ba-1961-0033.ch019

Surface Diffusion of Low Boiling Gases on Saran Charcoal J. R. DACEY

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Chemistry Department, Royal Military College of Canada, Kingston, Ontario, Canada

Hydrogen, deuterium, neon, argon, and methane flow through saran charcoal by both Knudsen and surface flow.

The latter is effected by the ad-

sorbed molecules sliding from site to site across the surface.

This is equivalent to a two-dimen-

sional Knudsen flow where the adsorption site acts as the wall of the three-dimensional case, and a slide across the surface is the same as a flight across the pore.

The activation energy for sur-

face diffusion is 75 to 8 0 % of the heat of adsorption.

It is possible to calculate theoretically the

relative contribution of each mechanism, while comparison

with

permits

experimental

its

He, which does

not

adsorb,

determination.

The

efficiency of surface flow is the ratio of the measured to the calculated value; this decreases as the size of the molecule increases, being 8 0 % for Ne and 1 2 % for CH . 4

lAfhen a gas passes, because of a pressure gradient, through a system of fine pores, the pressure may be sufficiently low and the pores sufficiently fine that the mean free path of the gas molecules is greater than the pore diameter. When this is so, the gas is transported by Knudsen flow and the amount of gas flowing is independent of the mean pressure but depends only on the pressure difference. When the pores are larger and the pressure is higher, the mean free path is smaller than the pore diameter. The gas is then transported by Poiseuille flow and the rate varies inversely as the gas viscosity. In this case the amount flowing at constant pressure gradient increases with the mean pressure. In any given case one may distinguish between these two methods of flow, as was shown by Adzumi, by plotting the amount flowing for constant pressure difference against the mean pressure ( 1 ). A horizontal line indicates Knudsen flow, while a sloping line indicates Poiseuille flow in addition. In the latter case the slope gives the Poiseuille flow and the intercept the Knudsen flow. When absorption occurs on the walls of 172

DACEY

173

Surface Diffusion of Low Boiling Gases

the pores, the adsorbed molecules may in some cases move along the surface, result ing in a transport of gas in the adsorbed phase. Such behavior has been found by Flood (8), Barrer (2, 3, 4), Carman (5), and others for a variety of porous solids. The present paper deals with the flow of small molecules through a porous form of carbon known as saran charcoal. Poly(vinylidene chloride) may be obtained from The Dow Chemical Co. as a white powder, designated saran A. To prepare saran charcoal from this powder it is first pressed into a convenient shape by use of a hydraulic press and steel die at a pressure of 15,000 p.s.i. The compressed polymer is then heated slowly in vacuo, starting at 1 2 5 ° C. and gradually increasing the temperature up to 7 5 0 ° C. The heating process takes about 3 weeks and the resulting piece of carbon retains the shape of the original polymer but is reduced in size in all directions by about 20%. Saran charcoal is a hard, strong, and highly porous form of carbon. The pores are believed to be very fine and uniform, slotlike in cross section, and be tween 12 and 15 A. in width in their narrowest dimension (6). In saran charcoal the pores are so small that molecules of the size of branched hydrocarbons, such as neopentane, iso-octane, and 2-methylpentane, to be in the pores at all are also on the pore walls. When such molecules are adsorbed, they pass into the charcoal by a process similar to the surface flow of adsorbed mole cules in larger pores. Such molecules move by an activated diffusion and activa tion energies have been determined from the temperature dependence of the rates of adsorption (6). Larger molecules such as α-pinene, tetraethylmethane, and sulfur hexafluoride, adsorb with great slowness, being too large to enter the pores easily. With small molecules up to 4 or 5 A. in diameter, Knudsen flow should be possible. However, gases such as H , D , Ne, and Ar are adsorbed so rapidly that their rates of adsorption cannot be readily measured. The present paper describes experiments designed to determine the flow mechanism of these small molecules through saran charcoal by measuring the transport of the gas under a pressure gradient through a thin diaphragm. 2

2

Experimental Methods Preliminary experiments indicated that a convenient charcoal diaphragm, permitting a reasonable flow rate of gas, was about 1 cm. in diameter and 0.2 to 1.0 mm. thick. A number of disks of carbon were made of this size by carbonizing slightly larger disks of compressed poly (vinylidene chloride) and smoothing them on each side by rubbing on fine emery paper. This made them flat, so that their thickness could be measured accurately. The disks were handled by dry-box technique to avoid adsorption of water or other contaminants from the air. The disk was mounted with Epon resin across the open end of a glass tube and the tube assembled as the inner tube of an ordinary trap. This trap is connected to the gas metering apparatus shown in Figure 1. This consists of a standard-bore tube of accurately known diameter, B, which contains the gas under investigation. The pressure is maintained constant by means of the tungsten contacts, E, which operate a relay, F, controlling a valve so that as the pressure drops the gas which has passed through the diaphragm is replaced by mercury, thus restoring the pressure. A similar metering device on the other side of the diaphragm measures the volume and maintains constant pressure of the gas leaving the charcoal. The rate of flow of the gas is measured by observing the level of the mercury in the standard bore tube by a cathetometer. The charcoal is located at C and may be held at constant temperature by immersion in a thermostat bath. The thermostat was a Dewar flask containing water for tem peratures between 0 ° and 1 0 0 ° C , and acetone or Freon for temperatures below zero. Cooling was accomplished by using an outer Dewar, the annular space be-

174

ADVANCES IN CHEMISTRY SERIES

tween being filled with liquid air. The gas pressure between the walls of the inner Dewar could be controlled to regulate the rate of cooling. A resistance wire wound around a support on the inner wall of the inner Dewar was used for heating. Temperature measurement and control to 0 . 0 1 ° C. were accomplished by a platinum resistance thermometer and a Miiller bridge. The off-balance current of the latter was amplified and used to operate the heating relay. Before being used for flow experiments, each disk was tested with helium for acceptability. The rate of helium flow at 10-cm. pressure gradient across the disk was measured at several mean pressures between 5 and 50 cm. Unless the mass of gas passing per unit time was constant—i.e., the flow through the disk followed Knudsen's law—the disk was rejected. About one disk in ten passed this test; the others showed increased flow at high pressures. Reproducible flow rates in the Knudsen region could be achieved with adsorbable gases only if the total amount adsorbed was small. Adsorption of 10% by weight, or greater, altered the permeability of the carbon. This effect on permeability may have been due in part to loosening of the cement but could not be wholly corrected by recementing. It is believed that the internal structure of the charcoal was altered in critical regions by strains produced by the adsorption of considerable amounts of adsorbate. For this reason all experiments on flow were carried out with less than 3% by weight adsorbed. Under these conditions results reproducible to within 5% were possible on any favorable sample for a considerable time. However, a charcoal disk would eventually change its flow properties, suddenly increasing in permeability. This may have been due to thermal shock, accidental exposure to too high a pressure, or some other cause. For this reason only a limited number of data were obtained from any one carbon disk and a number of different disks had to be used. During any series of runs the flow of helium was measured from time to time as a check on the condition of the carbon disk. A series of tests was made by measuring the helium flow rate after successive adsorption and desorption of ethane to 10% of the weight of the carbon. With a disk which originally exhibited only Knudsen flow, Poiseuille flow appeared and

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175


the Knudsen flow increased. After eight or nine cycles of adsorption and desorption the increase in flow stopped and a reproducible helium flow rate was established with a combination of Poiseuille and Knudsen flow. The adsorption isotherms were determined either gravimetrically with a quartz spiral balance or volumetrically by means of a modified B E T apparatus (9). The helium, argon, neon, and hydrogen were supplied by the Air Reduction Co. The methane was supplied by Phillips Petroleum Co. The deuterium was prepared from heavy water provided by Atomic Energy of Canada. The heavy water was reacted with an excess of the liquid alloy of Na and K, by breaking an ampoule of the alloy in the presence of 5 grams of heavy water contained in a closed system of 3-liter volume. Experimental Results A B E T plot of the adsorption data for argon at its boiling point gave a linear portion over the range p/p = 0.001 to 0.20. Taking 14.6 A. as the area of the argon atom, this gives a surface area for the carbon of 590 sq. meters per gram. The porosity of the carbon was calculated from the difference between helium and mercury displacement densities. The average value of ten disks, which agreed between themselves within 6%, was 0.44 cc. per gram. From these data an average pore radius, γ, may be determined by using the relation γ = 2e/A (7), where e is the porosity and A the area. The value obtained is 15 A. This assumes that the charcoal is made up of a large number of cylindrical pores. We know this is not true; the evidence of rates of adsorption shows that the pores are slotlike and less than 15 A. in diameter rather than radius (6). 0

P R E S S U R E IN cm. Figure 2.

Adsorption of neon at —35.0°, - 75.8° C.

—55.3°,

and

Figures 2 through 6 show the isotherms for neon, argon, hydrogen, deuterium, and methane. Heats of adsorption were calculated from these isotherms: Ne 1650, H 2350, D 2400, Ar 4900, C H 5900 cal. per mole. T h e carbon disks used for these experiments h a d been selected so that the 2

2

4

176


flow of helium was entirely Knudsen flow according to the Adzumi plot. This was confirmed by the measured temperature dependence, as seen in Figure 7 where the total amount of gas passing per unit time at constant pressure gradient

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Λ77

20 P R E S S U R E IN c m . Figure

40

5. Adsorption of deuterium at -70°, -35°, and 0° C.

1

6

8

P R E S S U R E IN c m . Figure 6.

Adsorption of methane at —30°, 0°, and 30° C.

varies inversely as the square root of the temperature. The helium flow is there fore taken to be a measure of the Knudsen permeability of the carbon disk and from it the Knudsen flow for any other gas can be calculated.

178


ι / VT Figure 7. Flow of helium through several different disks as a function of pressure All disks have approximately same thickness, 0.4 mm. The other gases used were examined in the same way as helium. In all cases the flow exceeded the Knudsen flow as predicted from the helium data. Figure 8 gives typical data; the flow in excess of the calculated Knudsen flow is attributed to surface diffusion of the adsorbed molecules. Instead of maintaining a pressure difference of 10 cm. across the carbon disk, one may select the proper pressures by reference to the adsorption isotherms so that the concentration gradient in the adsorbed phase remains constant. A pres sure gradient from 0.5 to 1% was chosen as suitable. Of the gases used, this technique is possible only with argon and methane, unless one uses very high pressures. The data in Table I were obtained in this way. Table I.

Flow of Gases for a Concentration Gradient in Adsorbed Phase of 0.005 to 0.010 Gram per Gram of Carbon Knudsen Flow,

Temp., °C.

Total Flow, Cc./Sec. Χ 70

-30 0 30 50

3.57 8.32 15.98 22.09

-30 0 30 60

1.87 4.80 13.48 28.15

Helium Data, Cc./Sec. X 10*

3

Surface Flow, Cc./Sec. X 10*

Argon 2.51 5.60 11.12 15.18

1.06 2.72 4.86 6.91

1.68 4.25 11.94 24.17

0.19 0.55 1.54 3.98

Methane

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179


01

I .05

Figure 8.

I .06

L_ .07

Gas flow as a function of pressure

Upper curves. Hydrogen and deuterium as compared with helium. Dashed line, disk 8 Lower curves. Neon and cahulated Knudsen flow of neon for disk 2

Discussion The Knudsen permeability of a porous system of unit area and thickness is 8 2RT given by Κ = =~^τ — — for unit pressure gradient, where κ is a structural conόκΑ

7ΓΜ

stant or shape factor. For any system of ideal cylindrical pores κ is equal to unity. With helium flowing through saran charcoal disks, the measured perme ability is between 4 and 8.5% of the ideal value. This means that κ lies between 25.0 and 11.7. The high value for κ indicates that this carbon does not resemble a system of ideal cylinders but rather that only a fraction of the void volume supports flow, the remainder being shut off from a continuous path or otherwise not functional. As can be seen from Figure 7, the resistance to flow of various disks is not proportional to the disk thickness. In fact, the value for κ for different disks varies over a range of about 200%, while the porosity varies only about 5%. The

180


proportion of pores supporting Knudsen flow in any given disk probably depends on random effects operating during its production. For this reason we cannot say that resistance to flow is the same at all depths throughout a single disk, and the pressure drop across a disk need not be linear with thickness. Hydrogen and deuterium both exhibit considerable surface flow, as seen in Figure 8. In both cases the temperature dependence gives an activation energy for surface diffusion of 1850 cal. per mole or 77% of the heat of adsorption. With these gases the total flow is always in the ratio 1:V2. Since this is the expected ratio for Knudsen flow, it follows that the surface flow also varies inversely as the square root of the molecular weight. It is therefore suggested that surface diffu sion is a two-dimensional Knudsen flow where fixed adsorption sites play the role of the walls and a slip across the surface is equivalent to that of a flight across a pore. The activation energy for surface diffusion is therefore the energy neces sary to break the bonds holding the molecule to the adsorption site while it still remains on the surface but is not free to slide to an adjacent site. This is to be contrasted with the activation energy for ordinary Knudsen flow, which is that necessary to remove the molecule from the surfaces and allow a free flight across a pore. The latter is equal to the heat of adsorption. Knudsen flow is not affected by the extent of adsorption. If two molecules of the same molecular weight have the same Knudsen flow—e.g., He and D —the former is not absorbed but the latter is. A molecule of a species which is strongly adsorbed spends a longer time on the wall than one of a more lightly adsorbed species, but at any instant the total number in flight across a pore is the same for each. For twodimensional Knudsen flow the same should be true. The species with higher surface concentration, for any given pressure, is more difficult to move laterally across the surface and spends more time at each fixed site than the less adsorbed one. As long as the ratio of the activation energy, E, for surface diffusion to the heat of absorption, ΔΗ, is the same for two gases, the surface diffusion would be expected to be proportional to l / V M . As seen below, size may play a part in surface diffusion; and the above statement may be true only if both species are of similar size. 2

Both the adsorption of neon and its surface flow are small. The accuracy of determining the activation energy for surface diffusion is therefore poor. A n average value of 1250 cal. is calculated from the data in Figure 8. This value is considerably greater than RT, indicating that we do have activated diffusion and not a mobile film. The data for argon and methane appear in Table I. The activation energies for these gases are, respectively, 3800 and 4450 cal. per mole. The ratio of e~ to e should give the number of times a molecule slides to an adjacent site within the surface for each time it leaves the surface for a flight across a pore. One would expect a single slip across the surface to be less effective in advancing the molecule than a single flight across a pore. Adsorption sites are perhaps only 2 or 3 A. apart, while a flight across a pore would advance a molecule 15 to 20 A. If we assume a factor of 7 for the relative value of a flight compared to a slip, we can arrive at an efficiency index for surface flow for each gas. For neon 2.6 surface slips occur for every Knudsen flight, but each flight is 7 times as effective as a slip; therefore, the calculated ratio of surface to volume flow is 0.37, the actual value is 0.29, and the efficiency for surface flow for neon is 78%. For methane the efficiency is only 12%. Figure 9 shows the efficiency plotted against the molecular diameter for the five gases used. On the assumption that molecular size does not affect ordinary Knudsen flow, one can conclude that E/RT

AH/BT

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DIAM.

Figure 9.

181

A .

Efficiency of surface flow as a function of molecular diameter

small molecules like Ne, H , and D move very efficiently across the surface while larger ones meet with surface hindrances and in effect must traverse a longer path. 2

2

Acknowledgment We acknowledge the financial assistance of the Defence Research Board of Canada under Grant 8220/12. Literature Cited (1) Adzumi, H., Bull. Chem. Soc. Japan 12, 285 (1937). (2) Barrer, R. M., Barrie, J. Α., Proc. Roy. Soc. (London) A213, 250 (1952). (3) Barrer, R. M., Grove, D. M., Trans. Faraday Soc. 47, 837 (1951). (4) Barrer, R. M., Strachan, E., Proc. Roy. Soc. (London) A231, 52 (1955). (5) Carman, P. C., Raal, F. Α., Ibid., A209, 38 (1951); Trans. Faraday Soc. 50, 842 (1954). (6) Dacey, J. R., Thomas, D. G., Ibid., 50, 740 (1954). (7) Emmett, P. H., de Witt, T. W., J. Am. Chem. Soc. 65, 1253 (1943). (8) Flood, Ε. Α., Tomlinson, R. H., Leger, A. E., Can. J. Chem. A30, 348, 372, 389 (1952). (9) Young, D. M., Beebe, R. Α., Bienes, H., Trans. Faraday Soc. 47, 1086 (1953). RECEIVED June 19, 1961.

ba-1961-0033.ch019

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