CONWAY PIERCE
1lS4
Vol. 64
THE FRENKELHALSEY-HILL ADSORPTION ISOTHERM ASD CAPILLARY CONDENSATION BY CONWAY PIERCE Department of Chemistry, University of California, Riverside, California Received March 7, 1960
Previous work has shown that the free surface adsorption of nitrogen, corrected for any capillary coiitlcnsation, is described by the equation ( V/Vm)2.76 = 1.305/(log palp). Investigation of other adsorbates shows that by suitable modification of the constants the equation is of general applicability for adsorption beyond the first layer. h single isotherm for a given adsorbate makes possible accurate prediction of the free surface isotherm of this adsorbate on any sample. Comparison of the computed free surface isotherm with the experimental one is used to detect capillary Condensation.
Frenkel, Halsey2 and Hill3 have independently suggested that a t high relative pressures, where a n adsorbed film is several molecular layers in thickness and its properties approach those of bulk liquid, the isotherm may be described by the equation
The observation that nitrogen adsorption in the multilayer region is independent of the substrate makes it of interest to investigate the applicability of the Frenkel (or Frenkel-Halsey-Hill) equation to other adsorbates and to see how the constants \ w y with different molecules and diff erent surfaces. To better control effects of capillary condensation selected samples, previously studied by nitrogen, were used. Ethyl chloride was chosen as adsorbate, as an example of a molecule whosc structure is quite unlike that of nitrogen.
where s is an exponent based upon the decay of surface forces with distance. Discussions of this general equation and applications to specific isotherms have been given by Bowers4 and by M e ~ e r . ~ Experimental Most of the published type I1 isotherms extendThrrc samples were used: Sterling h l T (3100), a grapliiing t o high relative pressures are for powder tized carbon black from Cabot.7 The nitrogen isotherm, samples. If the Frenkel equation is applied to reported by Holmes and Beebe,8 is reproduced in Fig. 1. these isotherms widely variant results are obtained. As previously noted6 there is no detectable interparticle The reason is that the isobherm of a powder sample condensation below 0.95~0.Silica, a fluffy Si02 powder, was studied by Young.9 The nitrogen isotherm is the sum of two effects, (1) adsorption in the multi- previously ehows no appreciable interparticle condensation below layer film on “free surface” and ( 2 ) capillary con- 0 . 9 5 ~ ~Graphon, . Lot 1925, a graphitized carbon black from densation a t contact points between particles. Cabot.7 Previous work has shown that a t high relative The relative magnitude of the two effects varies pressure there is extensive condensation between the particles make up an aggregate. from sample to sample because the amount of which All samples were evacuated a t 300°, to rrmove preadcapillary condensation depends upon the size and sorbed vapors. The physical appearance of the silica shape of the granules and upon the closeness of sample indicated that possibly somc water, taken up while packing or the average number of contacts per sealing i t into the adsorption bulb, was not removed by this treatment. The sample showrd a tcndenry to particle. agglomerate, not noted in the original matPrial. I n a previous studv of nitrogen isotherms6 it was Isotherms were determined gravimetrically a t 0” by found that the extent of interparticle condensation removing and weighing the bulb after each addition of could be evaluated by comparing the experimental vapor. After each weighing the adeorbed vapor was off before a new addition was made. This was data with a free surface isotherm that gave the mul- pumped to avoid any possible adsorption-desorption efferts attendtilayer adsorption not due to capillary condensa- ant upon the alternate warming and cooling of the bulb as tion. It was also observed that, the ideal nitrogen it was removed from the bath for wcighing The isotherm of graphite RIT is shown in Fig. 1 , with its isotherm was independent of the solid substrate. isotherm for comparison. Isotherms of silivn ~ ~number of nitrogen At all relative pressures above 0 . 2 the and Graphon are given in Fig. 2 . A11 me~siiremrntswcrc statistical layers was strictly a function of the rela- carried to 0 . 9 5 ~or 0 higher. The applicability of eq. 1 n-as tested by plotting the tive pressure. , a log-log scaje as mas done The ideal nitrogen isotherm fits a modification of amount adsorbed us. log p ~ / p on by Halsey.2 Log-log plots of the three isotherms are the multilayer equation, in the form shown in Fig. 3. To facilitate plotting, the amount adThis is in agreement with HalseyJ2who used data for a single sample, anatase, finding the exponent to have a value of 2.67. (1) J. Frenkel, “Kinetic Theory of Liquids,“ Oxford Cniversity Press. 1946. (2) G. D. Halsey, J . Chem. Phys., 16, 931 (1948). (3) T. L. Hill, “Advances in Catalysis,” Vol. LV, Academic Press, New York, N. Y.. 1952; J . Chem. Phys., 14, 263, 441 (1946); 16, 767 ,(1947); 11, 580, 668 (1949). (4) R. Bowers. Phzl. M a g , 171 44, 467 (1953). ( 5 ) L. Rfeyer, Z.phyaik. Chcm.. 16, 331 (1958). (6) C. Pierce, THE JOURNAL,63, 1076 (1959).
sorbed was for all samples reduced to an arbitrary power of 10 so that the initial adsorption falls in the first decade of the plot. This brings all plots to the same decade without altering the slope. A study of the isotherms and these plots yields the conclusions: 1. The slopes of the log-log plots are the same for the silica and carbon samples. That is, the multilayer adsorption is, like that of nitrogen, independent of the substrate surface. 2. The slope of the log-log plot for ethyl chloride is different from that for nitrogen. The isotherm for carbon (7) Provided through courtesy of W. R . Smith and W. B. Spencer. Godfrey L. Cabot, Inc., Cambridge, Mass. (8)J. 31. Holmes and R. A. Beebe, THISJOURNAL, 61, 1684 (1957). (9) G. J. Young, J . Colloid Sci., 13, 67 (1958).
FREXKEL-IIALSEY-HILL ISOTIIERAl AND
Sept., 1960
C h P I L L h R V CONDENSATION
1185
M T was used to compute the number of statistical layers, n, as a function of relative pressure. A Vm value of 2.52 mg./g. was chosen by the location of the inflection point, since the shape of the isotherm precludes use of a BET plot. The n values therefore are not absolute but probably good to 2 ~ 1 0 ~This ~ . uncertainty does not affect the relative values, only the absolute. A plot of the n values us. log p o / p is shown in the lower portion of Fig. 3. It is, of course, parallel to the plots taken directly from the isotherm. 3. The plot of n values for ethyl chloride fits the equation
The values of n for various relative pressures are given in Table I, which has for comparison the previously determined nitrogen values.
TABLE I XUMBER
LAYERSADSORBED ON SURFACE
O F STATISTICAL
A
P/PO
NZ
CzHaCl
CFzClz
0.30
1.30 1.54 1.70 1.90 2.17 2.58 3.35 4.40
1.27 1.43 1.63 1.80 2.22 2.75 3.85 5.40
1.17 1.36 1.60 1.95 2.35 3,05 4.70
.40
.50 .60 .70 .80
.90
.os
FREE
4 . The log-log plot for the Graphon isotherm is linear only up to 0.7~0.At higher pressures there is more adsorption than predicted by the straight line, which gives only the contribution of multilayer adsorption on a free 0 points fall above the surface. Above 0 . 7 ~ experimental straight line and the divergence increases with rising pressure. This divergence is due to the contribution of capilh r y condensation a t contact points behveen the particles. The existence of such condensation, not shown by the isotherm itself, is conclusively demonstrated by the divergence of the data from the straight line. Carman and Raal,’O Kiselev11 and others have experimentally compared isotherms for loose powders and porous materials having the same surface as the pon-der, to detect t,he effect of pores upon the isotherm. When there are no small pores that fill a t low relative pressure the powder data arc not needed. The isotherm is determined for the porous sample and the data plotted as in Fig. 3. The linear portion, ext,rapolated as needed, gives the isotherm that ~ o u l d be obtained from the pori-der. 5. Whcln the n values for a vapor have been determined from the isotherm of a sample whose adsorpt,ion gives a sufficiently long st.raight line interval in the log-log plot,, t,hese values can then be used to determine Vm from the isotherms of other snmples. A log-log plot of isotherm data is made as in Fig. 3. Within the linear region the ratio V / n for given relative pressures gives V,. A comput,ation from t,he silics isotherm is given in Table 11.
0.6 0.8 P/Po. Fig. 1.-Ethyl chloride isotherm of Sterling hIT (3100). The nitrogen isotherm of Holmes and Beebe is given for comparison. The crosses on the nitrogen are the adsorption computed from t h e n values. 0.2
0.4
TABLE I1 COMPCTATIUX O F
P/ PO
0.40 .50 .60 .70 .80 .90
I’m
Amoiint adsorbrd, 1,’ mg. CzHrCl
25 28 33 3D 48 68
PROM SILICA ISoTHERM
n
1.43 I ,68 1.89 2.22 2.75 3.85
Y/n = Vm (ing. C A C I )
17.5
17.5 17.6 17.4 17.6
(10) 1’. C . C a r m a n and r. A . Raal, I’roc. Roy. SOC. ( L o n d o n ) , AZ09, 59 (1951). (11) A. V. Kiselev, “The Structure and Properties of Porous hlaterials (Colston Papers) ,” Butterworth Scientific Publications, London,
1968.
0.4 0.6 U.8 PlPo. chloride isotherms of silica : ~ n dGraphon. 0.2
17.5 Fig. 2.-Ethyl
6 . The two isotherms of Fig. 2 show a distinct contrast in the primary adsorptions below V,. Silica adsorbs so weakly that there is no clearly defined inflertion in the isotherm when the first layer is completed. Graphon, on the other hand, adsorbs strongly and there is a sharp inflection a t the start of the multilayer adsorption. Despite these differences the adsorptions beyond the first layer are identical for the two samples. 7. The nitrogen and ethyl chloride isotherms of blT (Fig. 1) show some interesting effects of adsorption on a
CONWAY PIERCE
1186 0.95
0.90
PlPo. 0.80
0.60 0.40 0.20
c
20
log PolP. Fig. 3.-Log-log plots for ethyl chloridc isotherms of Graphon (G), silica (Sios) and Sterling )IT 3100 (MT). Lower plots are n values for CFzClz and C2H5Cl.
i
Vol. 6.2
Another effect of a uniform surface is found in the nitrogen isotherm of M T a t relative pressures between 0.3 and 0 . 4 ~ 0 .As previously discussed6 the isotherm fits eq. 2 above 0.4~0 but not below this value. The proposed explanation is tFat the first layer is not packed to the normal state of 16.2 A . 2per nitrogen atom when the inflection point is reached. Between 0.3 and 0 . 4 ~ 0normal packing is achieved and thereafter the multilayer adsorption is the same as for any other surface. Ethyl chloride does not show this first layer effect; the isotherm is normal throughout the multilayer region. The similarities and differences in the multilayer adsorptions of nitrogen and ethyl chloride suggest the possibility that the Frenkel equation, with suitable modification of the constants, may be of general applicability to type I1 isotherms. Halsey2 showed that i t applies to the adsorption of water and nitrogen by anatase and Bowers4 that it applied to adsorption of nitrogen, oxygen and argon by a metal foil. As a further test the isotherms of Carman and Raallo for CF2C12 on a fluffy silica and on Carbolac 1 were investigated. These isotherms are replotted in Fig. 4. Using Carman and Raal’s value of 1.17 mmoles for Vm the n values were computed for the silica sample -4 log-log plot of these values is shown in Fig. 3. Its slope differs appreciably from those of nitrogen and ethyl rhloride. The plot gives for Freon 12 (CF2ClQ) the equation
Selected n values are given in Table I. As previously showno from the nitrogen isotherm the adsorption by Carbolac 1 can be broken down into two parts, ( I ) adsorption in small pores and (2) adsorption on free surface not in these pores. A similar analysis was made of the CFzClz isotherm, using the n values of Table I. A cornputfation from the adsorptions a t 0.4 and 0 . 8 ~ 0gives a t 0.8 8.60 mmoles = 3.06 V , 0.4 5.95 mmoles = 1.35 V,
+ V, + V,
Solving, V , = 3.80 mmoles to fill the small pores and = 1.57 mmoles to cover the surface not in the small pores. The area of the free surface is computed by use of the silica data. Since 1.17 mmoles forms V , for a silica area of 300 m.2/g., 1.0 mmole covers 258 m.z. The free surface of Carbolac is therefore 1.57 mnioles/g. X 258 m.2/mmole = 405 m.2/g. A similar computation for nitrogen gave a free surface area of 460 m.’/g., an excellent agreement. As a further test of the comparison between nitrogen and Freon the volume of the small pores was computed. Using the V , values gave 0.29 ml. for I T 2 and 0.31 ml. for CF2C12. Here, too, the agreement is excellent. To test the validity of this analysis a corrected Carbolae isotherm was constructed by subtracting 8, values from the experimental ones. This free surface isotherm is shown as the middle curve of Fig. 4. A log-log plot from this corrected isotherm gave a straight line of proper slope, linear from 0 . 4 to 0.85pp. The uncorrected isotherm does not give any linear region.
V,
I
0.2
0.4 PlPo.
0.6
0.8
Fig. 4.-Frron 12 isotherms of Carbolac 1 and silica, from Carman and Raal. The free surface isotherm of Carbolac is obtained by subtracting the amount adsorbed in small pores from the total. uniform surface. On such a surface, where the adsorbed ~noleculecan movo about freely, the forces between molecules (lateral interactions) cause the isotherm to be convex to the pressure axis below V,. On uniform carbon samples this effect is pronounced in ethyl chloride isotherms** which do not complete the first layer until the relat,ive pressure is near 0 . 0 5 ~ or 0 higher. Nitrogen isotherms on such samples have a similar shape but V , is completed at such low pressure that ordinarily the convex sha e is overlooked. In extreme cases the lateral interaction effect is so strong that the isotherm becomes practically vertical below V,. Frequently this is referred to as a “phase transition.” (12)
J. Mooi, C. Pierce and R. N. Smith, Tais JOIXSAL, 67, G57
(1Q53).
Conclusions I n view of the general applicability of a modified Frenkel equation to the various isothernis studied it seems safe to conclude t h a t : (1) The Freiikel equation, with suitable adjustments of the two constants, will fit the multilayer region of most (or perhaps all) type I1 isotherms provided there is no capillary condensation. ( 2 ) A plot of volume adsorbed us. log p o / p , on a log-log scale, is a convenient test for capillary condensation. If there is no capillary condensation the points fall on a straight line, which represents the free surface isotherm. Condensation causes increased adsorption. ( 3 ) For a giT-en adsorbate the slope of the
E’HEXKEL-HA LSEY--HILL
Sept., 1960
ISOTHEIiM AND C A P I L L a R Y COlUDEsS.4TION
log-log plot is independent of the adsorbent. A single isotherm for a non-porous sample permits computation of generally valid n values for the adsorbate used. (4) I n the linear region of a log-log plot the monolayer volume, Vm, may be accurately determined from the ratio Vln after the n values have once been experimentally determined. This method can be used for isotherms which are convex t o the presiure axis below Vm, where the B E T plot is not possible. ( 5 ) The free surface adsorption of qamples with small pores and the volume in these pores may be separately computed from a single isotherm Ly use of simultaneous equations for the volume ad sorbed a t two relative pressures.
DISCUSSIOS .I. C.
(Ixhigh University).---Your loglog plots an for miall arid rathcr simple molecules. Kould %I:TTI,EAIWER
11S7
we expect the same slope, for example, for butyl alcohol? -41~0,are 1 he BET areas for Graphon and for a 350 m 2 graphite much in error due to capillary condensation?
CONWAY PIERCE --ils Halsey points out, the dopes vary greatly with different adsorbates. Butyl alcohol undoubtedly will give quite different values. I do not think the BET areas of the samples you mention are affected by the interparticle condensation. This occurE only a t high relative pressures, far above the ,T’ point. P. L. \J‘ALKER, JR. (Prniisylvania State L-niverbity).-You find a free surface area for Carbolac of 460 m.2/g. using nitrogen. The electron microscope surface area for Carbolac is about 350 rn.z/g. Do you interpret t h r difference as due to surface roughness? CONWAY PIERcE.-Either to that or to uncrrtainty in the electron microscope value. Various workers have told me personally that for the very fine Carbolac particles the microscope values are not as reliable as for blacks comprised of larger particles.
