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Pore Size Analysis of Wet Materials Via Low-Field NMR
F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids 11 0 1991 Elsevier Science Publishers B.V., Amsterdam
301
PORE SIZE ANALYSIS OF WET MATERIALS VIA LOW-FIELD NMR
Douglas M. Smith and Pamela J. Davis UNM/NSF CENTER FOR MICRO-ENGINEERED CERAMICS, University of New Mexico, Albuquerque, NM 87131 USA ABSTRACT
Conventional pore size analysis techniques require the use of dried materials but many materials undergo drastic structural rearrangement during drying (i.e., before analysis). The use of low-field NMR spin-lattice relaxation measurements is demonstrated for pore structure analysis for a number of wet solids including silica gels and ion exchange resins. INTRODUCTION
Most pore structure analysis techniques (adsorption/condensation, mercury porosimetry, TEM/SEM, etc.) are not appropriate for "wet" materials since they require the removal of Dore fluid before analysis. Since drying the sample can induce significant, irreversible changes (and is often a topic of study in its own right), a "nonintrusive" technique is required. The ability to monitor pore structure changes during materials processing would be of great utility for many materials. In general, changes during processing have been inferred from the pore structure of the final dried material. However, chemistry and structure often continue to evolve during drying and the interpretation of how a parameter affects the final pore structure is not straightforward. The few studies of pore structure evolution during processing use either scattering (SAXS, SANS), thermoporometry, NMR relaxation, or magnetic resonance imaging (MRI). BACKGROUND
Scattering has primarily provided information on nucleation and growth mechanisms in solution and/or the structure of the final dried material. The use of scattering for in-situ pore structure analysis suffers from limited length scales (1-20 nm, SAXS only), contrast problems, relation of results to pore size, multiple scattering, and
302
errors resulting from desmearing. However, the approach is quick, allows extraction of all length scales at once, and accesses closed porosity. Thermoporometry provides pore size information from comparison of melting and solidification thermograms (ie., the freezing/melting temperature of pore fluid is a function of pore size) [1,2]. This approach is useful for determining pore size distribution with pores in the size range of 1.5 to 150 n m but suffers from several limitations regarding its use. These include the fact that the pore fluid must be very pure (requires multiple washing which can change structure], is nonisothermal, requires a pore shape assumption to relate temperature to freezing point, suffers from network/percolation effects, and the volume changes associated with phase change can significantly affect the structure of the sample. In addition, the nature of the thermoporometry experiment precludes the continuous study of change in a single sample as it undergoes processing. The use of low-field NMR has been suggested as a pore structure tool and offers advantages [3,4]including the use of the existing pore fluid as the probe, a large pore size range (4nm to > 10 pm), the lack of percolation effects, and a pore shape assumption is only required for pores smaller than several nm. This technique is well suited for in-situ studies of gel structure as it is non-intrusive in the sense that the pore fluid is used as the probe, high purity fluids are not required, and the temperature is held constant. Pore size and surface area information are obtained from the fact that fluid near a surface will undergo spin-lattice (Ti) and spin-spin relaxation (Ti) at a faster rate than for the bulk fluid. From the two-fraction, fast exchange model, the measured Ti or T2 is related to the pore size by [51:
where the pore size, rp, is the hydraulic radius (2PV/As). The physical model associated with Equation 1 is illustrated in Figure 1. When the pore volume is large as compared to the surface area, (i.e., for pore size larger than 3-5nm) the volume of the surfaceaffected phase is small and the pore volume to surface area ratio is obtained directly from Equation 1. For smaller pores, assumptions concerning pore geometry
303
and the thickness of the surfaceaffected phase are required [61. The thickness of this surface-affected phase is typically 0.3 +/- 0.1 nm.
4 1
Bulk Fluid
I
U Pore Wall
Schematic diagram of pore fluid during a NMR experiment.
Figure 1
From relaxation measurements of fluid in the pores and the bulk fluid, the pore size maybe obtained if the surface interaction parameter,
p, is known. p is found by either
performing a series of relaxation experiments on partially saturated samples with different moisture contents [7] or by performing relaxation experiments on samples with submonolayer fluid coverage to directly obtain the surface relaxation time [81. For a porous solid, a distribution of relaxation times exists which must be extracted from the measured magnetization relaxation data. This requires the solution of Tlmax [1-2~p[-dT111f[T11 dT1
M(d = MO
(2)
Tlmin where M(T) is the measured magnetization at different delay times, 2, MO is the equilibrium magnetization, and f[T1] is the desired distribution of relaxation times which is directly related to the pore size distribution via Equation 1. Equation 2 may be solved bj a number of approaches such as the method of regularization [9].
EXPERIMENTAL Silica gels were prepared from tetraethyl orthosilicate using a two-step, basecatalyzed scheme described by Brinker and co-workers [lo]. This system was selected since it yields a fairly broad pore size distribution in both the initial(wet) and final (dried) states. The pore size distribution and surface area were determined durine
304
processing using a 20 M H z NMR and a 1800-~-900 pulse sequence as described elsewhere [3]. Before drying, samples were aged under various conditions including washing the samples with ethanol to remove the mother liquor (a mixture of water, ethanol, and unreacted TEOS),aging with various pH fluids (water and KOH), and aging in mother liquor for extended time. Samples were dried at ambient conditions for 1 week and then at 383 K. In addition to silica gels, commercial materials such as phase separated Vycor glass (Corning Glass) and ion exchange resins (Dow Chemical) were studied. For NMR pore size analysis, the Vycor was saturated by placing samples in an evacuated chamber and partially filling the chamber with ethanol such that only ethanol vapor contacted the sample. Ion exchange resins were both analyzed "as is" as well as after washing in distilled water. In addition to NMR,some samples were analyzed by thermoporometry using water as the pore fluid and a heating rate of 0.5 K/min. To convert the thermograms to pore size distributions, the method described by Eyraud et al. 121 was employed. N2 adsorption/condensation (77K)was used to obtain surface area [Spoint BET analysis (0.05
RESULTS AND DISCUSSION A significant part of pore structure characterization via NMR relaxation measurements is the determination of the surface-interaction parameter, required to relate relaxation time to pore size (see Eq. 1).
p, which is
p is a function of temperature,
fluid, surface chemistry, and field strength. As the field strength (and proton frequency)
p increases leading to greater sensitivity to pore size. Assuming that temperature and field strength are fixed, p for a given fluid-porous solid decrease, the magnitude of
combination can be found via several approaches. For high surface area materials, one can dry the sample sufficiently such that the magnitude of the surface relaxation time and the thickness of the surface-affected phase may be measured directly. Alternatively, one can measure relaxation on an unsaturated sample as the fluid content changes (effectivelychanging the ratio of bulk to surface-affected phases). If one knows the total surface area of the sample (for example, from nitrogen adsorption), a plot of 1/T1 versus
305
the product of Mv (mass of solid per volume of fluid) and surface area should be linear with a slope proportional to p. This type of plot is illustrated in Figure 2 for Vycor glass. In general, we have found that that the value of
p does not vary greatly (i.e. greater than
50%) for a given fluid and a wide range of solids if the solids do not contain a significant
concentration of paramagnetic impurities. With
p known, the pore size distribution
(PSD) may be calculated via the solution of Equation 2. The NMR-derived PSD as well as nitrogen condensation results (adsorption and desorption) are included in Figure 3 for Vycor. As expected, the NMR PSD exhibits a slightly broader distribution and a mean pore radius which is approximately 50% larger than the adsorption branch. This is a result of two factors: the skewing of condensation results to smaller pore size as a result of networklpercolation effects and the fact that NMR obtains the hydraulic radius (i.e., twice the pore volume to surface area) which only agrees with the condensation pore size when the sample contains uniform, smooth cylindrical pores.
0
1000
M v As
2000
3000
Figure 2 Variation of relaxation time with moisture content for Vycor.
306
1
10
100
r (nm)
Figure 4 Pore size distribution change during drying of a B2 silica gel. Also included is the PSD of the dried gel by nitrogen condensation and NMR. The synthesis of ceramics via sol-gel processing is an area for which the ability to study pore structure in-situ is of great practical importance. By changing processing conditions, the PSD of a wet gel--
be changed significantly to either change further
processing steps (e.g., drying) or the structure and properties of the final dried gel. How the pore sue distribution changes during drying is illustrated in Figure 4 for a base-
307
catalyzed silica gel as it dries over a one week period. After complete drying at 383 K, the sample was analyzed via N2 condensation and subsequently resaturated for NMR analysis. During the initial stages of drying, the large pores disappear as the wet gel shrinks and the entire gel remains saturated. As drying continues, the matrix eventually stiffens such that the vapor-liquid menisci penetrate the gel. From weight loss and volume measurements, we calculate this to occur at approximately 75% solvent loss. During this final stage of drying, a large decrease in pore size is noted as a result of the large capillary forces in pores less than 10 nm. The N2 and NMR results for the dried gel show good agreement. Often, the pore fluid in a wet gel is changed to modify the pore structure before drying. Larger pores in the wet gel imply lower capillary forces during drying and hence, faster drying rates without cracking and larger pore size in the final dried material [ll]. This increase in the pore size distribution is illustrated in Figure 5 for a gel washed repeatedly in water. Note that the smallest pore size is now 8 nm as compared to 3.5 nm for the gel washed in ethanol (see Figure 4). Water has the effect of increasing hydrolysis/condensation in the gel resulting in larger pores. Also shown in Figure 5 is the pore size distribution obtained from thermoporometry. Although the two techniques show reasonable agreement considering that they are completely independent, the thermoporometry is shifted to smaller pore size and also had a second peak at pore size greater than 1 pm. Pores this large are not contained in the wet gel since it is transparent. This is probably the result of structural rearrangement during freezing because of the fairly large cooling rates (0.5 C/min) associated with our instrument.
-
308
2o
,-I),
NMR
Themopommetry
10
01
. m
1
1
10
r (nm)
2500 A
m
1500-
U J
lWO;,
a
500-
Y
0
1000
unwashed EtOH washed 1 time A EtOH washed 5 times
W 0
2000-'i
2E
100
w 0
I
O
0
I
A.
1
I
For the study of some problems, the specific surface area is a more useful then the pore size distribution. This is illustrated in Figure 6 for three samples (unwashed, washed once in EtOH, and washed five times in EtOH) during drying. Previously, we have observed 181 a maximum in the surface area-solvent content curve in the vicinity of 4040% solvent loss. Also, it is often observed that when transparent wet silica gels are immersed in water, they become opaque and this is attributed to phase separation of formally unreacted TEOS in the pore fluid [ll]. We attribute the surface area increase during drying to this same effect. That is, as drying proceeds, the concentration of TEOS
309
and water in the pore fluid increases and results in the precipitation of high surface area silica. Evidence for this is presented in Figure 6 since only with extensive washing (5 times) does the surface area increase disappear.
J
d :: * m
,M m
ti
U A
&
M
1
I
p i
I I
Y
Figure 7
: ; .
2-
Y
....)..
Themopormetry
S I
10
r (nm)
100
Comparison of pore size distributions for Dow IX resin.
In addition to inorganic materials, NMR may also be used to study pore structure in organic materials such as ion exchange resins. A comparison between NMR and thermoporometry is presented in Figure 7. Good agreement is obtained between the techniques and the reason for the NMR peak at 70-80 nm is probably the result of "free" water on the outside of the small ion exchange particles. CONCLUSIONS
The use of low-field NMR appears to offer reasonable pore structure information (pore size distribution, surface area, etc.) for wet porous solids which could not be previously obtained by conventional methods. ACKNOWLEDGEMENTS
This work has been supported by Sandia National Laboratories (#05-5795) and
the UNM/NSF Center for Micro-Engineered Ceramics which is a collaborative effort of the NSF (CDR-8803152), Sandia and Los Alamos National Laboratories, the NMRDI, and the ceramics industry. The authors thank G. Johnston and K. Moore their help.
310
REFERENCES Brun, M., Lallemand, A., Quinson, J., and Eyraud, C., Thermochim. Acta, 1977, 1. 2. 3. 4.
5. 6.
7.
a.
9. 10. 11.
21,59. Eyraud, C., Quinson, J.F., and Brun, M., in CHARACTERIZATION OF POROUS SOLIDS, Eds. Unger, Rouquerol, Sig, Elsevier, Amsterdam, (1988). Gallegos, D.P., Munn, K., Smith, D.M., and Stermer, D.L., J. Colloid Interface Sci., 1987,119,127. Bhattacharja, S., DOrazio, F., T a r m n , J.C., Halperin, W.P., and Gerhardt, R, J.Am.Ceram.Soc., 1989, 72, 2126. Brownstein, K.R.,and Tam, C.E.,1. Mag. Resonance, 1977, 26, 17. Gallegos, D.P., Smith, D.M., and Brinker, CJ., J. Colloid Interface Sci., 1988, 124, 186. Davis, PJ., Gallegos, D.P., and Smith, D.M., Pow. Tech., 1987, 53,39. Glaves, C.L., Brinker, C.J., Smith, D.M., and Davis, P.J., Chem. Materials, 1989,1,
34. Gallegos, D.P., Smith, D.M., J. Colloid Interface Sci., 1988,122,143. Brinker, C.J., Keefer, K.D., Schaefer, D.W., Ashley, C.S., J. Non-Cryst. Solids, 1982,
48,47. Scherer, G.W., J. Non-Cryst. Solids, 1988, 100,77.
301
PORE SIZE ANALYSIS OF WET MATERIALS VIA LOW-FIELD NMR
Douglas M. Smith and Pamela J. Davis UNM/NSF CENTER FOR MICRO-ENGINEERED CERAMICS, University of New Mexico, Albuquerque, NM 87131 USA ABSTRACT
Conventional pore size analysis techniques require the use of dried materials but many materials undergo drastic structural rearrangement during drying (i.e., before analysis). The use of low-field NMR spin-lattice relaxation measurements is demonstrated for pore structure analysis for a number of wet solids including silica gels and ion exchange resins. INTRODUCTION
Most pore structure analysis techniques (adsorption/condensation, mercury porosimetry, TEM/SEM, etc.) are not appropriate for "wet" materials since they require the removal of Dore fluid before analysis. Since drying the sample can induce significant, irreversible changes (and is often a topic of study in its own right), a "nonintrusive" technique is required. The ability to monitor pore structure changes during materials processing would be of great utility for many materials. In general, changes during processing have been inferred from the pore structure of the final dried material. However, chemistry and structure often continue to evolve during drying and the interpretation of how a parameter affects the final pore structure is not straightforward. The few studies of pore structure evolution during processing use either scattering (SAXS, SANS), thermoporometry, NMR relaxation, or magnetic resonance imaging (MRI). BACKGROUND
Scattering has primarily provided information on nucleation and growth mechanisms in solution and/or the structure of the final dried material. The use of scattering for in-situ pore structure analysis suffers from limited length scales (1-20 nm, SAXS only), contrast problems, relation of results to pore size, multiple scattering, and
302
errors resulting from desmearing. However, the approach is quick, allows extraction of all length scales at once, and accesses closed porosity. Thermoporometry provides pore size information from comparison of melting and solidification thermograms (ie., the freezing/melting temperature of pore fluid is a function of pore size) [1,2]. This approach is useful for determining pore size distribution with pores in the size range of 1.5 to 150 n m but suffers from several limitations regarding its use. These include the fact that the pore fluid must be very pure (requires multiple washing which can change structure], is nonisothermal, requires a pore shape assumption to relate temperature to freezing point, suffers from network/percolation effects, and the volume changes associated with phase change can significantly affect the structure of the sample. In addition, the nature of the thermoporometry experiment precludes the continuous study of change in a single sample as it undergoes processing. The use of low-field NMR has been suggested as a pore structure tool and offers advantages [3,4]including the use of the existing pore fluid as the probe, a large pore size range (4nm to > 10 pm), the lack of percolation effects, and a pore shape assumption is only required for pores smaller than several nm. This technique is well suited for in-situ studies of gel structure as it is non-intrusive in the sense that the pore fluid is used as the probe, high purity fluids are not required, and the temperature is held constant. Pore size and surface area information are obtained from the fact that fluid near a surface will undergo spin-lattice (Ti) and spin-spin relaxation (Ti) at a faster rate than for the bulk fluid. From the two-fraction, fast exchange model, the measured Ti or T2 is related to the pore size by [51:
where the pore size, rp, is the hydraulic radius (2PV/As). The physical model associated with Equation 1 is illustrated in Figure 1. When the pore volume is large as compared to the surface area, (i.e., for pore size larger than 3-5nm) the volume of the surfaceaffected phase is small and the pore volume to surface area ratio is obtained directly from Equation 1. For smaller pores, assumptions concerning pore geometry
303
and the thickness of the surfaceaffected phase are required [61. The thickness of this surface-affected phase is typically 0.3 +/- 0.1 nm.
4 1
Bulk Fluid
I
U Pore Wall
Schematic diagram of pore fluid during a NMR experiment.
Figure 1
From relaxation measurements of fluid in the pores and the bulk fluid, the pore size maybe obtained if the surface interaction parameter,
p, is known. p is found by either
performing a series of relaxation experiments on partially saturated samples with different moisture contents [7] or by performing relaxation experiments on samples with submonolayer fluid coverage to directly obtain the surface relaxation time [81. For a porous solid, a distribution of relaxation times exists which must be extracted from the measured magnetization relaxation data. This requires the solution of Tlmax [1-2~p[-dT111f[T11 dT1
M(d = MO
(2)
Tlmin where M(T) is the measured magnetization at different delay times, 2, MO is the equilibrium magnetization, and f[T1] is the desired distribution of relaxation times which is directly related to the pore size distribution via Equation 1. Equation 2 may be solved bj a number of approaches such as the method of regularization [9].
EXPERIMENTAL Silica gels were prepared from tetraethyl orthosilicate using a two-step, basecatalyzed scheme described by Brinker and co-workers [lo]. This system was selected since it yields a fairly broad pore size distribution in both the initial(wet) and final (dried) states. The pore size distribution and surface area were determined durine
304
processing using a 20 M H z NMR and a 1800-~-900 pulse sequence as described elsewhere [3]. Before drying, samples were aged under various conditions including washing the samples with ethanol to remove the mother liquor (a mixture of water, ethanol, and unreacted TEOS),aging with various pH fluids (water and KOH), and aging in mother liquor for extended time. Samples were dried at ambient conditions for 1 week and then at 383 K. In addition to silica gels, commercial materials such as phase separated Vycor glass (Corning Glass) and ion exchange resins (Dow Chemical) were studied. For NMR pore size analysis, the Vycor was saturated by placing samples in an evacuated chamber and partially filling the chamber with ethanol such that only ethanol vapor contacted the sample. Ion exchange resins were both analyzed "as is" as well as after washing in distilled water. In addition to NMR,some samples were analyzed by thermoporometry using water as the pore fluid and a heating rate of 0.5 K/min. To convert the thermograms to pore size distributions, the method described by Eyraud et al. 121 was employed. N2 adsorption/condensation (77K)was used to obtain surface area [Spoint BET analysis (0.05
RESULTS AND DISCUSSION A significant part of pore structure characterization via NMR relaxation measurements is the determination of the surface-interaction parameter, required to relate relaxation time to pore size (see Eq. 1).
p, which is
p is a function of temperature,
fluid, surface chemistry, and field strength. As the field strength (and proton frequency)
p increases leading to greater sensitivity to pore size. Assuming that temperature and field strength are fixed, p for a given fluid-porous solid decrease, the magnitude of
combination can be found via several approaches. For high surface area materials, one can dry the sample sufficiently such that the magnitude of the surface relaxation time and the thickness of the surface-affected phase may be measured directly. Alternatively, one can measure relaxation on an unsaturated sample as the fluid content changes (effectivelychanging the ratio of bulk to surface-affected phases). If one knows the total surface area of the sample (for example, from nitrogen adsorption), a plot of 1/T1 versus
305
the product of Mv (mass of solid per volume of fluid) and surface area should be linear with a slope proportional to p. This type of plot is illustrated in Figure 2 for Vycor glass. In general, we have found that that the value of
p does not vary greatly (i.e. greater than
50%) for a given fluid and a wide range of solids if the solids do not contain a significant
concentration of paramagnetic impurities. With
p known, the pore size distribution
(PSD) may be calculated via the solution of Equation 2. The NMR-derived PSD as well as nitrogen condensation results (adsorption and desorption) are included in Figure 3 for Vycor. As expected, the NMR PSD exhibits a slightly broader distribution and a mean pore radius which is approximately 50% larger than the adsorption branch. This is a result of two factors: the skewing of condensation results to smaller pore size as a result of networklpercolation effects and the fact that NMR obtains the hydraulic radius (i.e., twice the pore volume to surface area) which only agrees with the condensation pore size when the sample contains uniform, smooth cylindrical pores.
0
1000
M v As
2000
3000
Figure 2 Variation of relaxation time with moisture content for Vycor.
306
1
10
100
r (nm)
Figure 4 Pore size distribution change during drying of a B2 silica gel. Also included is the PSD of the dried gel by nitrogen condensation and NMR. The synthesis of ceramics via sol-gel processing is an area for which the ability to study pore structure in-situ is of great practical importance. By changing processing conditions, the PSD of a wet gel--
be changed significantly to either change further
processing steps (e.g., drying) or the structure and properties of the final dried gel. How the pore sue distribution changes during drying is illustrated in Figure 4 for a base-
307
catalyzed silica gel as it dries over a one week period. After complete drying at 383 K, the sample was analyzed via N2 condensation and subsequently resaturated for NMR analysis. During the initial stages of drying, the large pores disappear as the wet gel shrinks and the entire gel remains saturated. As drying continues, the matrix eventually stiffens such that the vapor-liquid menisci penetrate the gel. From weight loss and volume measurements, we calculate this to occur at approximately 75% solvent loss. During this final stage of drying, a large decrease in pore size is noted as a result of the large capillary forces in pores less than 10 nm. The N2 and NMR results for the dried gel show good agreement. Often, the pore fluid in a wet gel is changed to modify the pore structure before drying. Larger pores in the wet gel imply lower capillary forces during drying and hence, faster drying rates without cracking and larger pore size in the final dried material [ll]. This increase in the pore size distribution is illustrated in Figure 5 for a gel washed repeatedly in water. Note that the smallest pore size is now 8 nm as compared to 3.5 nm for the gel washed in ethanol (see Figure 4). Water has the effect of increasing hydrolysis/condensation in the gel resulting in larger pores. Also shown in Figure 5 is the pore size distribution obtained from thermoporometry. Although the two techniques show reasonable agreement considering that they are completely independent, the thermoporometry is shifted to smaller pore size and also had a second peak at pore size greater than 1 pm. Pores this large are not contained in the wet gel since it is transparent. This is probably the result of structural rearrangement during freezing because of the fairly large cooling rates (0.5 C/min) associated with our instrument.
-
308
2o
,-I),
NMR
Themopommetry
10
01
. m
1
1
10
r (nm)
2500 A
m
1500-
U J
lWO;,
a
500-
Y
0
1000
unwashed EtOH washed 1 time A EtOH washed 5 times
W 0
2000-'i
2E
100
w 0
I
O
0
I
A.
1
I
For the study of some problems, the specific surface area is a more useful then the pore size distribution. This is illustrated in Figure 6 for three samples (unwashed, washed once in EtOH, and washed five times in EtOH) during drying. Previously, we have observed 181 a maximum in the surface area-solvent content curve in the vicinity of 4040% solvent loss. Also, it is often observed that when transparent wet silica gels are immersed in water, they become opaque and this is attributed to phase separation of formally unreacted TEOS in the pore fluid [ll]. We attribute the surface area increase during drying to this same effect. That is, as drying proceeds, the concentration of TEOS
309
and water in the pore fluid increases and results in the precipitation of high surface area silica. Evidence for this is presented in Figure 6 since only with extensive washing (5 times) does the surface area increase disappear.
J
d :: * m
,M m
ti
U A
&
M
1
I
p i
I I
Y
Figure 7
: ; .
2-
Y
....)..
Themopormetry
S I
10
r (nm)
100
Comparison of pore size distributions for Dow IX resin.
In addition to inorganic materials, NMR may also be used to study pore structure in organic materials such as ion exchange resins. A comparison between NMR and thermoporometry is presented in Figure 7. Good agreement is obtained between the techniques and the reason for the NMR peak at 70-80 nm is probably the result of "free" water on the outside of the small ion exchange particles. CONCLUSIONS
The use of low-field NMR appears to offer reasonable pore structure information (pore size distribution, surface area, etc.) for wet porous solids which could not be previously obtained by conventional methods. ACKNOWLEDGEMENTS
This work has been supported by Sandia National Laboratories (#05-5795) and
the UNM/NSF Center for Micro-Engineered Ceramics which is a collaborative effort of the NSF (CDR-8803152), Sandia and Los Alamos National Laboratories, the NMRDI, and the ceramics industry. The authors thank G. Johnston and K. Moore their help.
310
REFERENCES Brun, M., Lallemand, A., Quinson, J., and Eyraud, C., Thermochim. Acta, 1977, 1. 2. 3. 4.
5. 6.
7.
a.
9. 10. 11.
21,59. Eyraud, C., Quinson, J.F., and Brun, M., in CHARACTERIZATION OF POROUS SOLIDS, Eds. Unger, Rouquerol, Sig, Elsevier, Amsterdam, (1988). Gallegos, D.P., Munn, K., Smith, D.M., and Stermer, D.L., J. Colloid Interface Sci., 1987,119,127. Bhattacharja, S., DOrazio, F., T a r m n , J.C., Halperin, W.P., and Gerhardt, R, J.Am.Ceram.Soc., 1989, 72, 2126. Brownstein, K.R.,and Tam, C.E.,1. Mag. Resonance, 1977, 26, 17. Gallegos, D.P., Smith, D.M., and Brinker, CJ., J. Colloid Interface Sci., 1988, 124, 186. Davis, PJ., Gallegos, D.P., and Smith, D.M., Pow. Tech., 1987, 53,39. Glaves, C.L., Brinker, C.J., Smith, D.M., and Davis, P.J., Chem. Materials, 1989,1,
34. Gallegos, D.P., Smith, D.M., J. Colloid Interface Sci., 1988,122,143. Brinker, C.J., Keefer, K.D., Schaefer, D.W., Ashley, C.S., J. Non-Cryst. Solids, 1982,
48,47. Scherer, G.W., J. Non-Cryst. Solids, 1988, 100,77.