P a u l ß *tu *te tt
M EL LO N INSTITUTE O F INDUSTRIAL RESEARCH, PITTSBURGH, P A .
of Adsorbents
M e t h o d s for measuring surface areas b y gas adsorption m ay, for c o n v e n ie n c e , b e su bdivided into tw o groups. The first group is based on th e postulate o f the ex ist en ce o f multilayers o f p h ysi
cally adsorbed gas and makes use o f adsorption isotherms o f gases near their boiling points. The s ec o n d group assumes that the ad
sorption o f a vapor is a com bin atio n o f m onom ole cula r physical adsorption and of capillary condensatio n . Published proposals for measuring surface areas b y gas adsorption are critically discussed. It is co n clu d ed that the use of low-temperature adsorption o f s om e gas, such as nitrogen, near its b oilin g poin t is the best substantiated pro
cedure thus far describ ed , and that this procedure is c a p a b le of y i e l d ing relia ble values for the surface areas of porous and finely d ivid ed materials or even o f materials which have relatively small surface areas.
U
N T IL 1935 no satisfactory m ethod existed for m easuring the surface areas of both porous and nonporous adsorbents.F or nonporous solids a num ber of fairly satisfactory m ethods existed, including calculations based on the rate of sedi
m entation of particles in a suitable liquid, on the rate of fluid flow through packed beds of the adsorbent (6), on direct micro
scopic or ultramicroscopic particle counts, or on the adsorption (13, H ) of a suitable solute from solution. F or porous adsorb
ents, adsorption from solution and deductions based on the ad
sorption isotherm s of vapors, as interpreted by capillary con
densation, could be used. However, the only m ethod common to both porous and nonporous solids, the adsorption of solutes from solution, h ad m any lim itations when applied to a porous ad
sorbent. E quilibration was frequently slow because of the difficulty of diffusion of solute molecules through tiny capillaries filled with solvent. I t was also difficult to know the point on the liquid adsorption curves corresponding to th e form ation of a complete layer of adsorbed solute.
W ithin the last ten years, a num ber of new approaches to the problem have been m ade for measuring the absolute surface areas of both porous and nonporous solids. These new m ethods
involve the m easurem ent of the adsorption of gases by the solid adsorbents a t tem peratures close to the boiling points of the gases.
The purpose of the present paper is briefly and critically to summarize these published m ethods w ith a view to assessing their relative usefulness and general applicability.
F or convenience, the adsorption m ethods for m easuring surface areas m ay be divided into those th a t postulate ¿he existence of polymolecular adsorption a t pressures close to th e liquefaction pressures of the adsorbates and those th a t assume S-shaped adsorption isotherms to be a combination of monomolecular physical adsorption and capillary condensation. T o the first classification belong the m ethods proposed by the au th o r and co
workers (4, 5, 10) as well as those by H arkins and Ju ra (16, 17), by Askey and Feachem (1), and by Sm ith and Greene (£3). In this category, too, falls the work of Wooten and Brown (24) who showed how the adsorption m ethod can be applied to m aterials having surface areas so small as to be unm easurable by other procedures. In th e second category fall the recent works of H arvey (18) and of Kistler, Fischer, and Freem an (19), as well as earlier papers by M cBain (22), by Lowry (20), and by D raper (7).
MULTIMOLECULAR LAYER FO R M A T IO N
About ten years ago a search was begun a t the Fixed Nitrogen Research L aboratory for a m ethod by which the surface area of iron synthetic amm onia catalysts could be determ ined. I t was desirable to find a m ethod for measuring the surface area of re
duced catalysts w ithout, a t the same time, effecting any change in the extent or even the activity of the catalyst surface. To this end the adsorption of a num ber of gases was determ ined a t tem peratures close to the boiling points of the respective gases.
The results of this first series of determ inations are shown in Figure 1 (10). I t was suspected th a t the long linear p a rt of the isotherms consisted of the building up of m ultilayers of gas on the catalyst surface. If this were true, it was possible th a t the point corresponding to a monolayer m ight be selected on the isotherm
I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 37, No. 7
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alyst 9 p l e H
73
100 20 0 3 0 0 4 0 0 50 0 6 0 0 7 0 0 8 0 0 Pressure,mm.
Figure 1. Low-Temperature Adsorption Isotherms on a Pure Iron Synthetic Ammonia Catalyst ( 7 0 )
of one of th e in ert gases—nitrogen, for example. In succession, three different m ethods were used to select th e p o int on th e iso
therm corresponding to a m onolayer. I n each case th e m ulti
plication of th e num ber of -molecules in a m onolayer by the average cross-sectional area of each molecule would yield an absolute value for the surface area. T he first suggestion (4) was th a t th e extrapolation of th e linear p a rt of th e curve to the zero pressure axis (point A , Figure 2) would yield a value for the volume of nitrogen and hence the num ber of nitrogen molecules required to form a m onolayer. T his apparently was th e inter
p retatio n being placed on low -tem perature argon isotherm s inde
pendently by Askey and co-workers (1) in E ngland about the sam e tim e. A more detailed comparison of the adsorption of a num ber of different gases on several catalysts lgd to the conclusion th a t p oint B , where the long linear p a rt of the isotherm s begins, was th e best empirical choice of a point for calculating the surface area of the catalyst from the low -tem perature adsorption iso
therm . L ater a m athem atical trea tm e n t of th e theory of adsorp
tion in collaboration w ith Teller (5) led to a th ird and m ore useful way of interpreting the isotherm s. I t resulted in an equation from which the value of Vm, the volume of gas corresponding to a
p/ p s
Figure 2. Adsorption of Nitrogen on Iron-Alumina Catalyst at - 1 9 5.8“ C.
A , B , C , D , E represent definable points t o t e d In comparing surface areas by various 9ases (.10).
m onomolecular layer, could be determ ined by plo ttin g a portion of th e isotherm in such a m anner as to obtain a linear plot. T he fact th a t Vm an d the volume of nitrogen adsorbed a t p o in t B have alw ays agreed w ithin a b o u t 10% has given added w eight to the conclusions based on in terp retin g V m as th e volum e of gas re
quired to form a m onolayer over the adsorbent. T h e sim plicity of th e m ethod using th e linear equation for obtaining Vm has led to th e general adoption of this m ethod of in terp retin g th e low- tem perature adsorption isotherm s in our recent work. I t is believed th a t th e m ethod gives values for relative surface areas of different adsorbents th a t are accurate to a few per cent, an d values for th e absolute surface areas th a t ap p ear to be correct w ithin ab o u t 20% . T he details of this w ork will be briefly presented.
T he ap p aratu s for low -tem perature adsorptions has been de
scribed on a num ber of occasions (9, IS) an d need n o t be discussed here in detail. I t will suffice to p o in t o ut t h a t a stan d ard adsorption technique is employed, th e dead space around the adsorbent being determ ined by helium a t th e tem p eratu re a t which the m easurem ents are to be m ade (ab o u t —195° C., for example, if th e adsórbate is n itrogen).
B runauer, E m m ett, and T eller (5) showed th a t if th e S-shaped isotherm s, of th e type illu strated b y Figures 1 an d 2, are inter
p reted as representing th e building u p of m ultilayers a t the higher relative pressures, th ey can b e p lo tted according to the equation,
+ (C - 1) V
V(p„ - V) V mC ^ V mC Vo
(
1)
where V = volum e of gas adsorbed a t pressure p V m = volum e of gas required to form a m onolayer C = a c o n stan t
j>„ = liquefaction pressure of ad só rb ate used a t tem pera
tu re of experim ents
A plot of the left-hand side of the eq u atio n ag ain st p/p» yields a straig h t line, from the slope and in tercep t of w hich V m and C can be calculated directly. Figure 3 shows a ty pical se t of these linear plots (5).
Application of the m ethod to several th o u sa n d finely divided or porous substances (8, 11) has show n th a t a linear p lot of E quation 1 for nitrogen adsorption a t —195° C. is alw ays ob
tained betw een relative pressures of 0.05 an d a b o u t 0.35 except for a few porous solids such as charcoal an d chabasite in which m ost of the sorption capacity is centered in pores less th a n 20 Á.
in diam eter. T his relative pressure range correspond to a cover
age varying from a little less th a n a m onolayer u p to a b o u t 1.5 monolayers. I t does n o t extend to such relativ e pressures as would involve capillary condensation.
M any examples of surface area m easurem ents em ploying this m ethod have been published an d m ight be cited. F o r brevity, however, only a few will be given. T hey were selected because some independent estim ate of surface area is available in each instance.
Table I list surface area m easurem ents m ade on a selected group of zinc oxide sam ples (11); for com parison area determ ina
tions are shown b y several other m ethods. T he agreem ent be
tween the particle sizes calculated from adsorption surface areas and those obtained by C arm an ’s perm eability m ethod is excellent and well w ithin the combined experim ental error of th e two m ethods. T he particle sizes obtained by microscopic exam ina
tion and liquid phase adsorption are a little larger th a n those obtained by the gas adsorption m ethod. T his is to be expected in view of th e fact th a t th e gas adsorption m easurem ents include some surface of pores or sm all particles th a t would probably be missed by th e other procedures. T able I I gives area m easure
m ents on glass spheres (8, 9) prepared by Bloom quist and C lark (S). T he adsorption m easurem ents indicated an area about 40%
g reater th a n one would have expected from the size of the spheres as observed under a microscope. T o d em onstrate th a t this
dig-July, 1945 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 641
Table I. Surface Area Measurements on Zinc O x id e Pigments (7 7 )
P ig m e n t N o . F-1601 K-1602 G-1603
A rea b y a d so rp tio n , sq. m ./g . 9 . 4 8 8 . 8 0 3 .8 8 Av. p a rtic le size, m icrons
B y d ir e c t m icroscopic count® 0 .2 1 0 .2 5 0 .4 9 B y ad so rp tio n of m e th y l 0 .1 9 0 .2 4 0 .5 5
s te a r a te
B y ultram icro sco p io c o u n t 0 .1 3 5 0 .1 6 0 .2 6
B y p erm eab ility 0 . 1 2 0 .1 5 0 .2 5
B y ad so rp tio n of Na (liquid) 0 .1 1 5 0 .1 2 4 0 .2 8 By ad so rp tio n of Na (solid) 0 .1 3 5 0 .1 4 5 0 .3 3
° T his ca lcu lated v alu e is fro m m e asu rem en ts of th e n u m b e r of particles p er gram .
crepancy m ight well be due to some roughening of the bead sur
face by the washing w ith cleaning solution to which they had been subjected, a second washing by cleaning solution was em
ployed. T he area increased an additional 40% (Table II).
T his is a t least consistent w ith the idea th a t even the 40% dis
crepancy betw een the area estim ated by microscopic and adsorp
tive m ethods is due to a slight roughening of the glass spheres by exposure to cleaning solution. A third illustration is shown in Table I I I which summarizes d a ta obtained in recent m onths for the surface area of carbon black particles as judged by the particle size m easurem ents m ade by a n electron microscope in comparison with area m easurem ents m ade b y adsorption. T he two carbon blacks th a t show greater areas from the adsorption th a n the electron microscope m easurem ents have been so treated as to produce porosity. T he sta n d ard blacks th a t are supposedly non
porous show excellent agreem ent betw een th e areas determ ined by the two m ethods. In passing it should be emphasized th a t the electron microscope yields particle size directly an d n ot sur
face area; th e adsorption m easurem ents, on th e o th er hand, yield directly th e num ber of molecules required to form a monolayer and hence, with certain assum ptions, th e surface area. These three examples in themselves are strong evidence th a t the areas obtained by th e low -tem perature nitrogen adsorption m ethod are approxim ately correct.
Table II. Surface Area Measurements on Sized Glass Beads (8 , 9 ) A rea b y a d s o rp tio n of N 2 (liquid), sq. m ./g . 0 .5 3 2 Av. diam . calcd. from ad so rp tio n of N 2, microns
L iq u id 4 . 5 0
Solid 5 .3 0
D iam . b y microscopic o b serv atio n , m icrons 7 .0 0 Area after cleaning beads w ith soln., sq. m ./g . 0 .7 4 8
Table III. Surface Areas of Carbon Blacks (Square Meters per Gram)
E3Ï C a rb o n B lack B y N 2
A d so rp tio n
C alcd. fro m E lectro n M icroscope
M e a s u re m e n ts 0
P-33 (th e rm al decom position black) 2 0 .7 2 0 .9
« L am p b lack (ty p e T) 2 5 .5 2 3 .5
- L am p b lack (ty p e T a c tiv a te d ) 6 208 2 7 .4
w . A cetylene b lack (Shaw inigan) 6 4 .5 5 5 .9
G rad e 6 (channel black) 110 7 4 .8
M ogul Gong in k black) 450 8 5 .4
3 # a D e n s ity of 2.00 assu m ed in co n v e rtin g m icroscope d ia m eters to surface areas.
6 T r e a te d w ith air for 3 h o u rs a t 800° F.
3O
R ecently H arkins and J u ra (17) announced a m ethod for m easuring the absolute surface area of a finely divided nonporous solid th a t does n o t even require one to assume a cross-sectional area for the adsorbate molecule. T heir m ethod entails measuring sD®*' the he at evolved when a sample of finely divided titan iu m oxide is
immersed in w ater after having been p resaturated by exposure to a relative pressure of w ater vapor sufficiently high to form an icludf average of ab o u t five adsorbed layers. T he curve obtained by ily K plotting th e h e at evolved on immersion per gram of titanium
¡0- oxide against th e am ount of adsorbed w ater levels off ra th er lii'i quickly to a co nstant value. B y assuming th a t this constant lOfe value for th e h e a t of immersion is th e sam e as th a t of th e surface
;res energy of pure w ater (118 ergs per sq. cm.), th ey were able to
til-P/P.
Figure 3. Plot of Low-Temperature Nitrogen Adsorption Isotherms According to Equation 1 (5)
calculate the num ber of square centim eters of surface possessed by the titanium dioxide sample. T he result obtained by them was 13.8 square m eters per gram. T heir determ ination of the area of this sam e titanium dioxide b y the nitrogen adsorption m ethod m aking use of E q uation 1 yielded a value of 13.9 square meters per gram. T he agreem ent speaks for itself in adding weight to the contention th a t th e low -tem perature nitrogen isotherm m ethod yields approxim ately th e correct absolute value of the surface area. T he h e at of immersion m ethod is more use
ful as a separate procedure for checking th e areas of nonporous solids; it is probably too difficult experim entally to employ as a routine method.
H arkins and J u ra (17) also developed an independent m ethod for plotting the low -tem perature nitrogen adsorption d a ta and calculating surface areas. T hey discovered th a t plotting 1 / V 2 against log vlv » according to the equation
log p / p 0 = B - (A /V *) (2) where V is the volume of nitrogen adsorbed a t low tem perature a t the relative pressure p/po, yields a straig h t line over a long rela
tive pressure range extending usually from 0.05 to about 0.7.
From the absolute surface area m easurem ents employing the heat of immersion of partially satu rate d titanium dioxide described above, they showed th a t the area of th e titan iu m dioxide is given by the equation
area = k ( S ) l n (3)
where S = slope of p lot of E q uation 2
F or nitrogen, k has a value of 4.06. Thus by plotting the d a ta for adsorption of nitrogen a t —195° C. according to E quation 2 an d employing a value of 4.06 for k in E q uation 3, it becomes possible to obtain values for the surface areas of finely divided m aterials. T heir comparison of the results obtained by this m ethod w ith those obtained by using the plots for E quation 1 is shown in T able IV. T he agreem ent betw een the two m ethods is unbelievably close. I t should be borne in m ind th a t th e values obtained by H arkins and J u ra (17) by E quations 2 and 3 do not involve an y assum ption as to th e cross-sectional area of the
ad-642 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
Table IV. Comparison of A reas of Nonporous Solids Calculated by Harkins-Jura and by Brunauer-Emmett-Teller Methods
A rea from N 2 A d so rp tio n a t Average Diameters of Common Pigments
d ! in M icro n s“ m ethod to about eighty-six porous solids. In all cases the agree
m en t betw een the areas obtained by E quation 1 and those using a value of 4.06 for k in E quations 2 and 3 is w ithin 20% . I f they three peaks seem to occur corresponding to 14.05, 15.25, and 16.05 sq.
A.
T hey conclude th at, if one uses a value of 15.25 sq.A.
m aterials a different cross section of th e nitrogen molecule should be used for each solid in order to obtain accurate results. On the o th er hand, there is no assurance th a t constant k will be the same for porous and for nonporous materials. In any case, the agreem en t betw een the two m ethods is sufficiently good to w arrant the conclusion th a t the adsorption of nitrogen a t —195° C. can be is an independent check by direct microscopic observation. I t is evident th a t fair agreem ent exists betw een th e w a ter adsorption m ethod and the microscopic m ethod, though in som e cases t e results by the w ater sorption m ethod are several fold g re ater or sm aller th an those obtained by direct microscopic exam ination.
T he authors are fully cognizant, apparently, of several sources of error in th e m easurem ents and ta k e precautions to avoid them . T hey realize, for example, th a t strongly hygroscopic solids canrtot b e used w ith w ater vapor as th e adsórbate because of chemical reaction betw een the w ater vapor an d th e solid. T h e sam e would hold tru e for solids on which w ater vap o r is strongly chemisorbed.
I t is also necessary to avoid using th e w ater v ap o r m ethod on capillary condensation, since th e initial relative hu m id ity is in the neighborhood of 50% and is accordingly high enough to cause condensation in v ery fine capillaries. T h e authors believe they avoid all such complications by tak in g th eir equilibrium readings after an equilibration tim e so sh o rt as to preclude the occurrence adsorption now appears to be overwhelming, because S-shaped nitrogen adsorption isotherm s ha v e been found on a v a rie ty of
Table VI. Comparison of Surface A reas of Solid Adsorbents Calculated by Harvey (7 8 ) and Estimated b y
Brunauer-Emmett-Teller M ethod
July, 194S I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 643
a fte r preparation and, therefore, presum ably had no chance to form rough surfaces. Furtherm ore, adsorption on carbon black particles of a v ariety of sizes (as described in T able I I I ) , zinc oxide particles (11), and finely divided potassium chloride (4) and o ther nonporous crystals all yield uniformly S-shaped curves.
Since the same ty p e curve is obtained, regardless of the particle size, th e shape cannot be explained on the basis of capillary con
densation betw een the particles. I t m ust be recognized th a t capillaries too sm all to be seen microscopically m ight be present on all these solids. However, it would be fortuitous if the tin y cracks and capillaries happened to bo present on all of these various solids with sufficient uniform ity to produce substantially th e sam e ty p e of S-shaped adsorption isotherm . Finally, the agreem ent betw een th e m easurem ents by H arkins and J u ra (16) on titan iu m dioxide by the h eat of w etting m ethod and by the nitrogen adsorption m ethod argues against th e possibility th a t S- shaped nitrogen isotherm s on this substance are due to cracks or capillaries, since the la tte r would cause erroneous surface area results by the w ater immersion m ethod.
M O N O M O L E C U L A R PHYSICAL A D SO R PT IO N COM BINED WIThjl CAPILLARY C O N D E N SA T IO N
D uring the last two years, two different groups of workers have made interesting approaches to the old suggestion (21) of calcu
lating surface areas of porous m aterials by assuming th a t S- shaped adsorption isotherm s are m ade up of monomolecular physical adsorption combined w ith capillary condensation.
Even though it appears to be fundam entally incorrect thus to neglect m ultilayer adsorption, it is interesting to recapitulate briefly the results obtained by th eir respective procedures.
Even though it appears to be fundam entally incorrect thus to neglect m ultilayer adsorption, it is interesting to recapitulate briefly the results obtained by th eir respective procedures.