Langmuir 1994,10, 3842-3844
3842
Adsorption Hysteresis and the Pore Size Distribution of a Microporous Silica Gel Richard J. Murdey and William D. Machin* Department of Chemistry, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1B 3x7 Received June 15, 1994@ Isotherms for 2,2-dimethylpropane, 2,2,3-trimethylbutane, and ammonia adsorbed on a microporous silica gel all exhibit a steep segment in the desorption branch ofthe hysteresis loop. The extent of hysteresis decreases with increasing temperature and we utilize this phenomenon to derive the pore size distribution of the adsorbent. The pore size distribution is independent of adsorbate and, within a limited range of pore radii, is in reasonable agreement with the results of a method developed by K. S. W. Sing and coworkers. When adsorption hysteres in a mesoporous adsorbent arises from an irreversible, first-order, capillary phase change, capillary liquid to capillary gas, the size of the hysteresis loop decreases with increasing t e m p e r a t ~ r e . l - ~ Current theories of adsorption6 provide an explanation for this phenomenon and suggest that such irreversible phase changes should occur in adsorbents with pores of radii ( R p ) as small as two molecular diameters ( d ) ,i.e. for Rp 2 2d. Mesoporous adsorbents with a significant fraction of their pore volume in such pores exhibit temperature-dependent hysteresis. Anew method of pore size analysis based on this effect5 is also applicable to suitable microporous adsorbents. In this work we report isotherms determined at several temperatures for three adsorptives on a microporous silica gel and the pore size distribution (PSD) derived from these results.
Table 1. Isotherm Parameters for Silica Gel SG1
Experimental Section
adsorptive (dlnmp T/K V,b/cm3 g-' Vuc/cm38-1 0.312 ammonia (0.343) 243.15 0.050 2,2-dimethylpropane (0.626) 243.15 0.283 0.282 0.027 263.15 0.278 0.024 273.15 0.271 283.15 293.15 (0.266) 0.019 303.15 (0.255) 0.272 0.028 2,2,3-trimethylbutane(0.690) 273.10 0.023 0.271 297.10 0.015 313.10 (0.263) a Equilibrium molecular diameters are calculated using the method ofBen-Amotzand Herschback. Ben-Amotz,D.; Herschbach, D. R. J.Phys. Chem. 1990,94,1038. Calculated from the amount adsorbed at saturation pressure and bulk liquid density of the adsorptive. Values in parentheses are estimated by extrapolation from the highest measured pressure to saturation. Calculated from the amount adsorbed at PIP* = 0.01.
Prior to use, 2,2-dimethylpropane(DMP,Matheson,research purity)was stored over Cdzeolite for several days then purified by vacuum sublimation. Purity of this adsorptive,as determined by gas chromatography, is at least 99.97 mol %. Ammonia (Matheson,anhydrous, 99.99%)and 2,2,3-trimethylbutane(TMB, Pfaltz and Bauer, 99%) were sublimed twice under vacuum. Measurements were taken with a grease-free, volumetric adsorption apparatus incorporating metal bellows-seal valves (Nupro, type SS-4H)and a capacitance manometer (MKS,type 310 CH). Sample temperatures were controlled to ca. 0.05 K. The preparation and properties of the adsorbent, microporous A total of ten isotherms silica gel SG1, are described el~ewhere.~ are measured (cf. Figures 1 and 2) and relevant parameters are summarized in Table 1.
decreases as temperature increases (Figure 2). This latter effect has been noted elsewhere for various adsorptives on silica gel,5'9J0Vycor porous glass,lS2graphitic carbon: and controlled pore glass.4 In all of these systems hysteresis vanishes at a capillary critical temperature, T,,,where T,, < T,, the bulk critical temperature. Findenegg et ~ 1have . ~shown that this critical point shift is inversely proportional to the pore size, i.e. 1 - TJT, llRp. This observation is in accord with current theoretical models for the behavior of fluids in small pores. Evans et aL6J1have derived the approximate relation for a cylindrical pore of radius R,
Discussion All isotherms exhibit hysteresis and two trends are evident: (i) as the diameter of the adsorptive increases, the isotherm shape* changes from type IV with ammonia t o type I for TMB (Figure 1);(ii) the extent of hysteresis
* Author to whom correspondence should be addressed.
Abstract published in Advance A C S Abstracts, September 1, 1994. (1)Burgess, C. G. V. Ph.D. Thesis,University of Bristol, 1971. See also Burgess, C. G. V.; Everett,D. H.; Nuttal,S.Pure Appl. Chem. 1989, 61,1845. (2) Nuttal, S. Ph.D. Thesis, University of Bristol, 1974. See also Burgess, C. G. V.; Everett, D. H.; Nuttal, S. Langmuir 1990,6,1734. (3)Michalski, T.; Benini, A,; Findenegg, G. H. Langmuir 1991,7, 185. (4) Findenegg, G. H.; Gross, S.; Michalski, T.; Thommes, M. IUPAC Symposiumon the Characterization ofPoruusSolids,May 1993;Abstract @
9.
(5) Machin, W. D. Langmuir 1994,10,1235. (6)Evans, R.; Marconi,U. M. B.; Tarazona,P. J . Chem. Soc., Faraday Trans. 2, 1986,82,1763 and references therein. (7) Machin, W. D.; Golding, P. D. Langmuir 1989,5,608.
0~
1 - TJT,= dlR, where d is the molecular diameter of the adsorbate. A similar equation is obtained for slit-shaped pores. These authors suggest that this equation should be applicable within the limits 2 IRdd 5 20 and T,, O.95Tc. The lower limit, R , = 2d, is close to the boundary between primary micropores (R, < ca. 2d) and secondary micropores (2d < R , < ca. 5d).12 This implies that our earlier analysis of hysteresis in mesoporous adsorbents5 is applicable to appropriate microporous adsorbents, i.e. those that exhibit hysteresis arising from the irreversible, first-order, capillary phase change, capillary liquid to (8) Sing,K. S. W.; Everett,D. H.; Haul, R. A. W.; Moscou,L.; Pierotti, R. A.;Rouquerol,J.;Siemieniewska,T. Pure Appl. Chem. 1985,57,603. (9) Machin, W. D.; Golding, P. D. J . Chem. SOC.,Faraday Trans.
1990,86,175.
(10)Machin, W. D. J . Chem. SOC.,Faraday Trans. 1992,88, 729. (11)Evans,R.; Marconi, U. M. B.; Tarazona, P.J. Chem. Phys. 1986,
84, 2376.
0743-746319412410-3842$04.50/00 1994 American Chemical Society
Adsorption Hysteresis
Langmuir, Vol. 10, No. 10,1994 3843
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Re 1 a t i ve Pressure, P/P* Figure 1. Isotherms for 2,2,34rimethylbutane(TMB) and ammonia adsorbed on silica gel SG1: (a)TMB at 273.10 K; (b) TMB at 297.10 K, (c) ammonia at 243.15 K. Open points (0) denote desorption. The ordinate is displaced for clarity.
R e l a t i v e Pressure,P/P* Figure 2. Isotherms for 2,2-&methylpropane(DMP) adsorbed on silica gel SG1: (a)243.15 K; (b)263.15 K (c) 293.15 K. Open points (0)denote desorption. The inset shows the temperature dependence of AA for all the DMP isotherms.
capillary gas. For such a phase transition a t T < T,,, the difference in density, Ao, between the two phases depends on T as39599
in which AA, is the step observed at T,, the capillary critical temperature for each group of pores is Ti-1, and Ki is the fraction of the total pore volume within each group. When applied to a n appropriate set of isotherms, these equations allow the calculation of the pore size distribution (PSD) of the a d s ~ r b e n t . ~ The number of pore groups is determined by the number of isotherms, n, a t T < T,, and the range of pore radii within each group extends from Rn to Rn-l, such that (eq 1)
Ag = [l - TlTc,J1/3
(2)
It is clear from eq 1that for a n assembly of cylindrical pores of different radii a t temperature T,only those pores with radii greater than R, will contribute to hysteresis. Therefore, as T increases, the extent of hysteresis decreases from two effects, (i) fewer pores contribute to hysteresis and (ii)those pores that do contribute do so to a lesser extent according to eq2. The result of these effects is shown in Figure 2 for DMP adsorbed on SG1. For a given isotherm the extent of hysteresis can be expressed as AA, the difference between the amount adsorbed as capillary liquid and capillary gas at the phase transition, i.e.
R, = dl(1 - TnIT,) The volume fraction for each pore group, Ki,is obtained from eq 4 and the cumulative volume, V,,, in pores having radii greater than R, is n
V, = Vp
Ki i=l
where Ad is the amount adsorbed at the top of the step in the desorption branch, A, is the amount adsorbed at the lower closure point of the hysteresis loop, and A* is the amount adsorbed a t saturation pressure. For an assembly of pores of different radii where T, < Ti-1 n
f i n=
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i=l
(12) Carrott, P.J. M.; Roberts, R. A.; Sing,K. S . W . In Studies in Surfme Science and Catalysis, Vol.39, Characterization ofPomua Solids; Unger, K. K., Rouquerol, J., Sing,K. S. W., Kral, H.; Eds.; Elsevier: Amsterdam, 1988; p 89.
where V, is the total pore volume. Calculations for DMP and TMB isotherms are summarized in Table 2 and the PSD is shown in Figure 3. Note that results for both adsorptives are in close agreement and that the lower pore size limit for each is comparable to that suggested by Evans et a1.,6i.e. R, 2 2d. Also shown in this figure is the PSD obtained from the adsorption of ammonia. Not only do these results agree with those obtained with DMP and TMB a t large pore radii, R, > ca. 1.5nm, but also at very small radii, R, I2d (ca. 0.69 nm), the PSD extrapolates smoothly to the distribution estimated from the amounts adsorbed a t saturation and the diameter of the adsorptives.
Murdey and Machin
3844 Langmuir, Vol. 10,No.10,1994 Table 2. Pore Size Distribution Analysis for Silica Gel SG1
CI
0 \ 0 0
I.From DMP Isotherms 0 1 2 3 4 5 6
318.15 303.15 293.15 283.15 273.15 263.15 243.15
0 1 2 3
382.10 313.10 297.10 273.10
0.000 0.054 0.083 0.125 0.156 0.199 0.278
0.000 2.34 0.054 2.08 0.093 1.93 0.140 1.80 0.176 1.69 0.219 1.59 0.318 1.42 1I.From TMB Isotherms 0.000 0.000 2.46 0.219 0.219 1.68 0.253 0.269 1.57 0.337 0.369 1.42
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The results for ammonia are based on a single isotherm using the following p r ~ c e d u r e .At ~ a relative pressure, PIP*,less than that corresponding to the upper closure point of the hysteresis loop, the difference, AX, between the amounts adsorbed on the horizontal segment of the desorption branch and that on the adsorption branch is equivalent to a step a t an appropriate temperature, T,, such that
T, = T, 11 - d/Rpl[l -
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where AXis the step height and R, is the capillary critical pore radius for T, calculated from
(RP- d)’/RP= -2yV/[RT, ln(P/P*)l
(8)
where y is the surface tension and V the molar volume of bulk liquid adsorbate and R is the gas constant. The set of AX, T, values obtained for a range of relative pressures is analyzed as before using eqs 4-6. Equation 7 was originally presented as a semiempirical relation; however it is readily derived from eqs 1and 2 when eq 2 is expressed as
AX = [l - T/T,,]1’3
(9)
Several other methods for calculating the PSD in microporousadsorbents have been proposed. Most of these rely on the use of an isotherm equation such as the Langmuir or Dubinin-Radushkevich e q ~ a t i 0 n s . l In ~ a review of these methods, however, McEnaney and Mays13 conclude that they yield “ill-conditioned” solutions, that is, they do not provide a unique solution for the PSD. In a study of several microporous carbons, Carrott et a1.12 have proposed a method that does not rely on a n isotherm equation but requires only the total micropore volume, V,, and the volume adsorbed a t PIP* = 0.01. The latter quantity, Vu,is equated to the amount adsorbed in primary micropores, R, 5 ca. 2d (see Table 1)and the difference V, - Vuis equated to the volume in the larger secondary micropores. The PSD can be determined when isotherms are available for several adsorptives having a wide range of molecular diameters. The pores in microporouscarbons (13)McEnaney, B.; Maya, T. J. In Studies in Surface Science and Catalysis, Vol. 62, Characterization of Porous Solids II; RodriguezReinoso, F., Rouquerol, J., Sing, K. S. W., Unger, K. K., Eds.; Elsevier: Amsterdam, 1991;p 477.
> I
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P o r e Radius(Rp/nm) Figure 3. Cumulative pore size distribution for silica gel SG1 derived from 2,2-dimethylpropane isotherms (01, 2,2,3-trimethylbutane isotherms (O),and ammonia isotherms (+). Points marked (A) correspond to the total pore volume estimated from the amount adsorbed at the saturation pressure with the minimum pore radius taken as the radius of the adsorptive. Points marked (A)are derived from the amount adsorbed at P/P* = 0.01 following the procedure in ref 12. are often slit-~haped,’~ whereas the pore shape in globular adsorbents is less well defined. Consequently,the division between primary and secondary micropores in SG1 may occur a t a radius other than R, = 2d. When the method of Carrott et aZ.12is applied to our data, the results are in agreement with the present analysis if Vu is equated to the amount adsorbed in pores with R, 5 1.3d(see Figure 3). Our method of pore analysis assumes constant pore volume. All of the isotherms reach a well-defined plateau a t high relative pressures (Figures 1 and 2), a feature which is usually interpreted as saturation of the pore volume with capillary condensed liquid. Total pore volume, V,, should be constant when calculated from the amount adsorbed a t saturation pressure and the density of the bulk liquid a t that temperature. It is clear however (Table 11, that for several isotherms V, determined at higher temperatures are significantly smaller than the relatively constant values obtained a t lower temperatures. In part, this may result from the inability to continue these isotherms to saturation pressure when it is beyond the range of the pressure sensor, but the discrepancies are larger than we would expect. At the present time we cannot explain these observations, but further studies are planned.
Acknowledgment. The authors thank Dr. C. Flinn for analysis of the 2,2-dimethylpropane and Professor P. D. Goldingfor useful comment and discussion. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada. (14)Everett, D.H.; Powl, J. C. J. Chem. SOC.,Faraday Trans. I , 1976, 72, 619.
