Langmuir 1986,2, 151-154
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Characterization of Pore Structure: Porosimetry and Sorption W. C. Conner,* J. F. Cevallos-Candau, and E. L. Weist Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
J. Pajares, S. Mendioroz, and A. Cortes Instituto de Catcilisis & Petroleoquhica, CSIC Serrano, Madrid, Spain Received August 12, 1985. I n Final Form: October 17, 1985 Pore-size distributions measured by both mercury porosimetry and nitrogen adsorption are compared for a series of compressed aerosols. We conclude that both mercury intrusion and nitrogen desorption are characteristic of the constrictionswithin the void network. Mercury extrusion and nitrogen adsorption are related to the openings within the void network. By consideration of the void structure as a threedimensional network of interconnected pores of varying size, each technique is analyzed independently and in concert. These studies show the correspondence between the two techniques and the differences that are due to the sequential nature of the processes.
Introduction The most common methods of determining pore sizes in porous solids are mercury porosimetry and nitrogen adsorption-desorption. The data obtained from these methods are usually analyzed by assuming that the porous material consists of nonintersecting, cylindrical pores. This assumption fails to explain several features common to both methods, especially the presence of hysteresis between intrusion-extrusion and adsorption-desorption. This has led to controversy in choosing which branch of the hysteresis loops to use for analysis. Everett’ pointed out that a porous solid is best described by a network of interconnected pores. Recently, Conner and Lane et a1.2 have developed a three-dimensional, structural model consisting of spherical pores connected by volumeless, cylindrical throats to analyze mercury porosimetry. This model is now applied to the nitrogen adsorption process. In this work, the pore-size distributions given by mercury porosimetry and nitrogen adsorption are compared. The two processes are analyzed considering the influence of the statistical effects resulting from the sequential measurement of a network of interconnected pores. In particular, we demonstrate that there is a correspondence between mercury intrusion and nitrogen desorption and between mercury extrusion and nitrogen adsorption. Prior studies have focused on similar comparisons of the pore-size distributions derived from mercury porosimetry and nitrogen adsorption data. The following studies compared nitrogen desorption data to initial mercury intrusion data, except where noted. Joyner et al? found good comparison for data on bone char. Dubinin4 found satisfactory agreement in the intermediate and macropore range of activated charcoals. DeWit and Scholten5compared distributions from capillary-condensation (adsorption) data for zirconia and chrysotile and reanalyzed Zwietering’s617data on iron oxide-chromium oxide and ~~
Table I. Properties of Degussa Aerosils” aerosol particle size, 8, BET surface area, m2/g A130 160 130 200 A200 120 A300 90 300 A380 70 380 Composition (wt %): SiO, 99.8; A1,03 0.005; Fe2030.003; TiO, 0.03; HCl 0.025.
compressed aerosols to account for film thickness. Only the pore-size distributions for the zirconia samples gave excellent agreement, while in the others, nitrogen adsorption gave larger radii by 30%. Moscou and Lub8 found good comparison for aluminas, but nitrogen desorption gave steeper distributions for silicas. Brown and Lardg found good correlation between the pore-size distributions in low pore volume silicas but found large discrepancies with high pore volume silicas. They concluded that porosimetry causes the collapse of pore walls in silicas, forming “smaller pores” and “exaggerating” the measured macroporosity. On the other hand, Winslowlo concluded that mercury porosimetry does not damage aluminas. The application of intrusion porosimetry and of nitrogen desorption to the analysis of total surface area, another aspect of morphology, was recently compared by Davis.’l He concluded that mercury intrusion appears to predict higher areas than the BET method and that “packing and porosity, not contact angle, must be the major considerations” in the analysis of the two methods. Other researchers have proposed network models to describe the void structure of porous materials. Androutsopoulos and Mann12developed a square network to model oil recovery in porous solids. Mason’s13model shows that hysteresis in nitrogen adsorption is due to a network of pores connected by constrictions. Chatzis and Dullien14 have considered a network structure similar to that of Conner and Lane and applied percolation theory to predict
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(1) Everett, D. H. In “The Gas-Solid Interface”; Flood, E. A., Ed.; Dekker: New York, 1967; Vol. 2, p 1055. (2) Conner, W. C.; Lane, A. h4.;Ng, K. M.; Goldblatt, M. J . Catal. 1983, 83, 336. (3) Joyner, L. G.; Barrett, E. P.; Skold, R. J . Am. Chem. SOC.1951, 73, 3155. (4) Dubinin, M. M. In ”Chemistry and Physics of Modern Materials”;
Walker, P. L., Ed.; Dekker: New York, 1966; Vol. 2, p 83. (5) DeWit, L. A.; Scholten, J. J. F. J. Catal. 1975, 36, 36. (6) Zwietering, P.; Koks, H. L. T. Nature (London) 1954, 173, 683.
(7) Zwietering, P.; van Montfoort, A.; Tebben, J. H. In “Proceedings of the Third International Symposium on the Reactivity of Solids”; Madrid, 1956; Section IV, p 123. (8) Moscou, L.; Lub, S. Powder Technol. 1981,29, 45. (9) Brown, S. M.; Lard, E. W. Powder Technol. 1974, 9, 187. (10) Winslow, D. N. J . Colloid Interface Sci. 1978, 67, 42. (11) Davis, B. H. A p p l . Catal. 1984, 10,185. (12) Androutsopoulos, G . P.; Mann, R. Chem. Eng. Sci. 1979,34,1203. (13) Mason, G. Proc. R . SOC.London, Ser. A 1983, 390, 47. (14) Chatzis, I.; Dullien, F. A. L. Int. Chem. Eng. 1985, 25, 47.
0743-7463/86/2402-Ol51$01.50/0 0 1986 American Chemical Societv
152 Langmuir, Vol. 2, No. 2, 1986
Conner et al.
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F i g u r e 2. Comparison of the pore-size distributions obtained from mercury extrusion (- - -) and nitrogen adsorption data (..a).
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porosimetry curves i n sandstones. Further analysis b y Lane e t ai. indicates that t h e r e are substantial deviations between porosimetry and percolation p r o c e ~ s e s . ' ~
Experimental Section A series of nonporous, Degussa aerosols was pressed to 20 000 psig to create a void structure. Table I summarizes the properties of the aerosols. Mercury porosimetry experiments were performed a t the University of Massachusetts a t Amherst by using a Quantachrome Scanning Mercury Porosimeter capable of pressures up to 60000 psig. Samples were outgassed to less than 0.1 torr. The data were collected by an Analog Devices Macsym 350 computer. Nitrogen adsorption experiments were performed a t the Instituto de Catalisis y Petroleoquimica in Madrid, Spain by using a Micromeritics Digisorb 2500. Samples were outgassed to less than IO-" torr during 16 h a t 140 "C. The whole operation, preconditioning of the samples, nitrogen adsorption and desorption, and data recording and handling, was ordered through a PDP-8A computer from Datametrics. For the mercury porosimetry data, the void dimension as radius was determined from the pressure of intrusion or extrusion by using the Washburn equation with a contact angle of 140" and a surface tension of 480 dyn/cm2. The volume-distribution curves were found by taking the derivative of the volume intruded (or extruded) with respect to the radius of intrusion (or extrusion). Reintrusion and reextrusion of the samples were used to check for any irreversible damage due to compression during porosimetry. For the nitrogen adsorption experiments, the pore size was related to the partial pressure by using the method of Pierce,16 as modified by Orr and Dalla~alle.'~These data were then plotted as the cumulative pore volume in which nitrogen was adsorbed or from which nitrogen was desorbed vs. pore radius. The derivative of the cumulative pore volume with respect to pore radius gives the pore-size distribution. A modification of this method is also used to calculate the distributions assuming a void structure which consists of spherical pores connected by volumeless, cyl(15) Lane, A. M.; Conner, W. C.; Shah, N. J. Colloid Interface Sci., in press. (16) Pierce, C. J . Phys. Chem. 1953, 57, 149. (17) Orr, C.; Dallavalle, J. "Fine Particle Measurement"; MacMillen: New York. 1959; p 271.
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F i g u r e 3. Comparison of the pore-size distributions obtained from the nitrogen sorption isotherm for the compressed A200 Aerosil assuming cylindrical pores and pore-throat (-) void geometries. (e..)
indrical throats. This modification assumes that adsorption measures the spherical pores. Thus, the volume of the nitrogen layer building up on the pore wall is calculated by using spherical geometry. The desorption process is controlled by the radius of the volumeless throats; however, the liquid nitrogen layer to consider is in the spherical pores. Thus, it is necessary to assume a radius of the pore that has been accessed by the throat. It has been shown that for the porosimetry of compressed aerosols, the ratio of the radius of extrusion to the radius of intrusion is a constant of about 2.4.18 This assumption is used to estimate the radius of the pore connected to the throat of a given size. Intuitively, we might expect that the smaller throats would access the smaller pores, that is, there is a correspondence between the pore and throat sizes within the network.
Results The pore-size d i s t r i b u t i o n curves o b t a i n e d f r o m t h e m e r c u r y porosimetry and nitrogen a d s o r p t i o n data a r e c o m p a r e d in Figures 1 and 2. These figures show that mercury intrusion and nitrogen desorption give similar size d i s t r i b u t i o n s and that m e r c u r y extrusion and nitrogen a d s o r p t i o n c a n be similarly related. In e a c h case, distributions calculated from the mercury porosimetry data a r e narrower than those given by the nitrogen adsorption data. T h e distributions given b y intrusion a n d desorption a r e narrower with a m a x i m u m at a smaller radius than those given b y extrusion a n d adsorption. The d i s t r i b u t i o n curves derived f r o m t h e nitrogen adsorption data assuming different void-structure geometries (spherical o r cylindrical) a r e c o m p a r e d i n F i g u r e 3. No (18) Conner, W. C.; Neil, J.; Blanco, C.; Pajares, J. J . Phys. Chem., submitted for publication.
Langmuir, Vol. 2, No. 2, 1986 153
Characterization of Pore Structure
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significant difference results when the nitrogen adsorption data is analyzed assuming a void structure of spherical pores connected by cylindrical throats.
Discussion
It is not realistic to assume that a porous solid may be represented as a series of nonintersecting, cylindrical pores. Analysis of mercury porosimetry data using this assump tion has led to the conclusion that hysteresis is due to a change in contact angle from intrusion to e x t r u s i ~ n ? ~ ~ ~ ~ Conner et al. have questioned this view using thermodynamic arguments and observing that contact-angle hysteresis is inadequate in explaining many of the phenomena in porosimetry.21 More realistically, the void structure of a porous catalyst may be pictured as a series of interconnected channels of varying size as illustrated by Figure 4.
This has led Conner and Lane et a1.' to propose a three-dimensional network consisting of spherical pores connected by volumeless, cylindrical throats to represent a porous catalyst. A graphical representation of the Figure 8. (a)Visunlieatim of the mercury intrusion process: (h) %re-throat" model of Conner and Lane is given in Figure visualization of the nitrogen dernrption process. 5. This model can explain the phenomenon of hysteresis in both merporosimetry and nitrogen sorption, as well Since each pore is acceessible through more than one throat, as account for mercury retention in porosimetry. During the volume of the pore is measured at the largest, accesmercury porosimetry, the throats (the constrictions) consible throat size. Therefore, the larger throat sizes domtrol the intrusion process, while the pores (the openings) inate the measurement during the intrusion process control the extrusion process. ("nonlinkage"). Porosimetry is a sequential process, and The statistical influences that result from this analysis some throats are not measured at their corresponding are illustrated in Figures 6 and 7. These effects were pressure hecause they are not accessible to the mercury found by computer simulation using the pore-throat model until the mercury has reached them within the solid. with a given input distribution of pores and t h r 0 a t s . 2 , ~ ~ - ~ ~These throats me measured after the mercury has intruded smaller throats ("shadowing"). This leads to a shift in the (19) Lowell, S.; Shields, J. E. J. Colloid Interface Sci. 1980,80,192. (20) h e l l , 5.;Shields, J. E. Powder Technol. 1980,25, 37. 1211 Comer. W. C.: Lane. A. M.: Hoffman. A. J. J. Colloid Znterfnce ~, Sei. 1984, 100,'185. (22) Conner,W. C.; Lane, A. M. J. Cotol. 1984,89, 217,
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(23) Lapidw, G R: h e . A. M . : Ng, K. M.;Connor. W.C. Chsm. Em. Commun., in press. (24) Lane, A. M. Ph.D. Dissertation. University of Masssehuoetls, Amherst, MA, 19%.
154 Langmuir, Vol. 2, No. 2, 1986
Figure 9. (a) Visualization of the mercury extrusion process; (b) visualization of the nitrogen adsorption process.
distribution curve in the direction of smaller throat sizes. The extrusion process is also subject to the effects of shadowing; i.e., a pore can only be measured if an adjoining pore has been emptied earlier in the sequence. The pore size distribution curve is shifted to larger pore sizes. Due to the different paths of intrusion and extrusion, some mercury is retained within the pores during extrusion ("stranding"). The last t o extrude, the larger pores, are more likely to retain mercury. Thus, shadowing and retention lead to a narrowing of the extrusion distribution curve. In order to compare the methods in terms of an interconnected network of pores, the sequential nature of the two measurement processes is visualized in Figures 8 and 9. These figures depict the situations which may exist in a porous solid at some point during the mercury porosimetry and nitrogen sorption processes. Figure 8a has been drawn by arbitrarily assuming throat sizes and allowing mercury to invade the network from the outside through all throats which are larger than the chosen size. Similarly, Figure 8h was drawn by starting with the voids filled with condensed nitrogen and then allowing nitrogen to desorb at the gas-liquid interface from throats which were larger than the same radius chosen for Figure 8a. The figures show that at a given point during each process, nitrogen will still be condensed wherever mercury has not yet intruded. Figure 8 shows that mercury fding during intrusion and nitrogen removal during desorption are subject to the same statistical effects. Intrusion is a sequential filling of mercury into the porous solid, and desorption is a sequential emptying of nitrogen at a gas-liquid interface.
Conner et al.
Both the mercury intrusion and nitrogen desorption processes measure the larger radii first. Both processes exhibit nonlinkage and shadowing and measure the throat sizes as larger than they actually are. In Figure 9h, the void was fdled with condensed nitrogen wherever a pore was smaller than a chosen size. Figure 9a was drawn hy starting with the voids filled with mercury and allowing successively larger pores to empty until reaching the pore size chosen for Figure 9h. Mercury extrusion and nitrogen adsorption are similar in that both processes measure the smaller pore sizes first. However, they are not subject to the same network effects as found in the comparison of intrusion and desorption. Nitrogen adsorption is free of the sequential, shadowing effects because all areas of the porous solid are accessible to the nitrogen. Even if a pore fills with nitrogen, physical equilibrium dictates that the chemical potential across all interfaces throughout the network is the same. On the other hand, mercury extrusion, like intrusion, requires a continuum of mercury and is therefore subject to network effects. Further, the differences in the paths of intrusion and extrusion result in mercury retention; universal accessibility during adsorption precludes this effect. The result is that adsorption is devoid of the narrowing statistical influences of shadowing and retention exhibited by extrusion. Conclusions Mercury porosimetry and nitrogen adsorption are used to characterize the void structure of porous solids. For the region of pore radii in which the analyses overlap (Z(t300 A), the two methods give comparable information with regard to the void dimension. In particular, mercury intrusion corresponds to nitrogen desorption, and mercury extrusion corresponds to nitrogen adsorption. The two processes were examined in terms of the statistical effects of an interconnected network of pores. With this perspective, the effects on mercury intrusion and nitrogen desorption are equivalent. They reflect a shadowing due to the sequential nature of the measurement processes. However, nitrogen adsorption is free of such statistical effects, while the mercury extrusion process is subject to these network effects. No significant differences were evident in the pore-size distributions as a result of analyzing the nitrogen adsorption data assuming a void structure consisting of spherical or cylindrical pores connected by cylindrical throats (Figure 3). Mercury porosimetry and nitrogen adsorption may he used in conjunction to characterize the void structure in porous materials. This paper demonstrates the correspondence, strengths, and weaknesses inherent in these measurement techniques. Registry No. Hg,7439-97-6; N2,1727-37-9.
