., .

J Am Ceram Soc 73 [a] 2228-37 (1990)

Quantitative Electron Microscopic Investigation of the Pore Structure in 10 : 90 Colloidal SilicafPotassium Silicate Sol-Gels

Helen M. Kerch,* Rosario A. Gerhardt,*V+ and John L. GrazuV Department of Ceramics, Rutgers University,

Piscataway, New Jersey 08855

Transmission electron microscopy (TEM), scanning elec- tron microscopy (SEM), mercury intrusion porosimetry (MIP), and nitrogen sorption technique (BET) were utilized to characterize the microstructure of a 10:90 wt% colloidal silica/potassium silicate gel as first described by Shoup. Gels in the unsintered state (15% theoretical density) were prepared for microscopy by the techniques of ultramicro- tomy, Pt/C replication, and pore casting. Electron micro- scopic images of the ultramicrotomed thin sections (70 nm) show that the unfired gel possesses three distinct species of pores which are referred to as the micropores, mesopores, and macropores. The average micropore diameter was found to be 4 nm as determined by nitrogen desorption. Quantita- tive stereological analysis on the ultramicrotomed sections indicated that the average circular and lengthwise dimen- sions of the cylindrical mesopores were 0.15 and 0.39 pm, respectively. Similarly, this same analysis determined the av- erage spherical macropore diameter to be 0.83 pm. In con- trast, MIP results suggested that these gels possessed a unimodal pore size distribution centered around the 0.2-pm pore size. The discrepancy between MIP and microscopy can be explained by viewing the void space as a pore-throat network. Experimental evidence for this type of pore geome- try was obtained from stereo pairs of Pt/C replicas and thick microtomed sections (0.5 pm) which gave information about particle connectivity and pore casts which depicted the pore connectivity in three dimensions. [Key words: silica, sol-gel, porosity, microscopy, porosimetry.]

I. Introduction

OROSITY is a common microstructural feature in ceramic P bodies.' In some cases the porous phase is tailored to pro- duce specific properties in the materiaL2 For most ceramics, however, the ultimate goal is the reduction of porosity, and the raw materials processing and subsequent heat treatment are designed to achieve a product at or close to full density. With either scenario, the importance of accurate pore charac- terization is e ~ i d e n t . ~ - ~

Complete description of porosity involves a number of dif- ferent parameters including pore size and pore size distribu- tion, pore volume and density, surface area, pore texture and shape, and pore connectivity.6 Analytical techniques used to obtain these parameters are usually categorized by both the

T. E. Mitchell-contributing editor

Manuscript No. 198136. Received September 5 , 1989; approved March 23,

Presented at the 91st Annual Meeting of the American Ceramic Society,

Supported by the Fiber Optic Materials Research Program, Dr. George H.

*Member, American Ceramic Society. 'Author to whom all correspondence should be sent. 'Bureau of Biological Research.

1990.

Indianapolis, IN, April 24, 1989 (Glass Division, Paper No. 10-G-89).

Sigel, Jr., Director.

type of data they provide and their pore size detectability range. Included in such techniques are BETInitrogen sorption technique and mercury poro~imetry,~ X-ray microtomogra- phy? SANS (small angle neutron ~cattering),~ NMR (nuclear magnetic resonance),Io and electron microscopy." Since this paper will restrict itself to the discussion of pore characteriza- tion by mercury porosimetry and electron microscopy, only these techniques will be discussed in detail.

The pore size distribution of ceramics is commonly ob- tained by mercury intrusion porosimetry (MIP), which can detect pores with diameters between 2 nm and 100 pm." The technique is based on the idea that pressure must be applied to a nonwetting substance, in this case liquid mercury, in order for it to penetrate into a void space. By equating the cap- illary and applied forces within a cylindrical pore, Washburn13 derived an expression relating the applied pressure and pore diameter. In many cases, however, the pore geometry is un- known or has been characterized as being complex and irreg- ularly shaped. Nevertheless, the Washburn equation is often used to derive pore size information from mercury intrusion even though it should be applicable only to isolated cylindri- cal pores. MIP is also employed to determine pore volume.

Unlike MIP, which relies upon an assumed geometric model of the pore structure, electron microscopy allows direct ob- servation of the microstructure. Critics of this technique point to the difficulty in sample preparation and image inter- pretation as well as to the possibility of nonrepresentative ~amp1ing.l~ These are valid concerns; however, they are not insurmountable. It is true that sample preparation for electron microscopy can be time-consuming, but the microstructural information revealed is often unobtainable by other analytical methods. Also, with an understanding of the interrelationship between specimen preparation and image formation, the problem of interpretation can be resolved. Finally, quantita- tive microstructural information may be furnished which sat- isfies the statistical requirements if a proper sampling scheme is carried

Of the methods available for sample preparation of porous ceramics for TEM, ion milling17.'s and powder grinding and/ or d i~pers ion '~-~~ have been utilized in a number of investiga- tions. We feel that these preparation methods are not applicable to the study of our gels and materials with similar pore morphologies for the following reasons:

(1) Ion milling, which involves specimen thinning by argon ion bombardment at an acute angle, causes widening of the pores due to the preferential ion attack of the pore boundaries. This will cause a general shift in the pore size to larger values. In addition, with brittle and highly porous solids such as the one in this study, survival of the sample during ion bombardment is doubtful.

(2 ) The method of powder dispersion entails grinding the specimen into a powder and then dispersing it in a liquid medium by the use of either a deflocculant or an ultrasonica- tor. A TEM grid is then dipped into the liquid, causing ad- herence of the dispersed powder onto the grid. The ground material may be directly placed on a TEM support, thus elim- inating the dispersion step. With such a sample preparation

2228

August 1990 Quantitative Electron Microscopic Investigation of Pore Structure 2229

method, there is little question that destruction of the pore network has occurred on both the gross and local levels. This prevents the possibility of structural information to be derived from the resultant images. In addition, the sample thickness across the grid is variable and unknown because of the random manner in which the material is placed on the grid surface. Hence large pores can be masked by a layer or layers above or below it and small pores may be hidden from view altogether.

SEM s t ~ d i e s ' ~ - ' ~ of fractured and polished surfaces of porous materials may also be found in the literature. Interpre- tation of the images furnished by fracture surfaces, where the pore size scales with the fracture features, is ambiguous be- cause of the inability to distinguish between surface topogra- phy and true pores. Similarly, sample pullout may obscure the true morphology for specimens that are polished.

In performing the microscopic analysis of the colloidal gels in this investigation, the strategy was to use a variety of preparation techniques in order to maximize the amount and type of microstructural information. With many of the famil- iar methods eliminated, it became necessary to pursue those not often utilized in materials science. The methods chosen are ultramicrotomy," Pt/C replication,26 and pore ~asting.2~

Ultramicrotomy is a method by which ultrathin sections, typically 4 0 0 nm, are made by the cutting action of a glass or diamond knife against a resin-embedded specimen. Both ceramic and metallic materials have been prepared in this manner.28,29 For ceramics, the technique is usually chosen be- cause ultramicrotomed thin sections can reveal the inner structure of large particles or agglomerates. The resin simply provides the medium for holding the particles together during the thinning process. For our case, the resin represents the porous phase and its features are as important as the mono- lithic gel that it infiltrates.

The main advantages of using ultramicrotomy for viewing the pore microstructure are the maintenance of gel coher- ence, the ability to view a large number of fields, and, if serial sections are collected, the possibility of performing three- dimensional (3-D) reconstruction. In addition, because the sections produced are flat and ultrathin, stereological princi- ples may be applied to obtain quantitative information such as pore volume and pore size distribution.

Pore shape and degree of pore and particle connectivity are more difficult to quantify, but they may be readily obtained, at least qualitatively, by 3-D images afforded by TEM stereo pairs of microtomed thick sections and Pt/C replicas and SEM micrographs of samples prepared by pore casting. Pt/C replication involves the sequential evaporation of carbon and platinum at an angle onto a sample surface. The sample is etched away, leaving a replica of the specimen topography. Pore-cast samples are obtained by infiltrating a porous speci- men with an epoxy or other polymer material and then dis- solving the original sample. This way a negative of the solid is created which depicts the pore shape and connectivity.

The purpose of this study is to fully characterize the pore parameters utilizing both microscopy and the conventional techniques of mercury intrusion and BET. A comparison of the data obtained by the different methodologies will be pro- vided along with the rationale for any discrepancies between techniques.

11. Experimental Procedure

( I ) Gel Preparation Gel preparation is described in detail elsewhere7 and will

not be reviewed here. All silica monoliths were made with a mixture of 10 wt% colloidal silica$ and 90 wt% potassium silicate' which gels in the presence of formamide and water.

'Ludox HS-40, E. I. du Pont de Nemours and Co., Wilmington, DE. 'Kasil-1, Philadelphia Quartz Co., Lafayette Hill, PA.

The average particle diameter of the colloidal sol is 15 nm. The potassium silicate is comprised of a mixture of 20.8 wt% SiOz and 8.3 wt% K 2 0 with the balance being water. The proposed gelation mechanism is a destabilization of the col- loidal sol with a concurrent deposition of the potassium sili- cate onto the points of contact between colloidal particles. Clusters of colloidal particles are joined, causing the subse- quent formation of the 3-D gel structure.' The 10:90 wt% ratio was chosen because preliminary Hg porosimetry data, the sole source of pore size information at the time this work was started, indicated that it possessed a unimodal pore size distribution. Hence it was expected that this composition would have the simplest microstructure.

The gel monoliths were cut into equivalent-size disks with a diamond saw.** Sample blocks for both microscopic analy- sis and porosimetry were taken from the center of the disk, which in turn was taken from the median of the monolith. Two gel batches were made and subjected to identical prepa- ration and analysis to ensure batch-to-batch reproducibility. (2) Density Measurements

Bulk density was determined by geometrical measurements and mercury intrusion of cut disks obtained from the gel mono- liths. Density information was also derived from X-ray micro- tomography via mass fraction profiling.* The volume fraction of porosity, and hence the density, was also furnished by quan- titative stereological analysis of ultramicrotomed thin sections.

(3) Pore Size and Size Distribution Pore size and size information were obtained from micro-

graphs of gels prepared by the three different methods of ultramicrotomy, Pt/C replication, and pore casting. Quantita- tive stereological data were derived from the ultramicro- tomed thin sections and compared with mercury porosimetry and BET results.

(A) Preparation for Microscopic Analysis ( I ) Ultramicrotomy: In preparation for ultramicrotomy

the gel blocks were first dehydrated by three acetone replace- ment baths. This is necessary as the epoxy impregnant is not miscible with water. We chose to infiltrate the sample with Spurr3' epoxy as it had been used successfully with other ceramic materials. Also it possesses desirable rheological properties in the uncured state as well as the necessary me- chanical strength in the cured state.

A four-step infiltration schedule was carried out in the fol- lowing order with the ratios representing volume percent Spurr epoxy to propylene oxide: (1) 25:75, (2) 50:50, (3) 75:25, (4) 1OO:O. Each infiltration bath was performed in a rotator for a duration of 7 h. Samples were cured in Nalgenett molds for 48 h at 70°C. The tip of the infiltrated specimen block was then trimmed into a pyramidal shape as this keeps the orientation of the sample straight during cutting and aids in creating a distortion-free section. Microtomingtt was done with a biological-grade diamond knife'$ which enabled the production of coherent 70-nm-thick sections (see Fig. 1). Ran- dom thin sections were then collected onto carbon-coated TEM grids. Thick sections ranging from 0.25 to 1 pm were also obtained from an unfired gel.

(2) Pt/C Replication: Samples for replication were first fractured in air, then placed inside a freeze etch apparatus" in a vacuum of better than 1 x torr. Platinum was evapo- rated at an angle of 45" to a thickness of 2.5 nm followed by a 15-nm layer of carbon deposited at 90°C. The replicas were retrieved by immersing the gel in H F followed by a distilled water rinse.

(3) Pore Casting: Specimens for pore-cast analysis were dehydrated, infiltrated, and cured in the exact manner de-

**Isornet, Buehler Ltd., Lake Bluff, IL. "Size 00, Nalge Corp., Rochester, NY. '*Porter-Blum MT-2, Ivan Sorvall, Inc., Newton, CT. "Delaware Diamond Knives, Inc., Wilmington, DE. "BAF301, Balzers, Hudson, NH.

2230 Journal of the American Ceramic Society - Kerch et al. Vol. 73, No. 8

Fig. 1. TEM micrograph of ultramicrotomed trapezoid on speci- men grid.

scribed for ultramicrotomy. The tip of the sample block was cut with a diamond saw to expose the interconnected silica and epoxy phases. This surface was sequentially hand pol- ished with 6-, l- , and 0.25-pm grit size diamond paste followed by 0.05-pm alumina polish. The specimen was placed in a 45 wt% KOH solution for 30 min at 70°C to dis- solve the silica phase. The pore cast was then mounted on an SEM stud and sputtered with gold and platinum to reduce charging effects.

(B) Microscopy: Micrographs of the specimens prepared by ultramicrotomy and Pt/C replication were taken in bright- field mode at 100 kV.*** Stereo pairs were taken with a tilt angle of 10" between them. Pore-cast samples were observed under the SEM.ttt In addition, the thick microtomed sections were viewed with an intermediate voltage electron micro- scope (IVEM).~"

(C) Image Analysis: Quantitative stereological analysis of the ultramicrotomed sections was done with a digital image analyzer."' In order to achieve statistically significant data the following nested sampling scheme was carried out: from two silica monoliths originating from separate gel batches, two blocks were removed and prepared for ultramicrotomy. Three thin sections cut from each block were chosen ran- domly and three fields or micrographs at a magnification of 19000~ were obtained from each section. This yielded a total of 36 two-dimensional (2-D) fields from which the quantita- tive microstructural information was derived.

The basic stereological quantities obtained were average pore diameter (D,,,J, the total pore volume (K), and the num- ber of pore species per unit area and volume (N. and Nu, respectively).

(0) Mercury Porosimetry and BET: Pore size distribu- tion and pore volume data were obtained by mercury intru- sion porosimetry (MIP)." The maximum pressure that the gel was subjected to was 30000 psi ( ~ 2 0 0 MPa), which corre- sponds to a 3-nm pore radius. Values for contact angle and surface tension were taken as 135" and 0.484 N/m, respec- tively. Pores with smaller diameters were characterized with BET.**** The pore size distribution was derived from the ni- trogen desorption curve.

'**J.E.O.L. lOOCX, JEOL U.S.A., Inc., Peabody, MA. '"Hitachi S450, Hitachi Instruments, Inc., Santa Clara, CA. **'JEM-4000FX, JEOL U S A . Inc. :ha ecraft, Princeton Gamma Tech, Princeton, NJ.

*"*Omnisorp 360 Analyzer, Omicron Technology Corp., Berkeley Mofel 3005, Micromeritics, Norcross, GA.

Heights, NJ.

111. Results

(1) Density The homogeneity of the gel density, as determined by

X-ray microtomography, is a function of gel size as displayed in Fig. 2 for unfired gels consolidated in 12-, 7.5, and 125-mL containers.tttt As shown, the 12-mL gel has the most uniform density across the sample while gels made in larger containers exhibit a more concave density profile. For this reason all gels used in this study were made in 12-mL containers. Table I summarizes the density values obtained by geometrical meas- urements, mercury intrusion, X-ray microtomography, and stereological analysis. As can be seen, good agreement is found between all the methods.

(2) (A) Ultramicrotomy: Figures 3(A) to (C) depict represen-

tative images of a 70-nm thin section of an as-dried gel at three different magnifications. The light regions represent the epoxy or void space while the darker regions correspond to the silica gel. These micrographs indicate that in the micro- toming process we have cut across some large pores as well as directly through silica agglomerates. The images show that the gel samples were completely infiltrated as evidenced by the lack of voids at the silica/epoxy interfaces. The specimens also appear to have sustained no damage during sectioning. This observation is supported by the lack of rips, tears, or folds in the sections. The low-magnification image (Fig. 3(A)) demonstrates the uniformity of the colloidal gel microstruc- ture. The micrograph complements the recent NMR data which predicted that the homogeneity of the gel was on a scale of less than 5 pm."

Referring to Figs. 3(A) to (C), it is possible to designate qualitatively three distinct species of pores based on a knowl- edge of the consolidation process which gives rise to the following hierarchical gel network structure. The pores appearing as texture in Fig. 3(8) and labeled "a" in Fig. 3(C) are termed the micropores. The micropores comprise the interstices between the colloidal particles which come together as a result of the destabilization of the sol. As the destabi- lization process continues, the individual clusters of colloidal silica which have formed grow in dimension as more colloids become attached. Some of these clusters aggregate into larger agglomerates which are separated by the mesopores (labeled "b" in Fig. 3(B)). Other clusters form long chains or branches

Qualitative Description of the Microstructure

ttttThe drop in the center of the curves is an artifact of the analysis and hence does not represent an actual density decrease in the center of the gel.

0.500 I I

~ 0.400 I J

.-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 RADIUS r (cm)

Fig. 2. Graph of bulk density as a function of gel container size obtained by X-ray microtomography: (a) 125, (b) 75, (c) 12 mL.

August 1990 Quantitative Electron Microscopic Investigation of Pore Structure

Table I. Summary of Bulk Density Data Obtained by Various Techniques

2231

Density Theoretical density Pore volume Analytical technique (g/cm3) (”/.I (%)

Geometric measurements 0.32 r 0.01 14.5 85.5 Mercury intrusion* 0.328 ? 0.02 14.9 85.1 X-ray microtomography 0.339 ? 0.01 15.4 84.6 Stereology (areal analysis) 0.401 t 0.01 18.2 81.8 Stereology (pore frequency analysis)*,+ 0.268 ? 0.03 12.2 87.8

*Phi = 1/[(5) + (&,)I. Pbd = bulk density, = pore volume, pth = theoretical density. ‘Error obtained by calculating volume difference between a sphere and a cylinder.

which connect the agglomerates in three dimensions. The large pores, termed the macropores (labeled “c” in Fig. 3(A)), are formed by these silica branches.

To take full advantage of the method of ultramicrotomy 0.25- and 0.5-pm-thick sections of the gel were viewed in an IVEM. The arrangement of the pores in three dimensions can be seen via the stereo pairs of the 0.5-pm-thick sections presented in Fig. 4. The thick sections can be visualized as a superposition of approximately seven layers of the thinner ultramicrotomed sections as shown in Fig. 3. The proposed pore network described above is convincingly displayed by this stereo pair. Several sublayers of mesopores are visible within the thick section, confirming that their size is smaller than the section thickness (0.5 pm). On the other hand, por- tions of what appears to be only two layers of macropores can be seen, which would imply that their size is larger than 0.5 pm. The gel layers are stacked in such a way that the mesopore and macropores are displaced with respect

to the pores in the upper and lower layers. The reduction of the visible void space or light regions is caused by this stack- ing arrangement.

(B) PtlC Replication: Figure 5 displays a stereo pair of a gel fracture surface. With the aid of stereo visualization the silica particle connectivity and overall gel arrangement can be revealed. The most prominent feature in the replicas is the large ringlike structures that are formed by linking of several of the individual gel cluster units. At certain points about the rings are agglomerates which envelop somewhat smaller pore spaces. These structural units are similar to those found in the ultramicrotomed thick sections (Fig. 4). The rings are rather loosely packed and would account for the low theoreti- cal density (15%) demonstrated by the unfired gel. The micro- pores may not be characterized because of the resolution limit of the replication technique .31

(C) Pore Casting: Connectivity, shape, and size of the void space can be clearly discerned by a cast of the pores.

Fig. 3. Ultramicrotomed section (70 nm) of an unsintered gel taken at three different magnifications illustrating the three pore species: (A) micropores, (B) mesopores, (C) macropores.

2232 Journal of the American Ceramic Society - Kerch et al. Vol. 73 , No. 8

Fig. 4. dimensions.

Stereo pair of a thick microtomed section (0.5 pm) of an unfired gel showing arrangement of gel in three

Figure 6 is an SEM micrograph of a pore cast sample of an unsintered gel. A number of prominent features are illus- trated in the micrograph. On the surface of the cast are the concavities left from the silica particles which have been etched away during the dissolution process. This provides evi- dence that what is being viewed is the actual pore cast rather than artifacts produced by the polishing procedure.

In accord with the ultramicrotomed thin sections and the Pt/C replicas, the casts show the presence of both the macropores and mesopores. The imprint of the micropores on the pore cast was not resolvable because of the coating proce- dure. The mesopores appear to be cylindrical in shape while the macropores are best described as being spherical. The mesopores are seen to connect the macropores in the pore network. This connectivity is somewhat complex in nature; some macropores are linked by only a few mesopores while others are joined by many mesopore channels.

(3) Quantitative microstructural information pertaining to

pore volume, average pore size, and pore size distribution was furnished via stereological analysis of the ultramicrotomed thin sections. For comparison, the porosity was also charac- terized by BET nitrogen sorption and MIP.

(A) Pore Volume: Pore volume was calculated according to the stereological identity

Quantitative Analysis of the Microstructure

V, = A, (1)

That is, for a completely random structure the area fraction of a particular phase is equivalent to its volume fraction. A , was determined by the ratio of the total number of pixels occupy- ing the porous phase over the total number of pixels in the field. The average pore volume for the 36 fields examined was 81.78% ? 3.3, which is comparable to MIP data, geometric

Fig. 5. Stereo pair of a Pt/C replicated fracture surface for an unfired sample depicting particle connectivity.

August 1990 Quantitative Electron Microscopic

Fig. 6. SEM of a pore cast (unfired sample). Note pore shape and connectivity. Mesopores (circles) and macropores (boxes) are des- ignated in the micrograph.

density calculations, and microtomographic results listed in Table I.

It should be added that this analysis is valid for sufficiently thin sections only, as an erroneous pore volume of 35% would be obtained from the thick microtomed sections illustrating the importance of approaching a true 2-D sample. The dis- crepancy in pore volume between thick and thin sections is due to the overlapping arrangement of the gel (see Fig. 4) which conceals portions of the porous phase in the thicker sections.

(B) Pore Size and Pore Size Distribution of the Micro- pores: Figure 3(C) is a high-magnification image of a gel cluster which clearly depicts the micropores. Imaging the mi- cropores was possible by utilizing a defocus contrast tech- nique which has reviously been used to image voids32 and small inclusion^^^ in other materials. In an underfocused image, contrast arises due to the phase difference between the electrons originating from the silica phase and those coming from the pores. This phase difference manifests itself as dark rings which encircle the micropores, therefore making them visible. Within each cluster may be seen a distribution in the micropore size; however, a statistically complete de- scription of these pores has not yet been carried out but will be reported in a future publication.*"* They can, however, be quantified by nitrogen sorption technique. This method has shown that the as-dried gels have an average micropore size of 4 nm,' and this value scales well with the size of the micropores seen in the micrograph.

Investigation of Pore Structure 2233

(C) Pore Size and Pore Size Distribution of the Mesopores and Macropores: The data from the stereological analysis of the ultramicrotomed gels are given in Table 11. The pores were divided into 0.1-pm size class intervals with the largest pores considered having a diameter of 1.2 pm. Pores with diameters larger than this were not observed in the thin sec- tions. The total number of pores counted was 3385. The fre- quency of occurrence in each pore class is given in the second column of Table 11. The number of pores comprising a specific pore size interval per unit area of field (in this case 360 pm2) yields the quantity N, (third column). The calcula- tion of N, is less straightforward because the 2-D diameter of a pore in the image plane depends on how the actual 3-D pore was sectioned. For example, a 2-D pore with diameter D, may have originated from 3-D pores with diameters D, to D,,, where D,,, is the largest observable pore diameter, Fol- lowing the analysis given by Underwood34 for spherical pores,$§$* the contribution from each 3-D pore size interval to the 2-D distribution may be determined as follows:

In this system of notation the i refers to the 2-D section di- ameter while j refers to the 3-D sphere diameter. (N"), is the number of pores per unit volume of sizej, Z(Na), , ] is the num- ber per unit area of sections of size i obtained from spheres of size j , pl,i is the probability of a thin section intersecting a 3-D pore of diameter j and yielding a 2-D section of diameter i , and Di is the diameter of the 3-D pore of size j .

Utilizing this analysis, the term N, for each size interval was determined and is given in the fourth column of Table 11. This value was converted from a number quantity to a volu- metric term by multiplication with inverse bulk density and a term representing the volume of a sphere for each r, class size. This product provides a value for the pore volume for each pore size interval. The cumulative pore volume was then de- termined from the largest to the smallest pore species in order that the data (fifth column of Table 11) may be compared to MIP cumulative curves (Fig. 7(A)). There are a number of salient differences between the curves. First, the cumulative pore volume obtained by stereological analysis is larger than that indicated by MIP. Second, the pore size distribution ac- cording to mercury intrusion is shown to be unimodal as indi- cated by the smoothly varying curve. In addition, the curve furnished by image analysis reveals a much broader range of pore sizes, especially in the region of 0.5 pm and less. The curve exhibits a change of slope between 0.5 and 0.7 pm. For values larger than 0.7 pm, the pore volume falls off rapidly.

'"'For purposes of comparison, the defocus diameter of the micropores is reported in Table 111. The value should be comparable to the real size for the degree of defocus employed (0.7 rm).

*"'Although we have observed the mesopores to be cylindrical in shape, we do not expect a large error in the distribution curve by using the analysis for spherical pores. What we do expect from this assumption is an overesti- mation of the pore volume occupied by the mesopores (see Table I).

Table 11. Stereological Data for the Unsintered Gels Cumulative ore volume P

( r m ) Frequency (l/rmZ) (wm3) (cm /d (cm /g) 0-0.1 649 1.8 13.6 0.0222 3.2688 0.1-0.2 921 2.56 12.7 0.166 3.2466 0.2-0.3 705 1.07 3.46 0.153 3.0806 0.3-0.4 399 0.76 2.15 0.225 2.9276 0.4-0.5 153 0.43 1.04 0.213 2.7026 0.5-0.6 66 0.17 0.04 0.0141 2.4896 0.6-0.7 93 0.26 0.24 0.135 2.4755 0.7-0.8 103 0.29 0.27 0.226 2.3405 0.8-0.9 137 0.38 0.581 0.693 2.1145 0.9-1.0 132 0.37 0.847 1.39 1.4215 1.0-1.1 18 0.005 0.008 0.0174 0.0315 1.1-1.2 9 0.0025 0.005 0.0141 0.0141

Totals 3385 8.10 34.94 3.2688

Pore size interval N, N" Pore vplume

2234 Journal of the American Ceramic Society - Kerch et al. Vol. 73, No. 8

- U N E - U e U

0.50

0.00 .01 .1 1 10

pore diameter (microns)

(A)

20 I n .01 . 1 1 IC pore dze (mlsrona)

./ -

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

pore diameter (microns)

Fig. 7. Cumulative and differential pore size data obtained from intrusion meas- urements (0) and quantitative stereology (A). Insert in (B) is the pore size distribu- tion from the stereological analysis given on a logarithmic scale to better illustrate the break in the mesopore distribution at 0.25 j m .

The average pore size can be obtained from the differential form of the curve (Fig. 7(B)), specifically dv/dd where the derivative of the intruded volume is taken with respect to that of the pore diameter to eliminate the dependence on pore size. For MIP the average pore size is given as 0.2 pm. Stereological measurements indicate three maxima. One sharp maximum is observed about 0.9 pm and another much broader distribution contains the two other maxima and spans from 0.15 to 0.45 pm. The larger maximum is at- tributed to the macropores while the two smaller ones reflect contributions from the circular and lengthwise dimensions of the cylindrical mesopores. The mean pore diameters for both mesopore diameters and the macropores were calculated and found to be 0.15, 0.39, and 0.83 pm, respectively. By compar- ing the area under the curves, it is demonstrated that approxi- mately 75% of the pore volume is comprised of the macropores.

Dimensions for the mesopores and macropores may also be estimated by stereo viewing of the Pt/C replicas (Fig. 5) and by direct inspection of the pore-cast specimens (Fig. 6). The pores in the replicas were measured by averaging the longest and shortest chord across those pores which were situated parallel to the image plane. This averaging method was also used on the pore casts.

The pore size data for all the analytical methods employed are summarized in Table 111. The deviations shown for the ultramicrotomed sections were determined by a nested analy- sis of variance35 which takes into account the variance at each sampling level. It may be noticed that no standard deviation is listed for the average mesopore sizes because the errors were smaller than the number of significant figures. A complete statistical evaluation was not carried out for the pore di- ameters obtained from the replicas and pore casts and their

Table 111. Comparison of Analytical Techniques Utilized for Pore Characterization in This Study

Micropores Mesopores Macropores Analytical technique (nm) (m) (w) Nitrogen sorption 4 ? 0.2 Mercury intrusion 0.2 2 0.01 Ultramicrotomy* =4 0.15' 0.83 ? 0.05*

Pt/C replicationt 0.24 r 0.12 0.88 t 0.12 Pore castingt 0.23 ? 0.08 0.78 2 0.18

0.39*

"Determined from stereological analysis. 'Calculated by averaging the longest and short- est chord across the pores. 'Errors determined by a nested analysis of variance. Mesopores had negligible variance for both the circular and lengthwise dimensions.

August 1990

values are shown only for comparison. For nitrogen sorption and mercury intrusion, the errors reflect the standard experi- mental deviations.

Quantitative Electron Microscopic Investigation of Pore Structure 2235

IV. Discussion

TO the authors’ knowledge, this is the first time that ultra- microtomy has been employed to obtain a pore size distribu- tion curve. In addition to the usefulness of the statistically derived pore size distribution curve, the micrographs have re- vealed previously unknown information pertaining to the gel network. For example, we have been able to image the inter- stices or micropores between the colloidal particles (Fig. 3(C)) which are responsible for the majority of the surface area in the gels. Similarly, the pore volume is seen to arise primarily from the macropores which were so clearly observed in the 2-D ultramicrotomed sections as well as in the 3-D stereo rep- resentation of the Pt/C replicas, the thick microtomed sec- tions, and the pore casts. It is also found that the mesopores serve as the links between macropores, giving rise to a pore- throat network microstructure. Consistency in the results from all three TEM sample preparation methods assures us that what we are seeing is the actual microstructure of the gel and not artifacts of the preparation.

Pore volume results as obtained by stereological areal analy- sis of the 2-D images are in good agreement with those fur- nished by MIP. When the pore volume is converted to bulk density (see Table I), agreement is also found with values ob- tained by geometrical measurements as well as by X-ray mass profiling, suggesting the validity of the methods employed. The slight overestimation of the average density in the areal analysis case is probably due to the inability to quantify the micropore volume. The contribution of the micropores to the total volume is expected to be less than 9% based on BET results;’ therefore, the values obtained are quite reasonable. On the other hand, bulk density obtained from the cumula- tive pore volume curve errs in the opposite direction (see Table I and Fig. 7(A)). This is because the pores were as- sumed to be spherical and the volume of a sphere of diam- eter d will always be greater than the volume of a cylinder with height d . Since the mesopores are known to be cylindri- cal (Fig. 6), it may be concluded that the additional pore vol- ume stems from this oversimplification. Nevertheless, the estimated pore volume still falls within an acceptable stan- dard deviation.

A more striking difference between the results given by MIP and stereological analysis is provided by Fig. 7(B), in which the pore size distributions given by the two methods are compared. Detailed examination of the pore-cast images offers an explanation of this discrepancy between microscopy and porosimetry. In Fig. 6 we see that the larger macropores are interconnected by small channels and that the pores are not isolated as assumed by Washburn’s analysis. These chan- nels or throats comprise the mesopores. A nonbiased illustra- tion of the channels (mesopores) and sinks (macropores) is given in the binary image of an ultramicrotomed thin section which is presented in Fig. 8. During the intrusion process, the liquid mercury flows through the pore space via these chan- nels (marked by arrows) and subsequently fills the larger macropores as it reaches them.36 The pressure measured by MIP corresponds to the pressure required to force the mer- cury into these channels. The macropores are not “seen” by MIP because the mercury can only reach them through these channels. Experimentally one has surpassed the pressure re- quired to penetrate into the large macropores once intrusion through the mesopores begins. Thus we see no change in slope in the cumulative MIP curve at 0.83 pm (the average macropore size) and the total pore volume is erroneously as- signed to the mesopore population. Porosimetry can only de- tect the mesopores and the microstructure is characterized as being unimodal. One might consider performing an extrusion

Fig. 8. Binary image of thin section (70 nm) of unsin- tered gel. Black regions represent the pore space; gray re- gions are the gel. Arrows depict flow of mercury through “pore-throat’’ network.

experiment on a solid with this type of pore geometry in order to obtain the large void dimension. However, two additional conditions are imposed in order for mercury evac- uation from the pore space to take place. First, a pore path must be available to the mercury in order for it to retract at a specific pressure. Second, the mercury must be attached to the evacuating mercury or else it will be stranded in the pore?6 In addition, interpretation of extrusion curves is difficult be- cause there is a question as to whether the hysteresis observed between intrusion and extrusion porosimetry curves is due to contact angle differences or true pore m ~ r p h o l o g y . ~ ~ - ~ ~ Our results suggest that true morphology would be the cause of such a hysteresis.

Fairly good agreement is nevertheless found between the smallest average mesopore size as measured from the micro- graphs and that obtained from mercury porosimetry. This is because the smallest entrance will determine the force re- quired to intrude the pore space. For a cylindrically shaped pore,13 the applied force, F,,, is given by

Fa = rR2P (3) where P is the pressure across the cross section of the pore, rR2. The opposing capillary force F, is given by

14) where y is the surface tension of the mercury which acts in the direction determined by the contact angle, 0, over the perimeter 2rR, of the cylindrical pore. When the applied force equals the capillary force, mercury breakthrough can occur and infiltration of all the pore volume will take place if all the porosity is open. It is therefore not surprising that such good match between the bulk density measurements and that calculated from MIP was obtained.

The statistically derived averages of the mesopore cross- sectional diameter and height were surprisingly error-free (see Table 111). This is probably due to the large number of mesopores counted in the stereological analysis. It is interest- ing to note that the averages correspond with the peaks in the mesopore distribution in Fig. 7(B). Based on the stereology results, it may be argued that the mesopores have an aspect ratio of approximately 3 (length/circular width ratio). This is because in the ultramicrotoming process, sections were made across both the pore diameter and height as well as at oblique angles to the pore. However, because the N , calculation was strictly for spherical pores, the true ratio may be slightly dif-

F, = 2rrRy cos 0

2236 Journal of the American Ceramic Society - Kerch et al. Vol. 73, No. 8

ferent. In contrast, since the macropores are spherical, their dimensional analysis is more accurate and it closely matches what is seen in the 2-D micrographs and 3-D stereo pairs (Figs. 4 and 5) . As an additional note, the average pore sizes estimated from the biaxial viewing of the Pt/C replicas and pore casts agree quite well with the statistically derived values for the macropore case, but seem to give an average of the mesopore cross-sectional diameter and height. It is not pos- sible to comment further on the mesopore values supplied by the replicas and pore casts since a thorough quantitative study was not done on their images. These techniques were utilized primarily to furnish qualitative information about the gel microstructure.

This quantitative microscopic study of the pore size distri- bution in these silica colloidal gels suggests that the often re- ported agreement between MIP and powder dispersion samples claimed by previous investigators is misleading. We have provided experimental evidence that for a sample con- taining the “pore-throat” type geometry, MIP analysis only measures the small channels or mesopores and not the macropores or pore sinks. The fortuitous agreement between MIP and powder dispersion samples could only have come by partial destruction of the pore network during sample preparation or by masking of several layers of sample on the TEM grid.

K Conclusions

It has been shown that microscopy is a viable technique for pore characterization provided that proper sample prepara- tion is carried out. Ultramicrotomy, Pt/C replication, and pore casting together give the most thorough picture of the pore structure. Hg porosimetry, on the other hand, may only be used to describe the pore-throats (mesopores) in these gels. BET is necessary to quantify the micropores even though they may also be viewed by microscopic techniques.

While microscopic determination of pore size is neither quick nor easy, it allows the investigator to directly measure the pore size. From samples prepared via ultramicrotomy, we were able to determine a quantitative measure of the pore sizes and pore size distribution as well as information about the total pore volume.

Stereo visualization by Pt/C replicas and thick microtomed sections revealed gel connectivity and overall particle ar- rangement. At the same time, pore shape and connectivity were displayed by pore-cast specimens. Each sample prepara- tion technique provided different but essential information and together they furnished rich detail of the gel microstruc- ture not obtainable by the conventional methods of Hg porosimetry and BET sorption technique. This knowledge of the gel network may now be utilized to derive an understand- ing of the sintering mechanisms in these types of materials:’

Acknowledaments: ?ye. thank W. Q. Cao for his cooperation and suggestions. adeline Micell and Michelle Levin are acknowledged for their assistance in microscopy and sample preparation, respectively. We also thank Dr. Lee Peachey at the University of Pennsylvania for the use of the IVEM facilities there, and Dr. W. Glantschnig for the X-ray microtomography.

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