] O U R N A L OF
Journal of Non-Crystalline Solids 144 (1992) 45-52 North-Holland
NON-CRYSTALLIN SOLIDS E
Formation of microporous silica gels from a modified silicon alkoxide. I. Base-catalyzed gels William G. F a h r e n h o l t z , Douglas M. Smith and D u e n - W u H u a UNM / NSF Center for Micro-Engineered Ceramics, University of New Mexico, Albuquerque, NM 87131, USA Received 1 November 1991 Revised manuscript received 24 January 1992
Base-catalyzed silica gels have been prepared from mixtures of T E O S and a modified silicon alkoxide, methyltriethoxysilane. T h e ratio of modified ester to T E O S was varied in order to study the effect on gel structure. Low level additions of the modified ester resulted in an increase in the surface area of dried gels, but higher additions caused a decrease in the accessible area. This decrease in surface area corresponds to a significant change in physical morphology as probed with small angle X-ray scattering. 29Si M A S - N M R was used to determine the Q and T distributions of the gels and to estimate surface area and skeletal density based on the terminal group size. As the methyltriethoxysilane content was increased, the fraction of T 3 and T 2 species increased and the difference between the nitrogen surface area (accessible) and 'Q-derived' (total) surface area increased. Adsorption of carbon dioxide, methane, and water at 298 K was also measured.
1. Introduction
Modified alkoxysilanes such as methyltriethoxysilane (MTEOS) can be used to prepare organically modified silica gels or ORMOSILs [1-3]. In these studies gels and films have been prepared using only the modified ester, but other studies have shown that it is possible to form gels from mixtures of tetraethylorthosilicate (TEOS) and MTEOS [4,5]. Two advantages to using a mixture of esters as precursors would be to incorporate varying amounts of organic species into the gel and to tailor the mechanical properties of the gel. Since the pore structure of silica gels can be manipulated by the chemistry of the precursor solution, aging of the gel, and the drying process [6,7], it may be possible to prepare gels of controlled pore sizes with organic, hydrophobic surfaces. Such materials could find use as selective adsorbents or membrane coatings for any number of organic chemicals.
29Si magic angle spinning (MAS) nuclear magnetic resonance (NMR) is a powerful tool for investigating structure in silica-based materials [8-10]. NMR is sensitive to the bonding environment of the specific nucleus being studied [11]. As a result, information on both the first and second coordination spheres of silicon can be determined. Not only do NMR chemical shifts vary for Si-O as compared with Si-C bonds, but the difference between S i - O - S i and S i - O - R or S i - O - H bonds can also be determined. In fact, a special notation has been developed to describe these bonding environment [12]. For example, Q 4 indicates silicon in an S i - O - S i network where the silicon is bound to four other silicons through oxygens. Q3 indicates a silicon bound by three network-forming S i - O - S i bonds and one terminal group. The pattern follows with Q2 and Q1. Q0 silicons are isolated Si(OR) 4 or Si(OH) 4 molecules or monomers. OH and OR groups (R = CH3, C2H5, etc.) form terminal bonds since
0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
W.G. Fahrenholtz et al. / Formation of microporous gels. I
46
Table 1 29Si MAS-NMR chemical shifts for silicon species [11] Symbol Chemical shift Bonding
Si044 - species Q4 Q3 Q2
- 110 ppm - 102 ppm 96 ppm - -
complete S i - O - S i network 3 S i - O - S i bonds and one terminal 2 S i - O - S i and two terminal
H3C-Si033 - species T3 T2 TI
- 65 ppm - 58 ppm - 5 2 ppm
3 S i - O - S i , one CH 3 2 S i - O - S i , one terminal, one CIt 3 1 S i - O - S i , two terminal, one CH 3
The use of these figures can be justified using an average coordination argument and assuming that all of the silicon species are in the Si 4+ state. For each Q4 silicon, there are two oxygens ( 0 2-) and n o terminal species, in other words a fully developed S i - O - S i network. For each Q3 and T 3 silicon, there are 1.5 oxygens ( 0 2. ) and one terminal group ( O H - , O R - or R - ) . Q2 and T 2 silicons are bound to one oxygen and two terminal groups. Using the reported areas for each of the terminal groups, the surface area of a gel can be calculated using the following formula: SA=
they do not participate in network formation. For species with S i - C bonds, T notation is used. T 3 species are bound by one carbon and three network-forming bonds while T 2 silicons are bound by one carbon, one terminal group, and two network-forming bonds. 298i M A S - N M R can be used to determine the Q and T distributions of silica gels. Table 1 lists the N M R chemical shifts of several bonding environments [11]. Using NMR, it is possible to determine the n u m b e r of silicon species in each bonding environment by integrating the area of each peak. In theory, it should be possible to calculate the surface area of silica gels knowing the number of terminal groups, the size of each species, and assuming that all of the terminal groups are on exposed surface [13]. In reality, not all of the terminal groups will be accessible; thus this estimate can be considered an u p p e r limit of surface a r e a . Q 4 silicon can be assumed to provide no surface area since it is a fully bound network, but lower Qs and Ts will provide different amounts of surface based on the size of the terminal groups. For example, surface hydroxyls and methyls have a reported a r e a of 0.21 nm 2 (4.7 groups per nm2), while ethoxy groups have a reported area of 0.27 nm 2 (3.7 groups per nm 2) [14]. For a silica gel, the silicon species are normally Q 2 , Q3, o r Q 4 . If the fraction of species in each of these coordinations is x, y, and z, respectively, the formula for a silica gel can be expressed as Si.+y+zOx+x.Sy+2z(OR + O H + i ) 2 x + y , where
x + y + z = 1.
(1)
(2x +y)(NA)[(flA1) + (leA2) + (f3A3)] 1TIW
(2) where SA is the surface are, 2x + y is the number of terminal groups, N A is Avagadro's number, fn is the fraction of terminal group n, A n is the area of terminal group n, and mw is the formula weight of SiOx+l.Sy+zz(OR + O H + R)zx+y. Similarly, the density of the gel can be calculated assuming a value for the volume of each different type of silicon species. An amorphous Q4 network is assumed to have a volume of 0.455 cm3/g, a Q3 network has a volume of 0.525 c m 3 / g and a Q 2 network 0.580 cm3/g. The densities for the Q3 and Q 2 species were calculated based on the terminal groups being hydroxyls. Density can be calculated using a weighted average of these numbers as 100 Density = 0.455z + 0.525y + 0.580x "
(3)
Both the surface area and the density formulas can be extended to cover Q1 and T species.
2. Experimental procedure Gels were p r e p a r e d from solutions of T E O S and M T E O S in ethanol similar to the method described by Brinker et al. [15]. Gels ranging in composition from 0 to 75 mol% M T E O S (x = 0 75) were p r e p a r e d by mixing various ratios of stock solutions containing 50 or 75 mol% M T E O S
W.G. Fahrenholtz et al. / Formation of microporous gels. [
(x = 50 and 75) with a standard T E O S stock solution (x = 0). Stock solutions of identical concentration were p r e p a r e d by diluting the stoichiometric amount of esters to a standard volume with ethanol. W a t e r and HC1 were added and the resulting solution was refluxed at approximately 353 K for 4 h. The mole ratio of silicon to water to acid was 1:1:0.0007 in all of the stock solutions. After refluxing, the solution was aged for 24 h prior to gel formation. Gels were formed by adding 0.5M N H 4 O H to a mixture of stock solutions. The final ratio of silicon to water to N H 4 O H was approximately 1 : 2 : 0.02. Gels were formed at room temperature, ~ 295 K, in sealed glass vials. Gel time varied depending on the M T E O S content, x = 0 gels formed in less than 1 h but for x = 75 gel time was more than 48 h. After gelation, gels were aged at room t e m p e r a t u r e in the sealed vials for at least 24 h. Vials were then uncapped and the gels were exposed to the ambient atmosphere for drying. After 5 days of exposure, samples were placed in a 373 K drying oven for 24 h. Gels were transparent prior to drying but opaque after 24 h at 373 K. The surface area of all gels was determined by B E T analysis of nitrogen adsorption data collected at 77 K [16]. Gels were outgassed at 383 K under vacuum for at least 4 h prior to analysis. Five adsorption points were collected at relative pressures between 0.05 and 0.30. The error in B E T data is generally accepted to be around 10% of the measured surface area. The error in the fit of the B E T equation to the adsorption points was around 1% for all samples. The molecular crosssectional area of nitrogen was assumed to be 0.162 nm 2. Micropore area was determined from a plot of volume adsorbed versus the statistical thickness of the adsorbed layer, the t-plot method [16]. The total pore volume was determined by a single adsorption point at P / P o = 0.995. Surface area of selected gels was also determined by adsorption of methane and carbon dioxide at 298 K. For both m e t h a n e and carbon dioxide, adsorption data were reduced using the method of Dubinin and Radushkevich [16]. Methane data was collected between relative pressures of 0.0017 and 0.03 while carbon dioxide data was collected over a range of relative pressures from 0.0007 to
47
0.01. Molecular cross-sections of 0.170 and 0.178 nm 2 were assumed for C O 2 and CH4, respectively. Single point water adsorption data were collected at room t e m p e r a t u r e ( ~ 295 K) at a relative pressure of 0.23 (saturated LiC1 water solution), corresponding roughly to a single statistical monolayer. The size of a water molecule was assumed to be 0.108 nm 2. The adsorbed weight was measured and compared for gels with different M T E O S contents. Skeletal density was determined by helium pycnometry. A total of six measurements were made for each sample and the range was _+0.01 g / c m 3 in all cases. 29Si M A S - N M R data were collected at 79.459 M H z on a Varian spectrometer using TMS as the reference material. Samples were packed in zirconia rotors and spun at 3.0 kHz. An acquisition time of 0.02 s was used with a relaxation delay of 20 s. A total of 1520 free induction decays were collected for each spectrum. Spectra were deconvoluted in order to determine the Q and T distributions. Automatic deconvolution was performed using a multi-component fit and a Gaussian profile. Peak position, width, and integrated area were among the parameters included in the fitting routine. Small angle X-ray scattering was performed using Kratky optics on a Rigaku X-ray generator. X-rays were generated at a potential of 40 kV and 140 mA. D a t a were collected using a position sensitive detector. A standard desmearing program was applied to the data prior to analysis [17].
3. Results Nitrogen surface area, area of the micropores, and total pore volume data are plotted in fig. 1. The surface area and pore volume increased with small additions of the modified ester, but with larger additions both dropped dramatically. The reported data are for one set of samples; however duplicate samples were p r e p a r e d in the region where surface area dropped rapidly. Duplicate samples were within error (_+ 10%) of the reported data. The x = 0 sample corresponds to the two-step acid/base-catalyzed silica gels samples which are commonly denoted as B2 and which
W..G. Fahrenholtz et al. / Formation of microporous gels. [
48 1000
,
I
,
I
,
I
,
I
,
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,
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,
0.6
1000
i
872
85O
800
~
"~"%~-~
-
o.5
E
~'E
a00
.:.~
~-~-~-~,~i~'~t D
8 o e-
600 -
.~
400
~,
2o0
SURFACE AREA MICROPORE AREA
~-
"~ ~,
PORE VOLUME
.~ - 0,3
~
.._0.2 n-
\
-01
~~
NITROGEN NITROGEN MIC. PORe METHANE
Fiiiiil [] c, o ooxo
-0.4 ,~
[] ~
:,oo iiiiiii! 400
',~i
200
182
0 0
i
i
i
1
i
:
I0
20
3o
40
50
60
¢
x=0
7o
METHYLTRIETHOXYSILANE
x=40 (MOLE
%)
METHYLTRIETHOXYSBLANE (MOLE %)
Fig. 1. Surface area, micropore area, and pore volume of base-catalyzed gels. Lines are drawn through the data symbols as a guide for the eye.
typically have surface areas in the 800-900 m 2 / g range and pore volumes in the 0.4-0.8 c m 3 / g range [6]. The x = 20 gel had the highest surface area while the x = 70 had virtually no accessible surface area. The decrease in surface area is nearly three orders of magnitude, much greater than the estimated error in the measurement. The total pore volume followed a similar trend. The pore volume is essentially constant for x < 55 but rapidly decreases to zero as x increases to 70. Remarkably, the hydraulic radius of the samples, two times the pore volume divided by the surface area, was nearly constant over the entire range of composition, a value of 1.25 nm. The area of micropores, pores with radius less than 1 nm, reached a maximum at x = 50. The density as a function of composition as determined with helium displacement along with the density calculated using eq. (3) and silicon N M R data are given in fig. 2. Both density deter-
Fig. 3. Adsorption data for nitrogen, methane, and carbon dioxide.
mination methods decreased steadily as the percentage of methylated ester increased. The decrease in the measure density was well above the error in the measurement. Surface areas of the x = 0 and x = 4 0 gels were also determined by adsorption of carbon dioxide and methane. Again, an error of _+ 10% can be assumed, although the fit of the adsorption points predicted ~ 1% error. Unlike nitrogen adsorption at 77 K which probes the entire accessible surface, these gases probe specific surface adsorption sites which are usually polar in nature. Data are summarized in fig. 3 and results showed that the x = 40 has a lower affinity for carbon dioxide and methane despite having a slightly greater total specific surface area than the x = 0 gel. Adsorption of water was used to determine a relative degree of hydrophobic character for all of the gels. The total amount of water and the fraction of a monolayer of water
I
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2.2
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I
I
I
I
I
I
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O ADSORPTION - - E~- C O V E R A G E
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"~" []-~_~ O
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Z
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9
,,=
CALCULATED MEASURED ~ ~ ~ i 10 20 30 40 METHYLTRIETHOXYSILANE
0 =E <
0.4
,'D
]
,,=,
-0.8 ~, =o
0 ~ 50 (MOLE
i 60 %)
70
Fig. 2. Skeletal density of base-catalyzed gels. Lines are drawn through the symbols as a guide for the eye.
i
h
i
10 20 30 40 METHYLTRIETHOXYSILANE
0
i
50 60 (MOLE %)
70
Fig. 4. Water adsorption data and monolayer coverage for base-catalyzed gels. Lines are drawn through the data symbols as a guide for the eye.
W.G. Fahrenholtz et al. / Formation of microporous gels. I
49
0,7 t 3.49 • Q4 [] T3 0.50"61~ ~3.22 3.19 [m Q3 I~ Q2 I~T2 2.65 0.4 3.05 "
f I "
u. 0.3
0.2 0.1 0.0
x=70
0
10
25
40
50
60
70
METHYLTRIETHOXYSILANE (MOLE%)
x=60
Fig. 6. Q and T distributions and average number of bonds from 29Si MAS-NMR.
x=50
increased, the number of Q 4 species decreased, since the methylated silicons form T 3 species when fully condensed because of the unreactive carbon blocking the one site. Using the Q and T distribution data, an average number of network forming bonds per silicon was calculated for each gel. These data are also given in fig. 6. Surface area and density for the gels were calculated from Q and T distributions using eqs. (2) and (3). Surface area data are presented in fig. 7 and compared with data determined by nitrogen adsorption. Calculations were made assuming that all of the terminal groups were either ethoxy or methyl with the ratio of the two determined by the nominal composition of the starting solution. Unlike the measured values, the calculated numbers rose steadily with increasing amount of MTEOS. Calculated density data, presented in fig. 2, show a similar trend. That is, calculated values were consistently higher than
x =40
x=25
x=10 x = 0
o ' ' ' '-20
-io' -& ' -8' o ' -100 ' ' ' ' -120 -140 ppm
Fig. 5. ZgSi MAS-NMR spectra for x = 0 , x = 1 0 , x = 40, x = 50, x = 60, and x = 70 gels.
'
x=25,
covering the surface are displayed in fig. 4. The monolayer coverage was normalized by the nitrogen B E T surface area so that gels of varying area could be compared. 29Si MAS-NMR spectra are given in fig. 5. As the amount of methylated ester increased, the peaks between - 5 0 and - 7 0 ppm grew significantly in relative intensity. This was not surprising since this is the region of the spectrum assigned to silicons bound to three oxygens and one carbon. In addition to the change in the distribution between these two regions, there were also changes in the spectra in the range of - 8 5 to - 1 2 0 ppm. These spectra were deconvoluted to yield Q and T distributions which are summarized in fig. 6. As the amount of methylated ester
2500
I I I - O MEASURED ~ CALCULATED ~'E 2000CORRECTED < --
15oo
-
I
__
- - ~ - -
I __[]~ J
~
..~
I
- - ~ "
1000
0
10 20 30 40 50 60 METHYLTRIETHOXYSILANE (MOLE%)
70
Fig. 7. Surface area of gels calculated from Q and T distributions. Lines are drawn through the symbols as a guide for the eye.
50
W, G. Fahrenholtz et al. / Formation o f microporous gels. I
m e a s u r e d values. It was a s s u m e d t h a t t h e differe n c e in d e n s i t y was d u e to t h e f o r m a t i o n o f closed p o r e s , p o r e s i n a c c e s s i b l e to t h e p r o b e gasses. A c o r r e c t i o n f a c t o r for t h e s u r f a c e a r e a d a t a was c a l c u l a t e d b a s e d o n t h e d i f f e r e n c e bet w e e n c a l c u l a t e d a n d o b s e r v e d density. T h e r a t i o o f t h e o p e n v o l u m e ( r e c i p r o c a l m e a s u r e d density) to t h e t o t a l v o l u m e ( r e c i p r o c a l t r u e density) was set e q u a l to t h e r a t i o of t h e o p e n surface a r e a ( m e a s u r e d ) to t h e t o t a l s u r f a c e a r e a as shown in eq. (4):
MTEOSoddedB2 wef gel 102
. . . . . . . .
~
. . . . . . . .
=
100 10 -1 t10 -2
,4 k-
I 0 -~ 10 -4 1 0 -,s
A ~
IO-S
Vopen
SAopen
- --
Vopen -]- Vclosed
(4)
SAtotal '
w h e r e Vopen is t h e r e c i p r o c a l m e a s u r e d density, Vclosed is t h e d i f f e r e n c e b e t w e e n t h e r e c i p r o c a l s o f t h e t r u e d e n s i t y o f silica (2.2 g / c m 3) a n d t h e c a l c u l a t e d density, a n d SAopen is t h e m e a s u r e d N 2 s u r f a c e area. T h e s u r f a c e a r e a c o r r e c t i o n w o r k s well for the x = 0 gel, b u t was still b e l o w t h e c a l c u l a t e d value in all o t h e r cases. T h e s e d a t a a r e also p r e s e n t e d in fig. 7.
10 2
1o I M . TEOS 10-I i 10o
O~
lo_=
0 0
25%
~
/"
10 -3
¢-
£ L.
lo-* 1°-~
50% 60~o i
~
10 -s
lo_ 7
65%
lO-S
70~
D v
1o-. u
l o -10
75%
0.001
10 -7 10 -8 0.001
0.01
0.1
q (A -1 ) Fig. 9. Small angle X-ray scattering for wet gels.
X - r a y s c a t t e r i n g d a t a c o l l e c t e d by small a n g l e s c a t t e r i n g a r e given for d r i e d gels in fig. 8 a n d several w e t gels in fig. 9. D r i e d gels w e r e e x a m i n e d r a n g i n g in M T E O S c o n t e n t f r o m x = 0 to 75 (see fig. 8). T h e r a d i u s o f t h e f e a t u r e size in t h e x = 0 a n d x = 25 M T E O S gels was ~ 2.8 n m a n d 2.6 n m for t h e x = 50 to x = 65 gels. This size d e c r e a s e s d r a m a t i c a l l y to ~ 1.2 n m for t h e x = 70 a n d x = 75 gel. T h e s l o p e of t h e s c a t t e r i n g curves in t h e P o r o d r e g i o n (q from 0.09 to 0.4) was - 2.5 for t h e x = 0 gel, - 2.2 for t h e x = 25 a n d x = 50 gels, a n d - 2 for t h e x = 6 0 and x=65 gel. F i g u r e 9 shows s c a t t e r i n g results for w e t gels with x = 60 a n d x = 75. T h e s c a t t e r i n g curves w e r e qualitatively similar to t h e d r i e d gels of t h e s a m e c o m p o s i t i o n . T h e f e a t u r e size of t h e x = 75 gel a p p e a r s to b e significantly s m a l l e r t h a n t h a t for t h e x = 60 gel, s i m i l a r to t h e d r i e d samples.
4. Discussion
10-13 10 -16
. . . . . . . .
101
!
:
I [[[[!1
I
0.01
q
I ; ;;;;:1
;
: : ::::
0.1
(A-1)
Fig. 8. Small angle X-ray scattering for dried gels.
Initially, t h e r a p i d d e c r e a s e in t h e surface a r e a a n d p o r e v o l u m e with M T E O S c o n t e n t s a b o v e x = 55 was a t t r i b u t e d to t h e c o l l a p s e of p o r e s d u e to c a p i l l a r y forces d u r i n g drying. It was t h o u g h t
W.G. Fahrenholtz et aL / Formation of microporous gels. I
that the gel network weakened as Q4 species were lost [13]. Silicon N M R data confirmed that there were fewer Q4 species in gels with higher M T E O S content. SAXS data showed that the feature size of the dried gels, presumably the pore radius, also decreased dramatically at the point where surface area and pore volume went to zero. These data could be an indication that the pore structure of the gel collapsed as the methyl content increased. However, SAXS of the wet gels showed a similar trend to that for dried gels, a smaller feature size for the x = 75 gel as compared with gels with lower methyl contents. Smaller feature size is not necessarily an indication of collapse of porosity and loss of potential surface area for the wet gel; it could mean that the gel was more microporous. The total loss in surface area and collapse of pore volume in the dried gel was probably due to a combination of differences in the structure of the wet gel and collapse of the network during drying due to weakening of the network. Interestingly, the loss of surface area occurs in the region where the average number of oxygens (and carbons) per silicon (Stevel's R parameter) increases into the range of incomplete network formation [18]. R values in the range of 2-2.5 are common for glasses; values from 2.5 to 2.7 indicate an incomplete network containing isolate chain or ring species. R is 2.25 for the x = 0 gel and increases to 2.7 for gels of x > 60. R was calculated from the Q and T distributions determined by 29Si MAS-NMR. The decrease in skeletal density of the gels with increasing methyl content was consistent with what would be expected as surface groups are added and network formation is less complete, but the difference between the calculated density and the measured density may be an indication of closed porosity or free volume within the gel structure. If the decrease in density is attributed to the formation of closed porosity, a rough surface area correction can be calculated. As shown in fig. 7, the corrected surface area accounts for some of the difference between the calculated and observed values, but not all. Obviously, more than simple closed porosity is responsible for the decrease in surface area and density of these gels.
51
Adsorption of carbon dioxide, methane, and water was used to probe the surface of the gels in more detail. As shown in fig. 3, the nitrogen surface area and micropore area of the x = 0 and x = 40 gels were approximately equal. However, adsorption of m e t h a n e and carbon dioxide gave different results. The differences in the areas as determined by these three gases could be caused by differences in the polar nature of the surface of the gels, hydroxyl for the x = 0 gel and partially methylated for the x = 40 gel, in addition to actual differences in the surface area. In order to probe the nature of the surface more thoroughly, water adsorption experiments were carried out. W a t e r should be a sensitive probe to the number of hydrophobic methyl groups on the surface [14]. As shown in fig. 4, the water uptake decreases as the methyl content of the gels increase. In order to eliminate the effect of surface area, these numbers were normalized by the surface area to obtain the fractional monolayer coverage produced by adsorption of the reported amount of water. As expected, the amount of water adsorbed falls steadily as the methyl content of the gels increases until x = 60. The increase for gels of x = 60 and greater could be an artifact of the calculation which divides by the total surface area. For the low surface area materials, this produces a large number.
5. Conclusions
The surface area of base-catalyzed silica gels p r e p a r e d from T E O S and M T E O S was a function of composition. Above x = 50, the surface area decreased dramatically due to significant changes in the physical structure of the gels. Higher M T E O S contents led to less Q4 species in the dried gels which in turn led to smaller measured surface areas, but much larger calculated areas. Feature size of both wet and dried gels, as determined by SAXS, was consistent with the formation of smaller pores at higher methyl contents. The introduction of the methyl groups into the gels also affected the adsorption of water, methane, and carbon dioxide, indicating that the nature of the surface (i.e., degree of polarity and
52
W.G. Fahrenholtz et al. / Formation of microporous gels. I
hydrophobicity) was also changing. Calculation of the surface area and density from the Q and T distributions produced numbers significantly higher than the measured values, indicating the presence of closed or inaccessible porosity. The addition of the methyl-substituted ester had a effect on both the surface area of the gels as well as the nature of the surface. The authors would like to thank W. Ackerman of the Center for Micro-Engineered Ceramics for gas adsorption measurements and P.J. Davis of CMEC and Los Alamos National Laboratory for 298i NMR. In addition, the authors thank C.J. Brinker (CMEC and Sandia National Laboratories) and G.W. Scherer (E.I. DuPont de Nemours & Co.) for helpful discussions.
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