Langmuir 1988,4,977-982
977
Surface Roughness in Vapor-Phase Aggregates via Adsorption and Scattering Techniques Steven B. Ross and Douglas M. Smith* UNM Powders and Granular Materials Laboratory, Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico 87131
Alan J. Hurd and Dale W. Schaefer Division 1152, Sandia National Laboratories, Albuquerque, New Mexico 87185 Received December 1, 1987. I n Final Form: February 12, 1988 Fumed silica was studied by gas adsorption and small-angle scattering techniques to test whether the materials exhibit rough surfaces that would account for measurable differences in specific surface area. While the shapes of nitrogen and argon adsorption isotherms were identical for different grades of fumed silica, in disagreement with BET adsorption models of fractal surfaces, our other measurements support the notion that the roughness exists and differs from grade to grade. We attribute the failing of the BET fractal models to lateral interactions in the adsorbed layers.
Introduction In a previous study, Hurd, Schaefer, and Martin1 studied the fractal nature of surface roughness associated with vapor-phase aggregates. Three different fumed silica samples (CAB-0-SIL) representing a range of specific surface area between 200 and 390 m2/g were studied with a combination of light scattering and small-angle neutron scattering (SANS). The study confirmed that the mass structure of CAB-0-SIL is that of a fractal aggregate (i.e., primary particles in chain aggregates with low coordination number) similar to those found in simulations of diffusion-limited aggregation. However, contrary to the standard interpretation in which the primary particles are assumed to be smooth spheres, scattering results indicated a significant degree of surface roughness. The degree of surface roughness increased with increasing surface area with the surface fractal dimension D ranging from 2.0 for the 200 m2/g sample to 2.5 for the 390 m2/g sample. These scattering results indicate that the difference in surface areas for the various CAB-0-SIL grades involves surface roughness variation and not entirely primary particle size. In this work, we have applied a number of different techniques to analyze surface roughness of vapor-phase aggregates with a range of surface areas. Given the scattering results discussed above, CAB-0-SIL is a good model system to examine the consequences of roughness on adsorption measurements. Using several different adsorption methods as well as small-angle X-ray (SAXS)and neutron scattering (SANS), we have explored the nature of the surface in these vapor-phase aggregates as well as provided a comparative study of surface fractal dimensions obtained from the different methods. Although we find qualitative agreement between some of our techniques, we find that adsorption isotherms are insensitive to roughness.
Background Numerous studies of the surface roughness associated with adsorbents and porous materials have been conducted by using adsorption techniques. The fundamental approach is t~ use a family of probe adsorbates with different molecular cross sections, 6,and measure the number of moles in a monolayer, N,. The basic equation relating N, and u for a fractal surface is given by2 log N, = -D/2 log u + constant (1) (1) Hurd, A. J.; Schaefer, D. W.; Martin, J. E. Phys. Reu. A 1987,35, 2361.
0743-7463/88/2404-0977$01.50/0
From eq 1,a log-log plot of N, versus u will yield a straight line, and D is determined from the slope. The major uncertainty with this approach is in the assumed cross sectional area for the probe molecules. Even when a family of similar probe molecules is utilized, the value of u will depend upon the adsorbate/adsorbent chemical interaction and the physical nature (Le., roughness) of the surface. Instead of varying the size of the probe molecule, one may vary the size of the substrate. For this case, the measured surface area, 8,is related to the substrate diameter, d, by: log 8 = (D - 3) log d
+ constant
(2)
This approach has been applied by Avnir, Farin, and Pfeifer3 to study the surface roughness of fumed silica. AEROSIL (DeGussa Corp.) fumed silica with primary particle diameters ranging between 7 and 40 nm (from electron microscopy) was studied by using nitrogen adsorption. Application of eq 2 indicated a fractal dimension of ~ 2 . 0(i.e., that the primary particles are smooth spheres). This result contradicts the scattering findings of Hurd and co-workers' for lengths below 50 A even though there is general agreement that AEROSIL and CAB-0-SIL powders should be very similar. This approach of changing the substrate size suffers from several disadvantages, including the implicit assumption that the nature of the surface is not changing with the different samples and the fact that a range of substrate sizes is rarely available. Comparisons of the fractal dimension determined from adsorption and scattering methods for the same sample have been scarce in the literature. Hall4 studied the theoretical implications of scattering/adsorption analysis for microporous materials, but no experiments were conducted. Rojanski and co-workers5used a range of methods including adsorption (methods using eq 1and 2), electronic energy-transfer reactions, and SAXS to study the surface roughness of a single mesoporous silica gel sample. All four approaches agreed within the limits of experimental error and indicated a fractal dimension of =3. Finally, Drake et a1.6 studied silica gels with SAXS and adsorption (2) Pfeifer, P.; Avnir, D. J. Chem. Phys. 1983, 79,3558. (3) Avnir, D.; Farin, D.; Pfeifer, P. J. Chem. Phys. 1983, 79,3566. (4) Hall, P. J. Chem. Phys. Lett. 1986, 124,467. (5) Rojanski, D.; Huppert, D.; Bale, H. D.; Dacai, X.; Schmidt, P. W.; Farin, D.; Seri-Levy, A.; Avnir, D. Phys. Rev. Lett. 1986,56, 2505. (6) Drake, J. M.; Levitz, P.; Sinha, S. In Better Ceramics Through Chemistry Ik Brinker, C. J., Clark, D. E., Ulrich, D. R., Eds.; Materials Research Society Symposia Proceedings, 1986; Vol. 73, p 305.
0 1988 American Chemical Society
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Ross et al.
techniques and concluded that the structure is hierarchical with small primary particles (-14-47 A) associated together into 1000-A clusters. The evidence for fractal surfaces was inconclusive. Fractal Isotherms. Several investigators have proposed formulations of the BET equation for fractal surf a c e ~ . ~ ,In~ this J ~ case, the quantity adsorbed a t a given relative pressure is a function of the monolayer capacity, N,, the BET C constant, and D. Fripiat, Gatineau, and Van Damme7 have used a semiempirical approach to arrive at a general equation describing multilayer formation. The normalized uptake for adsorption restricted to a maximum of n layers is given by n
N/N, = C
2
i=l
n
n
xj/(l ;=1
above 77 K. After equilibration, the sample is cooled to 77 K and the surface area of the solid and solidified preadsorbed vapor is determined via nitrogen adsorption. The process is then repeated for a range of preadsorbate relative pressures. In principle, from the variation in the reduced surface area, Z/Z,, where Zo is the surface area measured with no adsorbate present, as a function of the preadsorbate relative pressure, information concerning surface roughness should be available. This type of measurement has been demonstrated for coordination number determination in particle packings by Smith and Olague12 but has not been previously applied to surface roughness analysis.
+ C r2= l x i )
(3)
where x is the relative pressure, PIP,. Equation 3 is derived by using the empirical scaling law for the ratio of moles in the ith adsorption layer (nJto moles in the first layer (nl): ni/nl = i-(p2). For D equal to 2 and taking the limit as n goes to a,eq 3 reduces to the conventional BET isotherm.s For a BET C value of 100 (i.e., a reasonable value for nitrogen adsorption on silica,’l eq 3 predicts a significant dependence of the normalized adsorption on D for a wide range of relative pressure. Even for PIPo of 0.3, a significant variation in N / N m is predicted. Pfeifer and co-workers9J0 have developed another approximation for the fractal BET isotherm using a variation of the BET equation for a restricted number of adsorption layers and a scaling law for the distribution of surface roughness. Their result is N _ Nrn
For calculations of N / N m versus PIPo for a BET C value of 100, eq 3 and 4 agree to within 10%. Both of these equations predict a decrease in the normalized uptake for increasing D a t a fixed C value and relative pressure. In principle, one could obtain adsorption data over a wide relative pressure range, find N,,, and C from the low-pressure data, and then fit eq 3 or 4 to the highpressure data to extract D. T o date, it does not appear that this technique has been attempted with adsorption data for materials for which D is known by other methods. This method has the significant advantage, as compared to using a range of adsorbates, that only a single adsorbate is required, which eliminates the uncertainty in D arising from the question of the correct molecular cross sectional area. Film-Surface Area Measurements. In addition to measuring the shape of the isotherms, we have also applied the so-called film-surface area measurement technique. It does not appear that this method for surface roughness determination has been previously suggested. In this approach, the sample surface area is determined from nitrogen adsorption measurements and BET analysis. Then, a suitable preadsorbate is equilibrated with the sample at a fixed relative pressure and a fixed temperature much (7) Fripiat, J. J.; Gatineau, L.; Van Damme, H.Langmuir 1986,2, 562. (8) Brunauer, S.; Emmett, P. H.; Teller, E. J.Am. Chem. SOC.1938, 60, 309. (9) Cole, M. W.; Holter, N. S.; Pfeifer, P. Phys. Reu. E: Condens. Matter 1986, 33, 8806. (10)Pfeifer, P., Preprint, IUPAC Symposium on Characterization of Porous Solids, Bad Soden, FRG,April, 1987. (11) Lowell, S.; Shields, J. E. Powder Surface Area and Porosity; Chapman and Hall: London, 1984.
Experimental Section Four grades of CAB-0-SIL fumed silica (L90D, MS7, HS5, EH5) with nominal surface areas in the range 90-380 m2/g were obtained from the Cabot Corp. Two of these grades (HS5 and EH5) were used by Hurd and co-workers in their previous scattering study of these materials.’ In addition, MS7 has the same nominal properties as the M5 that they used. Nitrogen and argon adsorption and desorption experiments at 77 K were conducted by using a Quantachrome Autosorb-1 volumetric adsorption analyzer. Before analysis, samples ( ~ 0 . g) 1 were outgassed at 373 K and 50 wm Hg for approximately 1 h. Adsorption isotherms were obtained over the relative pressure range 0.02-0.80 at increments of 0.02. Surface areas were determined from the nitrogen sorption isotherm by using BET analysis of data in the relative pressure range 0.05-0.38 and a nitrogen cross sectional area, u, of 0.162 nm2. Film surface areas were obtained by using a volumetric adsorption apparatus fabricated onto an Autosorb-1 nitrogen sorption analyzer. In this way, the quantity of the vapor preadsorbed on the sample was obtained as in a simple volumetric adsorption experiment and then the surface area of the solid and preadsorbed vapor was determined from nitrogen adsorption measuremenh. Both n-pentane (Aldrich, reagent grade) and n-heptane (J.T.Baker, reagent grade) at =293 K were used. The sample was first outgassed at 373 K and 50 wm Hg for 1h, and then the desired vapor was expanded into the sample chamber; equilibrium was attained after a few minutes. The sample was then cooled to 77 K, and a nitrogen adsorption surface area determination was performed in the usual manner (three-point BET). The sample was then outgassed, and the process was repeated for a different relative pressure. In addition to the reduction in nitrogen surface area as a function of vapor loading, the surface area was calculated from the adsorption measurements for n-pentane and n-heptane by using the BET equation and the appropriate molecular cross sectional area. Small-angle scattering was performed on all the samples with X-rays (SAXS) and with neutrons (SANS);in addition, the data in ref 1 have been used. SAXS was done at Sandia National Laboratories with a Kratky slit-collimatedX-ray system. The powders were run at two widely different packing densities to check for multiple scattering and interparticle interference: loosely packed but filled capillaries and capillaries whose walls had been lightly dusted with powder. No significant difference was found between these two sample preparations. The data were analyzed both in slit-smeared form and after desmearing by standard methods. SANS was performed on M5 and EH5 at the intense pulsed neutron source (IPNS) at Argonne National Laboratory and on LWD and MS-7 at LANSCE at Los Alamos National Laboratory. Good agreement was found with the Oak Ridge data in ref 1. For the HS5 we have used the data in ref 1 here, and for the L90D we have SANS data from LANSCE. In all cases, the scattering curves were fit to the form I(q)
-
Iq-”
(5)
where q is the scattering wave vector (q = [ 4 r / X ] sin (8/2), with X the wavelength and 0 the scattering angle). The scattering (12) Smith, D. M.; Olague, N. E. J.Phys. Chem. 1987,91, 4066.
Langmuir, Vol. 4, No. 4, 1988 979
Surface Roughness in Vapor-Phase Aggregates
-1
20 0
L90D
us7 HS5
I - 0
A E115 0.2
0.6
0.4
0.1
PPO
Figure 1. Nitrogen adsorption isotherms. Table I. Surface Areas (mZ/g)Determined from Nitrogen, n -Pentane. and n -HeDtane sample nitrogen n-pentane n-heptane Cabot corp. ~~
L90D MS7 HS5 EH5
109 f 3 200 f 6 350 f 10 385 f 12
98 f 15 159 f 24 298 f 45 297 f 45
89 f 14 142 f 21 258 f 39 229 f 34
90 f 15 200 f 25 325 f 25 380 f 30
exponent x is expected to be 6 - D,13where D is the surface fractal dimension. In the IPNS SANS data, an additional incoherent background was included in the fitting. In general, incoherent background corrections are most severe for the lower surface area materials and can lead to exponents x that are systematicallytoo small. Since we find x = 4 for the low surface area grade M-5, we are confident our results are not compromised.
Results and Discussion Nitrogen adsorption isotherms at 77 K are presented for all four powders in Figure 1. All isotherms are of type I1 according to the BDDT classification,14indicative of a nonporous powder or a porous solid without micropores. For one sample, EH5, the desorption branch was also measured, but no hysteresis was noted. Measurements were not conducted a t relative pressures greater than 0.8 in order to minimize condensation effects at the particleparticle contacts. I t was felt that negligible porosity/ surface roughness would exist with a feature size greater than the =5 nm associated with this upper relative pressure limit. Surface areas have been calculated from these isotherms and are reported in Table I. For all samples, the BET C constant is of order 150. Calculated surface areas were in good agreement with nominal values provided by the supplier. In order to probe the extent of surface roughness in these samples, if any, we have normalized the nitrogen and argon
adsorption isotherms by the monolayer uptake as determined from the BET analysis. These normalized isotherms are presented in Figure 2. Within the limit of our measurement precision, the curves are identical! This result implies either that the surfaces are all identical, possibly even smooth, or that the shape of the isotherms is insensitive to the surface texture. In view of the scattering results in ref 1and our own scattering studies, we adopt the latter point of view. Upon comparing our data with fractal BET isotherms that have been propo~ed,’~~J~ which are a function of the BET C value and the fractal dimension D , it is not surprising that we find generally poor agreement. In Figure 3, we have plotted the calculated fractal isotherms using eq 4 for a C value of 150 and a range of D values. This C value corresponds to the average value of the four samples. Also included are the normalized adsorption results for one sample, EH5. The theory for D = 2.5-2.6 fits the EH5 isotherm best, although deviations are increasingly serious a t high pressures where roughness effects should be most significant. A more rigorous test of the agreement between the fractal isotherm and our measurements would be a t even larger PIPo values; however, the onset of condensation a t the particle-particle contacts precludes this comparison. The deviation between our experimental uptake results and the smooth surface ( D = 2) BET isotherm is on the same order as the deviations observed by Harris and Sing15 for nitrogen adsorption on eight different silica samples and one alumina sample. In that work, when the isotherm for each sample was normalized by the BET monolayer capacity, all isotherms could be superimposed, and all deviated from the predictions of the BET model. With the exception of one silica sample, surface areas determined from electron microscopy and adsorption were in good agreement, indicating that the surfaces were smooth. One silica sample, which was chemically etched, had significant surface roughness. However, when the adsorption was normalized by the monolayer capacity, the effect of this roughness disappeared. On the basis of our findings, and supported by the Harris and Sing results, it appears clear that surface roughness effects are “lost” in the first adsorption layer. Thus it is not possible to extract surface roughness/fractal dimensions from adsorption isotherms of a single adsorbate. Adsorption isotherms a t 293 K for n-pentane and nheptane are presented in Figures 4 and 5. Both sets of isotherms are characterized by low BET C values (=lo) and may be classified as type I1 isotherms according to the BDDT classification. Surface areas have been calculated from these adsorption data by using the BET equation and are reported in Table I. The molecular cross sectional area is taken to be 0.492 nm2 for n-pentane and 0.631 nm2 for n-heptane.16 We should note that a wide range of values exist in the literature for these cross sectional areas. The values we use represent an average value for a range of materials referenced to nitrogen adsorption, but in fact, we would expect the actual value to be a function of the BET C value. It is interesting to note that this approach (measuring the surface area on a solid by using a range of adsorbates and adjusting the molecular cross sectional areas of the adsorbates so that the specific surface area matches that obtained from nitrogen adsorption) is only valid for solids with D = 2. For any other D value, the specific ~
(13) Bale, H.D.; Schmidt, P. W. Phys. Reo. Lett. 1984,53, 596. (14) Brunauer, S.;Deming, L. S.; Deming, W. S.; Teller, E. J. Am. Chem. SOC.1940,62, 1723.
~~
(15) Harris, M. R.; Sing, K. S. W.Chem. Ind. (London) 1959, 487. (16) McClellan, A. L.;Harnsberger, H. F. J. Colloid Interface Sci. 1967, 23, 557.
980 Langmuir, Vol. 4, No. 4, 1988
Ross et al.
3
Argon
Nitrogen 2.5
2
E
$ 1
-
LOOD
--
us7
--
HS5
. . ....
EH5
0.5
0
oi
1
0.i
0.6
0.2
0.1
0.4
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Figure 2. Normalized nitrogen and argon adsorption isotherms.
’ ’
10
0.16
0 = 2.0
0.u
8
--
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P)
n
E
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4
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0.6
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PRO
Figure 3. Calculated fractal isotherms for C equal to 150 and EH5 normalized isotherm.
Figure 4. Adsorption isotherms for n-pentane at 293 K.
surface areas should not be the same and the calculated u values may be significantly in error. This fact is one reason why the literature contains such a broad range of u values for various adsorbates. For example, for n-heptane adsorption on silica, u values between 0.292 and 0.836 nm2 have been reported.I6
Inspection of the surface areas in Table I for a particular powder shows a clear decrease with increasing u; this correlation suggests that a log-log plot of the number of moles in a monolayer versus u may be used to extract3 the fractal dimension D (i.e., as given by eq 1). These plots are presented in Figure 6. With the exception of the EH5 sample, our adsorption results fit this plot within the un-
Surface Roughness in Vapor-Phase Aggregates
*61*0 0.1)
-
-
Table 11. Fractal Dimension, D , from Adsorption and Scattering D calculated from SANS SANS sample e q 4 e q 1 ANL LANSCE SANS(1) SAXS L90D 2.5-2.6 2.1 NA" 2.0 NA 2.0
X
-
0.12
Langmuir, Vol. 4, No. 4, 1988 981
X
MS7
P a
X
0.10-
e
2.3
2.0 (M5)
2.1
NA
NA NA
2.6
2.1 (M5) 2.3 2.5
2.1 2.2 2.5
A
v)
?
2.5-2.6
HS5 2.5-2.6 2.3 EH5 2.5-2.6 2.5 Not applicable. 103
0.08-
8 r
X
e
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3
0 10'
0
Y
-
102
0
A
0
0.04
0
%
'b
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E
l
0
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0
x
0
1 00
0 BOD 0 us7 ns5
10-2
0
0.2
0.6
0.4
0.8
1
lo-'
PRO
t 10-3
Figure 5. Adsorption isotherms for n-heptane at 293 K.
10-2
lo-'
100
K (.%-')
Figure 7. Small-angle scattering curve of CAB-0-SIL grade EH5. The solid circles are SANS results from the intense pulsed neutron source at Argonne National Laboratory and the open circles are SAXS results from Sandia National Laboratory. The limiting slope indicates a surface fractal dimension of D = 2.65 f 0.1.
1000-
1 '.
f3
W
C
10-3
10-3
10-2
lo-' K
--
.
0.1
1
a(nm2) Figure 6. Molar monolayer capacity versus molecular cross sectional area. certainty of the u values that we use. The slope of a least-squares fit for each line yields of -012. The values of D calculated in this manner are reported in Table 11. Unlike the analysis of the nitrogen adsorption isotherm over a wide relative pressure range, a significant variation in D is noted. This variation ranges between 2.1 for L90D
100
(1-0
Figure 8. Small-angle scattering curve of CAB-0-SIL grade L90D. The curve was obtained at the Los Alamos Neutron Scattering Facility and indicates a fractal dimension consistent with smooth surfaces, D = 2.0 f 0.1. and 2.5 for EH5 and, in general, shows an increase in surface roughness with increasing surface area. Although not quantitative, this finding supports earlier scattering results1 and is consistent with the new scattering results. Typical scattering curves are shown for EH5 in Figure 7 and for L90D in Figure 8. The scattering at large wave vector is determined solely by the surfaces present, and the noninteger slope is indicative of rough surfaces, pow-
Ross et al.
982 Langmuir, Vol. 4, No. 4, 1988 1
Heptane
0 0 V
0
0
0.9
x
o
A
D
K
0
0.8
0
‘
4 ( A
Q X
0 LOOD
0.7
0 us7 X HS5
A M5
0.6 0.2
0.4
0.6
0.8
1
PPO Figure 9. Film surface area measurements obtained by using
heptane.
er-law polydispersity, or both.” In any of these cases, the attending surface area fits the descriptions given by eq 1 and 2; hence, neither gas absorption nor scattering can distinguish between rough surfaces and certain kinds of polydispersity. However, on the basis of published electron microscopy (CAB-O-SIL brochure) we believe that it is unlikely that polydispersity in the primary particles can explain our results. It is also possible that the scattering curves cover a crossover regime between two characteristic lengths (in this case the primary particle size and atomic spacings), which can give misleading slopes.l* We do not believe this to be the case since our curves exhibit about 1 decade of power law behavior; hence, the competing lengths are well separated. The surface fractal dimensions obtained by using eq 5 are shown in Table 11. The typical uncertainty is 0.1. In the case of SAXS, the results for the smeared and desmeared data agreed well. The values we report in Table I1 represent averages from the various scattering techniques we have used. An analysis based on self-affine surface roughne~s’~ would seem to be well motivated for fumed silica owing to its pyrogenic origin. A self-affine surface has roughness limited to a finite layer, such as a sandy beach ball, rather than self-similar roughness involving all length scales up to the size of the primary particles. Further, the topo(17) Wong, P.-2. Phys. Rev. E : Condens. Matter 1985, 32, 7417. Wong, P.-Z.; Howard, J.; Lin, J.-S. Phys. Rev. Lett. 1986, 57, 637. (18) Teixeira, J. In On Growth and Form; Stanley, H. E., Ostrowsky, N., Eds.; Martinus Nijhoff: Dordrecht, 1986; pp 145-162.
graphical relief of a self-affine surface is anisotropic and ideally has no overhanging cliffs. (A finite self-similar layer allows such overhangs but would be essentially indistinguishable from a self-affine surface in scattering and adsorption properties.) The scattering signature of such a system is a form like eq 5 at large wave vectors, with a slope between -3 and -4, steepening to an intermediate “Porod” slope of -4 at smaller wave vectors (positive curvature). Our data do not support the self-affine or any finite-layer interpretation because the curves have negative curvature, perhaps due to limited resolution. The failure of eq 4 could be attributed to the smoothing effects of surface tension in thick absorbate layers approaching condensation. Our data indicate that the layers absorbed after the first or second monolayer are little affected by the surface roughness. This observation is consistent with a rough layer of limited thickness (selfaffine), as the scattering results suggest. In addition to the scattering and adsorption measurements described previously, film surface area measurements were conducted with n-heptane as the preadsorbed vapor. For comparison purposes, surface areas (Z) are normalized by the surface area measured for samples with no n-heptane preadsorption (Eo). If a sample is smooth (i.e., D = 2 ) ) the surface area reduced in this way will change with increasing adsorbate coverage depending on the surface curvature. For a planar smooth surface, the reduced surface area should be equal to one, independent of preadsorbate loading. For a planar rough surface, Z/Zo will decrease as a function of preadsorbate PIPo. For smooth surfaces of positive curvature, Z/Zo will increase with coverage, and only the effects of surface roughness and/or condensation at particle contacts will cause Z/Zo to decrease. The reduction in surface area, via nitrogen adsorption, as a function of n-heptane relative pressure is given in Figure 9 for all four powders. A significant drop in surface area is noted for each sample even when the relative pressure of n-heptane is in the submonolayer region. In addition to surface roughness, particle-particle condensation may be contributing to this decline. Assuming that the CAB-0-SIL powders are formed of chains of smooth spheres with coordination number of 2, the change in Z/Zo with PIP, can be calculated by using the model of Smith and Olague.12 These calculations indicate that the surface area should be increasing and, hence, that there is a negligible effect of condensation on surface area reduction. Although a theory/model has not yet been developed for extracting D values from these film surface area measurements, qualitative information can be obtained from Figure 8. L90D is the smoothest material, followed by MS7, and HS5 and EH5 have similar roughness. These results agree well with the findings from scattering and multiple adsorbate analysis.
Acknowledgment. Support for this project has been provided by Sandia National Laboratories (Contract #02-2456) under US DOE Contract DE-04-76DP-00789, by Argonne National Laboratory under US DOE Contract W-31-109-ENG-38, and by the Los Alamos Neutron Scattering Center (LANSCE) under US DOE Contract W-7405-ENG.36. We thank P. Seeger, R. Hjelm, and P. Thiyagarajan for supervision and advice in data reduction. Registry No. Silica, 7631-86-9; nitrogen, 7727-37-9; argon, 7440-37-1; pentane, 109-66-0; heptane, 142-82-5.
