs most often at pressures of 10 to 10 torr (Reference 43); at higher pressures the buoyancy (compensation voltage) of a noninteracting mass on the balance is a linear function of the pressure. The deviation caused by TMF may be positive, negative, or a combination of both. The magnitude of the TMF depends on the geometry of the fiber trains and sample bulbs in the heated regions, the temperature gradients they undergo, and the pressure and the conductivity properties of the ambient gas. The TMF forces may be minimized experimentally. To accomplish this, the furnace is placed so that the sample bulb is at the center of the furnace. The counterbalance side is treated similarly. The magnitude of the TMF force can be adjusted by raising or lowering the furnace on the counterbalance side. The furnace surrounding the sample is never moved. This procedure is followed to maintain an accurate sample temperature. The temperature of the counterpoise furnace may be changed to achieve the same result. Czanderna (Reference 43) showed that the difference between the TMF forces caused by nitrogen and those caused by oxygen is slight. The maximum TMF force is found in the vicinity of 0.01 to 0.3 torr gas pressure. The vacuum point is usually found to be the terminal point of the high pressure extrapolation of the linear portion of the buoyancy curve. The effect is illustrated in Figure 24. 2.7.3. MEASUREMENT AND CALCULATION OF A Pr-O ISOTHERM. The first experiment to be discussed is the measurement of the total uptake of an adsorbate, which interacts with an adsorbent, as a function of the gas pressure. An example is the praseodymium oxide-oxygen 45

Institute of Science and Technology The University of Michigan +2 +1 0 0 15 perature and in an oxygen rate isotherms, one using oxygen and one using nitrogen (Figure 25). Since Nitrogen -2 2 18-3 0 1 2 3 4 5 6 7 8 PRESSURE (mm Hg) FIGURE 24. THE TMF EFFECT perature and in an oxygen pressure range of about 150 mm Hg (P 0 in air is about 150 mm). >; ~12 _~~2 rate isotherms, one using oxygen and one using nitrogen (Figure 25). Since nitrogen does not react with PrO under the conditions of the experiment, it is used to determine the combined x 2220 - E 10 14 O > 12 2 - * * * < Oxygen I I Nitrogen O 10 20 30 40 50 60 70 80 PRESSURE (mm Hg) FIGURE 25. RAW DATA OF A TYPICAL Pr-O ISOTHERM 46

Institute of Science and Technology The University of Michigan buoyancy and TMF effects on a sample of praseodymia as a functionof the gas pressure. To be exact, a noninteracting gas of molecular weight 32, with thermal conductivity properties the same as those of oxygen should be used; however, the difference between the buoyancy effect of nitrogen and that of oxygen is small when each gas interacts physically with an inert mass. The sample of praseodymia is exposed first to nitrogen (noninteraction) and then to oxygen (interaction); the progress of the interaction is measured by calculating the number of moles of oxygen taken up per mole of praseodymia; this is accomplished by graphical subtraction of the two buoyancy functions. Since the system studied in this experiment results only in species in which the ratio of oxygen to praseodymium varies (x in PrO ), the difference in buoyancy functions has a simple relation to x. A nitrogen isotherm is determined by carefully admitting nitrogen into the evacuated balance housing; the gas pressure is slowly increased to 150 mm at the temperature of the experiment. Approximately 15 minutes is allowed, to establish thermal equilibrium. The pressure is then reduced by removing small quantities of nitrogen (10-mm pressure increments) at ten-minute intervals; the corresponding pressure and compensation voltage are recorded at each stage. Additional points are taken at pressures where TMF is encountered, in order to establish the exact shape of this portion of the isotherm. The system is then evacuated and the sample allowed to establish a constant mass. The above procedure assures that the vacuum points of the nitrogen and the oxygen isotherms will coincide. After the sample mass is shown to be constant, small increments of oxygen are carefully admitted to the balance system, and each is allowed to equilibrate for periods from a few minutes to several hours. Equilibrium times depend upon the particular experiment and system being studied; the first is usually about an hour. The compensation voltages of the comparative nitrogen and oxygen isotherms are plotted on a piece of large-scale graph paper. Smooth curves are drawn through the plotted points. To obtain the final adsorption isotherm, the difference between the two curves is obtained at convenient pressure intervals and plotted as a function of pressure. 2.7.4. THE CALCULATION OF x IN PrO. The equation for the oxidation of Pr203 is PrO +- 0 PrO 1.50 2 2 1.50+y where y is the number of moles of oxygen added to the sample per mole of PrO1. Therefore, x = 1.5000 + y, where y = KAmv (20) 47

Institute of Science and Technology The University of Michigan Here Amv is the difference in millivolts of compensation voltage between the nitrogen and oxygen plots; K is a constant, represented as S (164.92 grams PrO 1.50/mole PrO 1.50 W 16 grams oxygen/gram atom oxygen In Equation 21, S is the balance sensitivity in grams per millivolt, and W is the weight in grams of PrO1.50 used in the experiment. More simply, the total uptake of oxygen may be calculated by multiplying the Amv by the sensitivity. The x values are considered reliable to ~0.0001 units. The data for atypical determination are illustrated in Figure 26. 1.85 1.80 - c~.75 - 1.70 1.65 0 50 100 150 OXYGEN PRESSURE (mm Hg) FIGURE 26. A TYPICAL (CALCULATED) Pr-O ISOTHERM 2.8. OTHER MEASUREMENTS 2.8.1. KINETIC STUDIES. Besides its use in the study of the total adsorption or reaction of a gas with a solid as a function of gas pressure, the microbalance described above has several other interesting applications. One such application is the measurement of kinetic processes. The oxidation of PrO1.50 will be discussed as an example (see also Reference 56). In the case discussed below, the rate of uptake is determined at essentially constant pressure. The volume of the working system is about two liters, and the sample size is about 50 mg. 48

Institute of Science and Technology The University of Michigan The amount of gas reacting, at say 10 mm or above, is so small that a pressure difference between the initial and final pressure conditions cannot be determined with a mercury manometer. Also, if a manometer similar to the one described in the volumetric adsorption section (Section 1.3.3) is used, essentially constant volume is also maintained. Recall that when the total uptake is determined as a function of pressure, two curves are needed to obtain the amount of gaseous oxygen which has reacted. Since the kinetic data are taken under isothermal and isobaric conditions, they describe the rate at which the chemical system moves along a vertical line between the curves for nitrogen and oxygen. A buoyancy correction at constant temperature and pressure enters into the calculations as a constant to be subtracted from all of the recorded mass increases. This "constant" varies as the pressure at which the kinetics is studied, and is a result of the slope of the nitrogen buoyancy curve. To obtain kinetic data, a nitrogen isotherm is determined, as described before, around the value of the oxygen pressure to be considered. Then the nitrogen is carefully pumped off and oxygen is admitted (in increments if necessary) until the operating pressure is reached. The moment of the first addition is taken as zero time. In this case about three to five minutes is needed for the gas to damp the balance and free it from oscillations before meaningful data can be recorded. The compensation voltage and time are recorded as the indicator hook passes the null position. When the operator has become familiar with the system, the potentiometer can be set to compensate for a prearranged voltage and the time recorded with increased accuracy. The process is continued as long as it is considered desirable. Equations 20 and 21 are used to transform the raw data to convenient units. As before, Amv is obtained by subtracting the nitrogen function from the oxygen function. Data taken in such a measurement are given in Figure 27 as a plot of millimoles of oxygen per mole of PrO1.50 versus the logarithm of time. 2.8.2. DETERMINING SURFACE AREA FROM NITROGEN ADSORPTION. The microbalance may be used to measure the surface areas of powders. As mentioned in Section 1.2, if the amount of a gas adsorbed in a monolayer on the surface of a solid can be calculated, and the area occupied by a single gas molecule is known, the surface area can be calculated. After the variation of surface coverage as a function of pressure has been established, the data may be interpreted in various ways in order to calculate the amount of gas in a monolayer. The Point B method (Reference 25) will be illustrated in this discussion, although the data could be treated in terms of the B.E.T. multilayer theory as well. Data from a measurement of a sample of TiO2 will be used as an illustration. 49

Institute of Science and Technology The University of Michigan 100 Z 80 0 0 60 O I 0.5 1.0 1.5 2.9 LOGARITHM OF TIME (minutes) FIGURE 27. RATE OF OXIDATION OF Pr 0 r23 To measure surface area, about 100 to 200 mg of sample is suspended from the balance in the manner described previously. The balance housing is then evacuated, and the sample temperature is raised to 500 C (see Section 1.5.2). The heating is continued until no further mass loss is observed. The furnace is removed, and a nitrogen bath is placed around the fused silica envelope that surrounds the sample. A few millimeters of helium pressure is then established inside the housing, and the system is allowed to equilibrate at 78~K; the system will reach thermal equilibrium in a few minutes. The helium is then removed and the system is pumped at 780K until no further mass changes are observed. Dry nitrogen is then admitted in increments to the balance housing, and the change in compensation voltage, a function of the total equilibrium pressure, is recorded. The first increments of gas must be added very slowly, or the balance may strike the arrest, shift its position, and thus change the reference point of the experiment. If a plot of the amount of nitrogen adsorbed versus the nitrogen gas pressure is made, the linear portion of the isotherm can be extrapolated to the ordinate. The point at which the experimental curve breaks away from the linear portion of the isotherm is taken as Point B. The specific surface area in square meters/gram is calculated from the equation specific surface = K(X/Y) (22) 50

Institute of Science and Technology The University of Michigan where X is the number of micrograms of N2 adsorbed at Point B, and Y is the sample weight in milligrams. K is a constant for nitrogen and is equal to 3.48; it is represented as aNN N2 K M (23) where N is Avogadro's Number, aN2 is the cross sectional area of an adsorbed N2 molecule, and M is the gram molecular weight of N2. A typical set of data is given in Table XI and illustrated inFigure 28. TABLE XI. SURFACE AREA DATA FOR THE ADSORPTION OF NITROGEN ON RUTILE AT 780K Nitrogen Nitrogen Nitrogen Nitrogen Pressure Adsorbed Pressure Adsorbed (mm Hg) (ig) (mm Hg) (ig) 10-6 0 123.1 1375 0.0025 123 150.8 1454 0.28 626 180.3 1532 0.67 706 223.0 1642 1.97 821 267.9 1752 3.3 890 383.7 2074 8.7 978 486.0 2585 16.0 1036 100.5 1319 23.2 1070 23.5 1072 47.0 1178 7.7 926 77.8 1255 10-6 14 107.1 1335 2000 - O 1000 z; 5 | Point B 100 200 300 400 500 PRESSURE (mm Hg) FIGURE 28. ADSORPTION OF NITROGEN ON RUTILE AT 780~A 51

Institute of Science and Technology The University of Michigan It must be noted that in order to calculate the masses of nitrogen adsorbed at various pressures, it is assumed that under the experimental conditions no correction is needed for the buoyancy effect of a noninteracting gas on the sample. The matter in question is not the TMF calibration, mentioned earlier, but the slope of the linear portion of the compensation voltage-pressure curve of a noninteracting gas. If this slope is very small, as it is in the case illustrated below, the amount of nitrogen adsorbed as a function of the pressure may be calculated as [Lg of N2 = (Amv) (sensitivity,,tg/mv) (24) where Amv is the difference between the value of the compensation voltage at the reference point of no adsorption (78 K, 10 6 mm Hg) and the value of the compensation voltage at succeeding equilibrium values of the total pressure. If a correction is needed, the variation of the compensation voltage with nitrogen pressure at 78 K is recorded (1) when the empty sample bulb alone is on the balance, and (2) when a sample is present. The reference points of the curves of the two experiments are then superimposed on the same piece of graph paper and the curves graphically subtracted. Amv in Equation 24 is now the difference between these two curves. 2.8.3. MAGNETIC SUSCEPTIBILITY. The microbalance may also be used to measure magnetic properties (Reference 57) of various substances by what in known as the Gouy method (Reference 58). A sample is placed between the poles of an energized magnet and the effect on it is observed. If a sample in a thin-walled tube is suspended between the poles of a magnet so that the lower end of the tube is cut by the maximum flux, the substance will be repulsed by or drawn into the field of the magnet. Paramagnetic substances experience a downward force, and diamagnetic substances experience an upward one. The force can be conveniently measured as a change in weight (AW) if the sample is suspended from a balance. For samples that weigh one gram or less, the values of AW range from a few micrograms to several hunded milligrams. These limits place the measurement of susceptibilities in the region of sensitivity and capacity of the microbalance. The susceptibility can be calculated as follows: 2gAW d X1 - _d2 = 2gX = W -(25) dll d2x2 = 2 where dl, X1 and d2, X2 are the densities and mass susceptibilities of the sample and of the surrounding atmosphere, respectively; g is the acceleration due to gravity; H is the magnetic field intensity; and A is the cross-sectional area of the sample. To obtain AW, Equation 24 is used. (Variations of the Gouy method are discussed by Dodd and Robinson, Reference 57.) 52

Institute of Science and Technology The University of Michigan Several standard samples of known magnetic susceptibility have been used to calibrate the field of a magnet. Powdered, crystalline ferrous ammonium sulfate or a solution of nickel chloride is commonly used, and HgCo( CNS)4 (Reference 59) has also been used. If the field strength is known and a substance of known susceptibility is measured, the balance sensitivity may be calculated by using Equations 24 and 25. However, this method is not as reliable as the absolute method (Section 2.6.1). The use of the microbalance to measure magnetic susceptibilities has been discussed by Kern (Reference 60) and Turner (Reference 61). An additional note must be made about this measurement and the microbalance. It is possible for the field of the magnet to interact with the Alnico needle and give spurious results; the effect of the interaction can be reduced by calibration and/or shielding, or by using small fields. 2.9. SUMMARY The microbalance has several important advantages. (1) Compared with other precision instruments, it is inexpensive and easy to maintain. (2) Although the balance must be handled with care, the construction is very rugged. (3) Small errors in the alignment of the balance appear to have no significant effect on the operation of the balance. (4) The long-term stability of the balance calibration is excellent. (5) A precision of 10 8 gram is readily attained. The microbalance may be used for many different experiments. However, some of its properties have not been explained or understood (Reference 62), and for this reason applying it to new problems may present new difficulties. More research needs to be done on this balance and balances in general so that their applicability may be extended. In the meantime, the device described above will serve to measure differences in mass in the microgram region. Appendix CROSS-SECTIONAL AREAS OF ADSORBED MOLECULES Table XII lists values for the cross-sectional areas of various molecular types used in adsorption research. It must be noted, however, that the data on one species but from different sources do not always agree. Irregularities in the surface of the adsorbent are a determining factor in the effective cross-sectional area occupied by the adsorbate molecule. The values of 16.2 and 19.5 A /molecule, for nitrogen and krypton respectively, are commonly used. It is recommended that the original papers be consulted before the values below are used for determinations where the accuracy is critical. 53

Institute of Science and Technology The University of Michigan TABLE XII. CROSS-SECTIONAL AREAS OF ADSORBED MOLECULES Particle Temperature Area Adsorbent Reference (Oc) (A /molecule) Ne -253 10.0 Ni foil 63, 64 Ar -195 13.7 (calculated) 65 -195 15.4 glass spheres 65 Kr -195 19.5 oxides and 30 porous glass Kr -195 15.2 (calculated) 29 -195 20.8 glass spheres, 29 metals, and oxides 02 -183 14.6 porous glass and 64 silica gel -183 14.1 (calculated) 3 H2 -253 8.3 Ni foil 63, 64 H20 25 10.6 oxides 66 24 10.6 oxides 27 26.5 10.8 (calculated) 65 D2 -253 7.2 Ni foil 63, 64 F- 12.9 67 Cl2 32-33 21.1 metals 68 Cl- 22 67 12 22.1 BaCI2, CaF2 67 N2 -195.8 16.2 (calculated) 3 N20 -78 20.4 2 charcoals and 64 a carbon black -80 16.8 (calculated) 3 NO -150 12.5 (calculated) 3 NO2 32-34 15.0 metals 68 NH3 -32.5 15.4 porous glass 65 -32.5 13.8 (calculated) 65 CO -183 16.8 (calculated) 3 CO2 -78 14.2 (calculated) 65 -78 20.1 porous glass 65 CO2 -56.6 17.0 (calculated) 3 CH4 -183 16.0 Ni foil 63, 64 17.2 (calculated) 69 C2H2 -78 22.2 porous glass 65 -78 15.2 (calculated) 65 54

Institute of Science and Technology The University of Michigan Particle Temperature Area Adsorbent Reference (~C) (A2/molecule) C2 H 6 -183 23 KCI and NaCL 70 -183 20.5 chrome -plated 71 Ni strips -183 24 TiO2 70 22.1 (calculated) 69 C3H8 27.4 (calculated) 69 C4 H 0 42.7 A1203, SiO2 29 0 30.5 (calculated) 29 n-C4H10 -78 43.4 glass spheres 29 and metals -78 29.7 (calculated) 29 0 46.9 tungsten powder 29 and ZnO 0 32.1 (calculated) 29 0 52, 41, 42 carbon and 72 Zn dusts 0 49 porous glass 65 0 56.6 glass spheres 73 C6 H6 25 27.0 titanium oxides 66 n-C7H16 24 55 oxides 27 24 44 graphite 27 CH3 OH 25 12 lignite 74 C2H5OH 0 20 glass spheres 19 C3H7OH 25 20 oxides 66 25 27 (calculated) 66 25 20 oxides 27 (CH3)2CO 25 26.9 (calculated) 7 CHCI2F -78 24.7 (calculated) 29 -78 37.5 glass spheres, 29 metals, and oxides 0 26.4 (calculated) 29 0 40.1 glass spheres, met- 29 als, and oxides C2 H Cl 0 23.9 (calculated) 75 0 26.1 graphite 75 CS2 0 23 (calculated) 72 55

Institute of Science and Technology The University of Michigan REFERENCES 1. E. V. Ballou and 0. K. Doolen, Anal. Chem., 1960, Vol. 32, p. 532. 2. S. Brunauer, The Adsorption of Gases and Vapors, Princeton University Press, Princeton, N. J., 1943. 3. P. H. Emmett and S. Brunauer, J. Am. Chem. Soc.,1937, Vol. 59, p. 1553. 4. J. H. DeBoer and C. Zwikker, Z. Phys. Chem., 1929, Vol. B8, p. 407. 5. I. Langmuir, J. Am. Chem. Soc., 1918, Vol. 40, p. 1361. 6. J. W. McBain, The Sorption of Gases and Vapors by Solids, G. Routledge and Sons, Ltd., London, England, 1932, p. 5. 7. S. Brunauer, P. H. Emmett, and E. Teller, J. Am. Chem. Soc., 1938, Vol. 60, p. 309. 8. G. D. Halsey, Advan. Catalysis, 1952, Vol. 4, p. 259. 9. G. D. Halsey, J. Am. Chem. Soc., 1951, Vol. 73, p. 2693. 10. G. Halsey and H. S. Taylor, J. Chem. Phys., 1947, Vol. 15, p. 624. 11. T. L. Hill, Advan. Catalysis, 1952, Vol. 4, p. 211. 12. A. V. Kiselev, Quart. Rev., 1961, Vol. 15, p. 99. 13. T. Wolkenstein, Advan. Catalysis, 1960, Vol. 12, p. 189. 14. E. P. Barrett, L. G. Joyner, and P. P. Halenda, J. Am. Chem. Soc., 1951, Vol. 73, p. 373. 15. R. C. Smith and H. C. Howard, Ind. Eng. Chem., 1942, Vol. 34, p. 438. 16. A. Cimino, E. Molinari, and E. Cipollini, Gazz. Chim. Ital., 1960, Vol. 90, p. 91. 17. L. G. Joyner, in Scientific Glass Blowing, ed. by W. C. Barr and V. J. Anhorn, Instruments Publishing Co., Pittsburgh, Pa., 1949. 18. R. Gilmont, Anal. Chem., 1948, Vol. 20, p. 474. 19. J. L. Shereshefsky and E. R. Russell, J. Phys. Chem., 1953, Vol. 57, p. 660. 20. J. M. Honig and L. H. Reyerson, J. Phys. Chem., 1952, Vol. 56, p. 140. 21. M. Feld and F. S. Klein, J. Sci. Instr., 1954, Vol. 31, p. 474. 22. F. G. Carpenter, Proceedings of the Third Technical Session on Bone Char, National Bureau of Standards, Washington, D. C., 1953. 23. I. F. Homfray, Z. Phys. Chem., 1910, Vol. 74, p. 129. 24. H. E. Reis, in Catalysis, ed. by P. H. Emmett, Reinhold Publishing Co., New York, N. Y., 1954, p. 12. 25. P. H. Emmett (ed.), Catalysis, Reinhold Publishing Co., New York, N. Y., 1954, p. 33. 26. P. H. Emmett, Advan. Colloid Sci., 1942, Vol. 1, p. 4. 27. H. K. Livingston, J. Am. Chem. Soc., 1944, Vol. 66, p. 569. 28. L. A. Wooten and J. R. C. Brown, J. Am. Chem. Soc., 1943, Vol. 65, p. 113. 29. R. T. Davis, T. W. DeWitt, and P. H. Emmett, J. Phys. Collid Chem., 1947, Vol. 51, p. 1232. 56

Institute of Science and Technology The University of Michigan 30. R. A. Beebe, J. B. Beckwith, and J. M. Honig, J. Am. Chem. Soc., 1954, Vol. 67, p. 1554. 31. F. W. Bloecher, Mining Engr., 1951, Vol. 3, p. 255. 32. W. E. Barr and V. J. Anhorn, Scientific Glass Blowing, Instruments Publishing Co., Pittsburgh, Pa., 1949, p. 205. 33. J. J. Meihuizen and C. A. Crommelin, Physica, 1937, Vol. IV, p. 1. 34. W. H. Keeson, J. Mazur, and J. J. Meihuizen, Physica, 1935, Vol. II, p. 669. 35. B. Dodge and H. Davis, J. Am. Chem. Soc., 1927, Vol. 49, pp. 610-620. 36. H. L. Ritter and L. C. Drake, Ind. Eng. Chem., Anal. Ed., 1945, Vol. 17, p. 782. 37. L. G. Joyner, E. P. Barrett, and R. Skold, J. Am. Chem. Soc., 1951, Vol. 73, p. 3155. 38. P. L. Kirk and F. L. Schaffer, Rev. Sci. Instr., 1948, Vol. 19, p. 785. 39. H. B. Klevens, J. T. Carriel, R. J. Fries, and A. H. Peterson, in Proceedings of the Second International Congress of Surface Activity, Solid/Gas Interface, Butterworths, London, England, 1957, p. 160. 40. J. Donau, Mikrochemie, 1931, Vol. 9, p. 1. 41. J. Donau, Mikrochemie, 1933, Vol. 13, p. 155. 42. I. M. Korenman and Y. N. Fertelmeister, Zavodsk. Lab., 1949, Vol. 15, p. 785. 43. A. W. Czanderna, PhD thesis, Purdue University, West Lafayette, Ind., 1957. 44. A. W. Czanderna and J. M. Honig, Anal. Chem., 1957, Vol. 29, p. 1206. 45. A. W. Czanderna and J. M. Honig, J. Phys. Chem., 1959, Vol. 63, p. 620. 46. Paul A. Faeth, PhD thesis, Purdue University, West Lafayette, Ind., 1961. 47. C. N. Cochran, Vacuum Microbalance Tech., 1961, Vol. 1, p. 23. 48. A. W. Czanderna, Vacuum Microbalance Tech., 1962, Vol. 2. 49. T. N. Rhodin, Advan. Catalysis, 1953, Vol. 5, p. 39. 50. F. A. Gulbransen, Advan. Catalysis, 1953, Vol. 5, p. 119. 51. E. W. Johnson and L. K. Nash, Rev. Sci. Instr., 1951, Vol. 22, p. 240. 52. A. W. Czanderna, private communication. 53. A. W. Czanderna, Vacuum Microbalance Tech., 1961, Vol. 1, p. 129. 54. R. E. Ferguson, E. D. Guth, and L. Eyring, J. Am. Chem. Soc., 1954, Vol. 76, p. 3890. 55. J. M. Honig, A. F. Clifford, and P. A. Faeth, J. Inorg Chem., in press. 56. P. A. Faeth and A. F. Clifford, to be published. 57. R. E. Dodd and P. L. Robinson, Experimental Inorganic Chemistry, Elsevier, New York, N. Y., 1957, p. 384. 58. L. H. Gouy, Compt. Rend., 1889, Vol. 109, p. 935. 59. R. S. Nyholm and B. N. Figgis, J. Chem. Soc., 1958, Vol. 284, p. 4190. 60. S. Kern, MS thesis, Purdue University, West Lafayette, Ind., 1957. 57

Institute of Science and Technology The University of Michigan 61. A. G. Turner, PhD thesis, Purdue University, West Lafayette, Ind., 1959. 62. J. M. Honig, Vacuum Mircobalance Tech., 1961, Vol. 1, p. 55. 63. A. Van Itterbeek and J. Borghs, Z. Physik. Chem., 1942, Vol. 50B, p. 128. 64. H. K. Livingston, J. Colloid Sci., 1949, Vol. 4, p. 447. 65. P. H. Emmett and M. Cines, J. Phys. Colloid Chem., 1947, Vol. 51, p. 1248. 66. D. Gans, U. S. Brooks, and G. E. Boyd, Ind. Eng. Chem., Anal. Ed., 1942, Vol. 14, p. 396. 67. J. H. DeBoer, Rec. Trav. Chim., 1946, Vol. 65, p. 576. 68. H. L. Wang and N. Hackerman, J. Phys. Chem., 1952, Vol. 56, p. 771 69. W. T. Grandquist, F. A. Mitch, and C. H. Edwards, Ind. Eng. Chem., 1954, Vol. 46, p. 358. 70. S. Ross, J. Am. Chem. Soc., 1948, Vol. 70, p. 3830. 71. C. Brown and H. H. Uhlig, J. Am. Chem. Soc., 1947, Vol. 69, p. 462. 72. P. H. Emmett and M. Cines, J. Phys. Colloid Chem., 1947, Vol. 51, p. 1329. 73. R. T. Davis and T. W. DeWitt, J. Am. Chem. Soc., 1948, Vol. 70, p. 1135. 74. N. Berkowitz and H. G. Schein, Nature, 1952, Vol. 169, p. 373. 75. R. N. Smith and C. Pierce, J. Phys. Colloid Chem., 1948, Vol. 52, p. 1115. BIBLIOGRAPHY Derjaguin, B. V., in Proceedings of the Second International Congress of Surface Activity, Solid/Gas Interface, Butterworths, London, England, 1957, p. 153. Juhola, A. J., and E. O. Wiig, J. Am. Chem. Soc., 1951, Vol. 73, p. 373. Pierce, C., J. Phys. Chem., 1953, Vol. 57, p. 149. Selwood, P. W., Magnetochemistry, Interscience, New York, N. Y., 1956. Simmons, J. H., G. L. Scheirer, Jr., and H. L. Ritter, Rev. Sci. Instr., 1953, Vol. 24, p. 36. 58

+ + + Div. 4/2 UNCLASSIFIED Div. 4/2 UNCLASSIFIED Inst. of Science and Technology, U. of Mich., Ann Arbor I. Faeth, Paul A. Inst. of Science and Technology, U. of Mich., Ann Arbor I. Faeth, Paul A. ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeth. ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeth. Oct. 62. 58 p. incl. illus., tables, 80 refs. Oct. 62. 58 p. incl. illus., tables, 80 refs. (Report No. 66100-2-X) Unclassified report (Report No. 66100-2-X) Unclassified report A volumetric adsorption apparatus and a gravimetric one A volumetric adsorption apparatus and a gravimetric one are described. The discussion of the volumetric method are described. The discussion of the volumetric method includes a detailed description of the construction and includes a detailed description of the construction and calibration of the basic apparatus, typical sample tubes, calibration of the basic apparatus, typical sample tubes, a special dewar, a heater, and special control devices. a special dewar, a heater, and special control devices. The procedures and methods of calculating specific sur- The procedures and methods of calculating specific surface area by the B.E.T. method using both nitrogen and face area by the B.E.T. method using both nitrogen and krypton, and of calculating true density, are presented krypton, and of calculating true density, are presented step by step. The measurement of pore volume distri- step by step. The measurement of pore volume distribution is also discussed. bution is also discussed. The gravimetric technique uses a quartz beam micro- The gravimetric technique uses a quartz beam micro(over) (over) UNCLASSIFIEDUNCLASSIFIED + + +IDiv. 4/2 UNCLASSIFIED Div. 4/2 UNCLASSIFIED Inst. of Science and Technology, U. of Mich., Ann Arbor I. Faeth, Paul A. Inst. of Science and Technology, U. of Mich., Ann Arbor I. Faeth, Paul A. ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeth. ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeth. Oct. 62. 58 p. incl. illus., tables, 80 refs. Oct. 62. 58 p. incl. illus., tables, 80 refs. (Report No. 66100-2-X) Unclassified report (Report No. 66100-2-X) Unclassified report A volumetric adsorption apparatus and a gravimetric one A volumetric adsorption apparatus and a gravimetric one are described. The discussion of the volumetric method are described. The discussion of the volumetric method includes a detailed description of the construction and includes a detailed description of the construction and calibration of the basic apparatus, typical sample tubes, calibration of the basic apparatus, typical sample tubes, a special dewar, a heater, and special control devices. a special dewar, a heater, and special control devices. The procedures and methods of calculating specific sur- The procedures and methods of calculating specific surface area by the B.E.T. method using both nitrogen and face area by the B.E.T. method using both nitrogen and krypton, and of calculating true density, are presented krypton, and of calculating true density, are presented step by step. The measurement of pore volume distri- step by step. The measurement of pore volume distribution is also discussed. bution is also discussed. The gravimetric technique uses a quartz beam micro- The gravimetric technique uses a quartz beam micro(over) (over) UNCLASSIFIED UNCLASSIFIED + + +

UNCLASSIFIED UNCLASSIFIE balance. The construction, manipulation, and calibration DESCRIPTORS balance. The construction, manipulation, and calibration DESCRIPTORS of the balance are described, along with procedures and of the balance are described, along with procedures and calculations for typical measurements based on mass Adsorption calculations for typical measurements based on mass Adsorption increases. These techniques include the measurement Chemistry increases. These techniques include the measurement Chemistry of sorption equilibirum, surface area, sorption kinetics, Krypton of sorption equilibirum, surface area, sorption kinetics, Krypton and magnetic susceptibility. Nitrogen and magnetic susceptibility. Nitrogen Gravimetric analysis Gravimetric analysis Volumetric analysis Volumetric analysis UNCLASSIFIEDUNCLASSIFIED + UNCLASSIFIED UNCLASSIFIED balance. The construction, manipulation, and calibration DESCRIPTORS balance. The construction, manipulation, and calibration DESCRIPTORS of the balance are described, along with procedures and of the balance are described, along with procedures and calculations for typical measurements based on mass Adsorption calculations for typical measurements based on mass Adsorption increases. These techniques include the measurement Chemistry increases. These techniques include the measurement Chemistry of sorption equilibirum, surface area, sorption kinetics, Krypton of sorption equilibirum, surface area, sorption kinetics, Krypton and magnetic susceptibility. Nitrogen and magnetic susceptibility. Nitrogen Gravimetric analysis Gravimetric analysis Volumetric analysis Volumetric analysis UNCLASSIFIEDUNCLASSIFIED

Div. 4/ 2 UNCLASSIFIED Div. 4/ 2 UCASE Inst. of Science and Technology, U. of Mich., Ann Arbor I. Faeth, Paul A. Inst. of Science and Technology, U. of Mich., Ann ArborIcath alA ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeth. ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeh Oct. 62. 58 p. inl. illus., tables, 80 refs. Oct. 62. 58 p. inc. illus., tables, 80 refs. (Report No. 66100-2-X) Unclassified report (Report No. 66100-2-X) Unclassified repor A volumetric adsorption apparatus and a gravimetric one A volumetric adsorption apparatus and a gravimetric one are described. The discussion of the volumetric method are described. The discussion of the volumetric method includes a detailed description of the construction and includes a detailed description of the construction and calibration of the basic apparatus, typical sample tubes, calibration of the basic apparatus, typical sample tubes, a special dewar, a heater, and special control devices. a special dewar, a heater, and special control devices. The procedures and methods of calculating specific sur- The procedures and methods of calculating specific surface area by the B.E.T. method using both nitrogen and face area by the B.E.T. method using both nitrogen and kryptor, and of calculating true density, are presented krypton, and of calculating true density, are presented step by step. The measurement of pore volume distri- step by step. The measurement of pore volume distribution is also discussed. bution is also discussed. The gravimetric technique uses a quartz beam micro- The gravimetric technique uses a quartz beam micro(over) (over) UNCLASSIFIED UCASFE Div. 4/ 2 UNCLASSIFIED Div. 4/2 UCASFE Inst. of Science and Technology, U. of Mich., Ann Arbor I. Faeth, Paul A. Inst. of Science and Technology, U. of Mich., Ann Arbor.Feh alA ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeth. ADSORPTION AND VACUUM TECHNIQUE by Paul A. Faeh Oct. 62. 58 p. inc. illus., tables, 80 refs. Oct. 62. 58 p. inc. illus., tables, 80 refs. (Report No. 66100-2-X) Unclassif ied report (Report No. 66100-2-X) Unclassified report A volumnetric adsorption apparatus and a gravimetric one A volumetric adsorption apparatus and a gravimetric one are described. The discussion of the volumetric method are described. The discussion of the volumetric method includes a detailed description of the construction and includes a detailed description of the construction and calibration of the basic apparatus, typical sample tubes, calibration of the basic apparatus, typical sample tubes, a special dewar, a heater, and special control devices. a special dewar, a heater, and special control devices. The procedures and methods of calculating specific sur- The procedures and methods of calculating specific surface area by the B.E.T. method using both nitrogen and face area by the B.E.T. method using both nitrogen and kryptom, and of calculating true density, are presented krypton, and of calculating true density, are presented step by step, The measurement of pore volume distri- step by step. The measurement of pore volume distribution is also discussed., bution is also discussed. The gravimetric technique uses a quartz beam micro- The gravimetric technique uses a quartz beam micro(over) (over) UNCLASSIFIED

UNCLASSIFIED UNCLASSIFIED balance. The construction, manipulation, and calibration DESCRIPTORS balance. The construction, manipulation, and calibration DESCRIPTORS of the balance are described, along with procedures and of the balance are described, along with procedures and calculations for typical measurements based on mass Adsorption calculations for typical measurements based on mass Adsorption increases. These techniques include the measurement Chemistry increases. These techniques include the measurement Chemistry of sorption equilibirum, surface area, sorption kinetics, Krypton of sorption equilibirum, surface area, sorption kinetics, Krypton and magnetic susceptibility. Nitrogen and magnetic susceptibility. Nitrogen Gravimetric analysis Gravimetric analysis Volumetric analysis (0 - - UNCLASSIFIED UNCLASSIFIED o____ + H 00UNCLASSIFIED UNCLASSIFIE 0 00 balance. The construction, manipulation, and calibration DESCRIPTORS balance. The construction, manipulation, and calibration DESCRIPTORS of the balance are described, along with procedures and of the balance are described, along with procedures and calculations for typical measurements based on mass Adsorption calculations for typical measurements based on mass Adsorption increases. These techniques include the measurement Chemistry increases. These techniques include the measurement Chemistry of sorption equilibirum, surface area, sorption kinetics, Krypton of sorption equilibirum, surface area, sorption kinetics, Krypton and magnetic susceptibility. Nitrogen and magnetic susceptibility. Nitrogen Gravimetric analysis Gravimetric analysis Volumetric analysis Volumetric analysis UNCLASSIFIED UNCLASSIFIED