Pore Structure Characterization of Catalyst Supports via Low-Field

Chapter 24

Pore Structure Characterization of Catalyst Supports via Low-Field NMR Spectroscopy 1

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Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 12, 2016 | http://pubs.acs.org Publication Date: October 3, 1989 | doi: 10.1021/bk-1989-0411.ch024

D. M . Smith , C . L. Glaves , D . P. Gallegos , and C . J. Brinker

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Center for Micro-Engineered Ceramics, University of New Mexico, Albuquerque, N M 87131 Division 1846, Sandia National Laboratories, Albuquerque, N M 87185

Two characterization techniques (mercury porosimetry and nitrogen adsorption/condensation) are widely employed for pore structure analysis of catalyst supports. Pore structure analysis is an important component of catalysis at several levels ranging from quality control for catalyst support production to the understanding of mass transfer resistance in laboratory experiments. Although porosimetry and adsorption/condensation are widely used, they suffer from several disadvantages. In an effort to avoid these disadvantages and to extract more detailed pore structure information, techniques such as small-angle x-ray/neutron scattering (SAXS/SANS), phase-change porosimetry, and low-field NMR spin-lattice relaxation measurements have been recently employed. In this paper, the application of low-field NMR to both surface area and pore structure analysis of catalyst supports will be presented. Low-field (20 MHz) spin-lattice relaxation (T ) experiments are performed on fluids contained in alumina and s i l i c a catalyst supports. Pore size distributions (PSD) calculated from these NMR experiments are compared to those obtained from mercury porosimetry and nitrogen condensation. 1

BACKGROUND - Conventional Pore Structure

Characterization

Mercury porosimetry employs t h e measurement o f mercury volume i n t r u d e d ( o r r e t r a c t e d ) i n t o a sample as a f u n c t i o n o f p r e s s u r e . The a p p l i e d pressure i s r e l a t e d t o t h e d e s i r e d pore s i z e v i a t h e Washburn Equation [1] which i m p l i e s a c y l i n d r i c a l pore shape assumpt i o n . Mercury porosimetry i s widely a p p l i e d f o r c a t a l y s t charact e r i z a t i o n i n both QC and research a p p l i c a t i o n s f o r s e v e r a l reasons i n c l u d i n g r a p i d r e p r o d u c i b l e a n a l y s i s , a wide pore s i z e range (~2 nm t o >100 /im, depending on t h e pressure range o f t h e instrument), and the a b i l i t y t o o b t a i n s p e c i f i c s u r f a c e area and pore s i z e d i s t r i b u t i o n i n f o r m a t i o n from t h e same measurement. Accuracy o f t h e method s u f f e r s from s e v e r a l f a c t o r s i n c l u d i n g c o n t a c t angle and s u r f a c e t e n s i o n u n c e r t a i n t y , pore shape e f f e c t s , and sample compression. However, t h e l a r g e s t d i s c r e p a n c y between a mercury porosimetryd e r i v e d pore s i z e d i s t r i b u t i o n (PSD) and t h e a c t u a l PSD u s u a l l y 0097-6156/89/0411-0251$06.00/0 © 1989 American Chemical Society

Bradley et al.; Characterization and Catalyst Development ACS Symposium Series; American Chemical Society: Washington, DC, 1989.


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CHARACTERIZATION AND CATALYST DEVELOPMENT

a r i s e s as a r e s u l t o f n e t w o r k / p e r c o l a t i o n e f f e c t s . An i m p l i c i t assumption i n porosimetry a n a l y s i s i s t h a t every i n d i v i d u a l pore i s i n d i r e c t c o n t a c t with the p e l l e t s u r f a c e . In f a c t , a p a r t i c u l a r pore i n a c a t a l y s t support w i l l be connected t o the s u r f a c e v i a a network o f v a r i o u s s i z e / s h a p e pores. Mercury w i l l i n t r u d e i n t o the pore not at the p r e s s u r e a s s o c i a t e d with the s i z e o f t h a t s p e c i f i c pore but at a p r e s s u r e c o r r e s p o n d i n g t o the s m a l l e s t c o n s t r i c t i o n i n the l a r g e s t branch o f the network c o n n e c t i n g the pore t o the s u r f a c e . T h i s e f f e c t w i l l r e s u l t i n the apparent PSD being skewed t o s m a l l e r pore s i z e s . When the p r e s s u r e i s lowered, ( i . e . , r e t r a c t i o n ) , a d i f f e r e n t p r e s s u r e w i l l be observed f o r the same pore as the r e t r a c t i o n w i l l occur through the path with the l a r g e s t constrictions. I n v e s t i g a t o r s have attempted t o model t h i s network problem using p e r c o l a t i o n t h e o r y i n an attempt t o e x t r a c t a d d i t i o n a l pore s t r u c t u r e i n f o r m a t i o n from the i n t r u s i o n curve. Using a pore model based on the pore space surrounding random packing o f s o l i d monodisperse spheres (a reasonable model f o r a c a t a l y s t support with a monodisperse pore s t r u c t u r e or with macropores surrounding a packing o f porous m i c r o s p h e r e s ) , Mason [2] concluded t h a t o n l y 16% o f the pores c o u l d be observed as a r e s u l t o f n e t w o r k / p e r c o l a t i o n e f f e c t s . R e c e n t l y , Smith, e t . a l . [3] r e f i n e d Mason's work and demonstrated t h a t a c t u a l l y 27% o f the pores c o u l d be observed with p o r o s i m e t r y but these would p r i m a r i l y be the s m a l l e r pores. In an attempt t o e x t r a c t f u r t h e r pore s i z e i n f o r m a t i o n , some i n v e s t i g a t o r s a l s o employ the d e p r e s s u r i z a t i o n ( r e t r a c t i o n ) curve. For example, Conner, e t . a l . [4] i n d i c a t e t h a t pore morphology i n f o r m a t i o n may be o b t a i n e d by comparing the i n t r u s i o n and e x t r a c t i o n c u r v e s . T h i s approach seems t o work r e a s o n a b l y w e l l f o r m a t e r i a l s with narrow, unimodal pore s i z e d i s t r i b u t i o n s . However, C i f t c i o g l u , e t . a l . [5] have r e c e n t l y demonstrated t h a t the r e t r a c t i o n curve may be dominated by the s i z e o f o n l y a few l a r g e i n t e r n a l pores and t h a t n e g l i g i b l e i n f o r m a t i o n c o n c e r n i n g the m a j o r i t y o f the pores i s o b t a i n e d i f the m a t e r i a l has a broad d i s t r i b u t i o n with a "well-connected" pore network. In p r i n c i p l e , f u r t h e r pore s t r u c t u r e i n f o r m a t i o n may be o b t a i n e d by performing repeated scanning curves i n the h y s t e r i s i s r e g i o n but the a d d i t i o n a l e f f o r t i s r a r e l y j u s t i f i e d i n terms o f the additional information obtained. N i t r o g e n a d s o r p t i o n / c o n d e n s a t i o n i s used f o r the d e t e r m i n a t i o n o f s p e c i f i c s u r f a c e areas ( r e l a t i v e p r e s s u r e < 0.3) and pore s i z e d i s t r i b u t i o n s i n the pore s i z e range o f 1 t o 100 nm ( r e l a t i v e p r e s sure > 0.3). As with mercury porosimetry, s u r f a c e area and PSD i n f o r m a t i o n are o b t a i n e d from the same instrument. T y p i c a l l y , the d e s o r p t i o n branch o f the isotherm i s used (which corresponds t o the p o r o s i m e t r y i n t r u s i o n c u r v e ) . However, i f the isotherm does not p l a t e a u at high r e l a t i v e p r e s s u r e , the c a l c u l a t e d PSD w i l l be i n e r r o r . For PSD's, n i t r o g e n condensation s u f f e r s from many o f the same disadvantages as porosimetry such as n e t w o r k / p e r c o l a t i o n e f f e c t s and pore shape e f f e c t s . In a d d i t i o n , a d s o r p t i o n / c o n d e n s a t i o n a n a l y s i s can be q u i t e time consuming with a n a l y s i s times g r e a t e r than 1 day f o r PSD's with reasonable r e s o l u t i o n . D e s p i t e the shortcomings o f these methods, they serve as the p r i n c i p l e a n a l y t i c a l t o o l s f o r c a t a l y s t support c h a r a c t e r i z a t i o n . I f one i s i n t e r e s t e d i n q u a l i t y c o n t r o l a p p l i c a t i o n s and s o l e l y l o o k i n g f o r q u a l i t a t i v e d i f f e r e n c e s between d i f f e r e n t batches o f the same or s i m i l a r supports, the e r r o r s a s s o c i a t e d with these methods


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are minor. However, i f one r e q u i r e s d e t a i l e d s t r u c t u r a l informat i o n , the use o f a d d i t i o n a l and/or more s o p h i s t i c a t e d techniques i s required.


BACKGROUND - Characterization v i a NMR

The a t t r a c t i v e n e s s o f s u r f a c e / p o r e c h a r a c t e r i z a t i o n v i a NMR s p i n - l a t t i c e r e l a x a t i o n measurements o f pore f l u i d l i e s i n the p o t e n t i a l advantages t h i s technique has as compared to the convent i o n a l approaches. These i n c l u d e : r a p i d a n a l y s i s , lower o p e r a t i n g c o s t s , a n a l y s i s o f wet m a t e r i a l s , no pore shape assumption, a wide range o f pore s i z e s can be e v a l u a t e d (0.5 nm to >1 /im), no n e t w o r k / p e r c o l a t i o n e f f e c t s and the technique i s n o n - d e s t r u c t i v e . When d e t e r m i n i n g s p e c i f i c s u r f a c e areas, NMR a n a l y s i s does not r e q u i r e o u t - g a s s i n g and has the p o t e n t i a l f o r o n - l i n e a n a l y s i s o f slurries. E a r l y s t u d i e s i n v o l v i n g NMR i n c l u d e the work by Hanus and G i l l i s [6] i n which s p i n - l a t t i c e r e l a x a t i o n decay c o n s t a n t s were s t u d i e d as a f u n c t i o n o f a v a i l a b l e s u r f a c e area o f c o l l o i d a l s i l i c a suspended i n water. S e n t u r i a and Robinson [7] and Loren and Robinson [8] used NMR to q u a l i t a t i v e l y c o r r e l a t e mean pore s i z e s and observed s p i n - l a t t i c e r e l a x a t i o n times. Schmidt, e t . a l . [9] have q u a l i t a t i v e l y measured pore s i z e d i s t r i b u t i o n s i n sandstones by assuming the value o f the s u r f a c e r e l a x a t i o n time. Brown, e t . a l . [10] o b t a i n e d pore s i z e d i s t r i b u t i o n s f o r s i l i c a , alumina, and sandstone samples by s h i f t i n g the T, d i s t r i b u t i o n u n t i l the best match was o b t a i n e d between d i s t r i b u t i o n s obtained from porosimetry and NMR. More r e c e n t l y , low f i e l d (20 MHz) NMR s p i n - l a t t i c e r e l a x a t i o n measurements were s u c c e s s f u l l y demonstrated by Gal legos and coworkers [11] as a method f o r q u a n t i t a t i v e l y determining pore s i z e d i s t r i b u t i o n s u s i n g porous media f o r which the " a c t u a l " pore s i z e d i s t r i b u t i o n i s known a p r i o r i . Davis and co-workers have m o d i f i e d t h i s approach t o r a p i d l y determine s p e c i f i c s u r f a c e areas [12] o f powders and porous s o l i d s . THEORY - NMR

The technique i s based on the observed decrease i n the s p i n l a t t i c e r e l a x a t i o n decay constant, T p o f a f l u i d i n c o n t a c t with a s o l i d s u r f a c e as compared with the T; f o r the f l u i d alone. W i t h i n t h i s f l u i d t h e r e are assumed to e x i s t two d i s c r e t e r e g i o n s : a s u r f a c e a f f e c t e d r e g i o n , i n which r e l a x a t i o n i s f a s t , and a r e g i o n which a c t s as bulk f l u i d . I f d i f f u s i o n between the r e g i o n s i s much f a s t e r than r e l a x a t i o n , than f o r a given pore s i z e , a s i n g l e T, w i l l e x i s t and can be d e s c r i b e d by the " t w o - f r a c t i o n , fast-exchange* model [13]. In terms o f the h y d r a u l i c pore r a d i u s , r , t h i s governing equation f o r a s a t u r a t e d porous medium i s g i v e n as [11]: 1/T, = a + p/r (1) where a i s the r e c i p r o c a l bulk f l u i d T, and j3 i s a s u r f a c e r e l a x a t i o n parameter i n v e r s e l y p r o p o r t i o n a l to the s u r f a c e phase T,, and i n c o r p o r a t i n g the s u r f a c e l a y e r t h i c k n e s s , a may be determined by performing a r e l a x a t i o n experiment on the f l u i d and i s a f u n c t i o n o f temperature and the f l u i d . . For water at ambient temperature, a i s on the order o f 0.3-0.5 s . p w i l l be a f u n c t i o n o f f l u i d , temp e r a t u r e , proton frequency and s u r f a c e chemistry. For d e c r e a s i n g proton frequency ( f i e l d s t r e n g t h ) , p w i l l i n c r e a s e r e s u l t i n g i n i n c r e a s e d pore s i z i n g s e n s i t i v i t y . A l s o with d e c r e a s i n g frequency, the s i g n a l to n o i s e r a t i o o f the 1, measurements w i l l decrease


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i m p l y i n g a decrease i n s e n s i t i v i t y . T h e r e f o r e , the optimum f r e quency w i l l depend upon both the pore s i z e and pore volume o f the sample. For most a p p l i c a t i o n s , f r e q u e n c i e s i n the range o f 10 t o 60 MHz are s a t i s f a c t o r y . The measured d a t a f o r a s i n g l e pore s i z e or a bulk f l u i d i s an e x p o n e n t i a l l y d e c a y i n g f l u i d m a g n e t i z a t i o n v e c t o r v e r s u s time i n which T, i s the decay c o n s t a n t . For a 180°-r-90° p u l s e sequence, the r e t a r n t o e q u i l i b r i u m o f the m a g n e t i z a t i o n v e c t o r i s d e s c r i b e d ^ M(r) = M [1 - 2 expC-r/T,)] (2) where M i s tne m a g n e t i z a t i o n at e q u i l i b r i u m . However, a t y p i c a l porous media w i l l have a d i s t r i b u t i o n o f pore s i z e s , r e s u l t i n g i n a m a g n e t i z a t i o n curve which r e c e i v e s c o n t r i b u t i o n s from each pore s i z e in the form o f d i f f e r e n t T j ' s . T h i s i m p l i e s t h a t the observed m a g n e t i z a t i o n i S j d e s c r i b e d by: M(r) = M | [1 - 2 e x p t - r / T j ) ] f ( T j ) dTj (3) T, i s the maxi expected v a l u e o f T, and i s u s u a l l y taken t o be the Tj f o r the bulk f l u i d . T . i s the minimum T j v a l u e and i s u s u a l l y taken t o be equal to tne s h o r t e s t 1, which can be measured with the p a r t i c u l a r instrument used. D e c o n v o l u t i o n o f Equation 3 t o y i e l d the d e s i r e d T, d i s t r i b u t i o n has been accomplished v i a nonn e g a t i v e l e a s t squares (NNLS) [14] ( d i s c r e t e d i s t r i b u t i o n s ) and r e g u l a r i z a t i o n [15] (continuous d i s t r i b u t i o n s ) a l g o r i t h m s . The d e s i r e d pore s i z e d i s t r i b u t i o n can then be determined from the T, d i s t r i b u t i o n v i a the a p p l i c a t i o n o f Equation 1. Equation 1 i s a p p l i c a b l e ( i . e . , no pore shape assumption) f o r pores with r a d i u s g r e a t e r than about 5 nm. However, the model has been extended to pores as small as 0.5 nm [16] by assuming a pore shape. In a d d i t i o n , the f r a c t i o n o f pore volume with pore s i z e s l e s s than 0.5 nm may be o b t a i n e d (assuming t h a t the concept o f pore s i z e i n t h i s s i z e range has p h y s i c a l s i g n i f i c a n c e ) although d i s t r i b u t i o n i n f o r m a t i o n i n t h a t r e g i o n can not be determined. The v a l u e f o r a can be determined independently but the magn i t u d e o f the s u r f a c e i n t e r a c t i o n parameter, must be found f o r the p a r t i c u l a r f r e q u e n c y / f l u i d / t e m p e r a t u r e / s o l i d system being s t u d i e d . Schmidt and co-workers [9] simply assumed a p v a l u e . Other workers [10,11] matched the NMR and mercury p o r o s i m e t r y d e r i v e d pore s i z e d i s t r i b u t i o n s t o e s t i m a t e p. More r e c e n t l y , Davis and co-workers [12] have shown t h a t p can be found v i a a s e r i e s o f T j experiments, v a r y i n g the q u a n t i t y o f f l u i d sorbed on the s o l i d s a r f a c e . In t h a t work i t was shown t h a t a p l o t o f i n v e r s e average Tj v e r s u s the s u r f a c e area (as determined v i a c o n v e n t i o n a l methods) times s o l i d c o n c e n t r a t i o n (SA*C) w i l l g i v e a l i n e with s l o p e (p/Z) and i n t e r c e p t a. T h i s value o f p can then be a p p l i e d t o f i n d unknown s u r f a c e areas and pore s i z e d i s t r i b u t i o n s u s i n g e x p e r i m e n t a l l y determined T.'s f o r s i m i l a r m a t e r i a l at the same f l u i d , frequency and temperature.


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EXPERIMENTAL

The pore s t r u c t u r e o f two types o f c a t a l y s t support m a t e r i a l were s t u d i e d : 7-alumina and s i l i c a a e r o g e l . The alumina samples were commercial c a t a l y s t supports made i n 1/8 i n c h diameter p e l l e t form by Harshaw Chemical. S i l i c a a e r o g e l s were prepared from s i l i c a g e l s s y n t h e s i z e d by a two step a c i d / b a s e c a t a l y z e d procedure employing TEOS with a water to s i l i c o n r a t i o equal to 3.7 [17] and ammonium hydroxide c o n c e n t r a t i o n o f 0.005 M (sample A) or 0.01 M


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(sample B). F o l l o w i n g g e l a t i o n , the samples were aged i n t h e i r r e s p e c t i v e l i q u o r at 323 K f o r 3 weeks (sample A) or 2 weeks (sample B). The aged samples were s o l v e n t exchanged with C 0 (at 298 K and 54 atm) and c r i t i c a l p o i n t d r i e d at 313 K and 81.7 aim t o produce a e r o g e l s . As we w i l l show, the aerogel pore s t r u c t u r e i s s e n s i t i v e to the ammonium hydroxide c o n c e n t r a t i o n employed i n the aging procedure. The pore s i z e d i s t r i b u t i o n o f the alumina m a t e r i a l was d e t e r mined v i a NMR and compared to r e s u l t s o b t a i n e d by mercury i n t r u s i o n and n i t r o g e n a d s o r p t i o n / c o n d e n s a t i o n t e c h n i q u e s . The pore s i z e d i s t r i b u t i o n s o f the two aerogel samples were measured v i a NMR and n i t r o g e n a d s o r p t i o n / c o n d e n s a t i o n o n l y ; the m a t e r i a l being too comp r e s s i b l e f o r porosimetry (the small pores o f the aerogel imply t h a t t h a t very high p r e s s u r e s are r e q u i r e d ) . NMR s p i n - l a t t i c e r e l a x a t i o n i n v e r s i o n r e c o v e r y (180°-r-90°) experiments were conducted on the samples u s i n g d i s t i l l e d water as the f l u i d probe. A d d i t i o n a l NMR experiments u s i n g cyclohexane were performed on the alumina m a t e r i a l . NMR experiments were performed using a Spin Lock L t d . CPS-2 p u l s e NMR at a frequency o f 20 MHz and temperature o f 303 K. R e l a x a t i o n curves were o b t a i n e d by measuring the f r e e i n d u c t i o n decay (FID) at approximately 30 d i f f e r e n t r v a l u e s between 10 ^s and 9 s. Samples f o r NMR experiments were s a t u r a t e d v i a a number o f t e c h n i q u e s . For f u l l s a t u r a t i o n , the alumina samples were immersed i n the f l u i d o f i n t e r e s t , whereas the aerogel samples were allowed t o e q u i l i b r a t e with vapor i n t r o d u c e d a f t e r e v a c u a t i n g the samples t o approximately 5 Pa. P a r t i a l s a t u r a t i o n was accomplished by e v a c u a t i n g the samples and then a l l o w i n g them t o e q u i l i b r a t e with vapor over s a l t s o l u t i o n s . F l u i d uptake was determined g r a v i m e t r i c a l l y . N i t r o g e n a d s o r p t i o n / c o n d e n s a t i o n measurements were performed u s i n g an Autosorb-1 a n a l y z e r to c a l c u l a t e sample s u r f a c e area and pore s i z e d i s t r i b u t i o n . BET a n a l y s i s at 77 K was a p p l i e d f o r ext r a c t i n g the monolayer c a p a c i t y from the a d s o r p t i o n isotherm and a N« m o l e c u l a r c r o s s - s e c t i o n a l area o f 0.162 nm was used to r e l a t e tne monolayer c a p a c i t y t o s u r f a c e area. PSD's were c a l c u l a t e d from the d e s o r p t i o n branches o f the isotherms u s i n g a m o d i f i e d form o f the BJH method [18]. Mercury i n t r u s i o n measurements were performed u s i n g an Autoscan-33 continuous scanning mercury p o r o s i m e t e r (1233000 p s i a ) and a c o n t a c t angle o f 140°.


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RESULTS AND DISCUSSION

Sample pore volumes and s u r f a c e areas v i a n i t r o g e n a d s o r p t i o n / condensation and mercury i n t r u s i o n are g i v e n i n Table I. For the alumina sample, the t o t a l pore volumes o b t a i n e d from condensation and mercury i n t r u s i o n are i n reasonable agreement. The l a r g e r v a l u e from mercury may be the r e s u l t o f sample compression and/or the presence o f pores «70 nm ( i . e . , c o r r e s p o n d i n g to the l a r g e s t r e l a t i v e p r e s s u r e used). For the s i l i c a a e r o g e l s , pore volumes c o u l d not be o b t a i n e d by porosimetry because sample compression e f f e c t s dominated the observed i n t r u s i o n (based on the o b s e r v a t i o n t h a t no mercury was e x t r a c t e d from the samples on the d e p r e s s u r i z a t i o n curve and v i s u a l i n s p e c t i o n o f the sample before and a f t e r a n a l y s i s ) . F o r the sample B a e r o g e l , n i t r o g e n a d s o r p t i o n i n d i c a t e d the presence o f a small amount o f m i c r o p o r o s i t y .


256


Sample

T a b l e I. Pore Volume and S u r f a c e Area Pore Volume (cc/g) S u r f a c e Area (m /g) Hg N N 2

2


Alumina Aerogel A Aerogel B

0.76

2

235 427 751

0.74 4.34 4.20

Magnetic r e l a x a t i o n d a t a from the NMR s p i n - l a t t i c e r e l a x a t i o n experiments on f u l l y s a t u r a t e d samples were d e c o n v o l u t e d i n t o cont i n u o u s T, d i s t r i b u t i o n s v i a the r e g u l a r i z a t i o n a l g o r i t h m . NMR experiments at d i f f e r e n t s a t u r a t i o n l e v e l s were used t o o b t a i n the a and p parameters which r e l a t e the T, d i s t r i b u t i o n s t o pore s i z e d i s t r i b u t i o n s (eq 1.) F i g u r e 1 i s a p l o t showing the r e s u l t o f these p a r t i a l s a t u r a t i o n experiments f o r water, w i t h the i n v e r s e average 1, ( o b t a i n e d from NNLS) p l o t t e d vs. the s u r f a c e area m u l t i p l i e d by the s o l i d c o n c e n t r a t i o n . The p a r t i a l s a t u r a t i o n e x p e r i ments f o r water e x h i b i t e d s i n g l e T, decay. The s l o p e and i n t e r c e p t o f the l i n e s i n F i g u r e 1 were used t o c a l c u l a t e p and a r e s p e c tively. Cyclohexane was a l s o used as a f l u i d f o r the alumina p e l l e t s . When p a r t i a l s a t u r a t i o n NMR experiments were performed u s i n g c y c l o hexane, the r e s u l t i n g T, d i s t r i b u t i o n s were very broad, making a p l o t s i m i l a r t o those i n F i g u r e 1 i m p o s s i b l e to c o n s t r u c t , a and p were i n s t e a d c a l c u l a t e d f o r the alumina/cyclohexane system v i a a one-point method, i . e . t a k i n g a t o be the i n v e r s e o f the T, f o r b u l k cyclohexane and c a l c u l a t i n g p from the average T, o f the f u l l y s a t u r a t e d sample (a s i n g l e decay) u s i n g : 1/Tj = a + p/2 SA * C (4) C was determined g r a v i m e t r i c a l l y and SA was taken as the N s u r f a c e area, a and p v a l u e s c a l c u l a t e d f o r the v a r i o u s samples are g i v e n i n T a b l e I I . A l s o i n c l u d e d are v a l u e s o f a f o r water and cyclohexane o b t a i n e d from experiments on bulk f l u i d . D i f f e r e n c e s between a v a l u e s f o r the same f l u i d are the r e s u l t o f u n c e r t a i n t y a r i s i n g from e x t r a p o l a t i o n and/or the presence o f d i s s o l v e d i m p u r i t i e s from the pore w a l l . R e g a r d l e s s , because o f the small pore s i z e s o f the m a t e r i a l s s t u d i e d , the c a l c u l a t e d pore s i z e i s o n l y a very weak f u n c t i o n o f a. P a r t i a l s a t u r a t i o n experiments f o r the aerogel m a t e r i a l were conducted o n l y on sample A. The a and p v a l u e s o b t a i n e d were assumed to be the same f o r sample B which was o f s i m i l a r c o m p o s i t i o n , d i f f e r i n g i n pore s t r u c t u r e o n l y . The v a l i d i t y o f t h i s assumption has been demonstrated i n o t h e r work [12] wherein samples o f s i m i l a r m a t e r i a l but d i f f e r e n t pore s t r u c t u r e f i t the same s t r a i g h t l i n e on p l o t s o f the type shown i n F i g u r e 1. 2

Table I I . a and p Values Material

Fluid

«(s )

Alumina Alumina Aerogel Bulk f l u i d Bulk f l u i d

Water Cyclohexane Water Water Cyclohexane

1.19 0.481 0.566 0.381 0.480

_ 1

£(nm/s) 105.5 8.28 8.64



SMITH ET AL.


40-1

F i g u r e 1.

SA*C p l o t s f o r d e t e r m i n a t i o n o f a and p.


257


258


-5000

Radius (nm)

F i g u r e 2.

M(r), D C M

and PSD p l o t s f o r cyclohexane i n alumina.



24.

SMITH ETAL.

Pore Structure Characterization ofCatalyst Supports

The c a l c u l a t i o n o f NMR pore s i z e d i s t r i b u t i o n s i s a t h r e e s t e p process once the values o f a and p are known. F i r s t a s p i n - l a t t i c e r e l a x a t i o n experiment i s undertaken on a s a t u r a t e d sample and a d a t a set o f m a g n e t i z a t i o n - d e l a y time, M(r), i s o b t a i n e d . The magnetizat i o n d a t a i s subsequently deconvoluted u s i n g r e g u l a r i z a t i o n t o o b t a i n a d i s t r i b u t i o n o f pore volume with T, [ i n t h i s work, the d i s t r i b u t i o n o f volume with the l o g o f T, i s c a l c u l a t e d , d V / d l o g ( T , ) ] . F i n a l l y , Equation 1 i s a p p l i e d t o c o n v e r t from T, t o pore s i z e and o b t a i n the d e s i r e d pore s i z e d i s t r i b u t i o n . S i n c e the pore shape which best d e s c r i b e s the a c t u a l pore shape i n these s o l i d s i s unknown, we simply use Equation 1. For 1 nm pores, e r r o r s o f up t o 10% c o u l d a r i s e from t h i s assumption depending on the a c t u a l pore shape [16]. T h i s c a l c u l a t i o n process i s i l l u s t r a t e d i n F i g u r e 2 f o r the alumina sample s a t u r a t e d with cyclohexane. The T j d i s t r i b u t i o n s o f f u l l y s a t u r a t e d samples were combined with the a and p values o f Table II t o produce pore s i z e d i s t r i b u t i o n s f o r each m a t e r i a l . The NMR pore s i z e d i s t r i b u t i o n s were compared f o r each type o f m a t e r i a l t o pore s i z e d i s t r i b u t i o n s obt a i n e d v i a n i t r o g e n a d s o r p t i o n / c o n d e n s a t i o n ( a l l m a t e r i a l s ) and mercury p o r o s i m e t r y (alumina samples). The r e s u l t s are shown i n F i g u r e 3 f o r alumina and i n F i g u r e 4 f o r the a e r o g e l s . In each case the NMR agrees f a i r l y well with the o t h e r t e c h n i q u e s , but i s seen t o r e s u l t i n s l i g h t l y l a r g e r pore s i z e s . T h i s i s c o n s i s t e n t with the l i m i t a t i o n s o f the other techniques which g e n e r a l l y r e s u l t i n s m a l l e r than a c t u a l pore s i z e measurements due t o c o n s t r i c t e d pores and n e t w o r k / p e r c o l a t i o n e f f e c t s . The d i f f e r e n c e between the two a e r o g e l s i s the r e s u l t o f the l o n g e r aging c o n d i t i o n s f o r Aerogel A. The NMR r e s u l t s f o r water and cyclohexane i n alumina should agree c l o s e l y . The d i f f e r e n c e noted i s probably due t o i n a c c u r a c i e s i n the cyclohexane a and p which had been c a l c u l a t e d u s i n g a one-point method. 2.5-1

Radius

F i g u r e 3. alumina.

NMR,

(nm)

n i t r o g e n condensation and p o r o s i m e t r y PSD's f o r


259


260


ACKNOWLEDGMENTS

T h i s work has been supported by Sandia N a t i o n a l L a b o r a t o r i e s (#556778) and t h e ALCOA Foundation. N i t r o g e n a d s o r p t i o n and mercury p o r o s i m e t r y measurements were performed by S.B. Ross. A e r o g e l s were prepared by Carol S. A s h l e y o f SNL. REFERENCES

[1] Washburn, E.W.; Phys. Rev., 1921, 17, 273. [2] Mason, G . ; J. Colloid Interface Sci., 1972, 41, 208. [3] Smith, D.M., Gallegos, D.P., Stermer, D . L . ; Powder Tech., 1987, 53, 11. [4] Conner, W.C., Weist, E.L., Pedersen, L . A . ; PREPARATION OF CATALYSTS IV: Delmon, Grange, Jacobs, and Poncelet Editors, Elsevier, Amsterdam, 1987. [5] Ciftcioglu, M., Smith, D.M., Ross, S.B.; Powder Tech., 1988, 55, 193. [6] Hanus, F., Gillis, P . ;J.Mag. Resonance, 1984, 59, 437.



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SMITH ETAL.


[7] Senturia, S.D., Robinson, J.D.; Soc. Pet. Eng. J., 1970, 10, 237. [8] Loren, J.D., Robinson, J.D.; Soc. Pet. Eng. J., 1970, 10, 268. [9] Schmidt, E.J., Velasco, K.K., Nur, A.M.; J.APPI.Phys., 1986, 59, 2788. [10] Brown, J.A., Brown, L.F., Jackson, J.A., Milewski, J.V., Travis, J.V.; Proceedings of the SPE/DOE Unconventional Gas Recovery Symposium, 1982, 201. [11] Gallegos, D.P., Munn, K . , Smith, D.M., Stermer, D.L.; J. Colloid Interface Sci., 1987, 19, 127. [12] Davis, P.J., Gallegos, D.P., Smith, D.M.; Powder Tech., 1987, 53, 39. [13] Brownstein, K.R., Tarr, C . E . ; J. Mag. Resonance, 1980, 39, 297. [14] Munn, K . , Smith, D.M.; J. Colloid Interface Sci., 1987, 119, 117. [15] Gallegos, D.P., Smith, D.M.; J. Colloid Interface Sci., 1988, 122, 143. [16] Gallegos, D.P., Smith, D.M., Brinker, C.J.; J. Colloid Interface Sci., 1988, 124, 186. [17] Brinker, C.J., Keefer, K . D . , Schaefer, D.W., Ashley, C . S . ; J. Non-Crystalline Solids, 1982, 48, 47. [18] S. Lowell and J. Shields, Powder Surface Area and Porosity; Chapman & Hall: London, 1984. RECEIVED January10,1989


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