Surface Diffusion of Hydrogen on Carbon
by Andrew J. Robell, E. V. Ballou, Lockheed Misrriles & Space Company, Palo Alto. California
and Michel Boudart University of California, Berkeley, California
(Received March 18, 1964)
The slow uptake of hydrogen on platinized carbon is due to activated diffusion of adsorbel hydrogen atoms away from platinum centers which chemisorb molecular hydrogen rapidly. The phenomenon has been studied both with hydrogen and deuterium, between 300 and 392 O, from 30 to 60 cm. of pressure on carbon samples containing 0.2 and 1% platinum by weight.
Introduction Physical adsorption of nitrogen is used routinely in the determination of the total surface area of porous adsorbents and catalysts. To determine the surface area of specific components, e.g., metals dispersed on an oxide support, it is sometimes possible to use selective chcmical adsorption. For instance, the surface area of platinum supported on alumina can be measured by means of chemisorption of hydrogen on the platinum component of the catalystU2 In this particular example, the success of the method relies on the fact that hydrogen after adsorption on the platinum sites is apparently unable to migrate on the nonmetallic sites of the support so that, a t selected temperatures and pressures, a one-to-one correspondence seems to prevail between exposed platinum atoms and adsorbed hydrogen atoms. This condition was found to fail for a part,icular system studied in our laboratory. The total number of hydrogen atoms taken up by a platinum-carbon sample exceedcd considerably the sum of two numbers: first, the number of hydrogen atoms taken up by the same weight of carbon sample in a separate measurement a t identical pressure and temperature, and second, the number of hydrogen atoms equal to the total number of platinum atoms in the platinum-carbon sample. Clearly, this observation suggests that a rather large fraction of the adsorbed atoms, after adsorption on the platinum sites, migrate to the carbon surface. A search of the literature revealed that the same phenomenon was reported in 1933 by Burstein, Lewin, and The .Journal of P h ~ s i c a lChrmistrU
Petrow,a who proposed the same interpretation, However, this explanation was later contested by Roginskii.4 I n order to elucidate the nature of the phenomenon further, it was decided to study systematically the adsorption of hydrogen on platinum supported on pure carbon. The effect of temperature, pressure, and amount of platinum on the rate of adsorption of hydrogen and deuterium on platinized carbon is reported and discussed in this work.
Experimental The carbon selected was Spheron 6 , a high purity channel black made by the Godfrey Cabot Corp., consisting of almost sphericaI nonporous particles, 150 A. in radius, with a B.E.T. nitrogen surface area of 100 m.*/g. Samples containing 0.2 and 1.0 wt. yo platinum were prepared by impregnation of the carbon with chloroplatinic acid. The amount of hydrogen adsorbed as a function of time at a constant pressure and temperature was measured volumetrically in an apparatus of standard design. Hydrogen and deuterium were purified by diffusion through palladium. Samples contained in quartz cells were reduced in flowing hydrogen a t 500” (1) St.mford ITriiser\it\ , Stanford. (‘:ill1 (2) L. Spenadel and M . Roudart, J . Phys. Chem.,64, 964 (1960).
(3) R. K. Burstein. P. Lewin, and 8. Pctrow. Physik. Z.,4, 197 (1933). (4) S. 2.Roginskii, “Adsorption and Catalysis on Heterogeneous Surfaces,” Moscow, 1948, p. 329.
SURFACE DIFFUS~ON OF HYDROGEN ON CARBON
2749
and evacuated a t 900" prior to and between the adsorption runs. Results are expressed as STP C I ~ of . ~ inolecular hydrogen taken up per gram of sample. After an adsorption run at 350", gases were pumped out a t temperature and analyzed: no more than 0.2% methane was found.
Results A typical run is shown in Fig. 1. It is seen that the amount of hydrogen taken up after 50 min. exceeds by about I erns3the sum of two quantities: the amount taken up by the carbon sample without the metal and thc amount corresponding to one hydrogen atom adsorbed for each platinum atom in the sample with the metal. This is the principal observation that was found in all the work described here. In what follows, we shall designate by "net adsorption" the amount adsorbed on a platinum carbon sample minus that adsorbed on the carbon blank alone. The effect of pressure on the net adsorption is illustrated in Fig. 2. Such studies showed that the net amount adsorbed a t a given time increases as the square root of the hydrogen pressure, p . S e t adsorption also increases with temperature (Fig. 3). l'rom such data, an apparent activation energy, E , can be calculated. It is found to be about 8 kcal./mole (see Fig. 4).
i.2,
O 00
20 *
.(0
'
30L
40 TIME MINI
50
7
60
Figure 2. Effect of pressure on net adsorption of Hz: data a t 300" on 1% Pt sample. Continuous curve, experimental values a t 30 cm.; 0, values a t 45 em. multiplied by (30/45)'/2; A, values a t 60 a n . multiplied by (30/60)'/?
01 0
I
I
I
I
1
10
20
30
40
50
I
TIME (MIN)
Figure 3. Effect of temperature on net adsorption of Hz: data at 60 rm. on 0.27; Pt sample: 3 , 300"; A, 350"; 0,392'.
I
01
10
0
I 20
I
I
30 40 TIME ( M I N I
I
50
I 60
Figure 1. Volume (STP rm.a/g.) of hydrogen adsorbed as a function of time, a t 350' and 60 cm.: 0, Spheron 6; A, Spheron 6 0.294 P t ; w, adsorption of hydrogen corresponding to one hydrogen atom per platinum atom (calculated).
+
1
70
Increasing the amoiirit of platinum by a factor of five also increases the net adsorption by a factor of less than five (Fig. 5 ) . A t later times especially, the sample with the higher content, of platinum exhibits an apparent saturation although the percentage of tho total carbon surface which is covered by hydrogen docs not Volume 08,Sunaher 10
Orlober. 1,964
2750
A. J. ROBELL, E. V. BALLOU, AND Ril. BOUDART
t5
1.6 1000
r
1.7
1.76
OK
Figure 4. Determination of apparent activation energy E: values of net adsorption F of H, a t various times t (min.) and pressures p (cm.): V, t = 10, p = 30; A, t = 5, p = 30; 0 , t = 10,p = 60; 0, t = 5 , p = 60.
OL
0
I 10
I
I
20
30
I 40
I
50
3
TIME ( MIN 1
Figure 6. Kinetic isotope effect a t 392' and 30 cm. Adsorption on carbon: 0, H2; 0 , D2. Net adsorption on 1% Pt sample: 0, Hz; B, Dz.
1.5 1.4
that of direct adsorption on the carbon blank (Fig, 6). Indeed, hydrogen is adsorbed faster than deuterium on the pure carbon samples, but the reverse is true for the net adsorption on platinized carbon. Although these data do not warrant a detailed analysis, they are compatible5 with the idea of activated adsorption of molecular hydrogen on pure carbon (with a normal kinetic isotope effect) and of activated diffusion of atomic hydrogen on the sample containing platinum (with an inverse kinetic isotope effect).
1.3 1.2
-
-
Q V V
B
>O
1.1 1.0 0.9
0.0 0.7
0.6
0.5 0.4
Discussion
0.3
All the data indicate that hydrogen molecules are adsorbed rapidly on platinum sites and then diffuse slowly away from them. It will now be assumed that the activated slow process is surface diffusion and not bulk diffusion. This assumption is supported by the apparent saturation occurring a t relatively low values of surface coverage. This apparent saturation would be even more difficult to understand if the slow uptake were due to diffusion into the interior of the carbon particles. Furthermore, absorption of hydrogen in carbon has never been reported. An attempt will now be made to explain the data quantitatively. Let us assume that the surface of carbon is covered with a certain number (n per gram)
0.2 0.1
t-
I TIME (MINI
Figure 5. Effect of amount of platinum on net adsorption of Ht a t 350". On 1% Pt: 0 , p = 60 cm.; 0, p = 45 cm.; p = 30 cm. 0 , p = 30 cm. On 0.270 Pt: B, p = 60 em.;
*,
exceed about 1%. This apparent saturation becomes noticeable at high platinum contents, long times, and high temperatures and pressures, all favoring a large net adsorption. Finally, the kinetic isotope effect shows distinctly that the nature of the net adsorption is different from The Journal of Physieal Chemistry
(5) J. Bigeleisen, J . Chem. Phys., 17, 675 (1949).
2751
SUItFACE D I F F U S I O N O F I l Y D H O G E N ON C A R B O N
of identical active zones associated with the platinum centers. Each zone is covered with hydrogen atoms in equilibrium with gaseous molecular hydrogen. Let the surface concentration of hydrogen atoms on each zone be co (number of atoms/cm.2). The value of co depends only on temperature and pressure and does not depend on time during an adsorption run. It is already apparent that the rate of net adsorption will depend on pressure through co. It will be seen later that it must be proportional to co. Therefore (Fig. 2), co must be proportional to p”*, This pressure dependence indicates dissociative adsorption in the low coverage region (Henry’s law). But studies of adsorption of hydrogen on platinum2 suggest that the surface of platinum ought to be almost completely covered with hydrogen a t least a t the lower temperature and higher pressure used in this work. Therefore, we are led to the hypothesis that the equilibrated zone serving as the source for surface diffusion consists of platinum centers surrounded by carbon centers. We now have to deal with a carbon zone in equilibrium with gaseous hydrogen, the rapid equilibration being brought about by the platinum centers. The rapid equilibration also suggests that hydrogen atoms are rather freely mobile on‘the equilibrated carbon zone. By contrast, the rate of diffusion of hydrogen on the carbon surface surrounding the equilibrated carbon zone is very slow, as indicated by the data. This situation can be understood if the equilibrated carbon zone consists of tasal planes of the graphite structure, whereas the surrounding carbon surface consists of more amorphous regions with a carboncarbon distance more characteristic of the distance (3.4 d.) between the basal planes in the graphite structure (Fig. 7). Thus we shall assume that the jump distance, d, on the carbon surface surrounding the carbon equilibrated zone is equal to 3.4 d. NOW,for the coefficient D of activated surface diffusion, we use the Einstein type of expression
4 where E, (kcal./mole) is the activation energy for surface diffusion and v is a frequency which, in the absence of further information, will be taken as equal to 1013sec. - *. With this picture in mind, we can write down and solve the differential equation for surface diffusion away from a constant circular source of radius a. The solution adapted from the analogous problem for heat transfer6 is shown in Fig. 8. In this doubly logarithmic plot, the abscissa is a dimensionless time
Dt
r = -
a2
The ordinate is a dimensionless amount of diffused particles a t time t 2F’
cp’ = coa
(3)
where F’ is expressed in number of atoms having diffused at time t/cm. of source perimeter.
Figure 7. Equilibrated adsorption on zone of radius a followed by surface diffusion.
/I
3 21
Figure 8. Solution of the diffusion equation; dimensionless pld of amount diffused us. time.
As can be seen in Fig. 8, the relation between log W and log r is linear in a restricted interval of dimensionless times. The data obtained on the 0.2% Pt samples can also be represented in a doubly logarithmic plot (Fig. 9) and the logarithm of the net amount F taken up a t time t is proportional to the logarithm of time t. The slope, at least a t short times, not larger than 10 min., is 0.6. The corresponding region of interest in Fig. 8 is therefore that which can be approximated by a straight line of slope equal to 0.6. This happens for -2 6 log r 6 1.3. In this region therefore N
log a’
=
N
0.6 log 7 -I- constant
(4)
(6) H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” Oxford University Press, London, 1959.
Volume 68, Number 10 Octnher, 1.9ciB
2752
A. J. ROBELL, E. V. BALLOU, AND M. BOUDART
P 0 Y
LL
0.05
c
fll lo,. -/
,
0.021 SLOPE , =OS4
0.04 0.7
2
I
IO
5
20
50
0.5
0.I IO0
TIME(MIN)
Figure 9. Net adsorption of HZa t 300” on 0.2% Pt sample: A, p = 60 cm.; 0, p = 30 cm.
Since a’ is proportional to P‘ and the latter is proportional to F , substitution of ( 2 ) and (3) into (4)gives
F 0: coD0.6 (3 Thus, as stated earlier, the amount adsorbed a t time t is proportional to q,and thus also to p”’ for adsorption with dissociation a t small coverage. The value of co depends exponentially on temperature co = Q’ e x p ( q / 2 R T ) X p”’
(6)
where q is the exothermic heat of adsorption of hydrogen on the equilibrated zone, in kcal./mole. From the measured temperature dependence of F , we get by substitution of (1) and (6) into (5) E’
=
10 d. A smaller value would be meaningless. A larger value, say 50 or 100 8., would lead to serious difficulties because the total area of equilibrated zones would correspond to a large amount of hydrogen taken up instantaneously. This is not observed. Then, if log 7 = log Dt/az must remain smaller than 1.3 for t = 10 nlin. and a = 10 ,&.,and if we use (l), we see that a must be larger than or equal to 0.58. We shall take (Y = 0.58 because larger values lead to correspondingly smaller values of the dzusivity, D, which in turn nccessitate unreasonably large values of n,the number of diffusion sources, required to fit the data. With a = 0.58, as will be seen, D already is quite small a t the temperatures of the experiments. With this value, eq. 10 gives s = 67.7 kcal./mole. Therefore, E, = 39.2 kcal./mole from (8), and q = 31.2 kcal./mole from (9). With E , = 39.2 and the assumed value of the jump distance d = 3.4 A., eq. 1 gives D = 3.4 X lo-’@and 5.8 X 10- cm.2/sec. a t 300 and 392”, respectively. Before adsorption curves can be calculated, two more parameters have to be chosen. One is the coefficient of proportionality co’ in eq. 6. This will be chosen &s large as possible because if it were small, a larger value of the number n of sources would be required to fit the data. The largest value of Q’ believed to be reasonable is that which gives co = 1015a t the experimental conditions of highest coverage, 300” and 60 cm. of pressure. This value of co corresponds to 10% surface coverage on the equilibrated carbon zones and it is recalled that a condition of small coverage for these zones is required by the pressure dependence of the data. The final parameter is n, the number of diffusion sources; it is a “scaling factor” and will be used to fit observed data. It is chosen equal to 3.16 X lo” for the samples containing 0.2% platinum. This is a reasonable figure. Indeed, if platinum atoms were atomically dispersed on carbon, n would be equal to 6 X 10l8,but a large fraction of the metal was shown by X-ray diffraction to be present as particles of 80 A. average diameter. The number of these, if all the platinum were accounted for by these particles, would be 2.8 X 10’4, a value about 1/1000 of that required if these crystals had to play the role of diffusion sources. The assumed values are summarized in Table I. As discussed above, these values are suggested by the physical picture of the process. They are reasonable values and there is surprisingly little leeway in their choice as was emphasized during the discussion.
0.6Ra - 0.5q = 8 kcal./moIe
(7) However, E, and q are related. Indeed, the activation energy for surface diffusion is expected to be a certain fraction a(O < a < 1) of the strength s of the bond between the diffusing species and the surface
E,
=
as
(8)
The heat of adsorption, q, is also related to s q
=
2s - 104.2
(9)
where 104.2 stands for the dissociation energy of molecular hydrogen. Substitution of (8) and (9) into (7) gives
+
0 . G a ~ 52.1 - s
=
8
(10)
A choice has now to be made for a. This choice is in turn influenced by the assumed value of the radius a of the source. The latter will be taken to be equal to
SURFACE DIFFUSION OF HYDROGEN ON CARBOX
Table I : Assumed Values for the Calculation of Surface Diffusion Quantity
Symbol
Value
Jump distance Frequency Radius of diffusion source Coefficient of proportionality Adsorption a t 300” and 60 cm. Number of diffusion sources
d
3.41 A. 10lSsec.-l 10A. 0.58 1016atoms/cm.* 3 . 1 6 x 1017
P
a a co
n
It can be seen frorn Table I1 that, with those values, a good agreement is obtained between calculated and experimental amounts of hydrogen adsorbed. I n other words, the explanation in terms of surface diffusion can be quantitative. At higher temperatures and longer times, calculated values are systematically higher than experimental values. This effect of “saturation” has been mentioned earlier. It may be due to an interference or overlap between diffusion zones which have been assumed to be separated and independent .
2753
interpreted successfully in terms of surface diffusion. Although it has been possible to propose a value of the surface diffusion coefficient, a quantitative treatment of the data is made very difficult by the number of parameters of the problem. Although there may be other cases where slow adsorption can be explained by surface diffusion from or to active centers, a quantitative explanation may prove even more difficult than for the very favorable case of platinized carbon considered in this investigation. In the determination of surface areas by selective chemisorption, the phenomenon may be quite troublesome.
Discussion R. A. VAN NORDSTRAND (Sinclair Research Co., Houston). Have you studied the reversibility of this chemisorption? It seems that your mechanism consists of readily reversible steps, so that simply by dropping the hydrogen pressure to zero you should be able to desorb and follow the process using the same equations.
s
Conclusion Qualitatively and to a certain extent quantitatively, the uptake of hydrogen by platinized carbon can be Table I1 : Comparison between Calculated and Experimental Amounts of Hydrogen Diffusion on 0.2% Platinum Sample Temp.,
Amount of surface diffusion, CC.of Hz (STP) Caled. Exptl.
O C .
Pressure, cm.
Time, min.
300
60
5 10 50
0.15 0.22 0.59
0.21 0.29 0.60
30
5 10 50
0.10 0.15 0.41
0.15 0.21 0.39
60
5 10 50
0.25 0.35 1.2
0.42 0.58 1.1
30
5 10 50
0.18 0.24 0.87
0.26 0.34 0.64
60
5 10 50
0.49 0.73 2.5
0.63 0.84 1.3
30
5 10 50
0.35 0.52 1.7
0.40 0.55 0 . 9 6 (est.)
350
392
A. J. ROBELL. No, we have not studied the reverse process. The desorption kinetics would not be predicted by the same mathematical solution. The boundary conditions to the unsteady-state diffusion equation would be different; the sourre would be a two-dimensional field of varying concentration, and the sink a small area of essentially zero concentration. We have noted that a n instantaneous reduction in the hydrogen pressure during an adsorption run produces a n immediate diminution in the rate of net adsorption, as predicted from our niodel.
J. W.’ E. COENENS([Jnilever, Netherlands). I n general I understand your wanting to “correct” your experimentally observed adsorption on platinum-carbon by subtracting the amount of gas adsorbed on carbon alone, but should it riot be borne in mind that we are primarily concerned with the direct experimental observation, rather than with a subtraction of the two? This is especially important in the case of the kinetic isotope effect. You actually did appear to observe such an effect with carbon but you found no effect on the carbon-supported platinum. But it seems to me that you cannot say that the kinetic isotope effect is reversed, although your observation is still significant enough. A. J. ROBELL. The experimental facts are ss follows: on the carbon alone, hydrogen adsorbs fsster than deuterium; on the platinized carbon, hydrogen and deuterium adsorb at essentially the same rate. Thus, “net” adsorption, as it is defined here, proceeds a t a faster rate with deuterium thcn with hydrogen. The point that I wish to bring out here with these observations is the following: the “normal” kinetic, isotope effect, i e . , the one in which hydrogen is faster than deuterium, observed in direct adsorption with carbon alone is not observed when platinum is dispersed on the carbon. This implies a different rate-(:ontrolling procese.
Volume 68,Number 10
October, 1964
