Langmuir 2005, 21, 8443-8451
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Influence of Surface Chemistry on the SAXS Response of Polymer-Based Activated Carbons Krisztina La´szlo´,*,† Orsolya Czakkel,† Katalin Josepovits,‡ Cyrille Rochas,§ and Erik Geissler§ Departments of Physical Chemistry and Atomic Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary, and Laboratoire de Spectrome´ trie Physique CNRS UMR 5588, Universite´ J. Fourier de Grenoble, BP 87, 38402 St. Martin d’He` res, Cedex, France Received February 11, 2005. In Final Form: May 2, 2005 Small-angle X-ray scattering (SAXS) measurements using contrast variation are reported for activated carbons prepared from poly(ethyleneterephthalate). The carbon surfaces are functionalized to different degrees by cold and hot nitric acid treatment. The latter treatment reduces the surface area by 75%, but the pore size distribution in the micropore range is hardly affected. Seven liquids, n-hexane, i-octane, i-propanol, cyclohexane, toluene, R-pinene, and nitrobenzene, in addition to water vapor, were used as contrast modifiers. Although the values of the specific surface area SX deduced from these measurements are relatively insensitive to the solvent, the detailed SAXS spectra reveal interactions occurring on different spatial scales that depend on the surface chemistry of the carbon and on the physicochemical properties of the solvent. In the most heavily oxidized sample, the amphiphilic molecule i-propanol stabilizes the surface structure, whereas nonpolar molecules make the rough surface smoother. In the untreated and the lightly functionalized carbons, water vapor at 50% relative humidity condenses only partially in the micropores at room temperature, whereas in the heavily treated sample condensation in the micropores is practically complete.
Introduction Recognition of the role of surface area and pore hierarchy in the performance of activated carbons has stimulated the commercialization of carbon adsorbents with tailormade porosity. Their design on the nanoscale level, however, has revealed the importance of an additional basic parameter, namely, their surface chemistry. The adsorption properties and the catalytic activity of these systems are both influenced by heteroatoms located along the edges of the turbostratic graphene layers or within them. The role of the different compounds of oxygen, nitrogen, sulfur, phosphorus, boron, and so forth formed with the carbonaceous matrix has been thoroughly studied over the past two decades.1-3 The band gap of the graphene sheets may be tuned by in-built heteroatoms4 that form stable nonstoichiometric surface compounds. These either originate from the precursor or may be introduced by further treatment. The polarities of the functional groups are influenced by the proximity of neighboring chemical structures. Polarity distribution functions, rather than discrete bond polarity values, should therefore be used to characterize these systems. The diversity of the O- and N-containing functional groups has been reviewed in detail.5-7 Recently, we reported measurements on a set of activated carbons derived from poly(ethylene terephtha-
late) (PET) that were functionalized at the surface by treatment with nitric acid.8 Scanning electron microscopy (SEM), small-angle X-ray scattering (SAXS), and nitrogen adsorption measurements showed that the microporous fraction in this carbon was almost entirely conserved despite a reduction in the surface area. The samples contained no measurable closed porosity. The present article is an attempt to investigate the effects of functionalization on the SAXS response of the same set of samples as in ref 8 using an extended range of contrast modifying liquids. Contrast matching has often been used to characterize the porosity of carbonaceous materials.9 Our goal is to draw attention to the importance of surface chemistry in the interpretation of results from SAXS combined with contrast variation.
† Department of Physical Chemistry, Budapest University of Technology and Economics. ‡ Department of Atomic Physics, Budapest University of Technology and Economics. § Universite ´ J. Fourier de Grenoble.
(6) Radovic, L. R. In Surface Chemistry of Activated Carbon Materials: State of the Art and Implications for Adsorption, Surfaces of Nanoparticles and Porous Materials; Schwarz, J. A., Contescu, C. I., Eds.; Marcel Dekker: New York, 1999; p 529. (7) Kapteijn, F.; Moulijn, J. A.; Matzner, S.; Boehm, H. P. Carbon 1999, 37, 1143. (8) La´szlo´, K.; Marthi, K.; Rochas, C.; Ehrburger-Dolle, F.; Livet, F.; Geissler, E. Langmuir 2004, 20, 1321. (9) Hoinkis, E. In Chemistry and Physics of Carbon; Thrower, P. A., Ed.; Marcel Dekker: New York, 1997; Vol. 25, p 72. (10) La´szlo´, K.; Bo´ta, A.; Nagy, L. G. Carbon 1997, 35, 593. (11) Bo´ta, A.; La´szlo´, K.; Nagy, L. G.; Copitzky, T. A. Langmuir 1997, 13, 6502. (12) La´szlo´, K.; Bo´ta, A.; De´ka´ny, I. Carbon 2003, 41, 1205.
(1) Tamon, H.; Okazaki, M. Carbon 1996, 34, 741. (2) Biniak, S.; Szymanski, G.; Siedlewski, J.; Swiatkowski, A. Carbon 1997, 35, 1799. (3) Lee, Y. J.; Uchiyama, Y.; Radovic, L. R. Carbon 2004, 42, 2233. (4) Strelko, V. V.; Kuts, V. S.; Thrower, P. A. Carbon 2000, 38, 1499. (5) Leon y Leon, C. A.; Radovic, L. R. In Chemistry and Physics of Carbon; Thrower, P. A., Ed.; Marcel Dekker: New York, 1994; Vol. 24, p 213.
Experimental Section Sample Preparation. Granular activated carbon (APET) was prepared from 2 × 3 mm2 PET pellets as described in ref 10. The surface chemistry and morphology of the precursors were characterized previously.11,12 The steam-activated carbon, obtained at 900 °C, was treated for 3 h with concentrated nitric acid at room temperature and at the boiling point of the carbonacid suspension to achieve different degrees of surface functionalization. The acidic samples were washed with distilled water and extracted in a Soxhlet apparatus until neutral pH was
10.1021/la050389+ CCC: $30.25 © 2005 American Chemical Society Published on Web 07/30/2005
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Table 1. Selected Data from Low-Temperature Nitrogen Adsorption and Helium Pycnometry parameter
APET W
APET A
APET B
SBET, m2/g Vtot, cm3/g W0, cm3/g W0/Vtot SDR, m2/g SBET/SDR wads, Å dHe, g/cm3 FC, e/Å3
1156 0.50 0.48 0.96 1352 0.86 8.6 1.74 0.524
1114 0.48 0.46 0.96 1293 0.86 8.6 1.82 0.548
304 0.14 0.12 0.86 337 0.90 9.2 1.50 0.452
attained. The yield at room temperature (APETA) was 100%, whereas at the boiling point (APETB) it fell to 94.5%. Virgin APET, after the same treatment in water (APETW), was used as a comparison. Adsorption Measurements. Nitrogen adsorption/desorption isotherms were measured at 77 K on the 0.25-0.35 mm powder fraction with a Quantachrome Autosorb-1 instrument. Surface areas were calculated from the BET model. The (micro)pore analysis was done by the Quantachrome software using the Dubinin-Radushkevich (DR) method. The true density of the carbon samples was determined by helium pycnometry with the same Autosorb-1 instrument. X-ray Photoelectron Spectroscopy (XPS). The surface chemical composition of the samples was determined by XPS using an XR3E2 (VG Microtech) twin anode X-ray source and a Clam2 (X-ray photoelectron spectroscopy) hemispherical electron energy analyzer. The base pressure of the analysis chamber was about 5 × 10-9 mbar. The Mg KR radiation employed (1253.6 eV) was not monochromatized. After the linear baseline was subtracted, curve fitting was performed assuming Gaussian peak shapes.13 Small-Angle X-ray Scattering. SAXS measurements were made on beam line BM2 at the European Synchrotron Radiation Facility (ESRF), Grenoble, France, at two different energies, 7.9 keV (λ0 ) 1.57 Å) and 18 keV (λ ) 0.69 Å). The sample-detector distances were 158 and 32 cm. An indirect illumination CCD detector (Princeton Instruments) with an effective pixel size of 50 µm was used. Intensity curves I(q), obtained by azimuthal averaging, were corrected for grid distortion, dark current, sample transmission, and for background scattering. At 18 keV, the values of the sample transmission lay in the range of 0.85-0.90; at 7.9 keV, where attenuation by absorption is stronger, the transmissions varied between 0.2 for the nitrobenzene-containing samples and 0.5 for the solvent-free carbons. The samples, ground in a ball mill, were inserted into 1.5-mm-diameter Lindemann capillaries and heated to 110°C for 24 h to remove trapped or adsorbed water. Contrast varying liquids were added immediately before sealing. A further set of samples was prepared by placing the capillary at room temperature in contact with air containing water vapor at 50% humidity. Intensities were normalized with respect to a standard (lupolen), assuming an effective sample thickness of 1 mm to account for the filling factor of the powder in the capillary tubes. This procedure implies that the stated intensities may be in error by a factor close to unity. The following liquids of increasing electron density were used: n-hexane, i-octane, i-propanol, cyclohexane, toluene, R-pinene, and nitrobenzene.
Results and Discussion The low-temperature nitrogen isotherms for the three samples display strong microporous character. The parameters deduced from these measurements are listed in Table 1. The pore width wads was calculated from the total pore volume Vtot and the BET surface area SBET, assuming slit-shaped pores. The micropore volume W0 and surface area SDR were derived using the DR model.14 Also listed (13) La´szlo´, K.; Tomba´cz, E.; Josepovits, K. Carbon 2001, 39, 1217. (14) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powders and Porous Solids; Academic Press: San Diego, CA, 1999.
Table 2. XPS Elemental Analysis of the Granular and Powdered Carbons and Deconvolution of the C 1s Regiona
sample
C O atom atom O/C % % %
APETW granular 91.2 powdered 94.0
8.8 6.0
I
II
III
IV
V
9.4 49.9 23.7 11.7 6.4 49.5 26.0 9.2
8.3 6.4 8.2 7.1
APETA granular 88.5 powdered 91.0
11.5 13 45.2 26.4 15.4 9.0 9.9 48.8 26.4 11.3
7.8 5.5 7.9 5.6
APETB granular 80.2 powdered 79.0
19.8 24.7 53.9 17.0 12.9 13.2 3.0 21.0 26.6 50.9 23.7 6.1 15.3 4.0
a The best fit of the typical asymmetric peak of the C 1s core spectrum was obtained by decomposition into five peaks: graphitic carbon (peak I, BE ) 284.2-284.4 eV), carbon present in phenolic, alcohol, or ether groups (peak II, BE ) 284.7-285.2 eV), carbonyl or quinone groups (peak III, BE ) 286.1-286.8 eV), carboxyl or ester groups (peak IV, BE ) 288.3-288.7 eV), and shake-up satellite peaks due to π-π* transitions in aromatic systems (peak V, BE ) 290.3-290.9 eV).
are the values of the helium density dHe measured by pycnometry. The electron density of the carbon is given by FC ) NAZdHe/M 10-24 electrons/Å3, where NA is Avogadro’s number, Z is the atomic number, and M is the atomic mass of carbon. The data in Table 1 and the pore size distribution8 confirm that all of the samples are highly microporous with very similar micropore distribution. The sample obtained by high-temperature acid treatment, however, displays a major loss of surface area. The surface chemical composition was determined by XPS. Because this technique yields information from a depth of only a few nanometers to study the homogeneity of the acid-treated carbons, both powdered and granular forms were analyzed (Table 2). The reproducibility in the values of the atomic concentration is (1%. No elements other than oxygen and carbon were detected with this technique in any of the samples. Comparison between granular and powdered carbons reveals the heterogeneity of the final carbon material. Differences between surface and bulk composition, greater than the experimental error, are observed in APETW and APETA. High-temperature acid treatment (APETB) virtually eliminates this difference. It can be concluded that functional groups appearing in peak II are more abundant in the bulk of the grains of APETW and APETB, whereas in all three samples the functionalities of peak III are more concentrated at the surface than in the bulk. For peaks IV and V, a homogeneous distribution was found. The principal finding, seen in Table 2, is that the O/C ratio increases with increasing severity of acid treatment. Parts a-c of Figure 1 show SAXS curves for the three samples APETW, APETA, and APETB in air and also in a selection of solvents. For clarity, not all solvents are shown in the Figure. All display the same overall shape, with extended power law behavior at low q (i.e., I(q)∝q-m), where the exponent m (3.5e m e4) indicates scattering from surfaces. Values of m < 4 correspond to rough surfaces.15 The size of the subgrains in the sample that cause this surface scattering is about 1 µm.8 In Figure 1, the plateau and the shoulder at intermediate q are characteristic of micropores. The scattering intensity beyond this shoulder comes from the pore walls as well as from atomic disorder in the carbon matrix. At the highest values of q in these Figures, all of the scattering curves converge as the broad peak because the turbostratic (15) Hasmy, A.; Anglaret, E.; Foret, M.; Pelous, J.; Jullien, R. Phys. Rev. B 1994, 50, 6006.
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Figure 1. (a) SAXS curves from powdered APETW in various contrast-varying liquids: red, air; black, hexane; green, toluene; blue, nitrobenzene; violet, cyclohexane. (b) SAXS curves from powdered APET A in different contrast-varying liquids: red, air; black, hexane; green, toluene; blue, nitrobenzene; violet, cyclohexane. (c) SAXS curves from powdered APET B in different contrastvarying liquids: red, air; black, hexane; green, toluene; blue, nitrobenzene; violet, cyclohexane. (d) Detail of part b showing the curve of APET A with water vapor: red, air; black, hexane; green, toluene; blue, nitrobenzene; violet, water vapor. Table 3. Physicochemical Data of the Solvents critical dimensions (nm)
electron density FS (e/Å3)
n-hexane
0.40 [16] 0.45 [17]
0.231
i-octane
0.59 [18] 0.55[19]
0.241
i-propanol
0.47 [14]
0.252
cyclohexane
0.48 [14] 0.54 [14] 0.50 [16] 0.66 [17]
0.267
toluene
0.40 [16] 0.66 [17]
0.283
6
R-pinene
0.70 [14]
0.288
7
nitrobenzene
na
0.377
8
water
0.27 [20]
0.334
solvent 0 1 2 3
air
4
5
interlayer spacing d (qmax ≈ 1.8 Å-1, d ) 2π/qmax ≈ 0.35 nm) is approached. Because the molecules investigated here (see critical sizes, Table 3) cannot penetrate into this confined space, the electron density contrast in this region is due to the difference between the electron density of carbon and that of free space. Because this is the same
for the various solvents, all of the signals are identical at high q. It is notable, however, that the signal from the samples containing water vapor (cf. Figure 1d) remains lower than the others in this region, indicating that this molecule can penetrate farther into the interlayer spacing than the other molecules. From the curvature of the shoulder in the SAXS curve, a radius of gyration RG of the turbostratic basic structural units (BSU) may be determined using the Guinier expression for single particles
(
I(q) ) exp -
)
q2RG2 3
(1)
The resulting values of RG calculated for each carbonsolvent pair are listed in Table 4. Except for APETB, where somewhat larger values are observed, RG does not vary notably with the different solvents. Owing to their high packing density, the BSUs are not randomly distributed. Local order is imposed by the minimum distance of approach L between nearest neighbors,8 which leads to an oscillatory structure factor S(q) associated with the total intensity I(q),
I(q) ) P(q) S(q)
(2)
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Table 4. Parameters Derived from SAXS Measurements APETW solvent
RG (Å)
L (Å)
air n-hexane i-octane i-propanol cyclohexane toluene R-pinene nitrobenzene water vapor
6.1 5.4 5.5 5.5 5.4 5.6 5.4 5.0
20 20 20 20 20 20 20 20
SX
(m2/g)
1930 1910 2080 1850 2090 1840 2070 1860 1790
APETA b
(cm-1) 0.099 0.045 0.045 0.042 0.048 0.046 0.048 0.062 0.052
RG (Å)
L (Å)
5.8 5.6 5.5 5.5 5.4 5.5 5.4 5.0
19 20 19 20 20 20 20 21
P(q), the form factor of the BSU, is approximated by the Debye-Bueche expression21
P(q) ) (1 + a2q2)-2
(3)
P(q) is found by fitting eq 3 to the shoulder in the experimental curve, which, by virtue of eq 2, allows S(q) to be calculated. In all of the samples studied here, S(q) displays a weak broad maximum, unlike the strong peak followed by oscillations that is characteristic of dense systems of monodisperse spheres. Examples of this structure factor are shown in Figure 2 for APETB in
SX
APETB
(m2/g)
1810 1890 2020 1910 2070 1710 1900 1700 1510
b
(cm-1) 0.082 0.045 0.040 0.040 0.043 0.048 0.042 0.037 0.047
RG (Å)
L (Å)
SX (m2/g)
b (cm-1)
5.7 6.0 8.0 7.8 8.1 6.0 8.6 5.9
19 27 34 23 34 22 30 22
920 540 620 810 630 610 700 750 280
0.073 0.056 0.041 0.031 0.048 0.049 0.050 0.052 0.023
thermore, because the volume fraction of carbon in the samples, φ ) (1 + VtotdHe)-1 where Vtot is the pore volume and dHe is the true density of the carbon, is not strictly identifiable with the filling factor of the BSUs in the material, φ is therefore undefined and becomes merely another fitting parameter in the modeling procedure. To circumvent these uncertainties and provide an estimator for L, for simplicity we adopt the Fournet expression
[
S(q) ) 1 +
]
24φ(sin qL - qL cos qL) (qL)
3
-1
(4)
despite the possibility that the effective filling factor may exceed the theoretical limit for the validity of this relationship. The position of the maximum qmax of S(q) is then defined by22
L)
Figure 2. Structure factor S(q) for APET B in different solvents, showing the shift of qmax and the corresponding increase in the inter-BSU spacing caused by the solvents compared to air: ×, air; b: hexane; O, cyclohexane; +, toluene.
different solvents. The weakness of the oscillation can be attributed to size polydispersity, whereas the increase in S(q) at higher q is an artifact due to scattering from the disorder of the atoms in the carbon substrate. The latter feature will be discussed in more detail below. The structure factor of dense systems of spheres may be described through a variety of models22-25 that can in principle accommodate polydispersity. The resulting parameters are, however, model-dependent, and the solution for the structure is of course not unique. Fur(16) Wood, G. O. Carbon 1992, 30, 0, 593. (17) Webster, C. E.; Drago, R. S.; Zerner, M. C. J. Am. Chem. Soc. 1998, 120, 5509. (18) Molina-Sabio, M.; Gonzalez, M. T.; Rodriguez-Reinoso, F.; Sepu´lveda-Escribano, A. Carbon 1996, 34, 4, 505. (19) Horvath, G.; Kawazoe, K. J. Chem. Eng. Jpn. 1983, 16, 470. (20) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. D. In Molecular Theory of Gases and Liquids; Wiley: New York, 1954; p 1110. (21) Debye, P.; Bueche, R. M. J. Appl. Phys. 1949, 20, 518. (22) Fournet, G. Acta Cryst. 1951, 4, 293. (23) Percus, J. K., Yevick, G. J. Phys. Rev. 1958, 110, 1. (24) Ashcroft, N. W.; Lekner, J. Phys. Rev. 1966, 145, 83. (25) Hayter, J. B.; Penfold, J. Mol. Cryst. 1981, 42, 109.
5.76 qmax
(5)
It can be seen from Table 4 that the value of L is identical within experimental error for all three samples in air (L ) 19 Å). For APETW and APETA, L is independent of the solvents examined here. For APETB, however, as found previously,8 L increases in the presence of n-hexane. Figure 2 shows the effect on S(q) of three different aliphatic solvents for APETB compared to air. Although toluene hardly modifies qmax with respect to its value in air, n-hexane, i-octane, R-pinene, and especially cyclohexane shift the maximum to an appreciably lower value, thus implying that the local structure of APETB swells. This behavior is consistent with its thin-walled structure and the low-pressure hysteresis observed in the nitrogen adsorption isotherms of this sample.8 On the macroscopic scale, however, optical microscopy measurements of APETB immersed in cyclohexane reveal that the powder grains swell only by 3%. It follows that the strong variations in L observed by SAXS, amounting to about 80%, are a nonaffine deformation that is essentially local. The specific surface area SX for each sample-solvent pair is calculated in the usual way, using the approximation that the samples contain only two phases.26 The validity of this strong assumption, however, needs to be verified. In the region beyond the shoulder 0.3e q e1.0 Å-1 where the intensity decreases, the scattering intensity can be expressed as27,28
I(q) ) Kq-4 + b
(6)
The final slope K and the atomic disorder parameter b are evaluated by plotting (26) Porod, G. In Small Angle X-ray Scattering; Kratky, O., Glatter, O., Eds.; Academic Press: New York, 1983. (27) Luzzati, V.; Witz, J.; Nicolaieff, A. J. Mol. Biol. 1965, 3, 367. (28) Ciccariello, S.; Goodisman, J.; Brumberger, H. J. Appl. Cryst. 1988, 21, 117.
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I(q)q4 ) K + bq4
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(7)
as a function of q4. The b parameters are listed in Table 4. From the SAXS data, the specific surface area is26
SX )
Vtot πK φ(1 - φ) πK ) Q dav Q (1 + VtotdHe)
(8)
where dav is the overall mass density of the sample. From eq 8, it can be seen that SX is a product of two terms. πK/Q, is obtained from scattering alone, whereas Vtot/(1 + VtotdHe) comes from independent gas adsorption and pycnometry measurements. The quantity
Q)
∫0∞(I(q) - b)q2 dq
is the second moment of the carbon-air scattering curve, where the carbon phase is assumed to be uniform. The lower limit of the integral is determined by the size (ca. 1 µm) of the subgrains that generate the low-q surface scattering.8 The upper limit of the integral is obtained from the relationship
∫q∞[I(q) - b]q2 dq ) ∫q∞Kq-4q2 dq ) qK0 0
0
Figure 3. Variation of [I(q) - b]q2 with q for APETA/air (O) and APETA/toluene (b), showing the low-q power law dependence. For clarity, only 50% of the APETA/air data points are shown. Arrows denote the Porod scattering region. The integration of Q was performed in three steps: by extrapolating and integrating the low-q power law behavior to 10-4 Å-1, numerically integrating the data displayed as far as the arrows, and finally, extrapolating to q ) ∞ beyond the arrows.
(9)
The contribution to Q from the two limits can amount to appreciably more than 10% and therefore cannot be overlooked. To illustrate the importance of the integration limits in eq 9, the integrand for two of the samples, APETA/ air and APETA/toluene, is shown in Figure 3. Because the apparent flattening for these curves at low q is an artifact,8 the curves were extrapolated to q ) 10-4 Å-1. Table 4 also lists the values of SX for each carbon-solvent pair. Apart from APETB, the variations of SX are small and, to a first approximation, independent of the solvent. This finding is illustrated in Figure 4, where values of the SAXSderived quantity K/Q are plotted for each carbon-solvent pair. For APETW and APETA, the values of K/Q are equal for the same solvent to within less than 5%, a result that is consistent with the estimated errors of the data evaluation procedure. The agreement between the values of K/Q highlights the similarity of these two samples. When K/Q for either APETW or APETA is compared in different solvents, however, the scatter in the values is greater because systematic variations occur among the different solvents. Thus, for toluene and nitrobenzene in APETW and APETA, K/Q is significantly lower than for n-hexane, cyclohexane, i-octane, and R-pinene. Pronounced differences among them appear when the solvent is polar (i-propanol and water vapor). The greater dispersion in Figure 4 for the results from APETB highlights the influence of surface chemistry for the different solvents. Although the values of SX for water vapor are also listed in Table 4, the surface area is ill-defined in this ternary system composed of carbon, condensed water, and water vapor, owing to the unique interaction between water and activated carbon surfaces that stems from the large dipole moment of water.29 The dispersion in K/Q with respect to the different solvents implies that the two-phase model is unsatisfactory. We have to consider the interfacial layer between the carbon and the liquid to be a third phase. Despite this being a ternary system, the second moment of the scattering curve can still be defined. Thus, if the com(29) Wang, Z.-M.; Kaneko, K. J. Phys. Chem. B 1998, 102, 2863.
Figure 4. Normalized final slope K/Q from SAXS data as a function of solvent in order of increasing electron density: A, air; B, n-hexane; C, i-octane; D, i-propanol; E, cyclohexane; F, toluene; G, R-pinene; H, nitrobenzene; I, water vapor. b, APETW; 9, APETA; O, APETB.
ponents are carbon (C), solvent (S), and a interfacial layer phase (P), then the intensity can be expressed as
I(q) ) (FC - FS)2SCC(q) + (FP - FS)2SPP(q) + (FC - FS)(FP - FS)SCP(q) (10) where the Sij(q) parameters are the partial structure factors for C-C, P-P, and C-P, respectively. The term SCP(q) is oscillatory, having a second moment equal to zero. The latter property follows from its definition as the Fourier transform of the probability of finding carbon and the interfacial layer phase in the same position (i.e., at a separation distance of r ) 0). The second moment of eq 10 thus becomes
Q)
∫0∞Iq2 dq ) (FC - FS)2∫0∞ SCC(q)q2 dq + ∞ (FP - FS)2∫0 SPP(q)q2 dq ) Q1 + Q2
(11)
In the binary case, to compare the effects of the different solvents, the scattering signal from each carbon-solvent
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Figure 5. (a) Relative density function p(q) for hexane (b), toluene (×), and nitrobenzene (+) in APETW. For clarity, only 20% of the data points are plotted. (b) Relative density factor p(q) for hexane (b), toluene (×), and nitrobenzene (+) in APETA. For clarity, only 20% of the data points are plotted.
Figure 6. Normalized SAXS spectra of APETW in air (dotted curves) compared with APETW in i-octane, cyclohexane, i-propanol, and R-pinene (continuous lines). Each pair of curves is separated by one decade. Exclusion effects in the shoulder region q can be seen in all samples but notably in cyclohexane and R-pinene. The rise in intensity at the highest q reflects solvent exclusion from the graphene interlayer spacing.
pair should be normalized by the respective contrast factor (FC - FS)2, where FC is the electron density of the carbon and FS is that of the solvent (Tables 1 and 3). This approach may be illustrated as follows. The ratio r(q) of the intensity scattered by a given carbon sample immersed in a solvent to that of the same sample in air may be expressed as
r(q) )
[I(q) - b]solvent [I(q) - b]air
)
[FC - p(q)FS]2 FC2
(12)
Figure 7. Normalized SAXS spectra of APETA in air (dotted curves) compared with APETA in i-octane, i-propanol, cyclohexane, and R-pinene (continuous lines). Each pair of curves is separated by one decade.
where p(q) is the relative density of the solvent with respect to its bulk value FS. Hence,
p(q) )
FC(1 - xr(q)) FS
(13)
In this model, where the atomic disorder parameter has been subtracted from the total intensity, the electron density of the carbon FC is taken to be uniform. It will be noted that the values of b in eq 12 are those of the carbon in the solvent and of the same carbon in air (Table 4);
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Figure 8. (a) Normalized SAXS spectra of APETB in air (dotted curve) compared with APETB in n-hexane (continuous line). (b) Normalized SAXS spectra of APETB in n-hexane (dotted curves) compared with APETB in toluene and nitrobenzene (continuous lines). The two pairs of curves are offset by one decade. (c) Normalized SAXS spectra of APETB in air (dotted curve) compared with APETB in i-propanol (continuous line). (d) Normalized SAXS spectra of APETB in n-hexane (dotted curves) compared with APETB in i-octane, cyclohexane, and R-pinene (continuous lines). The three pairs of curves are offset by one decade.
these quantities are different because the solvent molecules partially penetrate into the carbon skeleton. The relative density of the solvent p(q) depends on the micropore environment and hence is a function of the wave vector q. Although under normal physical conditions it is expected that p(q) e 1, densities in excess of the bulk liquid can occur in the first layers of molecules adsorbed at surfaces30-32 (i.e., for the present system, in the (30) Findenegg, G. H. J. Colloid Interface Sci. 1971, 35, 249. (31) Kern, H.; v. Rybinski, W.; Findenegg, G. H. J. Colloid Interface Sci. 1977, 59, 301. (32) Castro, M. A.; Clarke, S. M.; Inaba, A.; Arnold, T.; Thomas, R. K. J. Phys. Chem. B 1998, 102, 10528.
micropores). Parts a and b of Figures 5 show the results of this approach for APETW and APETA in the three solvents, n-hexane, toluene, and nitrobenzene. First, it should be stated that owing to the normalization procedure employed to match the different sequences of the SAXS curves the uncertainty in this representation is greatest at low q. Second, the maximum occurring around 0.8 Å-1 is an artifact due to the subtraction of the atomic disorder constant b. A density deficit is apparent for all three solvents in APETW around q ≈ 0.01 Å-1 and for toluene in APETA near q ≈ 0.03 Å-1, corresponding to distances on the order of 600 and 200 Å, respectively (i.e., the upper mesoporous/macroporous region). In the majority of
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Figure 9. Signal from APETB in air (+) and with water vapor at 50% humidity (b). For clarity, only 20% of the data points are shown.
reciprocal space occupied by the solvents, however, the mean value of the three curves for APETA is greater than unity, whereas the opposite is true for APETW. In Figure 5a, however, the strong reduction in p(q) in the case of nitrobenzene suggests that this solvent is partially excluded from the smallest pores in APETW. Although this finding may well indicate dense solvent in the micropores in APETA, caution is called for. The effective thickness of powdered samples dispersed in a liquid is difficult to control: a similar effect could result from a difference in the number of powder grains in the X-ray beam. It is, however, worthwhile to emphasize that because the intensity I(q) is the signal from the carbon alone the ratio K/Q is independent of the sample filling factor. The value of the surface area SX is affected neither by the intergranular space in the sample holder nor by the sample thickness. For systematic evaluations, the normalized curves [I(q) - b]/Q are compared for the same carbons. Although this approach works well for most of the spectra reported here, caution is still necessary because the scattering invariant Q is based on the assumption of a binary system. The procedure adopted here assumes that at the lowest spatial resolution (smallest q) where the contribution from voids is small the carbon-solvent curve is identical to that of carbon-air, which is taken as the reference. [I(q) - b]/Q is therefore adjusted by a factor close to unity such that at low q it coincides with the corresponding carbon-air curve. In this case, excess scattering above that of the carbon-air curve indicates voids or regions from which the solvent is excluded. The comparison of [I(q) - b]/Q for the other solvents in APETW with that in air is shown in Figure 6. Because their curves lie above those of air, it follows that cyclohexane and R-pinene, as well as nitrobenzene, are also partially excluded from the smallest pores. For APETA in the different solvents, the scattering curves are shown in Figure 7. It was seen in Figure 5b that n-hexane and toluene give full coverage with a tendency to form a dense interlayer, whereas nitrobenzene shows poorer matching over almost the entire q range. Figure 7 demonstrates that i-octane, cyclohexane, and especially i-propanol are also strongly excluded from the micropores. Surprisingly, in view of its size, R-pinene appears to be only slightly excluded from the micropores in this sample. For APETB, the curves equivalent to Figure 6 are shown in Figure 8a-d. It is obvious from Figure 8a that the
La´ szlo´ et al.
Figure 10. Occupation factor p(q) for water vapor in APETW (b), APETA (×), and APETB (+). Only in APETB is there complete condensation in the microporous region 0.1 Å-1 e q e 1 Å-1. For clarity, only 20% of the data points are shown.
APETB-air and APETB-n-hexane curves are dissimilar because the power law slopes at low q are quite distinct (m ) 3.5 and 3.75, respectively). They differ also, as already noted, in that n-hexane distorts the carbon matrix in the high-q region. Because all of the solvents except i-propanol show the same behavior, the APETB-air curve cannot be used as the reference; therefore, APETB-n-hexane is used instead. Figure 8b shows that APETB in toluene and nitrobenzene displays similar power law behavior at low q, but by virtue of the same argument as above, these solvents, especially nitrobenzene, are excluded from the micropores. An exception to this pattern is i-propanol (Figure 8c) because its power law response at low q is the same as that of APETB-air. The remaining solventss i-octane, cyclohexane, and R-pinene (Figure 8d)sfollow the same pattern as n-hexane, with increasing exclusion from the micropores as the critical molecular diameter increases. The difference in the power law slopes with APETB-air and APETB-i-propanol, on one hand, and the same carbon in the other solvents means that the rough surface structure (surface fractal dimension DS ) 6 - m ) 2.5) of the carbon-air interface is partly smoothed by the nonpolar molecules. Because the electron densities of the latter vary widely, it is difficult to attribute this smoothing to simple contrast matching. It is probable, therefore, that i-propanol stabilizes the surface functional groups and their surroundings, preserving their geometrical arrangement. On the other hand, the nonpolar molecules, which are attracted preferentially to the carbon substrate, smooth the more flexible outer regions of the surface. In the micropores where the functional groups tend to be fewer, polar or bulky nonpoplar molecules tend not to condense. To illustrate the effect of water vapor in these carbons, Figure 9 compares the measured intensity from APETB in air (unnormalized by Q) with that from the same sample prepared in an atmosphere with 50% relative humidity at room temperature. At low q, the two signals coincide, showing that little condensation occurs on the large surfaces. This differs from APETA (Figure 1b) where with water vapor the signal is smaller both at low q and in the microporous region, showing that a certain degree of condensation occurs in both sites. Because these samples are not immersed in the bulk liquid, effects of buoyancy or settling are not expected to change the packing factor of the powder, and it is justified to use the approach embodied in eq 13. Figure 10 shows the values of p(q) for
Influence of Surface Chemistry on Activated Carbons
the three carbon samples. In APETW and APETA, limited condensation, compatible with more- or less-dense clusters of water molecules, occurs both on the large subgrain surfaces at low q and in the micropores. In APETB, however, complete liquid condensation (p(q) ≈ 1) occurs in the micropores. The low degree of condensation observed at low q probably reflects the higher pumping efficiency of the micropores. Conclusions The effects of interactions between surface functional groups on the activated carbons investigated here and other molecules are revealed by SAXS when the samples are placed in contact with the corresponding liquid or vapor. Although estimates of the specific surface area, SX, are less sensitive to variations in the nature of the solvent, strong solvent-dependent effects are visible in the case of the most oxidized sample, APETB. In this sample, the microporous structure is flexible, displaying appreciable local swelling in n-hexane, i-octane, and cyclohexane. The macroscopic swelling of the sample is, however, modest.
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The fractal surface structure of the subgrains in the APETB sample is also deformed by the liquids. Under the interfacial pressure of nonpolar solvents, it becomes smoother, whereas the amphiphilic molecule i-propanol stabilizes the rough fractal surface. A solvent occupation factor p(q) is defined that indicates the relative density of the solvent in the sample as a function of the wave vector q. It is found that water vapor in an atmosphere at 50% humidity at room temperature is almost fully condensed in the micropores of APETB, whereas in the more lightly treated and untreated carbons the micropores are only partially filled. Acknowledgment. Access to small-angle beamline BM2 at the European Synchrotron Radiation Facility is gratefully acknowledged. We extend our warm thanks to E. Fu¨lo¨p and G. Bosznai for sample preparation. This research was supported by the National Research Fund (OTKA, grant no. T 046532) and the National Research and Development Programs (NKFP 3/043/2001). LA050389+
