Anal. Chem. 1985, 57, 2079-2084
formaldehyde, 50-00-0;formic acid, 64-18-6; 1-pentanol, 71-41-0; 1-hexanol, 111-27-3; 1-heptanol, 111-70-6; 1-octanol, 111-87-5; 1-nonanol, 143-08-8; 2-octanol, 123-96-6; 4-methyl-2-pentano1, 108-11-2; tert-amyl alcohol, 75-85-4; benzyl alcohol, 100-51-6; 2-phenylethanol, 60-12-8; 3-phenylpropanol, 122-97-4;heptanal, 111-71-7; octanal, 124-13-0; nonanal, 124-19-6; benzaldehyde, 100-52-7; anisaldehyde, 50984-52-6; p-tolualdehyde, 104-87-0; 5-nonanone, 502-56-7;4-methyl-2-pentanone, 108-10-1;aniline, 62-53-3; 2,6-dimethylaniline, 87-62-7; 1-octanethiol, 111-88-6; tert-butyl disulfide, 110-06-5;cyclohexene, 110-83-8;naphthalene, 91-20-3; 1-methylnaphthalene, 90-12-0; 2-pentanol, 6032-29-7; phenylacetaldehyde,122-78-1;acetone, 67-64-1;butanone, 78-93-3; N,N-dimethylaniline, 121-69-7; 2-hexene, 592-43-8; l-methylcyclohexene,591-49-1; 1-nitropropane, 108-03-2;2-nitropropane, 79-46-9; tetrahydrothiophene, 110-01-0;benzene, 71-43-2;toluene, 108-88-3;indole, 120-72-9;tetrahydrofurfuryl alcohol, 97-99-4; diethyl ethylphosphonate, 78-38-6; triethyl phosphite, 122-52-1; tri-n-butyl phosphite, 102-85-2; dibutyl phosphite, 1809-19-4; triethyl phosphate, 78-40-0; butanoic acid, 107-92-6;myrcene, 123-35-3;p-cymene, 99-87-6;limonene, 138-86-3; odanol,111-87-5; nerd, 106-26-3;geranial, 141-27-5;neryl acetate, 141-12-8;geranyl acetate, 105-87-3. LITERATURE CITED (1) Vratny, Petr; Brinkman, U. A. Th.; Frei, R. W. Anal. Chem. 1985, 57, 224-229. (2) LePage, James N.; Rocha, Ernest M. Anal. Chem. 1983, 55, 1360- 1364. (3) Honda, Kazumasa; Sekino, Jun; Imal, Kazuhiro Anal. Chem. 1983, 55, 940-943. (4) Sigvardson, Kenneth, W.; Kennish, John M.; Birks, John W. Anal. Chem. 1984, 56, 1096-1102. (5) Wendel, Gregory, J.; Stedman, Donald H.; Cantrell, Christopher A.; Damrauer, Lenore Anal. Chem. 1983, 55, 937-940. (6) Boilinger, Mark J.; Sievers, Robert E.; Fahey, David W.; Fehsenfekl, Frederick C. Anal. Chem. 1983, 55, 1980-1986. (7) Yamada. Masaaki; Ishiwada, Akira; Hobo, Toshiyuki; Suzuki, Shigetaka; Araki, Shun J . Chromatogr. 1982, 238, 347-356. (8) Kiopf. Lori L.; Nieman, Timothy A. Anal. Chem. 1983, 5 5 , 1080- 1083.
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(9) Brody, Sam S.; Chaney, John E. J . Gas Chromatogr. 1968, 4 , 42-46. (10) Bruening, Wiihelm; Concha, F. J. M. J . Chromatogr. 1975, 772, 253-265. (11) Kashihira, Nobuyuki; Makino, Kazuo; Kirata, Kuwako; Watanabe, Yoshichika J. Chromatogr. 1982, 239, 617-624. (12) Flne, David H.; Rufeh, Firooz; Lieb, David; Rounbehier, David P. Anal. Chem. 1975, 4 7 , 1188-1191. (13) Fine, D. H.; Lleb, D.; Rufeh, F. J. Chromatogr. 1975, 107, 351-357. (14) Drushel, Harry V. Anal. Chem. 1977, 49, 932-939. (15) Fine, David H. U.S. Patent 4066409, January 3, 1978. (16) Fontijn, A.; Sabadell, A. J.; Ronco, R. J. Anal. Chem. 1970, 42, 575-579. (17) Mehrabzadeh. A. A.; O'Brien, R. J.; Hard, T. M. Anal. Chem. 1983, 55, 1660-1665. (18) Matthews, Ronald D.; Sawyer, Robert F.; Schefer, Robert W. Environ. Sci. Technol. 1977, 7 7 , 1092-1096. (19) Winer, Arthur M.; Peters, John W.: Smith, Jerome P.; Pitts, James N., Jr. Environ. Sci. Technol. 1974, 8 , 1118-1121. (20) Joshl, Surendra 6.; Bufalini, Joseph J. Environ. Sci. Technol. 1978, 72, 597-599. (21) Ridley, B. A.; Howlett, L. C. Rev. Scl. Instrum. 1974, 45, 742-746. (22) McFarland, M.; Kley, D.; Drummond, J. W.; SchmeRkopf, A. L.; Winkier. R. H. Geophys. Res. Left. 1979, 6 , 605-608. (23) Bollinger, Mark J. Doctoral Thesis, University of Colorado, BouMer, CO, 1982. (24) Yates, D. J. C. J. Colloid Interface Sci. 1969, 2 9 , 194-204. (25) Galvagno, S.;Parravano, G. J . Catal. 1978, 55, 178-190. (26) Grob, K.; Grob, K., Jr. HRC CC, J. High Resolut. Chromatogr. Chromatogr. Common. 1978, 1, 57-64. (27) Nyarady, Stefan A.; Sievers, Robert E. J . Am. Chem. SOC. 1985, 107, 3726-3727. (26) Hodgeson, J. A.; Beii, J. P.; Rehme, K. A.; Krost, K. J.; Stevens, R. K. Proceedings of the Joint Conference on Sensing of Envlronmental Pollutants, Amerlcan Institute of Aeronautics and Astronautics, Paper No. 71-1067, Palo Alto, CA, 1971. (29) Nyarady, Stefan A.; Sievers, Robert E., patents pending. (30) Piam, Mlsha; Hutte, Richard S.,Slevers Research, Inc., 2905 Center Green Court, Boulder, CO 80301, personal communication, February 1985.
RECEIVED for review March 1,1985. Accepted May 1,1985. We are grateful to the National Science Foundation under Grant ATM-8317948, and to Sievers Research, Inc., for support of this research.
Determination of Pore Accessibility in Silica Microparticles by Small Angle Neutron Scattering Charles J. Glinka* Center for Materials Science, National Bureau of Standards, Gaithersburg, Maryland 20899 Lane C. Sander and Stephen A. Wise Center for Analytical Chemistry, National Bureau of Standards, Gaithersburg, Maryland 20899 Michael L. Hunnicutt and Charles H. Lochmiiller Department of Chemistry, Duke University, Durham, North Carolina 27706 The size, surface area, and, In particular, the accesslblilty of pores In slllca partlcles used In liquid chromatography have been studied by small angle neutron scattering (SANS). From SANS measurements on dry slllca samples, values for the speciflc surface area are obtained and have been compared wlth BET measurements. Pore accesslbilty has been studied by saturatlng the samples wlth an H20/D,0 solution whose neutron scatterlng length denslty matches that of silica. Any residual scattering observed under this condltlon can be attrlbuted to closed (unfilled) pores. Results are reported for slllca partlcles wlth nominal pore size ranging from 5 to 33 nm. I n additlon, other appilcations of SANS related to the use of porous slllca in chromatography and catalysis are dlscussed.
The physical structure of porous silica microparticles used
in liquid chromatography is normally characterized by parameters such as the average pore size, specific surface area, and specific pore volume as determined by gas adsorption techniques (Le., BET) or mercury porosimetry, for example. For microparticles with pores ranging in size from roughly 1 to 100 nm, small angle scattering of X-rays or neutrons provides an alternate means of characterizing the porosity which can potentially yield additional structural information not obtainable by these other techniques. For example, specific structural models for the pores, including their spatial organization and size distribution, can be tested by comparison with scattering measurements. Also, since both open and closed pores contribute to the small angle scattering, pore connectivity or accessibility can be investigated as well. This can be done, in principle, by comparing surface areas from scattering measurements with surface areas derived from nitrogen adsorption, which samples only the interconnected
0003-2700/85/0357-2079$01.50/00 1985 American Chemical Society
2 0 8 ~ ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER
i sI85
porosity. A more direct method, which avoids the difficulties of intercomparing the results of very different techniques, is to compare the scattering from dry samples with that measured from samples saturated with a liquid which (1)thoroughly wets the surfaces of the accessible pores and (2) has the same scattering density (or index of refraction) as the framework material. In this way scattering from filled pores is suppressed or masked relative to the scattering from the unfilled, closed pores. For porous silica, this pore masking technique is particularly well adapted to small angle neutron scattering (SANS) where H20/D20mixtures, which readily wet the highly polar pore surfaces in silica, can be used as the maskant. The neutron scattering length density of silica ((3.5 X 1010)/cm2)is intermediate between that of H20 ((0.56 X 101°)/cm2) and D20 ((6.34 X 101°)/cm2) which enables the scattering contrast to be varied over a wide range. Contrast variation is utilized extensively in SANS studies of polymers and biological macromolecules in solution but has only rarely found application in structural studies of solids. In this article present results from our initial efforts in using SANS to characterize the porosity of silica microparticles. In these first experiments, we have focused on those structural Parameters which can be obtained from diffraction data without recourse to any specific model for the pore structure. Among these is a mean chord length, which is a measure of pore size, and the specific surface area. These results are compared with manufacturers' values and our own BET measurements. We have, in addition, used H20/D20 contrast variation to study pore accessibility in silica microparticles with nominal pore sizes ranging from 5 to 33 nm. We find in all cases that over 99% of the pores are accessible and in one case observed the complete eliminatian of all pore scattering. Beyond demonstrating a highly ieterconnected pore structure, this result suggests that SANS with contrast variation would be a powerful method for the study of adsorbed phases free from interference from scattering by pores. Some implications of these results for the study of bondedphase silica and supported catalysts are discussed. EXPERIMENTAL METHODS Three varieties of commercialporous silica were studied in this work S1,consisting of 10 fim diameter spherical particles with 33 nm average diameter pores (Vydac TP, The Separations Group, Hesperia, CA);S2, having irregularly shaped 10 pm particles with 8.5 nm average diameter pores (Partisil 10, Whatman, Clifton, NJ); and S3, with spherical 10 fim particles with 6 nm diameter pores (Zorbax60, du Pont de Nemours, Wilmington, DE). The pore diameters are nominal values quoted by the manufacturers. These silica microparticles are typical of the types used as stationary phase supports in liquid chromatography and are manufactured to have both narrow particle size and pore size distributions. An extensive pore network permeates the particles and accounts for greater than 99% of their large specific surface area. Although exact procedures for the preparation of porous silica are often proprietary, general methods have been outlined by Unger ( I ) . One type of spherical silica microparticle is produced by agglomeration of colloidal silica with an organic polymer binder. The resultant particle is heated to remove the polymer and to sinter the colloidal subunits for structural integrity. The spaces between the subunits constitute the pore structure and thus pore diameter is dependent on colloid size in the original silica sol. An alternate procedure involves spray drying the silica sol to form spherical particles. Irregularly shaped particles are formed by grinding and sizing processes. The shape of the pores is thought to vary with the synthesis procedure and with postsynthesis treatments, such as hydrothermal treatment ( I ) . Each of the silica samples were dried at 150 OC under reduced pressure for 6 h prior to analysis by SANS. Quartz cells (20 mm diameter X 1mm) were filled with the silicas and then sealed to prevent water adsorption. Bulk densities were calculated from the silica mass and cell volumes, and these values were used to
obtain the mass of silica present in the neutron beam. For the SANS measurementson wetted samples, two methods of preparation were used which gave identical scattering results. In the fist case, small amounts of a water solution (preparedfrom measured volumes of D20 [99.8% D, from Aldrich Chemical, Milwaukee, WI] and HzO) were added directly to a quartz cell containing ultrasonically packed dry silica until an overlayer of liquid was present in the cell. Alternatively, silica and water were mixed externally to form a slurry which was then loaded into a sample cell in stages. After each partial loading, the cell was sonicated and any excess liquid was decanted. This process was repeated until a uniform filling was obtained. Following the measurements, the wetted silica was flushed into a beaker, slowly dried, and then weighed to determine the mass of silica actually present in each cell. Surface area measurementswere made on each of the samples by nitrogen adsorption ( I ) for comparison to the values obtained by SANS. Measurements were made at three or more helium/ nitrogen compositions within the range 0.1 I PIP, I 0.35 using a QuantasorbBET surface analyzer (Quantachrome,Inc., Syossett, NY). Prefers to the partial pressure of the adsorbate (nitrogen) within the flow mixture and Po,the saturated vapor pressure of the pure adsorbate. In all cases the linear regression fit parameters were better than 0.998. The small angle scattering measurements were carried out on the 8 m long SANS spectrometer (2)at the 10 MW NBS research reactor. The angular divergence of the incident neutron beam was 5 mrad, defined by circular cadmium irises of 27 and 12 mm diameter located at the entrance and exit, respectively,of a 4.5-m evacuated flight path which precedes the sample stage. The scattered neutrons were counted with a two-dimensional (65 X 65 cm2) position-sensitive proportional counter with a spatial resolution of 1cm, located in vacuum 3.5 m from the sample. The incident beam was in most cases offset from the center of the detector in order to increase the angular range covered in a single measurement. Incident neutron wavelengths ranging from 0.48 to 0.85 nm were used depending on the pore size of the sample; shorter wavelengths were used for small pore samples, longer wavelengths for the larger pore materials, in order to best match the angular extent of the scattering to the angular range subtended by the detector. Each data set was corrected for background, measured with the incident beam blocked at the sample position, and a small contribution from the unscattered incident beam itself, measured with an empty cell at the sample position and takingaccount of attenuation by the sample. The transmission (or attenuation) of each sample was determined by removing a beamstop from the face of the detector to measure directly the intensity of the incident beam, with and without a sample in place, having first attenuated the beam with a thin cadmium foil to avoid overloading the detector. The transmission of each dry silica sample studied was 95% or greater and thus multiple scattering effects were deemed to be negligible. After correcting for background, the observed scattering was in all cases axially symmetric about the beam direction. The data were, therefore, circularly averaged about the beam center to obtain the net scattering as a function of the magnitude of the scattering vector Q (1)
where X is the neutron wavelength and OB is half the scattering angle. For each choice of incident wavelength and instrument geometry used, the isotropic, incoherent scattering from a 3.2 mm thick flat plate of pure polycrystalline vanadium was also measured. The uniform level of this scattering, after being corrected for a small ( 10%) multiple scattering contribution (3),was used to put the silica data on an absolute scale of differential cross section per unit volume. N
SANS THEORY In small angle diffraction, the measured scattered intensity is proportional to a cross section per unit volume, dZ/dQ, which is related to a scattering density, p ( ? ) , through the general expression
ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER 1985
where the integration is over the entire specimen volume, V, ilIuminated by the incident radiation. For neutron scattering, the density p ( i ) a t position 2 is given by nb, where 6 is the coherent nuclear scattering amplitude ( 4 ) ,averaged over atomic dimensions, and n ( i )is the number of nuclei per unit volume a t 3. Equation 2 implies that the scattering observed at Q arises from structural features in the density p ( 7 ) with dimensions on the order of 2?r/Q. For the experimental conditions described in the preceding section, scattering over the Q range from 0.1 to 2.5 nm-l can be measured and, therefore, structure in p ( 2 ) which occurs over distances from roughly 2 to 60 nm can be studied. In order to interpret scattering data, some assumptions regarding p(i) must be made. For the expressions given below, the only underlying assumption is that the scattering volume consists of only two types of regions, or phases, which have a well-defined interface. Thus we treat the silica microparticles as consisting of uniform solid regions of silica with a constant scattering density p s and pores with a scattering density pp (p, = 0 for empty pores). The development of eq 2 for such a two-phase model can be found in many texts (5, 6). Here we simply summarize those results which wlll be used in the next section. At larger scattering angles in the small angle region, the intensity is expected to obey Porod’s law (7)
scattering experiment. If, for example, there are regions in the sample where the density is constant over distances of more than about 100 nm, the scattering from such regions will occur at immeasurably small angles and will not, therefore, be included in estimating the scattering invariant. With values for the surface area and volume fractions obtained from eq 3 and 4, a characteristic size, called the mean chord length, can be derived from ( 5 ) -
1, =
4v 4v ps 1, = 7 4 ,
where 4sand $p are the volume fractions of the solid and pore phases, respectively, and 4s+ 4p = 1. Equation 4 is called the scattering invariant and can be estimated from scattering data provided the measurements extend over a sufficiently wide Q range that accurate extrapolations of the intensity for both Q 0 and Q m can be made. If the scattering extends into the @ region, then Porod’s law can be used for the large Q extrapolation. The extrapolation to Q = 0 is, in principle, less critical because the Q2 factor in the integrand gives this portion of the scattering curve diminishing weight. For a porous material, the value for &, the volume fraction of the solid phase, obtained from 4 can be compared with the ratio of the bulk mass density of the specimen, db, to the skeletal, or theoretical, density of the material d (& = db/d). The two values should agree provided that no portion of the sample has structure on a scale which is outside that probed by the
- -
(5)
where I, for example, is the mean of all straight line segments in all directions which span the pores contained in the volume V. If the pores are roughly spherical in shape and nearly equal in size, then Ip will be approximately equal to 2 D p / 3 where D , is the pore diameter. Equations 3 and 4, and all other expressions for the cross section derived from a two-phase model, are proportional to (pa - P , ) ~ which is termed the contrast factor. This factor can be calculated if the compositions of the two phases are known and, for a porous material, can be varied by filling the pores with a fluid to change their scattering density. For pp = pa, scattering from filled pores is eliminated and any remaining scattering can be analyzed in terms of the structural parameters of the closed, unfilled pores. The background corrected scattered intensity I(Q) (neutrons per second) that is actually measured in an experiment is related to the cross section, dZ/dO, which characterizes the material, by
I(&) where S is the total interfacial surface area within the illuminated volume V. The scattered intensity will exhibit the &4 dependenceof Porod’s law provided the product Qr is large for all characteristic dimensions r of either phase. In the development of eq 3, density fluctuations due to atomic scale structure are not considered. Thus the product 84 dZ/dfl will not remain constant but will eventually increase when Q becomes so large that these fluctuations begin to be probed. For each material then there will be a range of Q over which the scattering is proportional to the surface area provided that the smallest dimensions of the scattering structure are appreciably larger than the distance of atomic density fluctuations. When this condition is met, the surface area S in eq 3 is the most meaningful parameter that can be determined from scattering data from an arbitrary structure. A second general result which follows from the assumption of a two-phase model relates the integrated scattered intensity to the fractions of the volume V occupied by each phase
2081
d2 dfl
ctT-(Q)
+ I,
(6)
assuming multiple scattering is negligible. In eq 6, t is the sample thickness, T its transmission, and c comprises a number of purely instrumental constants such as the flux of the incident beam and its cross-sectional area. The additive term, I,, represents a constant level due to isotropic incoherent scattering (4). For pure silica, I , is negligibly small while light water and vanadium, for example, scatter almost entirely incoherently. As mentioned in the preceding section, we measured the incoherent scattering from vanadium in order to put our silica data on an absolute scale. Dividing eq 6 by a similar expression for the intensity measured for vanadium, I,, all instrumental factors cancel and the cross section of interest is given by
(7) where dzl,/dfl = 0.0277 cm-l is the incoherent cross section for vanadium. To attempt to extract structural parameters from scattering data beyond those given in the above general expressions requires that a structural model be proposed. Often the density p(P) is assumed to be organized into discrete scattering centers, or particles, whose average size (or radius of gyration), shape, size distribution, and number density then enter as parameters to be determined by fitting part or all of the measured scattering curve. For porous silica, however, an interpretation in terms of discrete particles is probably not valid due to the extensive linking together of the elementary globules which make up the micrometer-sizedaggregates. An alternate model for a porous solid, proposed by Debye et al. (8),treats the pores as randomly distributed regions of arbitrary size and shape. The cross section derived from this model has a simple analytic form and does, we find, provide a good fit to some of our SANS data. In most cases, however, the scattering curves we measure have more structure than can be accounted for by the Debye model. Thus, in the
ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER 1985
2082
Table I. Summary of SANS and BET Results for Three Types of Porous Silica Microparticles with Nominal Pore Sizes of 33 (Sl), 8.5 (S2),and 6 (S3)nm silica (pore size) S1 (33 nm) S2 (8.5 nm) S3 (6 nm)
S',(BET), m2/g
S,(SANS), m2/g
= AV,/V
4 8
l', = 4V@,/S, nm
= db/d
60 i lob 70-9P 0.064 0.18 30 450 f 60 430 f 5* 0.11 0.15 3.7 375 f 50 430 f 5 0.15 0.21 4.6 aRange of values reflect differences between lots. bThe error bars for the SANS results include the uncertainties in fitting the data (5%) and in determining the absolute scattered intensity (10%). The BET error bars reflect only the reproducibility of the measurements.
- 1;jI:
1 o5
I
c
-5
s1 I -dry -in 39.5% H 2 0 / 6 0 . 5 %D 2 0
104 4-
a
0
u
lo3 I
c L 0
2
102
10
I
I
-
' k' I
r
0.2
1
0.5
I
I
I
1.0
1.5
2.0
52
.
1
A___
I\
1.0 2.0 Q (nrn-l) Figure 1. Small angle neutron scattering from dry samples of porous silica microparticles with nominal pore sizes of 33 (Sl),8.5 (S2),and 6 (S3)nm. The straight lines are Porod law fRs to the larger Q data 0.5 Scattering Vector
0.1
0 1000
I
I
0
0.5
1.0
1.5
2.0
0
0.5
1.0
1.5
2.0
in each case.
present study we have emphasized those results that are not predicated on an explicit structural model.
RESULTS The small angle scattering from dry samples of the three types of silica microparticles in which pore accessibility has been studied is shown in Figure 1. The data are plotted on a double logarithmic scale with each curve shifted vertically by an arbitrary amount for clarity. Consistent with a larger pore size, the width of the scattering from sample S1 (i-e.,the half maximum width in Q) is considerably less than that for the two smaller pore samples. At larger Qs, the scattering from all three samples exhibits the &4 dependence of Porod's law (eq 3), as indicated by the straight lines in Figure 1which have slopes of -4. The criterion for Porod behavior, namely, that Qr >> 1 for all characteristic dimensions r, suggests that the scattering from a larger pore material would begin to exhibit a q4dependence at smaller Q values than that from a small pore material. Such an inverse correlation with pore size can be seen in Figure 1 where the onset of Porod behavior occurs a t Q 0.5 nm-' for S1, and near Q = 1.2 nm-' for S2 and S3. The Porod region appears most restricted in the case of 53 where a straight line with a slope of -4 provides a good least-squares fit to the data only over the limited Q range from 1.5 to 1.85 nm-l. The departure from a Porod law seen in the last few points for S3, and for 52, may be due to incoherent scattering from hydroxyl groups on the pore surfaces or may mark the onset of scattering from near atomic scale density fluctuations. The fitted straight lines in Figure 1were used to extrapolate the measured scattering to Q = ~0 in order to calculate the scattering invariant (eq 4)and hence the silica volume fractions 9,. The extrapolations used for Q 0 are shown in Figure 2, where the data are plotted on a linear Q scale. From the data in Figure 1, the pore surface area and the volume fractions of each phase have been obtained from the expressions in the theory section. These results, along with
-
-
Scattering Vector Q (nm-' I
Figure 2. Effectiveness of pore masking In the three types of silicas studied is shown by comparing, on an absolute scale, the scattering from dry samples with that from samples saturated in an H20/D20 mixture whose Scattering density nearly matches that of silica. The dashed curves are the extrapolations to Q = 0 used in estimating the scattering invariant (eq 4). values for the surface area and volume fractions obtained from BET and bulk density measurements, respectively, are summarized in Table I. s, is the specific surface area, $s and $; are the silica volume fractions determined by SANS and bulk density measurements, respectively, and 1; is the mean chord length, which characterizes the skeletal framework of each type of microparticle. The SANS and BET values for the specific surface areas of the smaller pore samples, S2 and S3,are in reasonable agreement, considering the estimated uncertainties. The apparent percentage difference is greater for the larger pore sample, S1;however, in this case the measurements were not made on the same lot of material and subsequent BET data showed rather large differences between lots. The results in Table I are typical of measurements we have made on more than 20 different varieties of commercial porous silica (which will be reported separately (9))in that S, values obtained from SANS are, on the average, lower (but usually within 20%) than those given by BET, In a few cases, larger differences have been found with no apparent correlation observed between the magnitude of the discrepancy and the pore size of the material. This trend is similar to results found in some small
ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER 1985
angle X-ray scattering studies of porous silicas (10-13). Even more markedly different are the values in Table I for the volume fraction of the silica phase in each sample, 48and 4's. The values for are simply the ratios of the apparent or bulk density of each sample divided by the skeletal density which was taken to be d = 2.2 g/cm3 for amorphous silica (I). The much lower values for q5s obtained from the scattering invariant (eq 4) imply that the extrapolated scattering curves shown in Figures 1 and 2 severely underestimate the total scattering from the samples. This is rather surprising since the extrapolated regions in Figures 1 and 2 contribute no more than 20% to the integral in eq 4 and thus would have to be in error by more than 100% to account for the discrepancy with the bulk density measurements. The most likely explanation for such large deviations is, as noted following eq 4, that there are homogeneous regions of the silica phase which have dimensions greater than those which can be detected in our scattering measurements. It should be stressed, however, that even if this is the case, a surface area obtained from SANS should be the total area of all the silica regions because in the derivation of Porod's law only the interface between phases enters, independent of the size of the regions on either side of the interface. In the last column of Table I are values for the mean chord length of the silica phase in each sample, it, computed from the ratio of the volume fraction 4; (derived from the bulk density) to the surface area determined by SANS. The corresponding length or mean size of the pores, i,, cannot, in the present case, be estimated from the complementary volume fraction 4, = 1- 4sobtained either from scattering or density measurements alone. This is because (1 - 4s)includes not only the volume of the pores but also the space between the micrometer-sized particles and thus depends on how the particles pack in the sample cells. To determine a pore size from the expression for 1, (eq 5 ) would require a separate measurement, by mercury pycnometry for example, of the internal pore volume fraction of the particles. Nonetheless, the silica chord lengths in Table I do demonstrate a high degree of correlation between nominal pore size and the spacing between the pores in these materials. For the measurements of pore accessibility, samples of each type of silica were saturated, as described in the Experimental Section, in a solution of (HzO),(D20)l-x( x = volume fraction) with x near 0.41. At this concentration, the scattering length density (sld) of the solution is equal to that calculated for amorphous silica, ps = n6 = 3.5 x 1O1O cm-z (for an assumed density d = 2.2 g/cm3 and 6 = 1.58 X cm for a SiOz molecule), and thus filled pores should produce no small angle scattering. This sld matching condition was checked experimentally by preparing a series of samples of silica S1 saturated in solutions whose HzO concentration ranged from x = 0 (pure DzO) to 0.65 (corresponding to sld's from 6.34 X 1O1O cm-2 to 1.86 X 1O1O cm-2). The scattering from those samples with x appreciablydifferent from 0.4 was observed to have the same shape as the scattering from the dry S1 sample and to scale with the contrast factor, (pa - P,)~., which appears in eq 3 and 4, for example. This is illustrated in Figure 3 where the square root of the net intensity above the incoherent scattering from the solution is plotted vs. the percentage of HzO in the solutions. The plotted intensities are taken from the low Q end of the scattering curves, which is most sensitive to changes in contrast, and have been divided by the bulk density and transmission to correct for incidental differences among the samples. Plotted in this way the data point to a sld matching concentration of 40 f 1% HzO in DzO, close to the calculated value. The nearly linear dependence on the sld of the solution, or HzO fraction, is what would be expected for a two-phase model which implies (1) that virtually all of the pores are
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Percent H,O in pP Figure 3. Dependence of the small Q scattering from samples of silica S1, saturated in H 2 0 / D 2 0 mixtures, on the percentage of H 2 0 in the solution.
accessible and filled uniformly by the solution and (2) that the structure of the pores is unchanged. This latter conclusion was checked directly by measurements on two dry samples (of a smaller pore variety) of silica S1, one of which had been submerged in HzO (with a slightly acidic pH) for 2 weeks and subsequently k-edried. The scattering curves for these two samples were nearly identical in shape and the surface areas obtained from the Porod regions of the curves agreed within the combined experimental uncertainty of the two measurements (Le., within E % ) , thus demonstrating that the pore structure was unaltered. Although the data in Figure 3 point to a HzO concentration of about 40% as the sld matching point, the two measurements made near this concentration were not completely free of all small angle scattering. This can be seen in Figure 2 where SANS patterns for all three types of silica, saturated in HzO/DzO mixtures near the sld matching point, are shown along with the curves from the corresponding dry samples. For silicas S1 and 52, the intensity of the &-dependent scattering which persists at the smaller Q values is roughly 3 orders of magnitude lower than that from the dry samples. Furthermore, this residual scattering appears to be quite different in shape and becomes Q independent (due to the isotropic incoherent scattering from the HzO in the solution) well before reaching the Porod law regions found for the dry samples (see Figure 1). Thus it seems likely that essentially all of the small pores are filled with the solution and that the residual scattering is due to some larger scale inhomogeneities, perhaps within the silica framework itself. For silica S3, however, there is no residual Q-dependent scattering, only the flat incoherent scattering from the solution. This demonstrates unequivocallythat for this rather small pore material all of the pores are permeated by the sld matching solution.
DISCUSSION Our SANS measurements on dry porous silica demonstrate, consistent with previous X-ray scattering studies (10-13),that these materials have, in most cases, reasonably well defined Porod law regions from which the specific surface area of the pores, S,, can be obtained without assuming any structural model for the pores. For a homogeneously porous material, other model independent parameters, such as the specific pore volume and the mean pore chord length, 1,' can also be obtained directly from scattering data. For porous microparticles, however, scattering data must be supplemented by some independent measurement of the void volume between the particles. Our measurements on porous silica saturated in HzO/DzO mixtures demonstrate that virutally all of the pores in the
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 11, SEPTEMBER 1985
materials studied are interconnected and accessible. An additional result which follows from our contrast variation measurements is that these microparticles are nearly ideal realizations of a two phase model with sharp boundaries between the phases. Furthermore, the scattering density of the pore phase can be continuously varied over a wide range to enhance or diminish contrast with the silica framework, without altering the structure of the pores. For microparticles with a sufficiently uniform silica framework, all Q-dependent scattering is eliminated when the scattering density of the pores matches that of the matrix. This fact suggests that SANS with pore masking would be a powerful technique for studying the structure of adsorbed phases on these and other high surface area materials. One application would be in the study of bonded phase silica of the type used in reversed-phase liquid chromatography. Here SANS might provide information on the thickness and extent of coverage of the chemisorbed polymeric layers which would give new insight into the degree of pore mouth blocking or other alterations in the pore structure of chemically modified silica. That such information can be obtained with SANS remains to be demonstrated, however. For contrast variation measurements on such systems, mixtures of deuterated and hydrogenated nonpolar solvents would be required to promote wetting of the nonpolar surface of the bonded phase. Another potentially fruitful application of SANS with pore masking is in the study of metal catalysts (e.g., platinum or palladium) supported on porous silica. The use of pore masking to reduce the three phases in such materials (support, metal, and pores) to two has been tried in several small angle X-ray scattering studies (14,15)where high electron density liquids such as CHJz have been used to fill the pores of alumina or silica supports. However, a high degree of pore masking has not usually been attained in these studies possibly because of wetting problems or because an appreciable fraction of the pores were inaccessible. As a result it has been necessary to measure separately and subtract off the significant scattering from the masked, metal-free support. Furthermore, both the intensity and shape of this scattering have been found to depend on the concentration of pore maskant and thus considerable care must be taken to optimize and control the amount of maskant in each sample. Partly because of these experimental difficulties, some recent small angle X-ray scattering studies of supported catalysts have explored alternative approaches to pore masking (16). In the case of SANS measurements on the type of porous silicas studied
here, it should be possible to attribute all of the &-dependent scattering from a properly masked sample, at least in the Porod region, to the metal catalyst. The only difficulty would be in accurately measuring the necessarily weak scattering from the small volume fraction of catalyst above the incoherent scattering from the hydrogen in the masking solution. This should not be a major problem, however, provided the incoherent scattering can be isolated by extending the measurements to sufficiently large Q.
ACKNOWLEDGMENT We wish to acknowledge a number of helpful discussions and comments by Jon S. Gethner. Registry No. Silica, 7631-86-9.
LITERATURE CITED (1) Unger, K. K. ”Porous Sillca”; Elsevler: Amsterdam, 1979; p 5. (2) Gllnka, C. J., AIP Conf. Proc. No. 89, Neutron Scattering-1981; Faber, J., Ed.; 1982; pp 395-397. (3) Brockhouse, B. N.; Corliss, L. M.;Hastlng, J. M. Phys. Rev. 1955, 98, 1721-1727. (4) Bacon, G. E. “Neutron Dlffractlon”, 3rd ed.; Oxford Press: London, 1975. (5) Glatter, 0.; Kratky, 0. ”Small Angle X-ray Scattering”; Academic Press: London, 1982; Chapter 2. (6) Kostorz, G. “Treatise on Materials Science”; Academlc Press: London, 1979; Chapter 5, p 15. (7) Porod, G. Ko//oU-2. 1951, 124, 83. (8) Debye, P.; Anderson, H. R.; Brumberger, H. J . Appl. Phys. 1957, 28. 267-683. (9) Sander, L.; Glinka, C. J., to be submitted for publicatlon. ( I O ) Longman, G. W.; Wlgnall, G. D.;Hemmlng, M.;Dawkins, J. V. Co//o!d Polym. Sci. 1974, 252, 298-305. (1 1) Larson, B. C.; Bale, H. D. “Small-Angle X-ray Scattering”; Brumberger, H., Ed.; Gordon and Breach New York, 1967; pp 467-476. (12) RenOUDreZ, A.; Dalmal, G.; Weioel, D.; Imellk, B. J . Chim. Phys. 1987. ‘934-941. (13) Sashital. S. R.; Cohen, J. B.; Burwell, R. L.; Butt, J. B. J . Catal. 1977, 5 - -0,. 479-493 . . - .- -. (14) Whyte, T. E.; Klrklln, P. W.; Gould, R. W.; Helnemann, H. J . Catal. 1972, 25, 407-415. (15) Baston, A. H.; Potton, J. A.; Twlgg, M. V.; Wrlght, C. J. J . Caul. 1981, 71. 426-429. (16) Brurnberger, H. Trans. Am. Crystallop. Assoc. 1989, 19, 1-16.
RECEIVED for review January 28,1985. Accepted May 20,1985. Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose. Partial support (to C.H.L.) for this work was provided by NSF Grant CHE-8119600.
