9594
J. Phys. Chem. 1994, 98, 9594-9600
Inaccessible Pore Characterization of Less-Crystalline Microporous Solids M. Ruike, T. KasuJ N. Setoyama, T. Suzuki, and K. Kaneko* Department of Chemistry, Faculty of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263, Japan Received: February 25, 1994; In Final Form: July 16, 1994@
The pore structures of microporous carbon fibers having less-crystalline structures with different activation extents were examined by small-angle X-ray scattering (SAXS), N2 adsorption, and density measurements. The different kinds of porosities were associated with observable quantities and a new concept of an inaccessible pore was introduced. Inaccessible pores include closed pores and ultrapores which are accessible by He at 303 K but not by NZ at 77 K. The surface area of samples was determined by both the high-resolution a, plot of the N2 adsorption isotherm and the Debye-Bueche plot of the SAXS profile. The surface area a, from SAXS was greater than that a, from N2 adsorption. The difference a, - a, was associated with the volume and size of the inaccessible pores. The possibility for a general application of this inaccessible pore characterization was discussed.
Introduction Microporous solids are divided into crystalline and lesscrystalline ones. Zeolites are representative crystalline microporous solids whose microporosity can be evaluated by the X-ray diffraction data. On the other hand, the microporosity of less-crystalline solids such as activated carbon cannot be determined by the X-ray diffraction. Activated carbon which is a representative of less-crystalline microporous solids, however, has gathered much attention from separation, energy, and environmental sciences.l s 2 The great microporosity of activated carbon can offer molecular-order slit-shaped spaces for new reaction, storage, and adsorption regardless of the illdefined structure. Even physicists have basic interests in activated carbons, then they found unusual physical properties such as photoconductive behavior^.^ Recent molecular simulation researches have been studying model activated carbon system^.^-^ Also new microporous carbon materials have stimulated the fundamental sciences. Activated carbon fibers (ACFs) have been believed to have quite uniform micropores and exhibit better surface properties compared with classical granulated activated carbon^.^-^ Activated mesophase carbon microbeads have more ordered structure irrespective of greater surface area than ACFs.l0 Even fullerene crystals have microporous nature." These new microporous carbons should contribute to the understanding of molecules in the confined spaces. Therefore, more exact pore characterization of new microporous carbon has been expected to develop new chemistry on less-crytalline solids and molecular science in the confined micropore spaces. The activated carbon is made of micrographitic units and their binding parts.12 The pores develop mainly between micrographitic walls during activation process. All pores are not necessarily connected to the external surfaces; open and closed pores should be separately evaluated. In the case of the assessment of open porosity, N2 adsorption at 77 K has been widely used.13 Recently, effectiveness of He adsorption at 4.2 K was shown in evaluation of the ultramicrop~rosity.~~ Only molecular adsorption, however, cannot determine the detailed pore structure including the closed pores. Small-angle X-ray scattering (SAXS) has been used to evaluate whole porosities Research Center, Osaka Gas Co., Torishima, Konohana, Osaka 554, Japan. Abstract published in Advance ACS Absfracts, September 1, 1994. +
@
of open and closed pores. Analytical approaches to SAXS data on activated carbons have still important discussion^,^^^^^ and the previous SAXS studies cannot evaluate the number of closed pores easily. The combined approach of SAXS, molecular adsorption, and density measurements is desired to describe the exact microporosities of activated carbons. In this article, a new analysis for separated evaluation of open and closed microporosities of activated carbon fibres (ACFs) by the combined approach is given.
Combined Micropore Analysis We presume that ACFs have slight heterogeneous micropore structures. The micropores were classified into larger and smaller micropores, ultrapores, and closed pores. Figure 1 shows schematically these pores in terms of their volumes. The detailed definition of each pore will be given later. We must determine the volume, fraction, and specific surface area of each pore. Three kinds of examinations of SAXS, N2 adsorption, and density measurements are necessary for exact determination of these pore structures. How to combine these three methods will be described in the following. Micropore Volume and Specific Surface Area from N2 Adsorption. N2 adsorption at 77 K provides a definite micropore volume of a solid. Total micropore volume (W,) is determined by the a, plot.13 The heterogeneous micropore structure of smaller and larger micropores are determined from the analysis of the adsorption isotherm with the two-term Dubinin-Radushkevich (DR) equation: 14,17
W = W,, exp[-(A/EJ2]
+ WO2exp[-(A/EJ21
Ei = BEoi ( i = 1 and 2)
A = RTln(P4P)
(1)
where Wol and WOZcorrespond to the smaller and larger micropore volumes, respectively. The sum of Wol and W02 is equal to Was for the micropore system. Here the W02 was determined by the difference between W, and Wol (see eq 2).
The BET analysis is widely used for the determination of the specific surface area, while the routine BET analysis cannot determine the specific surface area in the case of microporous solids.ls Kaneko et al.,10919however, proposed a subtracting
0022-3654/94/2098-9594$04.50/0 0 1994 American Chemical Society
J. Phys. Chem., Vol. 98, No. 38, 1994 9595
Pore Characterization of Microporous Solids
of activated carbons. As both Vs and Vcp are exclusion volumes for He replacement at 303 K, the particle density by He replacement dHe is given by eq 5 . As He can occupy d l open
m
dHe= vs
Figure 1. Pore model of a microporous solid in terms of volumes. Here V,, Vmpl, Vmps, Vu,, and Vcp denote volumes of a solid, larger micropores, smaller micropores, ultrapores, and closed pores respec-
tively. pore effect (SPE) method using the high-resolution a, plot for the determination of the specific surface area, which is valid for microporous carbons whose pore width is greater than 7 8,. Relationships among Porosity, Density, and Pore Volume. Different kinds of densities and porosities are defined according to the experimental technique. We summarize the densities and porosities here because the detailed classification of porosity leads to exact micropore structures. Heterogeneous microporous solids have open and closed micropores with some distribution. From the view of molecular adsorption, the pore which does not communicate with the external surface through an adsorbed molecule is called a closed pore. This classification, however, is not sufficient from experimental aspects. Figure 1 shows the simple model of a porous solid using the volumes of solid part, larger and smaller micropores, ultrapores, and closed pores. The volumes of the solid, larger micropores, smaller micropores, ultrapores, and closed pores are expressed by V,, Vmpl, Vmps, Vup,and Vcp,respectively. When the total volume is expressed by V(=Vs -t Vmpl Vmps Vup Vcp),each volume fraction is given by eq 3.
+
+
+
In this article the term of closed pore is used for the pore which cannot be penetrated by He at 303 K. A new concept of an ultrapore is introduced; the ultrapore designates the smallest open pore in which He can diffuse at 303 K but N2 cannot at 77 K. It should be cautious that the ultrapore is not the same as the ultramicropore whose pore width is less than 7 8, defined by IUPAC.18 The open micropores are classified into larger and smaller micropores. Although there is no definite criterion between larger and smaller micropores yet, their volumes can be separately determined by the above two-term DR equation. The critical pore width may be 12-15 8, according to preceding examinations.1°J9 The above porosities can be associated with X-ray density d,, particle density dHe, and apparent particle density dap. In the following, these densities will be expressed by the mass of the system and above-mentioned volumes. The X-ray density d, is calculated from the lattice constant and atomic weight of the component. d, is the true density in the case of perfect crystals. The micrographites in activated carbon fibers, however, have greater c spacing than that of single-crystalline graphites. Then, the d, value of activated carbons is calculated using the true density (2.267 g ~ m - and ~ ) the c spacing (3.354 A) of the graphite20.21(eq 4),where &2 designates the c spacing
3.354 - m d, = 2.267 x 7 -TI u002
"s
(4)
+ vcp
spaces, the He replacement method is used for determination of particle density. In a gravimetric experiment, the buoyancy change of samples was measured in the wide He pressure range up to 8 MPa at 303 K." The buoyancy is proportional to He pressure and the particle density. Then, the linear buoyancy vs pressure plot leads to the correct particle density. If there is no closed pores, the particle density coincides with the X-ray density. The apparent particle density dapis determined by V and m: dap= m/V
(6)
The total volume can be determined by immersion of porous samples in a nonwetting liquid. As the carbon surface is hydrophobic, water is used for determination of dap. The experimental detail will be described later. Three densities have an order of dap< dH, < d,, where dHe equals to d, in the absence of closed pores. The above-mentioned volume fractions are given by the observable densities and pore volumes as follows: QS= daddx 'mps
= dapWo1
QP = 1 - daddx 'mpl=
dapW02
Consequently, the combination of NZ adsorption at 77 K and different density measurements provides a complete description of pore structures. The addition of the small-angle x-ray scattering analysis gives more detailed micropore structures including closed pores. Small-Angle X-ray Scattering and Pore Structure. One of the well-known parameters obtained from SAXS analysis is the gyration radius of scattering entities. This is determined from the Guinier plot, Le., logarithm of scattering intensity log Z(s) vs s2 (s = 4 n sin 6/A).*l The slope of this linear plot at a lower s region gives the radius of gyration. The radius of gyration has been generally interpreted as the dimension of pore in case of SAXS from porous solids. The sizes of pores and solid units, however, have almost the same dimensions on highly microporous solids. The important assumption of a dilute system does not hold for these systems any more. Therefore, we must be cautious for application of the Guinier analysis for SAXS from porous solids. On the other hand, Debye et al.23 showed that SAXS analysis based on the consideration of the correlation function together with density values leads to important information on porosity without the assumption of the dilute system. Thus this method gives the general and important information in the case of highly porous solids as well. The SAXS from porous materials mainly arises from the electron density difference between solid and pores. As the boundary of the solid and pores plays an essential role in SAXS from porous materials, the surface area is associated with SAXS. Theoretical relationship between specific surface area a, and a primary parameter obtained by analysis of the SAXS profile is given by eq 8, where asand QP are the solid and pore volume
Ruike et al.
9596 J. Phys. Chem., Vol. 98, No. 38, 1994
a, =
2.01
4 x 10~@.,@~ (m2/g> lmdap
I
fraction, re~pectively.~~ The ,I is the so-called length of inhomogeneity obtained from the SAXS analysis. This value is described by
where i(s) is the smeared scattering intensity observed at a line focus system. This equation involves the integration to infinity. Hence termination effects must be corrected. Debye et al.23derived the general relationships between the specific surface area and the correlation function as follows:
20 30 40 Time(min.) Figure 2. Time dependence of the density by water replacement. (e) P-5 and (0)P-10. Broken lines represent d*watcr calculated from eq 19.
0
10
relationships between these parameters and pore structures will be discussed. Where y'(0) is the tangent of correlation curve at r = 0. This correlation function can be derived from the observed SAXS by Fourier transformation. In case of random distribution of pores, the relationship is given by eq 11:
The solution of this equation is
This a, is given by
and this type of correlation function yields for the intensityZ5sz6 Z(s) =
A or (1 a2s2I2
+
I($>=
(1
+
A a2s2)3'2
(14)
The linear plot of ~(s)-1/2vs s2 (or l(s)-2/3 vs s2) gives the correlation length a from the slope and intercept of the linear plot:
a = v'slope/intercept
(15)
Furthermore, the average dimensions of solid segments asofid and pores uporecan be given by
asolid = a/@,
upore= a/@.,
(16)
These secondary parameters, asofidand spore, suggest the average sizes of the carbon wall and the micropore, respectively. Thus, the Debye analysis is effective for characterization of the randomly distributed pore system. Ruland studied a variety of activated carbons with SAXS to apply both Guinier and Debye analyses; the radius of gyration is unambiguous, but the specific surface area still has a definite physical meaning in the dense system.27 a,, asolid,and aPre will be evaluated later, and the
Experimental Section Samples. Four kinds of pitch-based activated carbon fibers (P-5, 10, 15, and 20), which had been activated by HzO were used in the present measurements. They have different porosities, which were obtained by different bumoff conditions. The number in the sample name is about one-hundredth of the specific surface area. Detailed surface parameters of these ACF samples were described e1~ewhere.l~ Small-Angle X-ray Scattering Measurements. We measured SAXS spectra by use of a two-axial three-slit system (Mac Science Model No. 3310) with Cu Ka radiation with a nickel filter to reduce the Cu K,8 radiation. The scattered X-rays were detected by a linear-type position-sensitive proportional counter (PSPC) with a window 50 mm long and 10 mm wide. The scattering parameters ranging from 0.01 to 0.6 A-1 was covered. All measurements were carried out in transmission geometry for the specimen. The fibrous samples were packed in the slitshaped SAXS cell. With the X-ray tube operated at 30 kV and 20 mA, it took ca. 3 h to measure each of the SAXS spectra. The data were corrected for the parasitic scattering and absorption, and absorption correction was negligible for ACFs. Density Measurements. The apparent particle density was measured by water replacement method at 303 K using deionized-distilled water with the aid of a Gey-Lussac type pycnometer (14 mL) after pretreatment at 383 K under 0.1 mP for 3 h. The time dependence of the apparent particle density after immersing into water was measured. The particle density values are quoted from previous paper.12 X-ray Diffraction Measurements. The X-ray diffraction (XRD) patterns were measured by use of an automatic X-ray diffractometer with Cu Ka under the conditions of 45 kV and 30 mA. Results and Discussion Porosity from Density and N2 Adsorption. As the adsorption isotherms of water vapor by these ACF samples are of type 111,28the whole pore surfaces of ACFs do not instantaneously wet to liquid water; the larger micropores close to the mesopores can be wetted instantaneously, while the complete wetting process of smaller micropores is slower due to vapor diffusion and adsorption. Figure 2 shows the changes in the apparent density with the water replacement. The density increases with time owing to vapor diffusion and then becomes constant; the rate of increase is different from one sample to another, which
Pore Characterization of Microporous Solids TABLE 1: Micropore Volumes of ACFs sample W, (cm3g-*) Wol (cm3g-l) P-5 P-10 P-15 P-20
0.34 0.47 0.77 0.97
J. Phys. Chem., Vol. 98, No. 38, 1994 9597 TABLE 3: Volume Fractions of ACFs Wo2 (cm3g-1)
0.31 0.41 0.54 0.62
0.03 0.06 0.23 0.35
2.14 2.24 2.19 2.20
1.91 1.95 2.04 2.13
0.36 0.31 1 .o
TABLE 2: Various Densities of ACFs P-5 P-10 P-15 P-20
0.44
P-10 P-15 P-20
1.15
1.11 0.99 0.78 0.68
1.05 0.95 0.90
0.56 0.64 0.69
0.06 0.18 0.24
0.40 0.42 0.42
0.06 0.07 0.02 0.01
0.03 0.02 0.02
P '
I
ultrapores
smaller micropores
2.5 +graphite
larger micropores
2.0
r
5 .-
-
solid
M
v
h
1.5
i;
&
'"0
1 .o
0.5
I
I
I
1
1
J
0.8 1 1.2 0.2 0.4 0.6 Total micropore volume WaS(cm'p'')
0.2 0.4 0.6 0.8 1 1.2 Total micropore volume Was (cm'g')
Figure 4. Fraction changes of various spaces and solid volume with activation process. Here each volume fraction is expressed by the perpendicular length between two solid lines. 100.0
1
I
Figure 3. Relationships of density and micropore volume for ACF samples: (0)d,; (W ~ H C ; (+) dwatcr; (0) dap.
depends on the porosity. The apparent density extrapolated to time = 0 (dwater) and that after sufficient time (d*water) have their own well-defined meanings. The density from extrapolation should have the meaning given by eq 17, if only both
external surface and pore-wall of the larger micropores are instantaneously wetted to water. Furthermore, dwarer provides dapthrough eq 18. Micropore volumes from DR analysis (W%,
dwater
daP
=1
+ WO2dwater
WOI, and W02) are summarized in Table 1. As smaller micropores are also fitted with water except ultrapores and closed pores after a long time, dwawr must become constant (d*WatCr), which is predicted with the value of dwawr through eq 19. This is shown by the broken lines in Figure 2, agreeing with the experimental value.
Four kinds of densities of all ACF samples are summarized in Table 2. Both dWam and dapbecome smaller with the progress of activation. On the other hand, d, and dHe tend to increase with the activation. The changes of these densities due to activation are shown in Figure 3. The volume fractions calculated from eq 8 with these values were tabulated in Table 3, and those for different ACF samples are shown in Figure 4. Figure 4 shows clearly that the fraction of larger micropores increases while those of solids and closed pores decrease with the increase of total micropore volume, i.e., the activation extent.
Total micropore volume V&"cm'g'') Figure 5. Fraction change of open pore with activation process.
The data suggest the activation mechanism of carbons; first, smaller micropores are produced from the solid part and opening close pores, and then part of smaller pores are widened with the progress of activation. During such activation process the percent of smaller and larger micropores, Le., open micropores goes over 95%, as shown in Figure 5. Structural Information from SAXS and XRD. XRD provides information on the micrographitic structure of the micropore wall, that is, the ordered solid parts. SAXS leads to the average structural unit of pores and solids including both ordered micrographites and disordered intermicrographitic parts. Hence whole consideration on XRD and SAXS data should give a detailed picture of less-crystalline microporous carbon structures. Figure 6 shows SAXS spectra of P-10. The scattering intensity decreases gradually wtih the increase of the scattering parameter. There is no peaks, which indicates the absence of the long-range ordered structure. The SAXS profiles of other ACF samples had similar features. Figure 7 shows the DebyeBueche plots for P-5 and P-10. The linearity is guaranteed in the wide s region, and the correlation length, a, was obtained. Equation 18 leads to the average dimensions of asofid and upore. Three values of each sample are collected in Table 4. Table 4
Ruike et al.
9598 J. Phys. Chem., Vol. 98, No. 38, 1994
z20000
0.2 0.3 0.4 s ( A') Figure 6. SAXS intensity from P-10. 0
0.1
0.5
0.6
0.0 12 0.010 0.008 $ w
0.006
Figure 8. Average size parameters of solid walls and crystallites: (+) stacking width
0.004
La; (W)
stacking height Lc; (0)average dimension of
0.002
d
0.62
0.64 0.66 0.b8 0.'1 s ( A-2) Figure 7. Debye-Bueche plot of ACFs: (a) P-5; (b) P-10.
4 16.0 .I
v)
cr 14.0
TABLE 4: Structural Size Parameters from SAXS,XRD,
.-gEi 12.0
and Nz Adsorption P-5 P-10 P-15 P-20
6.8 7.1 7.3 7.1
14.2 12.7 11.4 10.3
8.4 7.9 8.9 7.9
17.5 17.6 17.5 12.9
13.1 16.1 20.3 22.9
-
-
g 10.0 .Q
7.5 7.9 10.1 11.3
8.0
-
6.0
-
I I
I
also contains Lc and La from XRD and the pore width determined from N2 adsorption. Here Lc and La are the stacking height and stacking width of the micrographites. The correlation length does not change seriously with the activation extent, whereas both asobd and apE change significantly. The activation gives the decrease of asofid and the increase of upre. On the other hand, both Lc and La values of P-5-P-15 are almost constant. Only La of P-20 is smaller than those of other ACF samples. The disagreement of SAXS and XRD results leads to further structural informations. The XRD detects the ordered structure of the micrographitic unit, whereas SAXS provides an assembly structure of micrographites including intermicrographitic parts, as illustrated in Figure 8a. In this case, XRD determines the Lc and La values of the micrographite, while SAXS gives an average dimension of the solids asolid, Le., the micrographite assembly. The activation process is divided into two steps from the results of SAXS and XRD. In the f i s t step, the micrographite assembly becomes smaller with the activation extent, but no significant changes occur in the size of unit micrographite (see Figure 9). Namely, the activation process takes the micrographite-assembly a part (Figure 8b). In the second step, the gasification occurs at the edge part of the micrographite unit, lessening the graphitic unit, as shown in Figure 8c. Consequently, the SAXS analysis together with XRD
0
I
1
I
I
0.2 0.4 0.6 0.8 1 1.2 Total micropore volume W, $ c m3g")
Figure 9. Schematic model of activation process for micrographitic carbon.
examination is very powerful to elucidate the assembly structure of primary units in the less-crystalline solids. Evaluation of Size and Number of Inaccessible Pores. The Debye approach for the SAXS data leads to the specific surface area a, due to all pores regardless of open or closed ones. The detailed comparison of the specific surface area a, from the SAXS analysis with the specific surface area a, from N2 adsorption gives the information of closed pores. Here we determined the a, value from SPE method. In Figure 10 the comparison is made of a, and a,. The a, values other than that of the most activated sample (P-20) are greater than a,, while a, agrees with a, for P-20. Therefore, the condition of a, 2 a, is hold for all samples. This difference between a, and a, values indicates directly the presence of the closed pores and ultrapores. The ultrapores are not available for an N2 molecule, as defined earlier. Then ultrapores can be regarded as a kind of closed pores from the viewpoint of the N2 adsorption. Here we introduce the concept of the inaccessible pores which include both closed pores and ultrapores. At the same time, smaller
Pore Characterization of Microporous Solids
J. Phys. Chem., Vol. 98, No. 38, 1994 9599
1800 1600
1400 n
M
"6 1200 v
,
ox
lo00 800
800
lo00
1200
1400
1600
1800
as(m*g")
Figure 10. Comparison of specific surface area from SAXS and SPE method for Nz adsorption.
E 70.0
8 60.0
k 50.0
1.5 E
r:
40.0
I
'Ii30.0
1 .o
.e 20.0
Y
c
10.0
O
0.5
3
e, 0.0
e
0
a'
0.2
0.4
0.6
0.8
1
1.2
Total micropore volume Was(cm3g.')
Figure 11. Volume and number fraction changes of latent pores: (0) volume fraction; (0)number fraction; (W) ratio of the size rilrem.
and larger micropores are denoted as effective micropores because of their good accessibility to NZmolecules. When the specific surface areas and volumes for the inaccessible and effective micropores are expressed by Si, Vi, Sem, and Vem, respectively, the ratios of Vil(Vem Vi) and Si/(Sem iSi) can be derived from the known porosities, as shown in
+
--Vi
Vem
+ Vi
- @'.p + @cp @P
_-
niri3 nemre,3
_-
+ nirf - E
(20)
samples. The data are very important for a perfect eluciation of properties of less-crystalline microporous carbons. This approach first enables us to assess the structure of inaccessible pores. The least-activated sample P-5 has an abundant number of inaccessible pores, but not so large a volume fraction. This is indicative that there are many inaccessible pores in P-5, but most of them are much smaller than effective micropores. This size is ca. 4.2 8,from the consideration of rilrem= 0.56, whereas the slit-shaped pore width from NZ adsorption is 7.5 A. The inaccessible pore size of ca. 4.2 8, is quite reasonable in comparison with the N2 molecular size of 3.5 8,. This is because the Lennard-Jones interaction energy of an N2 molecule with the graphitic micropore of 4-5 8, in the width is about 700 K, which often gives rise to the entrance blocking.29 Such narrow micropores should work as inaccessible pores for N2 molecules. The number fraction steeply drops with the activation extent, while the volume fraction gradually decreases. In this stage, the activation dissociates the micrographite assembly, as discussed above. The inaccessible pores are isolated from the external surface by the micrographitic walls. Consequently, partial dissociation of the micrographite assembly makes inaccessible pores communicated with the external surface and increases the effective micropores. As inaccessible pores are very close to each other because of their high concentration, the inaccessible pores are easily merged with each other by little defaults of the micrographitic walls. Thus the average size of inaccessible pores increases steeply, accompanied by the abrupt decrease of the number fraction of the inaccessible pores. The size and the number of inaccessible pores were evaluated from SAXS, NZ adsorption, and density measurements. This combined approach can elucidate the closed-pore structures of not only activated carbon but also other less-crystalline porous materials. Also this approach should be helpful to study chemical processes in closed spaces or solid defect chemistry.
Acknowledgment. The authors are greatly indebted to Dr. Matsuoka of Kyoto University, Dr. Nishikawa of Yokohama National University, and Dr. Fukao for their generous encouragements and valuable suggestions for SAXS studies. We thank Mr. Ishii for XRD measurements. This work was partially supported by Grant-in-Aid for Scientific Research of Ministry of Education, Japanese Government. Nomenclature a asdid
Here ni and nem are the number of inaccessible and effective micropores respectively. Furthermore, if we assume a symmetrical shape of their characteristic dimensions (q and rem) such as a sphere or a cube for the inaccessible pores and the effective micropores, these fractions are expressed by their characteristic dimensions, ni and nem. Here the ratios of nil(ni nem) and Tilrem are derived from eqs 22 and 23. Thus we
+
can evaluate the ratios of the number and characteristic dimension of the inaccessible pores from the observed quantities. Figure 11 shows the number and volume fractions of the inaccessible pores and the ratio of the size rilrem for ACF
apre
correlation length (A) average dimension of solids (A) average dimension of pores (A) specific surface area determined by Nz adsorption with SPE analysis (m2 g-I) specific surface area determined by SAXS with the Debye method (m2 g-l) adsorption potential (kl mol-') affinity coefficient Characteristic adsorption energy (kl mol-') structural parameter (kl mol-') scattering intensity smeared scattering intensity stacking height (A) stacking width (A) wavelength (A) mass of the system (g) number of effective micropores number of inaccessible pores scattering angle (rad)
9600 . I Phys. . Chem., Vol. 98, No. 38, 1994
VCP V, Vem
wo
1
w02
W% W
characteristic dimension of effective micropores characteristic dimension of inaccessible pores scattering vector (A-1) specific surface area of inaccessible pores (m2 g-l) specific surface area of effective micropores (m2 g-I) total volume (cm3) volume of a solid (cm3) total pore volume (cm3) volume of smaller micropores (cm3) volume of larger micropores (cm3) volume of ultrapores (cm3) closed pore volume (cm3) volume of inaccessible pores (cm3) volume of effective micropores (cm3) volume of smaller microprobes determined by DR analysis (cm3 g-I) volume of larger micropores determined by DR analysis (cm3 g-l) micropore volume determined by a, analysis (cm3 g-') pore width (A)
References and Notes (1) Teng, H.; Suuberg, E. M. J . Phys. Chem. 1993, 97, 478. (2) Rodriguez-Reinoso, F.; Molina, M.; Munecas, M. A. J. Phys. Chem. 1992, 96, 2707. (3) Kuriyama, K.; Dresselhause, M. S. Phys. Rev. B 1991, 44, 8256. (4) Seaton, N. A.; Walton, J. P. R. B.; Quirke, N. Carbon 1989, 17, 853. ( 5 ) Balbuena, P.; Gubbins, K. E. Langmuir 1993, 9, 1801. (6) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir, in press.
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