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Analysis of nitrogen adsorption isotherms on porous and nonporous silicas by the BET and αs methods
Analysis of Nitrogen Adsorption Isotherms on Porous and Nonporous Silicas by the BET and ~8 Methods M . R. B H A M B H A N I , I P. A. C U T T I N G , 2 K. S. W. S I N G , ~X'D D. H. T U R K
Department of Chemistry, Brunel University, London, England Received December 14, 1970; accepted March 19, 1971 Nitrogen adsorption isotherms were determined on a wide range of porous and nonporous silicas. Isosteric heats of adsorption were calculated from the isotherms (over the temperature range - 192 ° to - 178°C) on representative materials. Standard data for nitrogen adsorption at -196°C on nonporous hydroxylated silica are tabulated for the p/po range 0.001-0.90. The results indicate that certain high-area silicas are truly nonporous, but some grades of commercial Aerosil are porous. Surface areas are calculated from the isotherms by means of the BET method and the new a~-method. The latter is a graphical procedure in which the amount adsorbed is plotted against a , for the standard adsorption data, where a, is the ratio of the amount adsorbed (at the given p/po) to the amount adsorbed at p/po = 0.4. Deviations of the a,-plots from linearity are explained in terms of micropore filling and capillary condensation. In the absence of micropore filling, the surface areas calculated from the slope of the a,-plots are in excellent agreement with the BETareas. Enhanced isosteric heats and C values are associated with micropore filling; the isotherm is therefore distorted in the BET range and the BET-area is not valid. In certain cases, when micropore filling and monolayer coverage at low p/po are followed by multilayer formation and capillary condensation at higher p/po, a nearly linear a,-plot results, but again neither the BET-area nor the a~-area can provide a meaningful value of the internal surface area.
INTRODUCTION The influence of Stephen Brunauer's work in many different areas of pure and applied science has been prodigious. Indeed, it is possible to trace the stages in the development of his work--from the early days of the B and E partnership, through the period of BET and BDDT to the silicate, surface energy, and porosity studies--by noting the impact of his ideas on the scientific literature. In spite of this truly impressive record, Brunauer is not content to rest on past achievements; we can look forward to other major contributions in his years of "retiremont." No satisfactory alternative to the BET i Present address: Glaxo Laboratories
Limited,
Greenford, Middlesex, England. 2Present address: The Gas Council, London Research Station, Michael Road, London S.W. 6, England. Copyright @ 1972 by Academic Press, Inc.
m e t h o d (1) has y e t b e e n d e v e l o p e d for t h e r o u t i n e d e t e r m i n a t i o n of surface area. T h e t h e o r e t i e a l l i m i t a t i o n s of t h e B E T m o d e l are recognized, b u t in p r a c t i c e t h e v a l i d i t y of t h e B E T a r e a m u s t be assessed e m p i r i c a l l y for each gas-solid s y s t e m . U n f o r t u n a t e l y , m a n y of t h e e x p e r i m e n t a l i n v e s t i g a t i o n s of a d s o r p t i o n r e p o r t e d i n t h e l i t e r a t u r e were m a d e on p o o r l y c h a r a c t e r i z e d solids a n d t h e n u m e r o u s a t t e m p t s to c o m p a r e B E T a r e a s a n d a d j u s t m o l e c u l a r cross-sectional a r e a s were o f t e n m a d e o n a r a t h e r a r b i t r a r y basis. G e n e r a l l y , e m p h a s i s was p l a c e d on m o n o l a y e r - m u l t i layer coverage and capillary condensation, a n d t h e i m p o r t a n c e of t h e m i e r o p o r e filling m e c h a n i s m was n o t f u l l y a p p r e c i a t e d . V a r i o u s e m p i r i c a l m e t h o d s of i s o t h e r m analysis have been introduced in the past few y e a r s ; t h e b e s t k n o w n of t h e s e is p r o b a b l y t h e t - m e t h o d of L i p p e n s a n d de B o e r (2), w h i e h p r o v i d e s a s i m p l e a n d d i r e c t
Journal of Colloid and Interface Science, Vol. 38, No. 1, January 1972
109
110
BHAMBHANI E T AL.
means of interpreting nitrogen isotherms. The amount of nitrogen adsorbed is plotted against t, the statistical multilayer thickness for the adsorption of nitrogen on a nonporous reference solid. Any deviation in shape from the standard isotherm is therefore detected on the t-plot as a departure from linearity. Recently, the so-called universal t-curve of de Boer and his coworkers (3) has been criticized (4-7) on the grounds that it cannot represent an accurate nitrogen isotherm on all nonporous solids, and that the calculation of t necessarily involves assumptions concerning the nature of the packing and stacking of adsorbate molecules (8). The t-method was amended by Sing (9) to take into account the process of micropore filling and to provide under certain conditions an assessment of the micropore volume. It has been pointed out by Brunauer (4) and others (5, 6) that since t is itself calculated from V/V~, the t-method is necessarily dependent on the BET evaluation of the monolayer capacity. It is clear that this limitation must restrict the scope of the method to those systems where the BET monolayer capacity is well defined (10). To avoid this difficulty, the t-method has been modified (5, 6) and t has been replaced by ( V / V ~ ) ~ , termed a~, where V~ is the amount adsorbed at a selected relative pressure (p/po)~ • The reduced standard isotherm on the nonporous reference solid is therefore arrived at empirically and not via V~. In principle, ¢~ could be placed equal to unity at any convenient point on the standard isotherm; in practice, with a number of vapors (including nitrogen at -196°C) it seems reasonable to place a. = i at (p/po)~ = 0.4. With nitrogen, monolayer coverage and mieropore filling occur at p/po < 0.4 and any hysteresis loop present is located at p/po > 0.4. The scope of the ~,-method has been discussed only in outline and its application has been restricted so far to a few adsorption systems (6, 7, 11, 12). In this paper, standard data are presented for nitrogen adsorption on nonporous silica, and isotherms on a wide range of porous and nonporous silicas are analyzed by the ~,-method. The chief aim of this work was to exploit the new method in order to throw light on the mechanisms of
physical adsorption and to examine the validity of the BET monolayer capacity, especially in relation to microporosity. Isoteric heats of adsorption are discussed from the same standpoint. MATERIALS AND METHODS The results of preliminary investigations (6) had indicated that certain high-area silicas could serve as nonporous reference materials. Thus, two Degussa products TK70, and TKS00, were found to consist of discrete spherical particles, the degree of aggregation being lower than in the commercial grades of Aerosil. Another grade of nonporous hydroxylated silica studied was Fransil; in this case the surface area determined by electron microscopy (36 m2/gm) was in fairly good agreement with the BET nitrogen area (38.7 m2/gm), and the reduced nitrogen isotherm corresponded very closely with that obtained on various samples of low-area crystalline and amorphous silica. The original batch of Fransil was used again in the work reported here and is referred to as Fransil-I. Other new batches of Fransil and TK800 were Fransil-II, TK800-II, and TKS00-III (TK800-I being the original batch). Various grades of Aerosil (200, 300, and 50X) were supplied by the manufacturers (Degussa Forschung Chemic). A portion of Aerosil 300 was soaked in water for several days and dried at room temperature. The various silica gels were specially prepared and supplied by the Unilever Chemical Development Centre; they were selected to provide a wide range of surface properties with pore structures within the micropore and mesopore range. Gel I( was calcined in air at 900°C to give K(900). The nitrogen adsorption isotherms were determined volumetrically using both a semimicro apparatus of the type designed by Harris and Sing (13) and an apparatus based on the design of Lippens, Linsen, and de Boer (14). The nitrogen was of 99.9 % purity and was dried by slow passage through a cold trap. Helium (99 % purity) was used for the dead space measurements. All equilibrium pressures were measured on a mercury manometer with the aid of a cathetometer (to 4-0.001 cm). Cryostat bath temperatures
Journal of Colloid and Interface Science, Vol. 38, No. 1, J a n u a r y 1972
ADSORPTION ISOTHERMS ON SILICAS were measured with a vapor pressure thermometer (oxygen or nitrogen) at the time of each adsorption reading; an accurate value of p/po was then calculated for each point on the isotherm. The isosteric heats of adsorption were calculated from nitrogen isotherms determined using a Cahn RG Electrobalance and a cryostat with a modified hangdown tube, as described by Cutting (15). In this case, the pressure measurements were made to within ~=0.1 torr with a C.E.C. pressure transducer, which had been calibrated against a mercury manometer. The temperature of the sample was checked with a copper-eonstantan thermoeouple to within 4-0.05°C. All samples were outgassed for prolonged periods (usually 15-20 hours) at 25°C and the reproducibility of most isotherms was checked. In some eases (e.g., Fransil-I, Fransil-II, and Gel A) outgassing was also conducted at temperatures up to 200°C; no change in the isotherm could be detected. RESULTS
111
TABLE I STANDARD ADSORPTION DATA FOR ~ITROGEN AT -196°C ON NONPOROUS HYDROYLATED SILICA
(FRANSIL-I) Relative pressure #/po
0.001 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0 90
Adsorption per unit Reduced adsorption area (tLmole/m~) as(= V/V~.4)
4.0 5.4 6.2 7.7 8.5 9.0 9.3 9.4 9.7 10.0 10.2 10.5 10.8 11.3 11.6 11.9 12.4 12.7 13.0 13.3 13.6 13.9 14.2 14.5 14.8 15.1 15.5 15.6 16.1 16.4 17.0 17.8 18.9 19.9 21.3 22.7 25.0 28.0 37.0
0.26 0.35 0.40 0.50 O.55 0.58 0.60 0.61 0.63 0.65 0.66 0.68 0.70 0.73 0.75 0.77 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.01 1.04 1.06 1.10 1.14 1.22 1.29 1.38 1.47 1.62 1.81 2.4
The nitrogen adsorption data given in Table I were obtained on Fransil I, which had been previously adopted as the nonporous hydroxylated silica reference material. The adsorption per unit area in column 2 is expressed in micromoles per square meter (following the practice of Kiselev), taking the surface area as the BET vMue of 38.7 m2/gm. The reduced adsorption a~ in column 3 is V/Vo.4, where V0.4 is the adsorption at the standard state of p/po = 0.4. t~epresentative isotherms and a~-plots are shown in Figs. 1 and 2. The linear plots in Fig. l(b), and the corresponding Type II isotherms in Fig. l(a), are the result of unrestricted monolayer-multilayer adsorption on the nonporous solids Fransil-II, TI4800-I, and Aerosil 300. The other samples which gave linear a~-plots over a wide range condensation. Other gels which gave similar of P/po were TK70, TKS00-II, TKS00-III, a~-plots were H, K, K(900), L, and P. and Aerosil 200. The isotherms in Fig. 1(c) The a~-plots on the mieroporous gels D exhibit hysteresis and are characteristic of and E are shown in Fig. 2(b) with the coradsorption on mesoporous solids. That this responding Type I isotherms in Fig. 2(a). is the case is confirmed by the shape of the Gel M gave a very similar a,-plot to that of a~-plots (Fig. l(d)), which are all linear over E. The a,-plots in Fig. 2(d) are more complex the initial range of p/po and deviate upwards in nature, probably owing to a combination from linearity with the onset of capillary of monolayer-multi]ayer coverage, micropore Journal of Colloid and Interface Science, Vol. 38, ~o. i, January 1972
BI-IAMBHANI ET AL.
112 2ooj a
"
'
jJ
,oo!./J 5Ojf_O
I
I
I
E
Q_
500~
hS(
3O(
)
~5o~ J C
o
0.2
0.4
0-6
0.8
~-0
05
PtPo
I.O
1.5
2-0
2.5
Gs
FIG. 1. Nitrogen isotherms and ~-plots on nonporous snd mesoporous silicas. Open symbols, adsorption points; closed symbols, desorption points. filling, and capillary condensation. The mixed gel, E q- J, was made up of equal parts by weight of gels E and J. Aerosil 50X and soaked Aerosil 300 both gave curved a~-plots, indicative of porosity. The surface areas are shown in Table II. The BET surface areas, SB~T, in column 2 were calculated in the usual way, with the nitrogen molecule in the close-packed monolayer ~ssumed to occupy an average area of 16.2 A2. The value of p/po corresponding to the upper limit of the initiM linear region of the a,-plot is indicated in column 4. The values of S~ have been calculated from the slope of the linear part of the a~-plot (taking a line through the origin), using the relation S~ = 2.89 V / a , , [1]
where V is the volume of nitrogen adsorbed, expressed in cubic centimeters (S.T.P.)/ gram and the factor 2.89 has been obtained by calibration against the BET area of Fransil-I. In cases where the ~,-plot is not linear the value of $8 shown in brackets has been calculated from the slope of the line drawn from the origin to the initial adsorption points. The value of the external surface area is also given in those eases where the a,-plot is linear in the multilayer range (6, 9). The isosteric heats of adsorption Q,t on Fransil-I and gels A, B, and D are plotted against loglop/po in Fig. 3. This procedure has the advantage over the conventional plot of O,, against V/V,-. in that no assumption has to be made about the mechanism of adsorption or the magnitude of surface area.
Journal of Colloid and Interface Science, VoL 38, No. 1, J a n u a r y 1972
ADSORPTION ISOTHERMS ON SILICAS
113
4oo! I
300~
] // // ----
/
E
/
D
,1 / E
oi
I
I
I
T
I
I
I
I
co 400 ~
F
©
./
o!2
o!4
o!o
o!8
1-o
P/Po
o
o!s
i!o
i!s
2!o
2.s
~s
FIG. 2. Nitrogen isotherms and a,-plots on mieroporous and mixed pore silicas. Open symbols, adsorption points; closed symbols, desorption points. Essentially, Q,t is expressed as a function of the difference in chemical potential. D ISCUSSION The fact that. the ~,-plots in Fig. l(b) and also those for all the nonporous solids listed in Table II are linear over a wide range of P/po appears to confirm the reliability of the standard adsorption data in Table I. The values of a, show a considerable difference from those calculated from the data of Lippens, Linsen, and de Boer (14), which provided the basis for their universal t-curve. On the other hand, our data are in fairly good agreement (to P/po ~ 0.8) with the reduced adsorption data of Linsen (16) and Pierce (8). Linsen has already noted the lack of agreement between his t-curve on a sample of Aerosil and t h a t of Lippens (14,
17) on a calcined (apparently nonporous) alumina. He attempted to explain this difference in terms of the geometry of the higharea silica b y postulating that the areas where elementary particles touch are rendered inaccessible to adsorbate molecules. The present results, along with those reported previously (18) on low-area nonporous silicas, demonstrate t h a t within wide limits the effect of particle size on the standard isotherm is negligible. It is now clear that certain batches of Aerosil have a small but significant degree of porosity. For example, the c~,-plot on Aerosil 50X was curved over the monolayer range but almost linear in the multilayer region. The small amount of mieroporosity was sufficient to reduce the external surface area (calculated from the slope of the linear section of the
Journal of Colloid and Interface Science. ¥ o l . 38, N o . 1, J a n u a r y lg72
114
BHAMBHANI E T AL. TABLE I I C O M P A R I S O N OF SURFA.CE A R E & S C R L C U L & T E D BY B E T A.ND ~s M E T H O D S Silica sample
SBET (m2/gm)
Nonporous solids Fransil-I Fransil-II TK 70 T K 800-1 TK 800-II TK 800-III Aerosil 200 Aerosil 300 Mesoporous solids Gel A Gel G Gel H Gel J Gel K Gel K (900) Gel L Gel P Mieroporous solids Gel D Gel M Gel E Aerosil 50X Mixed micro- and mesoporous solids Gel B Gel F Gel N Gel 1~ Aerosil 300 (soaked) Gel (E + J)
4]
Ss (m2/gm)
Upper limit of linear region of ~zs-plot
(~/$0)
38.7 34 36 154 148 160 194 313
33 36 153 150 165 193 318
--
->0.9 >0.9 >0.9 0.9 >0.7 >0.9 0.8
300 504 460 349 376 207 369 274
303 503 458 350 376 208 372 272
0.4 0.3 0.3 0.3 0.4 0.3 0.4 0.7
767 637 631 38
(810-960) 35~ (770) 17~ (730) 20° (37) 25a
Not linear Not linear Not linear <0.2
500 550 463 536 321 440-470
(505) (560) (480) (531) (320-340) (465-485)
<0.3 <0.12 <0.4 <0.2 Not linear Not linear
These values are calculated from the linear part of the a,-plot in the multilayer range.
C3 ATENT HEAT
--
02.5
]
-2.0
I
---1-5
L
-1-0
f
-0"5
togl0P/Po FIG 3, Isosteric heats for nitrogen on nonporous and porous silicas. ¢ Fransi]; I I Gel A ; A Gel B; • Gel D .
a , - p l o t ) to a b o u t 25 cm~'/gm, cf t h e B E T a r e a of 38 m2/gm. C o m p a r i s o n of o u r d a t a w i t h t h e results of A r i s t o v a n d K i s e l e v (19) has r e v e a l e d a s m a l l b u t significant a m o u n t of m i c r o p o r o s i t y in t h e R u s s i a n s a m p l e of Aerosil. I n t h e case of A e r o s i l 300, t h e a,p l o t (Fig. l ( b ) ) e x h i b i t s a n u p w a r d d e v i a t i o n f r o m l i n e a r i t y a t p / p o > 0.8. T h i s m a t e r i a l c o n t a i n e d m a n y s m a l l p a r t i c l e s a n d i t seems likely that interparticle capillary condensation contributed to the adsorption at high P/Po • A f t e r t h e A e r o s i l 300 h a d b e e n s o a k e d i n w a t e r , t h e a~-plot g a v e e v i d e n c e of b o t h m i c r o p o r o s i t y a n d m e s o p o r o s i t y , i.e., d e v i a t i n g f r o m l i n e a r i t y a t low a n d a t h i g h p / P o • All t h e s e r e s u l t s confirm o u r earlier suggest i o n t h a t F r a n s i l a n d T K 8 0 0 are m o r e s a t i s f a c t o r y as n o n p o r o u s reference silicas
Journal of Colloid and Interface Science, Vo]. 38, No. 1, J a n u a r y 1972
ADSORPTION ISOTHEI~MS ON SILICAS than are the normal commercial grades of Aerosil, which have been adopted in the past. The agreement (usually to within 1%) between the values of SBET and So in Table II for all the nonporous and mesoporous solids is noteworthy and serves to confirm the validity of Eq. [1]. On the other hand in the case of the microporous solids the values of $8 (in brackets) are mostly higher than those of SBET • In the study of porous and nonporous carbon blacks, de Boer and his coworkers (20) also noted that values of St, calculated from the slope of the t-plot, were higher than those of S~ET. These authors (3, 20) suggest that St provided a more reliable estimate of the total surface than did SB~T • Brunauer (4) has rightly pointed out that in the analysis of an isotherm by the tmethod, it is essential that a correct t-curve be employed. His view differs from ours, however, in that he suggests that the appropriate t-curve should be based not on the chemical similarity of the absorbent surface but rather on the magnitude of the heat of adsorption. According to Brunauer, the BET C constant is frequently adequate for testing the appropriateness of the t-curve, but that a more reliable cheek is the measure of agreement between SBET and St. The application of a~-method is helpful within the context of this discussion. Although the values of S, in Table II are based on the value of SBEr for Fransil-I, the use of the a~-method as a comparative method for surface area determination is independent of the BET method. Gregg (21) has stressed the normalizing, or scaling, principle of the ~8-method: that for a series of isotherms of identical shape the uptake at a given pressure is directly proportional to the surface area. In principle, therefore, if the surface area of the reference solid could be determined accurately by another means (e.g., electron microscopy) the a~-method could be made entirely independent of the BET method. In our view, the differences noted above between S~ and SB~T are the direct result of micropore filling in changing the shape of the nitrogen isotherm; the implication is that neither SB~T nor S~ has any
115
physical meaning. As expected, this discrepancy is associated ~dth a difference in the C value. Nitrogen adsorption at - 196°C on a nonporous hydroxylated silica gives a C value of about 110; with mieroporous gels, C is increased to 170-190. To understand the significance of these results, we must examine the theoretical basis for the concept of micropore filling. Dubinin (22) has defined mieropores as those pores in which the adsorption potentials are substantially enhanced owing to a significant overlap of the adsorption forces from the pore walls on either side of the adsorbate molecule; he and others (6, 8, 9, 10, 23, 24) have argued that the concept of layer-by-layer surface coverage then loses its physical meaning. If we accept the possibility of mieropore filling as a primary mechanism of physical adsorption, which operates at low P/po (as distinct from the secondary process of capillary condensation), we are still faced with the problem of characterizing the adsorption mechanism in practice. Two questions naturally arise: 1) What is the critical value of pore width which marks the boundary between filling and monolayer-multilayer adsorption in mesopores? 2) Does the mieropore filling mechanism govern all eases in which pore filling has restricted the muitilayer adsorption, i.e., approaching a Type I isotherm? We cannot give definitive answers to these questions at the present time because the theory of physical adsorption is not sufficiently developed. Dubinin (22) places the upper limit of micropore width at. about 30 A, but some authors (20, 25) favor a lower value ( < 10 A). Strictly, the effect of pore narrowing on the adsorption potential must depend on the nature of the adsorbentadsorbate interactions and the size of the adsorbate molecule. Related to the influence of pore narrowing on the shape of the isotherm is its effect on the heat of adsorption. As Brunauer and his eoworkers (4) have pointed out, the C constant is directly related to the free energy of adsorption (or change in chemical potential) rather than to the heat of adsorption. The magnitude of C also depends on the
Journal of Colloid and Interface Science, VoI. 38, No. 1, J a n u a r y 1972
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BHAMBHANI ET AL.
P/po range of linearity of the B E T plot.
Differential, or isosteric, heats of adsorption, on the other hand, provide a basis for the comparison of interaction energies involved in different adsorption systems (29). Thus, according to the Dubinin criterion, the process of micropore filling is accompanied b y an enhanced differential heat over that given b y monolayer coverage (under the same conditions of p and T) of the open surface. The isosteric heats Q~ plotted in Fig. 3 reveal an interesting difference between the three gels A, B, and D: Q~ remains reasonably constant over the range of p/po for both Fransil-I and gel A, whereas at low p/po Q~t is enhanced for gels B and D. I t has already been noted that gel D gave a T y p e I isotherm and an a,-plot characteristic of micropore filling; the high Q~ is therefore to be expected. The case of gel B is more complex, but the evidence of Fig. 3 suggests t h a t in this case also, micro-
pore filling played a significant part in the adsorption process at low p/po. If this is true, in spite of their close agreement, neither SBET nor S~ has any real meaning for gel B. Six samples have been placed in the mixed pore category in Table If. All these isotherms, except that on Aerosil 300 (soaked), exhibited hysteresis and gave evidence of capillary condensation. In most cases, the a~-plots were either not linear or deviated from linearity at low p/po ( < 0.2). The case of gel N is interesting because this material gave a linear a,-plot to a higher p/po ( N 0.4), which appeared at first sight to conform to the requirement for monolayer-multilayer coverage followed b y capillary condensation. On the other hand, the B E T plot on gel N was linear over a somewhat restricted range of p/po (0.05--0.25) and the C value was high (~-d60). I t appears therefore that gels B and N were rather similar in character in t h a t the pore size distribution in each ease resulted in a compensating effect between the restrictive adsorption in mieropores and the capillary condensation in mesopores, which gave rise to a nearly linear a~-plot obscuring the influence of mieropore filling (30). I t is possible that certain of the other gels placed in the mesoporous category were also microporous to some extent. Journal of Colloid and Interface Science~ Vol. 38, No.
Firm conclusions about the mechanism of adsorption should not be drawn on the basis of an isotherm of a particular vapor at a single temperature. We have suggested elsewhere (6) that a useful diagnostic test of micropore filling is the comparison of values of apparent surface area obtained b y the application of the as-method to isotherms of a number of different vapors on the porous solid. Such an approach is time consuming, however, and for routine work we must obtain as much information as possible from a single isotherm. The results presented here illustrate the way in which the a~-method m a y be used to supplement the B E T procedure. Particular care is, of course, required to ensure t h a t the a,-plots are restricted to t h a t part of the isotherm covered b y reliable standard data. ACKNOWLEDGMENTS The authors wish to thank the Gas Council, London, and Unilever Chemical Development Centre, Warrington, for their support. They also their thanks to Degussa Forschung Chemic, Frankfurt, for supplying certain samples; and to J. D. Carruthers and R. E. Day for some isotherm data.
1, January 1972
REFERENCES 1. BRAUNAUER, S., EMMETT, P. H., AND TELLER,
E., J. Amer. Chem. Soc. 60, 309 (1938). 2. LIPPENS,B. C., ANDDE BOEa, J. H., d. Catal. 4, 319 (1965). 3. DE BOER, J. H., LINSEN, B. G., AND OSINGA,
TH. J., J. CaSal. 4, 643 (1965); BROEKOFR, J. C. P. AND LINSEN, B. G., inB. G. Linsen, Ed., "Physical and Chemical Aspects of Adsorbents and CatMysts," p 23. Academic Press, London, New' York, 1970; DE BoEn, or. H., LIP:PENS, B. C., LINSEN, B. G., BROEKHOFF, or. C. P.~ VAN HEUVEL, A.,
ANDOSlNOA,Tm J., J. Colloid Interface Sci. 9.1, 261 (1966). 4. MIKHAIL,R. SH., BRUNAUER,S., AND BODOR, E. E., J. Colloid Interface Sei. 26, 45 (1968); BRUNAUER, S., SKALNY, or., AND BODOR,
E. E., ibid. 30, 546 (1969); BRUNAUER, S. in D. H. Everett and R. H. Ottewill, Eds., "Surface Area Determination," p 63. Butter-
worths, London, 1970. 5. SING, K. S. W., Chem. Ind. (London) 1968, 1520; Carruthers, or. D., CUTTING, P. A.,
DAy, R. E., HARRIS, M. i~., MITCHELL, S. A., AND SING, K. S. W., Chem. Ind.
ADSORPTION ISOTHERMS ON SILICAS (London) 1968, 1772; Payne, D. A., .~xI) SING, K. S. W., Chem. Ind. 918 (1969). 0. SING, K. S. W., in D. H. Everett and R. H. Ottewill, Eds. "Surface Area Determination," p 25. Butterworths, London, 1970. 7. NICOL~ON, G. A., J. Chim. Phys. 66, 1783 (1969); NICOL.~ON, G. A., AND TEICHNER, S. J., J. Chim. Phys. 66, 1816 (1969). 8. PIERCE, C., J. Phys. Chem. 72, 3673 (1968). 9. SING, K. S. W., Chem. Ind. (London) 829 (1967). 10. ~REGG, S. J., AND SING, K. S. W., "Adsorption, Surface Area and Porosity." Academic Press, London and New York, 1967. 11. ALDCnOFT, D., BYE, G. C., ROmNSON, J. G., AND SING, t(. S. W., J. Appl. Chem. 18, 301 (1968). 12. CARRUTIIERS, J. D., PAYNE, D. A., SING,
13. 14.
15.
16. 17. 18.
19.
K. S. W., STRYKER, L. J., dr. Colloid Interface Sei., in the press. HARRIS, M. R., AND SING, K . S. W., J. Appl. Chem. 5, 223 (1955). LIPPENS, B. C., LINSEN, B. G., DE BOER, J. H., J. Catal. 3, 32 (1964). CUTTING, P. A., in C. H. Massen and H. J. Van Beckum, Eds. "Vacuum Microbalance Techniques," Vol. 7, p 71. Plenum Press, New York and London, 1970. LINSEN, B. G., Thesis, p 64, Delft, The Netherlands, 1964. LIPPENS, t3. C., Thesis, p 145, Delft, The Netherlands, 1961. I'IARRIS, M. R., AND SING, I~. S. W.~ Chem. Ind. (London) 1955, 487. ARmTOV, B. G., AND Ig/ISELEV, A. V., Kolloid. Zh. 23, 299 (1965).
117
20. DE BOER, J. HI.~ LINSEN, B. G., VAN DEI~ PLkS, TH., AND ZONDERVAN, G. I., J. Catal. 4, 649 (1965). 21. (3I~JCGG, S. J., in D. I-I. Everett and R. LI. Ottewill, Eds., p 41. Butterworths, London, 1970. 22. DUBIN1N, M. M., J. Colloid Interface Sci. 21, 387 (1966); ibid., 23, 487 (1967); in D. }I. Everett and R. H. Ottewill, eds. "Surface Area Determination," p 123. Butterworths, London, 1970. 23. PIERCE, C., J. Phys. Chem. 63, 1076 (1959); ibid., 64, 1184: (1960). 24. MARsh, H., ~ND R~ND, B. J., J. Colloid Interface Sci. 33, 101 (1970); ibid., p 478 (1970). 25. MIKHAIL, R. Sift., AND SHEBL, F. A., J. Colloid Interface Sci. 32,505 (1970). 26. H_
Journal of Colloid and Interface Science, ¥oi. 38, No. l, Jam~ary 1972
Department of Chemistry, Brunel University, London, England Received December 14, 1970; accepted March 19, 1971 Nitrogen adsorption isotherms were determined on a wide range of porous and nonporous silicas. Isosteric heats of adsorption were calculated from the isotherms (over the temperature range - 192 ° to - 178°C) on representative materials. Standard data for nitrogen adsorption at -196°C on nonporous hydroxylated silica are tabulated for the p/po range 0.001-0.90. The results indicate that certain high-area silicas are truly nonporous, but some grades of commercial Aerosil are porous. Surface areas are calculated from the isotherms by means of the BET method and the new a~-method. The latter is a graphical procedure in which the amount adsorbed is plotted against a , for the standard adsorption data, where a, is the ratio of the amount adsorbed (at the given p/po) to the amount adsorbed at p/po = 0.4. Deviations of the a,-plots from linearity are explained in terms of micropore filling and capillary condensation. In the absence of micropore filling, the surface areas calculated from the slope of the a,-plots are in excellent agreement with the BETareas. Enhanced isosteric heats and C values are associated with micropore filling; the isotherm is therefore distorted in the BET range and the BET-area is not valid. In certain cases, when micropore filling and monolayer coverage at low p/po are followed by multilayer formation and capillary condensation at higher p/po, a nearly linear a,-plot results, but again neither the BET-area nor the a~-area can provide a meaningful value of the internal surface area.
INTRODUCTION The influence of Stephen Brunauer's work in many different areas of pure and applied science has been prodigious. Indeed, it is possible to trace the stages in the development of his work--from the early days of the B and E partnership, through the period of BET and BDDT to the silicate, surface energy, and porosity studies--by noting the impact of his ideas on the scientific literature. In spite of this truly impressive record, Brunauer is not content to rest on past achievements; we can look forward to other major contributions in his years of "retiremont." No satisfactory alternative to the BET i Present address: Glaxo Laboratories
Limited,
Greenford, Middlesex, England. 2Present address: The Gas Council, London Research Station, Michael Road, London S.W. 6, England. Copyright @ 1972 by Academic Press, Inc.
m e t h o d (1) has y e t b e e n d e v e l o p e d for t h e r o u t i n e d e t e r m i n a t i o n of surface area. T h e t h e o r e t i e a l l i m i t a t i o n s of t h e B E T m o d e l are recognized, b u t in p r a c t i c e t h e v a l i d i t y of t h e B E T a r e a m u s t be assessed e m p i r i c a l l y for each gas-solid s y s t e m . U n f o r t u n a t e l y , m a n y of t h e e x p e r i m e n t a l i n v e s t i g a t i o n s of a d s o r p t i o n r e p o r t e d i n t h e l i t e r a t u r e were m a d e on p o o r l y c h a r a c t e r i z e d solids a n d t h e n u m e r o u s a t t e m p t s to c o m p a r e B E T a r e a s a n d a d j u s t m o l e c u l a r cross-sectional a r e a s were o f t e n m a d e o n a r a t h e r a r b i t r a r y basis. G e n e r a l l y , e m p h a s i s was p l a c e d on m o n o l a y e r - m u l t i layer coverage and capillary condensation, a n d t h e i m p o r t a n c e of t h e m i e r o p o r e filling m e c h a n i s m was n o t f u l l y a p p r e c i a t e d . V a r i o u s e m p i r i c a l m e t h o d s of i s o t h e r m analysis have been introduced in the past few y e a r s ; t h e b e s t k n o w n of t h e s e is p r o b a b l y t h e t - m e t h o d of L i p p e n s a n d de B o e r (2), w h i e h p r o v i d e s a s i m p l e a n d d i r e c t
Journal of Colloid and Interface Science, Vol. 38, No. 1, January 1972
109
110
BHAMBHANI E T AL.
means of interpreting nitrogen isotherms. The amount of nitrogen adsorbed is plotted against t, the statistical multilayer thickness for the adsorption of nitrogen on a nonporous reference solid. Any deviation in shape from the standard isotherm is therefore detected on the t-plot as a departure from linearity. Recently, the so-called universal t-curve of de Boer and his coworkers (3) has been criticized (4-7) on the grounds that it cannot represent an accurate nitrogen isotherm on all nonporous solids, and that the calculation of t necessarily involves assumptions concerning the nature of the packing and stacking of adsorbate molecules (8). The t-method was amended by Sing (9) to take into account the process of micropore filling and to provide under certain conditions an assessment of the micropore volume. It has been pointed out by Brunauer (4) and others (5, 6) that since t is itself calculated from V/V~, the t-method is necessarily dependent on the BET evaluation of the monolayer capacity. It is clear that this limitation must restrict the scope of the method to those systems where the BET monolayer capacity is well defined (10). To avoid this difficulty, the t-method has been modified (5, 6) and t has been replaced by ( V / V ~ ) ~ , termed a~, where V~ is the amount adsorbed at a selected relative pressure (p/po)~ • The reduced standard isotherm on the nonporous reference solid is therefore arrived at empirically and not via V~. In principle, ¢~ could be placed equal to unity at any convenient point on the standard isotherm; in practice, with a number of vapors (including nitrogen at -196°C) it seems reasonable to place a. = i at (p/po)~ = 0.4. With nitrogen, monolayer coverage and mieropore filling occur at p/po < 0.4 and any hysteresis loop present is located at p/po > 0.4. The scope of the ~,-method has been discussed only in outline and its application has been restricted so far to a few adsorption systems (6, 7, 11, 12). In this paper, standard data are presented for nitrogen adsorption on nonporous silica, and isotherms on a wide range of porous and nonporous silicas are analyzed by the ~,-method. The chief aim of this work was to exploit the new method in order to throw light on the mechanisms of
physical adsorption and to examine the validity of the BET monolayer capacity, especially in relation to microporosity. Isoteric heats of adsorption are discussed from the same standpoint. MATERIALS AND METHODS The results of preliminary investigations (6) had indicated that certain high-area silicas could serve as nonporous reference materials. Thus, two Degussa products TK70, and TKS00, were found to consist of discrete spherical particles, the degree of aggregation being lower than in the commercial grades of Aerosil. Another grade of nonporous hydroxylated silica studied was Fransil; in this case the surface area determined by electron microscopy (36 m2/gm) was in fairly good agreement with the BET nitrogen area (38.7 m2/gm), and the reduced nitrogen isotherm corresponded very closely with that obtained on various samples of low-area crystalline and amorphous silica. The original batch of Fransil was used again in the work reported here and is referred to as Fransil-I. Other new batches of Fransil and TK800 were Fransil-II, TK800-II, and TKS00-III (TK800-I being the original batch). Various grades of Aerosil (200, 300, and 50X) were supplied by the manufacturers (Degussa Forschung Chemic). A portion of Aerosil 300 was soaked in water for several days and dried at room temperature. The various silica gels were specially prepared and supplied by the Unilever Chemical Development Centre; they were selected to provide a wide range of surface properties with pore structures within the micropore and mesopore range. Gel I( was calcined in air at 900°C to give K(900). The nitrogen adsorption isotherms were determined volumetrically using both a semimicro apparatus of the type designed by Harris and Sing (13) and an apparatus based on the design of Lippens, Linsen, and de Boer (14). The nitrogen was of 99.9 % purity and was dried by slow passage through a cold trap. Helium (99 % purity) was used for the dead space measurements. All equilibrium pressures were measured on a mercury manometer with the aid of a cathetometer (to 4-0.001 cm). Cryostat bath temperatures
Journal of Colloid and Interface Science, Vol. 38, No. 1, J a n u a r y 1972
ADSORPTION ISOTHERMS ON SILICAS were measured with a vapor pressure thermometer (oxygen or nitrogen) at the time of each adsorption reading; an accurate value of p/po was then calculated for each point on the isotherm. The isosteric heats of adsorption were calculated from nitrogen isotherms determined using a Cahn RG Electrobalance and a cryostat with a modified hangdown tube, as described by Cutting (15). In this case, the pressure measurements were made to within ~=0.1 torr with a C.E.C. pressure transducer, which had been calibrated against a mercury manometer. The temperature of the sample was checked with a copper-eonstantan thermoeouple to within 4-0.05°C. All samples were outgassed for prolonged periods (usually 15-20 hours) at 25°C and the reproducibility of most isotherms was checked. In some eases (e.g., Fransil-I, Fransil-II, and Gel A) outgassing was also conducted at temperatures up to 200°C; no change in the isotherm could be detected. RESULTS
111
TABLE I STANDARD ADSORPTION DATA FOR ~ITROGEN AT -196°C ON NONPOROUS HYDROYLATED SILICA
(FRANSIL-I) Relative pressure #/po
0.001 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0 90
Adsorption per unit Reduced adsorption area (tLmole/m~) as(= V/V~.4)
4.0 5.4 6.2 7.7 8.5 9.0 9.3 9.4 9.7 10.0 10.2 10.5 10.8 11.3 11.6 11.9 12.4 12.7 13.0 13.3 13.6 13.9 14.2 14.5 14.8 15.1 15.5 15.6 16.1 16.4 17.0 17.8 18.9 19.9 21.3 22.7 25.0 28.0 37.0
0.26 0.35 0.40 0.50 O.55 0.58 0.60 0.61 0.63 0.65 0.66 0.68 0.70 0.73 0.75 0.77 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.01 1.04 1.06 1.10 1.14 1.22 1.29 1.38 1.47 1.62 1.81 2.4
The nitrogen adsorption data given in Table I were obtained on Fransil I, which had been previously adopted as the nonporous hydroxylated silica reference material. The adsorption per unit area in column 2 is expressed in micromoles per square meter (following the practice of Kiselev), taking the surface area as the BET vMue of 38.7 m2/gm. The reduced adsorption a~ in column 3 is V/Vo.4, where V0.4 is the adsorption at the standard state of p/po = 0.4. t~epresentative isotherms and a~-plots are shown in Figs. 1 and 2. The linear plots in Fig. l(b), and the corresponding Type II isotherms in Fig. l(a), are the result of unrestricted monolayer-multilayer adsorption on the nonporous solids Fransil-II, TI4800-I, and Aerosil 300. The other samples which gave linear a~-plots over a wide range condensation. Other gels which gave similar of P/po were TK70, TKS00-II, TKS00-III, a~-plots were H, K, K(900), L, and P. and Aerosil 200. The isotherms in Fig. 1(c) The a~-plots on the mieroporous gels D exhibit hysteresis and are characteristic of and E are shown in Fig. 2(b) with the coradsorption on mesoporous solids. That this responding Type I isotherms in Fig. 2(a). is the case is confirmed by the shape of the Gel M gave a very similar a,-plot to that of a~-plots (Fig. l(d)), which are all linear over E. The a,-plots in Fig. 2(d) are more complex the initial range of p/po and deviate upwards in nature, probably owing to a combination from linearity with the onset of capillary of monolayer-multi]ayer coverage, micropore Journal of Colloid and Interface Science, Vol. 38, ~o. i, January 1972
BI-IAMBHANI ET AL.
112 2ooj a
"
'
jJ
,oo!./J 5Ojf_O
I
I
I
E
Q_
500~
hS(
3O(
)
~5o~ J C
o
0.2
0.4
0-6
0.8
~-0
05
PtPo
I.O
1.5
2-0
2.5
Gs
FIG. 1. Nitrogen isotherms and ~-plots on nonporous snd mesoporous silicas. Open symbols, adsorption points; closed symbols, desorption points. filling, and capillary condensation. The mixed gel, E q- J, was made up of equal parts by weight of gels E and J. Aerosil 50X and soaked Aerosil 300 both gave curved a~-plots, indicative of porosity. The surface areas are shown in Table II. The BET surface areas, SB~T, in column 2 were calculated in the usual way, with the nitrogen molecule in the close-packed monolayer ~ssumed to occupy an average area of 16.2 A2. The value of p/po corresponding to the upper limit of the initiM linear region of the a,-plot is indicated in column 4. The values of S~ have been calculated from the slope of the linear part of the a~-plot (taking a line through the origin), using the relation S~ = 2.89 V / a , , [1]
where V is the volume of nitrogen adsorbed, expressed in cubic centimeters (S.T.P.)/ gram and the factor 2.89 has been obtained by calibration against the BET area of Fransil-I. In cases where the ~,-plot is not linear the value of $8 shown in brackets has been calculated from the slope of the line drawn from the origin to the initial adsorption points. The value of the external surface area is also given in those eases where the a,-plot is linear in the multilayer range (6, 9). The isosteric heats of adsorption Q,t on Fransil-I and gels A, B, and D are plotted against loglop/po in Fig. 3. This procedure has the advantage over the conventional plot of O,, against V/V,-. in that no assumption has to be made about the mechanism of adsorption or the magnitude of surface area.
Journal of Colloid and Interface Science, VoL 38, No. 1, J a n u a r y 1972
ADSORPTION ISOTHERMS ON SILICAS
113
4oo! I
300~
] // // ----
/
E
/
D
,1 / E
oi
I
I
I
T
I
I
I
I
co 400 ~
F
©
./
o!2
o!4
o!o
o!8
1-o
P/Po
o
o!s
i!o
i!s
2!o
2.s
~s
FIG. 2. Nitrogen isotherms and a,-plots on mieroporous and mixed pore silicas. Open symbols, adsorption points; closed symbols, desorption points. Essentially, Q,t is expressed as a function of the difference in chemical potential. D ISCUSSION The fact that. the ~,-plots in Fig. l(b) and also those for all the nonporous solids listed in Table II are linear over a wide range of P/po appears to confirm the reliability of the standard adsorption data in Table I. The values of a, show a considerable difference from those calculated from the data of Lippens, Linsen, and de Boer (14), which provided the basis for their universal t-curve. On the other hand, our data are in fairly good agreement (to P/po ~ 0.8) with the reduced adsorption data of Linsen (16) and Pierce (8). Linsen has already noted the lack of agreement between his t-curve on a sample of Aerosil and t h a t of Lippens (14,
17) on a calcined (apparently nonporous) alumina. He attempted to explain this difference in terms of the geometry of the higharea silica b y postulating that the areas where elementary particles touch are rendered inaccessible to adsorbate molecules. The present results, along with those reported previously (18) on low-area nonporous silicas, demonstrate t h a t within wide limits the effect of particle size on the standard isotherm is negligible. It is now clear that certain batches of Aerosil have a small but significant degree of porosity. For example, the c~,-plot on Aerosil 50X was curved over the monolayer range but almost linear in the multilayer region. The small amount of mieroporosity was sufficient to reduce the external surface area (calculated from the slope of the linear section of the
Journal of Colloid and Interface Science. ¥ o l . 38, N o . 1, J a n u a r y lg72
114
BHAMBHANI E T AL. TABLE I I C O M P A R I S O N OF SURFA.CE A R E & S C R L C U L & T E D BY B E T A.ND ~s M E T H O D S Silica sample
SBET (m2/gm)
Nonporous solids Fransil-I Fransil-II TK 70 T K 800-1 TK 800-II TK 800-III Aerosil 200 Aerosil 300 Mesoporous solids Gel A Gel G Gel H Gel J Gel K Gel K (900) Gel L Gel P Mieroporous solids Gel D Gel M Gel E Aerosil 50X Mixed micro- and mesoporous solids Gel B Gel F Gel N Gel 1~ Aerosil 300 (soaked) Gel (E + J)
4]
Ss (m2/gm)
Upper limit of linear region of ~zs-plot
(~/$0)
38.7 34 36 154 148 160 194 313
33 36 153 150 165 193 318
--
->0.9 >0.9 >0.9 0.9 >0.7 >0.9 0.8
300 504 460 349 376 207 369 274
303 503 458 350 376 208 372 272
0.4 0.3 0.3 0.3 0.4 0.3 0.4 0.7
767 637 631 38
(810-960) 35~ (770) 17~ (730) 20° (37) 25a
Not linear Not linear Not linear <0.2
500 550 463 536 321 440-470
(505) (560) (480) (531) (320-340) (465-485)
<0.3 <0.12 <0.4 <0.2 Not linear Not linear
These values are calculated from the linear part of the a,-plot in the multilayer range.
C3 ATENT HEAT
--
02.5
]
-2.0
I
---1-5
L
-1-0
f
-0"5
togl0P/Po FIG 3, Isosteric heats for nitrogen on nonporous and porous silicas. ¢ Fransi]; I I Gel A ; A Gel B; • Gel D .
a , - p l o t ) to a b o u t 25 cm~'/gm, cf t h e B E T a r e a of 38 m2/gm. C o m p a r i s o n of o u r d a t a w i t h t h e results of A r i s t o v a n d K i s e l e v (19) has r e v e a l e d a s m a l l b u t significant a m o u n t of m i c r o p o r o s i t y in t h e R u s s i a n s a m p l e of Aerosil. I n t h e case of A e r o s i l 300, t h e a,p l o t (Fig. l ( b ) ) e x h i b i t s a n u p w a r d d e v i a t i o n f r o m l i n e a r i t y a t p / p o > 0.8. T h i s m a t e r i a l c o n t a i n e d m a n y s m a l l p a r t i c l e s a n d i t seems likely that interparticle capillary condensation contributed to the adsorption at high P/Po • A f t e r t h e A e r o s i l 300 h a d b e e n s o a k e d i n w a t e r , t h e a~-plot g a v e e v i d e n c e of b o t h m i c r o p o r o s i t y a n d m e s o p o r o s i t y , i.e., d e v i a t i n g f r o m l i n e a r i t y a t low a n d a t h i g h p / P o • All t h e s e r e s u l t s confirm o u r earlier suggest i o n t h a t F r a n s i l a n d T K 8 0 0 are m o r e s a t i s f a c t o r y as n o n p o r o u s reference silicas
Journal of Colloid and Interface Science, Vo]. 38, No. 1, J a n u a r y 1972
ADSORPTION ISOTHEI~MS ON SILICAS than are the normal commercial grades of Aerosil, which have been adopted in the past. The agreement (usually to within 1%) between the values of SBET and So in Table II for all the nonporous and mesoporous solids is noteworthy and serves to confirm the validity of Eq. [1]. On the other hand in the case of the microporous solids the values of $8 (in brackets) are mostly higher than those of SBET • In the study of porous and nonporous carbon blacks, de Boer and his coworkers (20) also noted that values of St, calculated from the slope of the t-plot, were higher than those of S~ET. These authors (3, 20) suggest that St provided a more reliable estimate of the total surface than did SB~T • Brunauer (4) has rightly pointed out that in the analysis of an isotherm by the tmethod, it is essential that a correct t-curve be employed. His view differs from ours, however, in that he suggests that the appropriate t-curve should be based not on the chemical similarity of the absorbent surface but rather on the magnitude of the heat of adsorption. According to Brunauer, the BET C constant is frequently adequate for testing the appropriateness of the t-curve, but that a more reliable cheek is the measure of agreement between SBET and St. The application of a~-method is helpful within the context of this discussion. Although the values of S, in Table II are based on the value of SBEr for Fransil-I, the use of the a~-method as a comparative method for surface area determination is independent of the BET method. Gregg (21) has stressed the normalizing, or scaling, principle of the ~8-method: that for a series of isotherms of identical shape the uptake at a given pressure is directly proportional to the surface area. In principle, therefore, if the surface area of the reference solid could be determined accurately by another means (e.g., electron microscopy) the a~-method could be made entirely independent of the BET method. In our view, the differences noted above between S~ and SB~T are the direct result of micropore filling in changing the shape of the nitrogen isotherm; the implication is that neither SB~T nor S~ has any
115
physical meaning. As expected, this discrepancy is associated ~dth a difference in the C value. Nitrogen adsorption at - 196°C on a nonporous hydroxylated silica gives a C value of about 110; with mieroporous gels, C is increased to 170-190. To understand the significance of these results, we must examine the theoretical basis for the concept of micropore filling. Dubinin (22) has defined mieropores as those pores in which the adsorption potentials are substantially enhanced owing to a significant overlap of the adsorption forces from the pore walls on either side of the adsorbate molecule; he and others (6, 8, 9, 10, 23, 24) have argued that the concept of layer-by-layer surface coverage then loses its physical meaning. If we accept the possibility of mieropore filling as a primary mechanism of physical adsorption, which operates at low P/po (as distinct from the secondary process of capillary condensation), we are still faced with the problem of characterizing the adsorption mechanism in practice. Two questions naturally arise: 1) What is the critical value of pore width which marks the boundary between filling and monolayer-multilayer adsorption in mesopores? 2) Does the mieropore filling mechanism govern all eases in which pore filling has restricted the muitilayer adsorption, i.e., approaching a Type I isotherm? We cannot give definitive answers to these questions at the present time because the theory of physical adsorption is not sufficiently developed. Dubinin (22) places the upper limit of micropore width at. about 30 A, but some authors (20, 25) favor a lower value ( < 10 A). Strictly, the effect of pore narrowing on the adsorption potential must depend on the nature of the adsorbentadsorbate interactions and the size of the adsorbate molecule. Related to the influence of pore narrowing on the shape of the isotherm is its effect on the heat of adsorption. As Brunauer and his eoworkers (4) have pointed out, the C constant is directly related to the free energy of adsorption (or change in chemical potential) rather than to the heat of adsorption. The magnitude of C also depends on the
Journal of Colloid and Interface Science, VoI. 38, No. 1, J a n u a r y 1972
116
BHAMBHANI ET AL.
P/po range of linearity of the B E T plot.
Differential, or isosteric, heats of adsorption, on the other hand, provide a basis for the comparison of interaction energies involved in different adsorption systems (29). Thus, according to the Dubinin criterion, the process of micropore filling is accompanied b y an enhanced differential heat over that given b y monolayer coverage (under the same conditions of p and T) of the open surface. The isosteric heats Q~ plotted in Fig. 3 reveal an interesting difference between the three gels A, B, and D: Q~ remains reasonably constant over the range of p/po for both Fransil-I and gel A, whereas at low p/po Q~t is enhanced for gels B and D. I t has already been noted that gel D gave a T y p e I isotherm and an a,-plot characteristic of micropore filling; the high Q~ is therefore to be expected. The case of gel B is more complex, but the evidence of Fig. 3 suggests t h a t in this case also, micro-
pore filling played a significant part in the adsorption process at low p/po. If this is true, in spite of their close agreement, neither SBET nor S~ has any real meaning for gel B. Six samples have been placed in the mixed pore category in Table If. All these isotherms, except that on Aerosil 300 (soaked), exhibited hysteresis and gave evidence of capillary condensation. In most cases, the a~-plots were either not linear or deviated from linearity at low p/po ( < 0.2). The case of gel N is interesting because this material gave a linear a,-plot to a higher p/po ( N 0.4), which appeared at first sight to conform to the requirement for monolayer-multilayer coverage followed b y capillary condensation. On the other hand, the B E T plot on gel N was linear over a somewhat restricted range of p/po (0.05--0.25) and the C value was high (~-d60). I t appears therefore that gels B and N were rather similar in character in t h a t the pore size distribution in each ease resulted in a compensating effect between the restrictive adsorption in mieropores and the capillary condensation in mesopores, which gave rise to a nearly linear a~-plot obscuring the influence of mieropore filling (30). I t is possible that certain of the other gels placed in the mesoporous category were also microporous to some extent. Journal of Colloid and Interface Science~ Vol. 38, No.
Firm conclusions about the mechanism of adsorption should not be drawn on the basis of an isotherm of a particular vapor at a single temperature. We have suggested elsewhere (6) that a useful diagnostic test of micropore filling is the comparison of values of apparent surface area obtained b y the application of the as-method to isotherms of a number of different vapors on the porous solid. Such an approach is time consuming, however, and for routine work we must obtain as much information as possible from a single isotherm. The results presented here illustrate the way in which the a~-method m a y be used to supplement the B E T procedure. Particular care is, of course, required to ensure t h a t the a,-plots are restricted to t h a t part of the isotherm covered b y reliable standard data. ACKNOWLEDGMENTS The authors wish to thank the Gas Council, London, and Unilever Chemical Development Centre, Warrington, for their support. They also their thanks to Degussa Forschung Chemic, Frankfurt, for supplying certain samples; and to J. D. Carruthers and R. E. Day for some isotherm data.
1, January 1972
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Journal of Colloid and Interface Science, ¥oi. 38, No. l, Jam~ary 1972