PHASE TRANSITIONS OF ARGON ADSORBED ON GRAPHITE' GEORGE JURA
AND
DEAN CRIDDLE
Department of Chemistry, University of Calzfornia, Berkeley, California Received August 10, 1960 I. INTRODUCTION
The detailed investigations of the adsorption of n-heptane on ferric oxide (12) and graphite (11) have demonstrated that first-order transitions of the adsorbed gas occur a t sufficiently low temperatures and pressures. These films exhibit critical temperature phenomena. Many such transitions are known but only the above two have been studied in detail. The above investigations revealed a number of unexpected facts. First, below the critical temperature and a t pressures below the transition temperature, the normal temperature coefficient of adsorption is reversed; the higher the temperature, the greater the amount adsorbed a t a given pressure. Second, the heats of transition are considerably higher than the corresponding gas-liquid transition in three dimensions. The heats are computed on the assumption that the surface is homogeneous. If the transition occurred on only part of the surface, the heats are indeterminate, and in previous work would be lower. Third, the values for the critical constants are a t variance with those predicted by the theories of either Deronshire (3) or Hill (7). In order to further elucidate the transitions, the study of the argon-graphite system was undertaken. Several factors favored this choice: the ease with which pure materials could be obtained, the convenient temperature range in which the transitions were expected to occur, and the fact that this system would more closely approximate the assumptions in the simplified available theories of the transition. This paper reports the results of the adsorption studies of argon on graphite from 63.8"K. to 77.3"K.The observed relations are more complex than has been previously observed for any other system. As many as four transitions were found in a single isotherm. In other respects-namely, temperature coefficients and heats of transition-the isotherms were normal. The temperature coefficient was always that expected and the heats of transition are small. 11. EXPERIMENTdL
The graphite used was obtained from Dr. M. Corrin, who in turn had obtained it from Dr. L Winters of the National Carbon Company The sample was supposedly free of oxygen complexes on the surface and had an ash content of less than 0.001 per cent. The specific area, 3.22 m.2g.-', was determined by 1 Presented a t the Twenty-Fourth National Colloid Symposium, which u a s held under the auspices of t h e Division of Colloid Chemistry of the American Chemical Society at St. Louis, Missouri, June 15-17, 19m. 163
164
GEORGE JURA A S D D E . 4 5 CRIDDLE
Dr. Corrin by nitrogen adsorption a t 77.3’B. The argon was of Airco “spectroscopically pure” grade. The analysis supplied claimed less than 0.01 per cent impurity. The purity was checked in the following manner. A sample of the gas was condensed a t about G4’K. The vapor pressure \vas measured, a part of the argon was removed by the vacuum pumps, and the vapor pressure of the remaining solid was determined. The vapm pressure of the residual argon was the same as that of the original. The measurements indicated that the amount of any impurities present was less than 0.1 per cent.
=TO MANOSTAT
r
‘TO NITROGEN INTAKE
MANOSTAT
FIG.1. A schematic drauing of the cryostat; the head is shown in detail
The solid was degassed in a high vacuum a t 450°C. for a period of 16-20 hr. Before heating the sample was evacuated for about 12 hr. a t room temperature, in order to minimize the formation of the oxygen complex on the surface. The cryostat used is a low-temperature calorimeter with the electrical leads removed, as described by Giauque and coworkers (4). A schematic diagram of the cryostat is shown in figure 1. The liquid used in the cryostat was nitrogen. Temperature was controlled by the rate of pumping of the nitrogen in the large Dewar flask. Two manostats, one for the large outside Dewar and another on the small constant-temperature Dewar, controlled the pumping rate through relays which operated magnetic solenoid valves as well as the current for the pumps. The maximum variation in the temperature in the inner bath corresponded to a nitrogen pressure of f 0 . 1 mm. of mercury. The temperature was determined with a nitrogen vapor-pressure thermometer and was computed from the equation:
+
log p = -339.8/T 6.71057 as proposed by Giauque and Clayton (5).
- 0.005628GT
PHASE TRAKSITIONS OF ARGON ON GRAPHITE
165
The isotherms were determined volumetrically. The final pressures were so low that no correction was essential for the unadsorbed gas. The isotherms were obtained from successive additions from a buret of about 10-ml. capacity and a pressure of about 10 mm. The equilibrium pressures were determined by a McLeod gauge. In general, the equilibrium gas pressures were such that the mean free path of the gas was of the order of the diameter of the connecting tubing. Thus it was essential to correct the observed pressures for thermal transpiration. The necessary corrections were measured a t 7i.3"K. by the following procedure. Two U-tubes were constructed: the first was formed from a tube having an inside diameter of 8 mm. and a tube having an outside diameter of 50 mm.; the second with a tube having an inside diameter of 8 mm. and a series of twelve capillary tubes 0.4 mm. in diameter. Each arm of the U-tube was connected to a calibrated McLeod gauge. The closed end of the U-tube was maintained at a constant depth of immersion in a liquid-nitrogen bath. The argon pressure was then varied, and readings were taken on both arms. If the mean free path is long compared to the diameter of the tube, the equation relates the true pressure to the observed pressure (13). If the mean free path is short compared to the diameter of the tube, then the pressures are related by the equation
where pq
=
PI
+ P Z / +~ W l a
The former of the two relations was used in conjunction with the U-tube, one arm of which was constructed of capillaries, while the latter was used with the 50-mm. U-tube. I t was thus possible to relate the pressure of the gas a t room temperature to that existing in the adsorption chamber. The choice of the tubes was such that a short region of the pressure range could not be directly measured. This region was approximated by connecting the two branches of the curve shown in figure 2 . Since the temperature variation used in this investigation is not large, it is believed that no appreciable error is introduced when the where the correction for thermal results a t 77.3"K. were multiplied by (T~/!!'Z)''~, transpiration is necessary. The dispersion of the sample in the container was found to be important. The most satisfactory was one in which the powder was distributed on a number of shelves. A center tube, perforated along its entire length, permitted ready access of the gas to all parts of the adsorption chamber. The time necessary to establish equilibrium between the solid and the gas with this container was 10 min., whereas a solid bed required as much as 24 hr.
166
GEORGE JURA AND DEAN CRIDDLE I
1
I
I l"p &served
preltwo
I
.I
FIG.2. The thermal transpiration correction f o r argon between the temperatures of 77.3OK. and 298°K. The internal diameter of the tube is 8 mm.
o 0.7
.
8
F I G 3. . The isotherms of argon on graphite from 63.8"to 77.3'K. Note t h a t a monolayer requires approximately 0.75 ml. of argon. 111. RESULTS AND DISCUSSION
The isotherms were determined to the highest pressure that could be read on the McLeod gauge used,-about 0.l.mm. or until approximately a monolayer was adsorbed. A determination of the complete isotherm would require a different apparatus from that necessary for the low-pressure region. From the area
PHASE TR.4NSITIONS OF ARGOS O S GR.4PHITE
167
as determined by nitrogen adsorption a monolayer of argon on this sample would require approximately 0.75 ml. The isotherms from G3.8"K. to 77.3"K. are exhibited in figure 3. The values for PO were computed from the constants in the International Critical Tables (10). In figure 3 the experimental points a t the lowest pressures are omitted. This region is shown in figure 4.Figure 5 shows the region in which the transitions occur, while figure G exhibits two duplicate determinations a t 65.16'K.
FIQ.4. The adsorption of argon on graphite at very low pressures
There are a number of features of particular interest. First, the shape of the curves below the formation of a monolayer. The isotherms are sigmoid with two points of inflection. This behavior is general after a monolayer has been formed. Similar isotherms of argon on the alkali halides have been found by Orr (14). A careful analysis of the data indicates that the only transitions are those exhibited in figure 5. I t appears that the film is gaseous, even though the curve is sigmoid. A virial equation of state for the adsorbed gds is capable of describing the shape of the isotherms. Further investigations of this region from the theoretical point of view are in progress. The second feature is the apparently large temperature coefficient below the pressures a t which a monolayer is formed. The differential heat of adsorption
168
G E O R G E J U R A AXD D E A N CRIDDLE:
in this region is about 3000 cal. mole-l, not abnormally high. It should be noted that the temperature coefficient is normal a t all coverages, both above and below the transitions. This behavior is in contrast to that observed in the transitions previously studied--heptane on graphite and ferric oxide-where there is an inversion of the temperature coefficient in passing over a transition. One other aspect of the effect of temperature is noticeable. From the data available it appears that the lower the temperature the lower the relative pressure a t which the amount of gas corresponding to urn is adsorbed. The above is based on the assumption that vrn = 0.78 ml., and will vary only slightly with temperature.
OOOP MM Hc FIG.5. T h e first-order transitions observed in the adsorption of argon on graphite. The experimental points are shown in figure 6.
The transitions observed in this system are shown in figure 5 . For the sake of clarity the experimental points in this figure have been omitted. The experimental points and reproducibility are illustrated in figure 6, which exhibits duplicate determinations a t 65.16dK. A minimum of two determinations was made at each temperature. No poorer checks were obtained in any instance than those illustrated in figure 6. I n figure 5 no attempt has been made to average the values of the various isotherms. The first determination a t each temperature was used in the compilation of figure 8. By a judicious choice a more consistent set of curves could be shown. The startling fact is the number of observed transitions: four a t 65'K., two a t 66"K., and one a t 67.25'K. There also is some evidence that there are no transitions a t 63.80'K.; none could be found with the present means of pressure measurement. However, the change in pressure over the region in which the transitions are expected to appear is too small to be determined by a McLeod gauge. A more precise means of pressure determination is essential before any
PHASE TILZSSITIOXS OF A R G O S OS GRAPHITE
169
positive statement can be made concerning the existence or nonexistence of any transitions below 64°K. There are two possible explanations for the number of transitions that have been found. The first would depend upon a heterogeneous surface, the second upon the occurrence of polymorphic transitions in the adsorbed film. Or, there may he a combination of the two explanations. The amount of work performed to date does not permit any conclusive decision. The writers believe that the concept of polymorphic changes is to be favored. The arguments for this follow.
.45
I
I
0 0 .
103P
FIG.7 FIG.6 . Duplicate determinations of argon on graphite at 65.16'K. FIG.7. The adsorption of water on anatase a t 25°C. The specific area of t h e titanium dioxide is 13 8 m,*g,-1 FIG.6
Let us first consider the possibility of a heterogeneous surface. First, consider the adsorption of some gas on an ideal crystal of anatase. Further assume that the crystals are in the form of rectangular parallelopipeds. There are then present two crystalline faces, the 100 and 001. Each of these faces mill adsorb gas, depending on their respective energies. In general, the isotherms would be different, especially in the low-pressure region where any specific relations would be observable. If transitions occur, it is probable that the pressure of the gas a t which the transition occurs will be different for each of the two faces. I t is probable that two transitions rather than one will be observed when a gas is adsorbed on anatase. Figure 7 exhibits the isotherm of water on anatase a t 25OC. Similar results have been obtained with n-heptane and propyl alcohol (6). The extension of this idea to the present system would require that there be present on the graphite four different surfaces and also that two of these surfaces pos-
170
GEORGE JURA A N D DEAN CRIDDLE
sess approximately the same critical temperature. The latter is required by the reduction from four to two transitions as the temperature is increased. Another possibility of explaining the number of transitions would require only one surface but a surface which was energetically inhomogeneous. This follows from the work of Hill (8). The extension of the work of Hill would require a maximum of two surfaces to account for the number of transitions that are found. The main argument against the crystallographic heterogeneity of the surface must arise from the structure of graphite. It is much cheaper to cleave graphite than t o break the bonds. Any process of diminution would lead to a preponderance of the c surface. I t appears probable that any means of manufacture of a fine graphite would yield an almost uniform crystallographic surface. Thus, if the surface is heterogeneous, it must be energetically so. There are several factors which favor the idea that the transitions are polymorphic changes. First consider the heats of transition. Computing the heats of transition by means of the Claperon equation, dn
AH
zF=Tarr where K is the film pressure, T the temperature, u the area of the surface available per molecule, and AH the heat of transition per molecule, it is found that the heats of transition vary from 50 to 100 cal./mole. This figure is exceedingly low, The magnitude of the heat change is characteristic of polymorphic phase changes rather than a phase change involved in a gas-liquid or gas-solid change. The above heats are computed on the assumption that the surface is homogeneous. If the surface were not homogeneous, the computed heats would be indeterminate but approximately as given provided the various "surfaces" adsorbed approximately the same amount a t a given pressure. The heat effects appear to be too small to favor heterogeneity. Barrer (l),in his studies of the adsorption of argon on graphite, has concluded that there was a 500 cal. barrier to the translation of an argon molecule on the surface of graphite. R T , the possible translational energy of the molecule on the surface, is small in this investigation compared to the height of the barrier. Therefore the film is nonmobile and the symmetries of the adsorbed layer should be fixed by the lattice of graphite. A large number of symmetrical arrangements of argon on graphite are possible, but only centered hexagonal symmetries are considered. Tetragonal symmetries are also possible, but in these two of the next nearest neighbors are almost the same distance away as the four nearest neighbors. Many such arrangements are possible, several of which are a t reasonable interatomic distances for interaction of the argon atoms. These would lead to transitions each of which would require only 10 per cent more gas adsorbed than that observed for the transitions. This agreement between the predicted and observed values for the volume positions of the transitions is a strong argument in favor of the idea of a polymorphic transition. It is this coincidence of observed and found positions, coupled with the magnitude of the heats of transition, which makes it appear that polymorphic changes might account for the
PHASE TRANSITIONS OF ARQON ON QRAPAITE
171
number of transitions that are observed. Table 1 lists the observed volumes a t which transitions occur and the computed volumes of transition. This evidence is not sufficiently conclusive to permit a certain conclusion. The only possible precedent for this conclusion is to be found in the work of Copeland and Harkins, who observed such a change in the films of the long-chain alcohols on water (2). Sufficient data are available for a rather complete computation of the thermodynamic quantities related to the adsorption of argon on graphite. The isosteric TABLE 1 The comparison of observed and computed volumes of transition
v
V (COYPUTLD)
0.76 0.51 0.37 0.27 0.16
(OBSrnVrn)'
0.42t o 0.46 0.35 t o 0.32 0.32 t o 0.34 0.28 to 0.31
~
I
* V (observed) is taken from the midpoint of the transition. The.two values given are the highest and lowest values at which this transition is found t o occur.
V VOLUME ABSORBED, C C E T P ) Gi
ae 04 06 VOLUME ADSORBED. CC(STP)G"
08
FIG.8 FIG.9 FIG.8. The isosteric heat of adsorption of argon on graphite FIG 9 The effect of t h e adsorption of argon on the surface free energy, heat content, and entropy.
heats of adsorption are shown in figure 8. It is of interest to make all the possible computations indicated by Hill (9). Many of these quantities make use of the derivatives of various functions. Their accuracy cannot be as high as that yielded by direct measurement, which is contemplated. Therefore, the discussion of the thermodynamic quantities is reserved until the completion of the heat measurements. The similarity of these curves with "stepwise" adsorption should be noted. What occurs in the argon-graphite system is similar and yet different in that the steps do not persist with temperature.
172
QEOROE JURA AND DEAN CRIDDLE
It is evident that a great amount of further work is essential before any real comprehension of the adsorption of argon on graphite is possible. The present measurements are sufficient merely to outline in block form the actual complexity of the adsorption process. A real understanding probably will be had only when thermal measurements are available and the present adsorption measurements repeated with a high degree of precision. The limitation of the present measurements is the use of a McLeod gauge as a means of determination of pressure. Undoubtedly a Pirani gauge could be used; this would yield the necessary precision in the measurement of the equilibrium pressure. IV. SUMMARY
The adsorption of argon at low surface coverages was measured on graphite. Four first-order phase changes were found a t 65'K. A possible explanation for the number may be that the surface is heterogeneous or that the adsorbed film undergoes polymorphic transitions. Insufficient evidence is available to make any conclusion certain. The authors favor the explanation of polymorphic changes for two reasons: first, the heats of transition are low, 50 to 100 cal. mole-'; second, the structure of graphite would permit many symmetrical arrangements of the adsorbed molecules in the region in which the transitions are observed. If the number of transitions are due to heterogeneity, it appears certain that the heterogeneity is energetic rather than crystallographic. The adsorption of argon on graphite is sigmoid even a t surface coverages less than that required for a monolayer. A few of the possible thermodynamic quantities of interest obtainable from the data are presented. REFERENCES ( 1 ) BARRER, R.
M.:Proc. Roy. Soc. (London) A161, 476 (1933).
W. D . : J. Chem. Phys. 10,272 (1942). (2) COPEIAND, L. E., AND HARKINS, A. F . : Proc. Roy. SOC. (London) A163, 132 (1937). (3) DEVONSRIRE, (4) GIAUQUE, W . F . : Private communication. (5) GIAUQUE, W. F., AND CLAYTON, C . : J. Am. Chem. Soc. 66,4879 (1933). (6) HARKINS, W.D . , AND LOESER,E . : Unpublished work. (7) HILL,T. L . : J. Chem. Phys. 14, 263 (1946). (8)HILL,T. L.: J. Chem. Phys. 17, 520 (1948). (9) HILL,T. L.: J. Chem. Phys. 18, 246 (1950). (10) International Critical Tables, Vol. 111, p. 208. McGraw-Hill Book Company, Inc., New York (1928). (11) JURA,G., HARKINS, W . D . , AND LOESER,E. H . : J. Chem. Phys. 14, 344 (1946). (12) JURA,G., LOESER,E. H . , BASFORD, P . R . , AND HARKINS, W . D . : J . Chem. Phys. 14, 117 (1946). (13) KENNARD, E. H . : Kinetic Theory of Gases, pp. 330-3. McCraw-Hill Book Company, Inc., New York (1938). (14) ORR,W. J. C . : Proc. Roy. SOC. (London) A173, 349 (1939).
