354
CONWAY PIERCE AND R. NELSON SMITH
HEATS OF ADSORPTION. I11 METHANOL ON CARBON^ CONWAY PIERCE
AND
R. KELSON SMITH
Department of Chemistry, Pomona College, Claremont, California Received M a y 8 , 1949
Recent papers by Halsey ( 5 ) and by the writers (11) have independently given arguments supporting the view that adsorbing surfaces of solids are nonuniform in physical adsorptions. This view is not new, but it has largely been ignored in recent years because of the success of the B.E.T. equation, which is based upon the assumptions that the heat of adsorption is uniform in the first layer and that after the first layer is completed further adsorption is on a uniform and liquidlike surface. Actually, these assumptions are not needed in the basic B.E.T. concept of multimolecular adsorption in layers of varying thickness, and Joyner and Emmett (7) stress the fact that El as used in the equation does not necessarily agree with direct experimental values for heat of adsorption in the first layer. There is, however, a general tendency to ignore the fact that these assumptions are simplifications needed to carry out the mathematical derivation of the B.E.T. equation and to accept them as rigorously true. In our previous work we concluded that (1) surfaces have sites of varying activity, each of which can hold adsorbate at a given relative pressure; (2) a type I1 isotherm is the result of two separate processes, adsorption on a bare surface and on a previously covered surface, and these can be described by a two-term equation
I.'=- ax 1
+ bx +x-1
Cy2
(1)
in which the first term gives adsorption on the bare surface and the second adsorption beyond the first layer*; (3) the net heat of adsorption does not become zero until p = P O ; (4) in layers beyond the first the net heat is related to relative pressure by the equation
E
- E,
= K(l
- X)
(2)
We have found further evidence for our views in a new type of adsorption isotherm, that of methanol on nonporous carbon surfaces, which is described herein. EXPERIMENTAL
Isotherms were determined for methanol on graphite KC-1, Graphon, and activated charcoal S600H. 1 This is a progress report on work done under Contract N8 onr 54700 with the Office of Naval Research. 9 Halsey ( 5 ) expresses the same idea by the relation e = ec-, 1 in his discussion of the B.E.T. equation.
+
HEATS O F ADSORPTIOK. I11
355
Graphite SC-1 \vas obtained from the Sational Carbon C ~ m p a n yIt . ~has an ash content below 0.001 per cent and is free of oxygen complex. The nitrogen area4 is 4.0 sq. m. per gram. The sample was from the lot previously used for determination of the isotherms of ethyl chloride, ammonia, and water (11). Graphon5 is graphitized Spheron Grade 6 carbon black. The sample was from the same batch as that used by Beebe and associates (1) and by Joyner and Emmett ( 7 ) .The nitrogen area is ca. 80 sq. m. per gram. Charcoal S600H was prepared by the carbonization of Saran. Its preparation and properties have been described in a previous publication from this laboratory (8). Isotherms were determined at temperatures of 0' and 28.9"C. when isosteric heats were desired, otherivise at 0°C. only. All isotherms were determined by a gravimetric method of removing and weighing the sample bulb after each addition of vapor. At 0°C. the vapor pressures \yere read by a modified McLeod gage. The complete isotherm for S C - 1 a t 28.9"C. is shorn in figure 1. Figure 2 shows the low pressure region for the NC-1 isotherms at 0' and 28.9"C. and a portion of t'he 0°C. isotherm for Graphon. The latter was extended to 167 ml. (S.T.P.) a t z = 0.98. The 0°C. isotherm for S600H is shown in figure 6. The lower curve gives the low pressure values on expanded scale. DISCIJSSIOK
The isotherms of figures 1 and 2 are of a type not previously reported. In line with Brunauer's classifications, we suggest that they be designated as type VI. As shown in figures 1 and 2, these isotherms start out convex to the pressure axis, or as type I11 or V, then become concave and change to a type I1 shape. From point B on they are exactly like the type I1 et'hyl chloride isotherms on the same adsorbents. These type VI isotherms provide evidence for our postulate that adsorption in the first layer must be treated as a separate process from adsorption in layers beyond the first. For both graphite and Graphon the amount taken up at point B corresponds closely viith the computed value of V,, based on the kn?wn nitrogen surface areas of the samples and a computed area of 16.2 sq. A. for the methanol molecule. S C - 1 has a computed V,,, value of 0.89 ml. (S.T.P.), as compared with a point B value of near 0.9, and Graphon has a computed Vm value of 18.7 ml., as compared with a point B value of about 19 ml. These isotherms, therefore, show that the first layer is essentially filled before there is appreciable multilayer adsorption, even though the first layer does not fill a t the low relative pressures which are characteristic of type I1 isotherms (where point B is usually located a t relative pressures below 0.1). Isosteric heats of adsorption for methanol on graphite are shown in figure 3. a Through the courtesy of Dr. Lester 1,. Winter, Kational Carbon Company, Cleveland, Ohio. Determined by Professor R. A . Beebe and Miss hf. H. Polley of hmherst College. Furnished by Dr. Walter Smith of the Godfrey L . Cabot Company, Boston, hlaassohusetts.
356
CONWAY PIERCE AND R. KELSON SMITH
As might be predicted from the shapes of the isotherms, the net differential heats of adsorption are quite different from those previously reported (11) for ethyl chloride on the same adsorbent. For ethyl chloride E - E L is above 1800 cal. per mole until after completion of the first layer; then it drops rapidly to the low values characteristic of adsorption beyond the first layer. The net heat for
I
2
I
I
I
I
9
5
4
' 3 2
w/ I I II 1 I
c
.3
.4
.5 P / po
.6
II ,7
II .e
II .9
FIG.1. Isotherm of methanol o n graphite SC-1 a t 28.9"C.
methanol drops from 3000 cal. per mole for the first portions adsorbed to about 600 cal. per mole at about O.5Vm, then remains fairly constant until the first layer is completed, after which it drops to the low value for multilayer adsorption. The shape of the methanol heat-volume curve indicates nonuniformity of the surface. Only a small fraction of sites can hold adsorbate at low relative pressure,
HE.\TS
357
O F ADSORPTIOX. I11
but as pressure is increased the active fraction of the surface increases rapidly and complete coverage occurs at relative pressure near 0.3. After this occurs another type of distribution of active sites governs adsorption beyond the first layer. The similarity of the isotherm to that for ethyl chloride after point B is passed indicates that the same distribution of sites is effective for both ethyl chloride and methanol after the first layer is completed.
1.6
80
I .4
70
z
-
0.
4:
I
1.2
60
1E
L
ur
5
1.0
50
L .8
40
3
-
J
L
2m a c
-
1' .6
30
i
cn 20 6
3
0
.-.
j .4
+"
IO
.2
.I
.2
.3
.4
.S P/
po
.6
.7
.0
.9
FIG.2. Isotherms of methanol on graphite and Graphon
The flattening of the heat-volume curve in the region 0.5V, to I', may be due either to a uniform activity of the last half of the surface (after the most active sites have been covered) or to the influence of previously adsorbed molecules after the surface has become partially covered. The data do not permit one to prove either explanation to the exclusion of the other. The discovery of type VI isotherms as intermediate between types I1 and I11 permits a generalization as to the relation between heat of adsorption and the type of isotherm that is obtained. When the heat of adsorption is high at all
>'
358
CONWAY PIERCE AKD R. KELSON SMITH
sites, the first layer is formed at low relative pressure and the isotherm is type 11. When only a small fraction of sites can adsorb at low relative pressure the first layer is not completed until pressures are so high that multilayer adsorption is extensive. In this case there is no break in the isotherm at completion of the monolayer and the isotherm is type 111,convex t o the pressure axis at all relative pressures. Finally, when surface activity is low but all sites can adsorb a first layer before the pressure is high enough for much multilayer adsorption, a type VI isotherm is obtained. I
I
I
I
3000d
A 0
H
a
$!
2000
tn
wa
0
J
a 0
I
w
I 2 3 4 VOLUME ADSORBED, CC.(S,T.P.) PER GRAM FIG.3 . Isosterio heats of adsorption for methanol on graphite
Type I11 isotherms are exceedingly rare; in fact, we know of but one example, water on graphite. In a previous paper (11) we listed ammonia on graphite as belonging to type 111, but re-examination of the data now leads t o classifying it as type VI. There is a small discontinuity near 0 . 5 ~ 0and the points are better fitted by drawing the isotherm as type VI. Moreover, the rise occurs where the amount adsorbed is about that computed for a monolayer, as in the methanol isotherms. We were aware of this apparent break in the curve at the time the isotherms for ammonia were determined but assumed the break to be due to experimental error. That the isotherm is really type VI now seems probable.
HEATS OF ADSORPTION. I11
359
In early applications of the B.E.T. theory Brunauer, Deming, Deming, and Teller (3) listed the isotherms of bromine and iodine on silica gel, determined by Cameron and Reyerson (4), as belonging to type 111. ilctually, this is not consistent with the typical type I11 isotherm later given by Brunauer in his book ( 2 , page 150). The typical isotherm is a smooth convex curve extending to near po, while the bromine and iodine isotherms when plotted on a relative pressure basis as in figures 4 and 5 are rising too steeply to be type 111. Since silica gel is known to have capillaries me believe that the bromine and iodine isotherms if continued to high relative pressures lyould be type V, or like the isotherms of water on charcoal. On the basis of the B.E.T. treatment and the extension given by Brunauer, Deming, Deming, and Teller (3) it is customary to assume that when an isotherm is concave to the pressure axis C > 1 or E, > E,. Conversely, it is held that a convex isotherm is indicative that C 2 1 or El 2 E L . Our data for methanol show conclusively that these assumptions are incorrect. The methanol isotherms are initially convex where the net heat of adsorption has a high positive value and they become concave in a region where the net heat is small, some 600 cal. per mole. Our interpretation is, as stated above, that n-hetbr an isotherm is concaw or convex depends upon the distribution of acthe sites and the manner in which the distribution changes with increase in pressure. Our data in this and the preceding papers show that for both convex and concave isotherms the net heat is positive. We cannot agree with the interpretation given by Brunauer, Deming, Deming, and Teller for the isotherms of bromine and iodine on silica gel. The original adsorption data are replotted on a relative pressure basis in figures 4 and 5. To make these plots we used the vapor pressure data of the International Crztical Tables for iodine and the values of Scheffer and Voogd (10) for bromine. With the exception of a few scattered points the bromine data for temperatures of 58', 79", and 99.9"C. fall on one curve and the data for 117.5" and 137.7%. on another curve which is displaced to the right or in a direction to indicate a positive net heat of adsorption. If the net heat is zero, as assumed, all points should lie on the same curve. There is considerable spread in the iodine points and for all temperatures except 98°C. the data fall near a median curve; the 98'C. points fall to the right or in a direction to indicate a negative net heat. We feel, however, that this shift is not conclusive in view of the spread in points for all other temperatures. Our interpretation of the relative pressure plots of the isotherms is that the data do not justify a positive conclusion regarding the sign of the net heats of adsorption. They do indicate that the net heats of adsorption are small. Certainly they do not warrant the assumption made that El - E , for iodine is -3500 cal. For a heat difference of such magnitude there should he a wide spread between the isotherms for the various temperatures, when these are plotted against relative pressures. None of the existing isotherm equations will fit a type VI isotherm throughout the entire relative pressure range, nor does it appear feasible to devise a single
3 60
COK'WAY PIERCE AKD R. KELSOK SMITH
equation which will fit. The difficulty is that the term which fits the first portion must be of such a nature as to become constant when the monolayer has been
.36
.32
= 98' e = 137.6' 0 = 158.3' 0 = 178.4'
0
0
= 198.5'
.20
a4i .24 L (3
2 .20
P
cn .I6 0
-I J
I
.I2
.O 8
.04
.I
.2
.3
P/
p,
.4
.5
.6
FIG.4. Isotherms of iodine on silica gel; data of Cameron and Reyerson (4)
completed. From point B on, however, the isotherm can be fitted by an equation of the form
361
HEATS OF ADSORPTIOK. I11
.2
.3
P/ Po
.4
FIG.5 . Isotherms of bromine on silica gel; data of Cameron and Reyerson (4)
v=vm+---
Cy2
1
- px
The second term of this gives the adsorptions beyond the first layer, as previously shown for numerous isotherms. In a recent paper (8) we showed that activated charcoal will hold a given
im
;:::\
c
1 140 a 100
,
I
,
!
#
I
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I
I
,
.
:
c -
c:
4000
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;
u
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22000-
E
i -
to
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I
TABLE 1 C o m p u t a t i o n of integral heat of adsorption of methanol o n charcoal from heats of wetting Data of Raaouk (9)
O.Oo0 0.002 0.008 0.017 0.040
0.079 0.173 0.273 0.372 0,521 0.621 0.780 0.884 0.972 1 .ooo
O.oo00 0.0192 0.0391 0.0477 0.0673 0.0810
0.0963 0.1054 0.1117 0.1197 0.1239 0.1288 0.1328 0.1343 I 0.1350
(3)
(4)
(5)
(6)
YOLKS ADSORBED P E P 237 0 . CHARCOAL
I E A T OF WEITING
ICPBASK IN SEAT DF W E m N G PEP
I T E O U L HEAT OF ADSOPPTlON COLUXN 5 X 237)
O.OO0 0.142 0.29 0.354 0.50 0.60 0.715 0.78 0.825 0.887 0.917 0.955 0.98 0.995 1 .oo
own
cd./gram
cd.lgram
17.0 12.5 9.8 8.9 6.9 5.5 4.0 2.8 2.3 1.7 1.3 0.7 0.3 0.1 0.0
0.0 4.5 7.2 8.1 10.1 11.5 13 .O 14.2 14.7 15.3 15.7 16.3 16.7 16.9 17.0
0 1065 1710 1920 2390 2720 3080 3360 3480 3620 3720 3860 3950 4Mx)
4030
laries of charcoal. The adsorption of methanol gives a good example of this effect. The isotherm of methanol on a fine-pore charcoal, charcoal S600H,is shown in
HEATS OF ADSORPTIOK. I11
3 63
figure 6. Comparison with figures 1 and 2 s h o w that the initial convex portion of the isotherm has practically disappeared in charcoal adsorption and that at a relative pressure of 0.1 the charcoal holds some 80 per cent of its saturation volume. As previously discussed, we believe that there is capillary condensation in charcoal pores at pressures even lower than those which produce a monolayer on a plane carbon surface. With our data for graphite and the data of Razouk (9) for heats of wetting, we can compare relative heats of adsorption for methanol on charcoal and graphite. Razouk measured heats of wetting for charcoal samples previously brought to equilibrium with various partial pressures of methanol vapor. 4 s shown by Harkins and Jura (6), integral heats of adsorption can be computed from such data, since the heat of wetting for a partially saturated sample is less than that of a dry sample by an amount equal to the heat evolved when the given amount of vapor was adsorbed. Details of the calculation from Razouk's data are shown in table 1. His original values are given in terms of 1 g. of charcoal and are converted to values per mole of alcohol adsorbed by multiplication with the factor 237, which is the weight of charcoal to adsorb 1 mole of methanol at saturation. The integral heats of adsorption so computed mere plotted and the differential heats obtained from the slope of this curve. 4 plot of the differential heats for charcoal is shown in figure 7. Comparison with figure 3 shows that the heats of adsorption on charcoal are much greater than on graphite; the last portions adsorbed by charcoal show as high a net heat as the first portions on graphite. This great increase in heat of adsorption we attribute to the effects of neighboring walls of the capillaries. SUMMARY
The isotherm for methanol on a nonporous carbon surface is a new type, which is designated as type VI. It starts as a type 111isotherm, up to completion of a monolayer, then s h o w multilayer adsorption similar to a type I1 isotherm. The first layer is essentially completed before there is appreciable adsorption in multilayers. Isosteric heats of adsorption were computed from isotherms at 0" and 28.9"C. They show that it is not necessary to assume zero or negative net heats of adsorption for a convex isotherm. Rather, it is shown that the shape of the isotherm depends upon the distribution of active sites that can adsorb at given pressures and the way in which this distribution varies with change in pressure. Isotherms of methanol on nonporous and porous carbon surfaces are compared. The heat of adsorption on charcoal is much greater than on graphite. REFERESCES (1) BEEBE,POLLEY, S.\IITH, A N D WENDELL: J . Am. Chem. SOC.69,2294 (1947). The Adsorption of Gases and Vapors. Princeton University Press, Prince(2) BRUNAUER: ton, New Jersey (1943). (3) BRUNAUER, DEMING, DEMING, A N D TELLER: J. Am. Chem. SOC.62, 1723 (1940). (4) CAMERON A N D REYERSON: J. Phys. Chem. 39, 169 (1935). (5) HALSEY: J . Chem. Phys. 16, 931 (1948). (6) HARKINS AND JURA:J. Am. Chem. SOC.66, 919 (1944).
364
RAYMOND A. BROWN AND J O H N R. CANN
(7) JOYNER A N D EMMETT: J. Am. Chem. Soc. 70, 2353 (1948). (8) PIERCE,WILEY,AND SMITH:J . Phys. & Colloid Chem. 65, 669 (1949). J. Phys. Chem. 46, 190 (1941). (9) RAZOUK: (10) SCHEFFER AND VOOOD: Rec. trav. chim. 46, 214 (1926). J. Phys. & Colloid Chem. 62, 1115 (1948). (11) SMITHAND PIERCE:
EXTENSIO?; OF T H E THEORY OF REVERSIBLE ELECTROPHORETIC BOUKDARY SPREADING OF PROTEINS' RAYMOKD A. BROWN
AND
JOHN R . CANN
Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California Received February 7 , 194.9
There are two criteria for the electrophoretic homogeneity of a protein. The first is that under the influence of an electric field the protein should migrate as a single boundary in buffers of various hydrogen-ion concentrations and ionic strengths. The second is that the rate of spreading of the protein boundary under conditions such that convection and anomalous electrical effects are avoided should be no greater than that due to diffusion alone. In the absence of spreading due to convection and conductivity or pH differences, boundary spreading indicates heterogeneity. The boundary of an inhomogeneous protein is spread simultaneously by diffusion and by the differences in the mobilities of the differently charged ions. Sharp and coworkers (9) have shown that the mobility distribution may be obtained from the refractive-index gradient curves. In particular they showed that, in the case in which spreading due to diffusion is negligible compared to electrical spreading, the standard deviation of the mobility distribution, H, may be calculated from the relation
where Au/At is the time rate of change of the standard deviation of the gradient and E the electric field strength. H i s called a heterogeneity constant. Recently Alberty and coworkers (1, 2, 3) have considered the case in which diffusion of the protein is not negligible and the mobility distribution may be represented by the Gaussian probability function. Assuming that the diffusion constant, D, is the same for all protein ions, they showed that in this case the refractive-index gradient will have a Gaussian form. A heterogeneity constant, h, may be calculated from the equation
Contribution KO.1381 from the Gates and Crellin Laboratories of Chemistry.
