Morphological Investigation of Chemically Treated Poly(ethylene

Langmuir 2004, 20, 1321-1328

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Morphological Investigation of Chemically Treated Poly(ethylene terephthalate)-Based Activated Carbons Krisztina La´szlo´,*,† Katalin Marthi,‡ Cyrille Rochas,§ Franç oise Ehrburger-Dolle,§ Fre´de´ric Livet,| and Erik Geissler§ Department of Physical Chemistry, Budapest University of Technology and Economics, H-1521 Budapest, Hungary, Research Group for Technical Analytical Chemistry, Hungarian Academy of Sciences, Department of General and Analytical Chemistry, Budapest University of Technology and Economics, H-1521 Budapest, Hungary, Laboratoire de Spectrome´ trie Physique UMR 5588 CNRS-Universite´ J. Fourier de Grenoble, BP 87, 38402 St. Martin d’He` res Cedex, France, and Laboratoire de Thermodynamique et Physico-Chimie Me´ tallurgiques UMR 5614 CNRS-Institut National Polytechnique de Grenoble, BP 75, 38402 St. Martin d’He` res Cedex, France Received October 21, 2003. In Final Form: December 16, 2003 Complementary techniques, including low-temperature nitrogen adsorption and small-angle X-ray scattering (SAXS), are applied to detect the effects of surface functionalization on the morphology of activated carbon derived from poly(ethylene terephthalate) (PET). Scanning electron microscopy (SEM) is also employed as an auxiliary method to visualize the surface below the micron scale. The SEM images reveal a micron-sized ridgelike texture. Room temperature acid treatment makes the ridges become more pronounced, while treatment with boiling acid uncovers fiberlike structures of roughly 1 µm diameter. All samples display an apparent surface fractal dimension of Ds ) 2.4 in the wave vector range 0.001-0.02 Å-1. Nitric acid at room temperature increases the surface oxygen content only by 3 at. %, while all the adsorption properties and structural parameters reported in this paper are virtually unaffected. Significant differences in the morphology at submicron scales appear only after boiling acid treatment. The resulting carbon remains highly microporous, but the loss of Brunauer-Emmett-Teller (BET) surface area from about 1150 to 304 m2/g is approximately 75%. In addition to the principal peak at around 8 Å, fresh peaks appear in the polydisperse Horva´th-Kawazoe (HK) pore size distribution owing to the burnoff of intervening walls. The average width of the slitlike pores calculated from the Dubinin-Radushkevich (DR) plot increases from 8.4 to 11 Å. The minimum slit width where the applied probe molecules, that is, nitrogen and hexane, can enter increases from about 5 to about 5.4 Å. The separation distance of the basic structural units is practically unchanged. When, however, this carbon is in contact with hexane, this distance expands from about 19 to 27 Å. The swelling is consistent with the deformable nature of this sample also illustrated by the low-pressure hysteresis and the reduced helium density. Particular attention was paid to the surface areas derived from low-temperature nitrogen adsorption and X-ray measurements. Owing to the wide spatial range of the structures in these samples, estimates of the specific surface area of activated carbons can be substantially in error unless both upper and lower q ranges of the SAXS spectra are taken into account. Surface areas derived from the adsorption data either by the BET or the DR approaches were always below the values obtained by standard SAXS. As an example, the carbon sample functionalized at room temperature gave surface area values of 1114, 1293, and 1970 m2/g, respectively. The possibility that this difference is caused by inaccessible pores was excluded by contrast variation measurements with hexane.

1. Introduction The performance of activated carbons is strongly influenced not only by the contact surface area and porosity but also by the chemistry of the surface.1 Introduction of heteroatoms can significantly influence both the adsorption properties and the catalytic activity, and it is therefore of practical concern to enhance their effect. The most * To whom correspondence should be addressed. E-mail: klaszlo@ mail.bme.hu. † Department of Physical Chemistry, Budapest University of Technology and Economics. ‡ Research Group for Technical Analytical Chemistry, Hungarian Academy of Sciences, Department of General and Analytical Chemistry, Budapest University of Technology and Economics. § Laboratoire de Spectrome ´ trie Physique UMR 5588 CNRSUniversite´ J. Fourier de Grenoble. | Laboratoire de Thermodynamique et Physico-Chimie Me ´ tallurgiques UMR 5614 CNRS-Institut National Polytechnique de Grenoble. (1) 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.

frequent and most important among surface groups are oxygen complexes. These are modified when activated carbons are treated with various oxidative chemicals, for example, nitric acid.2,3 Such surface chemical treatment, however, may produce changes in the morphology of the carbons. Studies of the effects of surface chemical treatment should therefore also include consideration of the collateral damage inflicted on the carbon matrix. Active carbons typically have a large internal surface resulting from micropores, or rather nanopores, with a width up to 20 Å. The standard method of measuring surface area and pore volume is by the adsorption of gases, most often nitrogen at 77 K. However, because the width of the pores is of the same order of magnitude as that of the probe molecules, analysis of adsorption isotherms requires specific approaches4 that are different from the (2) Rodriguez-Reinoso, F.; Molina-Sabio, M.; Munecas, M. A. J. Phys. Chem. 1992, 96, 2707. (3) La´szlo´, K.; Josepovits, K. 25th Biennial Conference on Carbon, July 14-19, 2001, Lexington, KY; CD ROM of Extended Abstracts. (4) Gregg, S. J.; Sing, K. S. Adsorption, Surface Area and Porosity; Academic Press: London, 1982.

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standard Brunauer-Emmett-Teller (BET) model, which was developed for adsorption on flat or mesoporous surfaces. Introduction of heteroatoms also influences the interaction between the gas and the solid surface.5 The possibility of supplementing adsorption measurements by an independent nonintrusive method such as smallangle (neutron or X-ray) scattering arose nearly 40 years ago.6 Most papers on activated carbons published during the following period7 report spatial features covering a range of 10-1000 Å or less. Recent developments in instrumentation have extended the available range of transfer wave vectors. This allows new information to be gained about the micropore network arrangement.8 Unlike gas adsorption, small-angle X-ray scattering (SAXS) measurements of the internal surface area, based on the Porod final slope method, are in principle modelindependent.9 In this paper, the two techniques are compared for a set of activated carbon samples prepared from a synthetic polymer, poly(ethylene terephthalate) (PET). Nitrogen adsorption and SAXS results are complemented by scanning electron microscopy (SEM). The limitations of the SAXS determination are also examined. It is shown that a crucial consideration in evaluating the specific surface area by SAXS is the wide range of characteristic distances that prevails in these systems. One of the aims of the present article, therefore, is to investigate the effect of extending the resolution range of the measurements both to low and to high transfer wave vectors. Also, unlike gas adsorption which is unable to “see” any closed pores that may be present, SAXS detects both closed and open pores and thus may yield a larger surface area. Moreover, it has been demonstrated10,11 that SAXS can in principle discriminate between open and closed porosity if combined with contrast variation. Addition of a contrast varying fluid partly mimics the gas adsorption measurements. The method provides further information on the morphology of the sample and highlights some causes of the observed discrepancies between SAXS- and adsorptionderived surface areas. 2. Experimental Section 2.1. Sample Preparation. Granular activated carbon (APET) was prepared from 2 × 3 mm PET pellets as described by La´szlo´ et al.12 The surface chemistry and morphology of the precursors have been characterized previously.13,14 This steam-activated carbon, obtained at 900 °C, was treated for 3 h with concentrated nitric acid at room temperature (RT) and at the boiling point (BP) of the carbon-acid suspension to achieve different degrees of surface functionalization. The acidic samples were washed with distilled water and extracted in a Soxhlet apparatus until a neutral pH was obtained. The yield was 100% at RT (APETA) and 94.5% at the elevated temperature (APETB). Virgin APET, (5) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: London, 1992. (6) Dubinin, M. M.; Plavnik, G. M.; Zaverina, E. D. Carbon 1964, 2, 261. (7) Hoinkis, E. In Chemistry and Physics of Carbon; Thrower, P. A., Ed.; Marcel Dekker: New York, 1997; Vol. 25, p 72. (8) Pfeifer, P.; Ehrburger-Dolle, F.; Rieker, T. P.; Gonzalez, M. T.; Hoffman, W. P.; Molina-Sabio, M.; Rodriguez-Reinoso, F.; Schmidt, P. W.; Voss D. J. Phys. Rev. Lett. 2002, 88, 115502. (9) Porod, G. In Small-Angle X-ray Scattering; Glatter, O., Kratky, O., Eds.; Academic Press: London, 1982. (10) Hua, D. W.; D’Souza, J. V.; Schmidt, P. W.; Smith, D. M. Stud. Surf. Sci. Catal. (Characterization of Porous Solids III) 1994, 87, 255. (11) Mitropoulos, A. Ch.; Stefanopoulos, K. L.; Kanellopoulos, N. K. Microporous Mesoporous Mater. 1998, 24, 29. (12) La´szlo´, K.; Bo´ta, A.; Nagy, L. G.; Frischkorn, C. B. Carbon 1997, 35, 593. (13) Bo´ta, A.; La´szlo´, K.; Nagy, L. G.; Copitzky, T. A. Langmuir 1997, 13, 6502. (14) La´szlo´, K.; Bo´ta, A.; De´kańy, I. Carbon 2003, 41, 1205.

La´ szlo´ et al. Table 1. Surface Composition Determined by XPS sample

C, atomic %

O, atomic %

100 O/C

APETW APETA APETB

94 91 79

6 9 21

6.4 9.9 26.6

after the same water only treatment (APETW), was used as a comparison. The surface composition of the samples, determined by X-ray photoelectron spectroscopy (XPS), is shown in Table 1. All measurements reported here were made on samples ground in a ball mill. 2.2. Scanning Electron Microscopy. Surface morphological investigations were made on a JEOL 5500 electron microscope in low vacuum mode with a secondary electron detector. The accelerating voltage was 20 kV, and the working distance 20 mm. The samples were fastened to the copper sample holder by adhesive carbon tape. 2.3. Adsorption Measurements. Nitrogen adsorption/desorption isotherms were measured at 77 K, using a Quantachrome Autosorb-1 computer-controlled apparatus. The 250-350 µm powder fraction was measured. The apparent surface area was derived according to the BET model. (Micro)pore analysis was performed by the Quantachrome software using the DubininRadushkevich (DR) and Horva´th-Kawazoe (HK) methods. 2.4. Density Measurements. The true density of the carbon samples was determined by helium pycnometry using the AUTOSORB-1 instrument. 2.5. Small Angle X-ray Scattering. The activated carbon samples studied here exhibit a wide range of characteristic sizes. To take account fully of all the contributions to the scattering spectrum, it is essential to probe as wide a range as possible of transfer wave vectors q ()4π/λ sin θ/2, where λ is the wavelength of the incident radiation and θ is the scattering angle). For this reason, the SAXS measurements were made at a synchrotron source, beamline BM2 at the European Synchrotron Radiation Facility (ESRF), Grenoble, France. Two different experimental configurations were used. Ultra-small-angle measurements (USAXS) were made using an incident energy of 7.9 keV (λ ) 1.57 Å), the distance between sample and detector being D ) 216 cm. In this configuration, the beam-stop, a cross-hair of 300 µm platinum wire, yielded measurements between ca. 7 × 10-4 and 10-2 Å-1. In a second configuration, providing data in the range of ca. 4 × 10-3 Å-1 e q e 1.4 Å-1, the incident energy was set to 18 keV (λ ) 0.69 Å) and the sample to detector distances were 157 and 32 cm. In this case, the beam-stop was a lead disk of 2 mm diameter, fixed to Kapton foil just before the flight tube exit window. In all cases, an indirect illumination CCD detector (Princeton Instruments) with effective pixel size of 50 µm, cooled by a Peltier effect device, was used. Intensity curves I(q), obtained by azimuthal averaging, were corrected for grid distortion, dark current, sample transmission, and background scattering. Intensities were normalized with respect to a standard sample (lupolen), assuming an effective sample thickness of 1 mm. The powder samples were contained in capillary tubes of diameter 1.5 mm. To remove trapped or adsorbed water, they were heated to 110 °C for 24 h before sealing. For contrast variation measurements, hexane was used to modify the electron density contrast between regions of the sample of different density. Carbons to be placed in contact with hexane were first heated to 110 °C and then connected for 24 h to an atmosphere with a partial pressure of hexane p/p0 ≈ 0.4. Alternatively, liquid hexane was introduced into the tube.

3. Results and Discussion 3.1. Scanning Electron Microscopy. Scanning electron micrographs of the three samples are displayed in Figure 1. These micrographs reveal an alternating structure of characteristic size about 1 µm. As the chemical treatment progresses, these large-scale features become more pronounced. With the BP treatment, the process culminates in the formation of filaments having a diameter of about 1 µm. The images suggest that the carbon is not homogeneous in density on this length scale.

Morphology of Activated Carbons

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Figure 2. Low-temperature nitrogen adsorption isotherms of the carbon samples. From top to bottom: APETW, APETA, and APETB. Table 2. Characteristic Data Derived from the Low-Temperature Nitrogen Adsorption Data SBET, m2/g Vtot, cm3/g W0, cm3/g W0/Vtot SDR, m2/g SBET /SDR wads, Å wDR, Å

Figure 1. SEM micrographs of (a) APETW (×10 000), (b) APETA (×20 000), and (c) APETB (×10 000). Note how the skeleton structure is revealed by the acid.

3.2. Analysis of the Adsorption Isotherms. The lowtemperature nitrogen adsorption/desorption isotherms of the powdered samples are shown in Figure 2. The type I isotherms reveal a typically microporous structure with a very narrow hysteresis loop of type H4, indicating slitshaped porosity. The total pore volume (Vtot) was calculated from the amount of nitrogen vapor adsorbed at a relative pressure close to unity, on the assumption that the pores are then filled with liquid nitrogen. The surface areas were calculated according to the BET model (SBET). Since the

APETW

APETA

APETB

1156 0.50 0.48 0.96 1352 0.86 8.6 8.4

1114 0.48 0.46 0.96 1293 0.86 8.6 8.6

304 0.14 0.12 0.86 337 0.90 9.2 11.0

mechanism of adsorption in narrow pores is by volume filling rather than surface layer formation, the DR approach was used to determine the micropore volume, W0, from which a surface area SDR was extracted. This latter calculation involves the assumption that the molecules filling the pores are in contact with the pore walls. The characteristic energy, E0, was deduced from the slope of the DR plot with β ) 0.34. The pore width w of slit-shaped micropores is taken to be 2k/E0, where k is a constant (9-13 kJ nm/mol). Here the value k ) 9 kJnm/ mol was adopted.15,16 An average pore width wads ()2Vtot/ SBET) was derived from the total pore volume and SBET, assuming slit-shaped geometry as revealed by the hysteresis loops. The data derived from the adsorption isotherms are listed in Table 2. The divergence between SBET and SDR results from the difference in the models. Both methods may underestimate the specific surface area when the pores are so narrow that only a single layer can be completed. On the other hand, SDR may be overestimated if the pore accommodates more than two layers, that is, when “excess layers” are no longer in contact with the walls. Another cause of underestimation of the surface area derived from low-temperature gas adsorption stems from the kinetic hindrance due to the low energy of the gas particles, especially in the case of narrow micropores or constrictions. (15) Stoeckli, F.; Lo´pez-Ramoń, M. V.; Hugi-Cleary, D.; Guillot, A. Carbon 2001, 39, 115. (16) Nguyen, C.; Do, D. D. Carbon 2001, 39, 1327.

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Table 3. Helium Density and Solid Volume Fraction O sample

FHe, g/cm3

φ

APETW APETA APETB

1.74 1.82 1.50

0.53 0.53 0.83

The temperature of the nitric acid treatment affects the low-temperature nitrogen adsorption properties and thus the morphology of the activated carbon. The control sample APETW is highly microporous with SBET and SDR of 1156 and 1352 m2/g, respectively. RT treatment, which alters the surface chemistry17 (Table 1), has practically no effect on the adsorption surface area of APETA but slightly decreases the total porosity and the volume of the micropores, listed in Table 2. The ratios of the pore volumes W0/Vtot and of the adsorption-derived surface areas SBET/ SDR are, however, unaffected. At elevated temperature (BP), the acid treatment is more destructive (APETB). The surface area is sharply reduced, but the remaining structure is still strongly microporous. The micropore volume ratio W0/Vtot decreases by only 10%, from 96% to 86%. These high values are an indication that pore filling occurs in one step.18 The decreased microporosity and the concurrent widening of the filled micropores slightly increase the SBET/SDR value. The heavy damage to the pore structure is also reflected in the low-pressure hysteresis (LPH), observed only in this carbon:19 the pore walls become very thin. The structure can be distorted by stress from adsorption, leading to irreversible trapping of the adsorbate molecules. These molecules, however, are removed when the evacuated sample is raised to room temperature. Entrapment takes place in pores otherwise inaccessible for the gas molecules. The narrower the pore, the more pronounced the intercalation.20 In numerous cases, desorption is influenced by the state of the adjacent pores, that is, by whether there is a clear channel between the pore and the outer surface (the network effect).4 The greater hydrophilic character also contributes to the collapse of micropores when samples prepared in an aqueous medium are dried.21 The low helium density of APETB (Table 3) is a sign of a severely weakened skeleton and/or selective conservation of regions with closed porosity. The HK approach reveals a polydisperse pore size distribution in the micropore range (Figure 3). APETW has a single local maximum at 8.4 Å and a shoulder at 10 Å. For APETA, the first maximum is at 8.1 Å, while the previous shoulder becomes a second maximum at the same position. In APETB, the first peak shifts to 8.0 Å and the second remains at 10 Å. Two new peaks appear at 15.6 and 18.7 Å. These results show that the boiling acid completely destroys some of the existing pores. According to the semiempirical HK approach derived for slit-shaped pores, this effect is most pronounced in the range 7.5-15 Å. However, the peaks appearing at 15.6 and 18.7 Å reflect an enlargement of part of the micropores. The burnoff of single graphene layers contributes to the weakening of the pore walls and effectively doubles (from 8 to 15.6 Å) the distance between the remaining adjacent walls. These values are in good agreement with the pore width listed (17) La´szlo´, K.; Kerepesi, P.; Tombaćz, E.; Josepovits, K.; Geissler, E. Carbon ’02 International Conference on Carbon, September 15-19, 2002, Beijing, China; CD ROM of Extended Abstracts E046, 4 pp. (18) Carrot, P. J. M.; Roberts, R. A.; Sing, K. S. W. Carbon 1987, 25, 59. (19) La´szlo´, K.; Bo´ta, A.; Nagy, L. G. Carbon 2000, 38 (14), 1965. (20) Rodriguez-Reinoso, F.; Linares Solano, A. In Chemistry and Physics of Carbon; Thrower P. A., Ed.; Marcel Dekker: New York, 1989; Vol. 21, p 11. (21) Pamula, E.; Rouxhet, P. G. Carbon 2003, 41, 1905.

Figure 3. Differential pore size distribution computed by the HK method. From top to bottom: APETW, APETA, and APETB.

Figure 4. SAXS spectrum of the three samples APETW, APETA, and APETB in air, showing the four zones described in the text. APETA and APETB have been shifted vertically downward by one and two decades, respectively.

in Table 2. Recent model calculations indicate that underestimation of the surface area due to single layer completion is limited to pore widths between 6.9 and 9.1 Å and overestimation starts at 14 Å.22 Owing to the polydispersity, none of the previously discussed effects can be excluded. 3.3. SAXS Measurements. The SAXS curves of the three APET samples in air are shown in Figure 4. In this figure, four main regions of interest can be identified, labeled I-IV. In the low q region I, the prominent feature of the scattering intensity I(q) exhibits power-law behavior, with a slope of about -3.6, characteristic of scattering from a fractal surface of dimension Ds ) 2.4. The smallest q value measurable by the X-ray camera, about 7 × 10-4 Å-1, defines the size of the largest objects that can be detected in these measurements, that is, a radius of gyration of some 2500 Å. In region I at q e 0.001 Å-1, a flattening in the response is observed, which, without further information, might be interpreted as defining the size of the largest structures present. The curvature, however, is probably spurious, since the product I(q)t, where t is the sample thickness, greatly exceeds unity in the lowest q region. Multiple scattering at very small angles is therefore unavoidable. Distortion of the overall response by multiple scattering over wider angles, (22) Lastoskie, C.; Gubbins, K. E.; Quirke, N. J. Phys. Chem. 1993, 97, 4786.


Langmuir, Vol. 20, No. 4, 2004 1325

associated with turbostratic basic structural units (BSUs),26 that is, bricks consisting of a pile of a few polyaromatic molecules. From the Scherrer expression for a peak of width dq (i.e., dS ) 0.9 × 4π/dq), the average diameter dS of the bricks can be estimated from the feature at 3 Å-1 as dS ) 16 ( 2 Å, which is consistent with the above value of d. The Guinier relation,

P(q) ∝ exp(- q2RG2/3)

(1)

which represents the form factor at small q for a single particle of radius of gyration RG, yields a reasonable fit for the shoulder but overestimates the intensity in the plateau region (continuous curve in Figure 5a). The same phenomenon is encountered also in samples APETA and APETB. An alternative description for the shoulder region, which is also used to estimate the surface area, is due to Debye and Bueche.27 This can be expressed formally in terms of a nominal radius of gyration Rg,

P(q) )

Figure 5. (a) Detail of the SAXS spectrum of APETW, showing the fit to the Guinier equation (solid line). The difference between the curve and the data reveals spatial correlation among the BSUs. The dashed line is the Debye-Bueche description (eq 2) of random pores in a solid (ref 27). Zones I-IV are as in Figure 4. (b) Structure factor S(q) ) I(q)/P(q) calculated for sample APETW, where P(q) is given by eq 2.

however, as described elsewhere,23 is almost certainly insignificant in these measurements, since the attenuation of the primary beam is moderate and is due essentially to absorption. As will be mentioned below, insertion of a contrast varying fluid yields information on the extent of multiple scattering in this region. In particular, it is found that the deviation from power-law behavior observed at low q in Figure 4 is not an indicator of the maximum size of the particles. A more reliable estimate of the size (ca. 1 µm) of the objects producing the surface scattering, however, is provided by the SEM micrographs shown in Figure 1. A close-up of the SAXS response of the activated carbon sample before HNO3 chemical treatment (sample APETW) is shown in Figure 5a. In region II, a plateau occurs around 0.1 Å-1, over which the carbon density is approximately uniform. This plateau is terminated by the shoulder at III, from which an apparent Guinier radius RG ) 6.1 ( 0.1 Å can be deduced. The estimated error represents the statistical uncertainty from the data in the q region used to calculate RG. If, for simplicity, it is assumed that this scattering is caused by uniform spheres, then their outer diameter d ()2.58RG) is 15.8 ( 0.3 Å. Previous wide-angle X-ray scattering measurements24 revealed two broad peaks, respectively at q ≈ 1.7 Å-1 and at q ≈ 3.0 Å-1, typical of nongraphitic carbons,25 which are usually (23) Perret, R.; Ruland, W. J. Appl. Cryst. 1971, 4, 444. (24) La´szlo´, K.; Marthi, K.; Djurado, D.; Ehrburger-Dolle, F.; Geissler, E. Carbon ’03 International Conference on Carbon, July 6-10, 2003, Oviedo, Spain; CD ROM of Extended Abstracts (ISBN 84-607-8305-7); Linares-Solano, A., Cazorla-Amoros, D., Eds.; D10, 5 pp.

1 (1 + q Rg2/6)2 2

(2)

The fit to eq 2 is shown as a dashed line in Figure 5a. Owing to the difference in the fit at low q, the numerical value of Rg (9.0 Å) is of course different from that of expression 1. The shortfall in the measured scattering intensity in the plateau region is the signature of spatial correlation between particles due to repulsive interactions, such as occur in dense atomic or molecular fluids.28 In the present case, a similar correlation would be expected from BSUs forming a disordered nanoporous carbon matrix. The total scattered intensity from the assembly of such particles may be approximated by the product of the particle form factor P(q) and the structure factor S(q),

I(q) ) S(q) P(q)

(3)

where S(q) describes the interference due to interparticle correlation. Figure 5b shows the structure factor S(q) ) I(q)/P(q) calculated for sample APETW in the shoulder region III of Figure 5a, where expression 2 has been used for P(q). S(q) exhibits a weak maximum around qm ≈ 0.3 Å-1, corresponding to a mean separation L between the BSUs. If the latter were arranged in crystalline order, a diffraction peak would be observed at qm ) 2π/L. In disordered interacting systems, however, the peak is broadened. Expressions for S(q) have been developed for hard spheres29 and for assemblies of electrostatically repulsive spheres in solution.30 The former approach has been recently employed to describe the distribution of micropores in activated carbon fibers.31 In the present case of a frozen assembly of objects of irregular shape, however, no general analytical expression exists for S(q). The following simple empirical fitting function,32 however, has been found to give reasonable agreement with computer simulations of S(q):33

S(q) )

1 1 + 3p(sin qL - qL cos qL)/(qL)3

(4)

(25) Warren, B. E. Phys. Rev. 1941, 59, 693. (26) Oberlin, A. In Chemistry and Physics of Carbon; Thrower, P. A., Ed.; Marcel Dekker: New York, 1990; Vol. 22. (27) Debye, P.; Bueche, R. M. J. Appl. Phys. 1949, 20, 518. (28) Enderby, J. E.; March, N. H. Adv. Phys. (Philos. Mag. Suppl.) 1965, 14, 453. (29) Percus, J. K.; Yevick, G. J. Phys. Rev. 1958, 110, 1.

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determined by a combination of gas adsorption and helium pycnometry results (Tables 2 and 3). In these samples, the invariant

Q)

∫0∞(I(q) - b)q2 dq

in the denominator of eq 7 is sensitive both to the upper and lower limits of the integral. Knowledge of the scattering behavior at q ) 0 and q ) ∞ is therefore essential, since the whole of the scattering curve must be included. The contribution from the upper limit is, from eq 5

∫q∞

Figure 6. Plot of Iq4 vs q4 for APETW in air.

max

(I(q) - b)q2 dq )

∫q∞

max

K dq ) K/qmax q2

(8)

Table 4. Parameters Derived from SAXS sample

b, SX , R G, Å L, Å cm-1 m2/g

APETW air hexane APETA air hexane APETB air hexane

6.1 5.4 5.8 5.6 5.8 6.0

19.6 19.6 19.1 19.8 18.9 27.2

0.099 0.045 0.082 0.045 0.078 0.056

2000 1980 1970 2050 860 520

SBET/SX (SDR/SX)

wmin ) 2Vtot/SX, Å

0.58 (0.68) 0.58 (0.68) 0.56 (0.58) 0.54 (0.63) 0.35 (0.39) 0.58 (0.65)

5.0 5.1 4.9 4.7 3.3 5.4

where the amplitude of the correlation peak is described by the parameter p. The position of the first maximum of eq 4 at qmL ) 5.76 indicates a separation of L ≈ 19 Å between the BSUs. The estimated values of L for the three samples (Table 4) decrease slightly for APETA and APETB. The presence of a correlation peak implies that the model associated with eq 2 is not suitable for determining the specific surface area of the activated carbon for X-rays. Instead, the Porod approach is employed.9 A region of the scattering spectrum is required where the Porod law holds, that is, where the intensity varies as q-4. To attain values of the surface area comparable to SBET, that is, of the order of 1000 m2/g, the corresponding part of the spectrum must lie in region IV of Figure 5a. The observed slope in IV, however, is only -2.5. Owing to atomic disorder in the surrounding material, this region at high q contains an additional signal that varies only weakly with q. In what follows, it is assumed that the background signal from atomic disorder, b, is constant and independent of q in this region. The total intensity is then

I(q) ) Kq-4 + b

(5)

I(q) q4 ) K + bq4

(6)

Hence

Figure 6 shows the data from the high q region IV of the APETA curve of Figure 5a fitted to eq 6. The value of K is defined by the intercept of the least-squares straight line fit at q ) 0. The values of the slope b are listed in Table 4. The specific surface area SX ) A/VFav, where Fav is the macroscopic sample density and A/V is the area per unit volume of sample, is then found from9

A ) V

πφ(1 - φ)K

∫0 (I(q) - b)q2 dq ∞

(7)

The values of the volume fraction φ and the density Fav are (30) Hayter, J. B.; Penfold, J. Mol. Cryst. 1981, 42, 109. (31) Hoinkis, E.; Ziehl, M. Carbon 2003, 41, 2047.

where qmax is the highest value of q explored in the fit to eq 6. For the present samples, owing to the high surface area, K is large. For qmax ) 1.0 Å-1, this contribution amounted generally to about 20% of the total value of the invariant. The lower limit of the integral in Q is more delicate to evaluate, since the second moment of the power law at low q diverges if q tends to zero. The choice of the lower limit in the calculation of Q is therefore important. The electron micrograph images of Figure 3, which suggest typical sizes close to 1 µm, indicate a lower limit of qmin ) 10-4 Å-1. The resulting contribution to Q from the region qmin e q e 0.01 Å-1 was found to amount to 15-25% of the total. The above considerations thus suggest that estimates of the specific surface area of activated carbons can be substantially in error unless both upper and lower q ranges of the SAXS spectra are taken into account. The resulting values of SX are listed in Table 4. These are smaller than the notional limiting value of the graphene unit (ca. 2600 m2/g) but still larger than the surface areas derived from adsorption data (SBET and SDR), as indicated by the ratio SBET/SX or SDR/SX. In section 3.2, the assumptions leading to the estimate of the adsorption surface areas were already discussed. The possible contribution from inaccessible pores can be directly verified by contrast variation. This technique consists in bathing the carbon in a low molecular weight fluid, which reduces the signal from regions in the sample that are penetrated by the liquid, while leaving unaffected the intensity scattered by regions from which the liquid is excluded. Figure 7 shows, as a typical example, three SAXS responses of the same sample (APETA), in the dry state, with hexane vapor (partial pressure p/p0 ≈ 0.4), and also in contact with liquid hexane. At low q, the response of the hexane vapor sample is identical to that of the dry specimen, that is, the space between the surfaces of the large structures is filled with hexane vapor. At higher q, the hexane vapor curve deviates to join that of the sample containing liquid hexane. The hexane fills the micropores in the condensed state, thereby reducing the electron density contrast in that region of the spectrum. At the upper end of the explored range of q (≈1.25 Å-1), the carbon-air and carbon-hexane curves meet again, demonstrating that the hexane molecules are totally excluded from this part of the spectrum. This value of q corresponds to an exclusion size limit dmin ≈ 2π/q ) 5 Å. The carbon-liquid hexane curves can be analyzed using eqs 6-7, in the same way as above, to calculate the surface (32) Posselt, D.; Pederson, J. S.; Mortensen, K. J. Non-Cryst. Solids 1992, 145, 128. (33) Hasmy, A.; Anglaret, E.; Foret, M.; Pelous, J.; Jullien, R. Phys. Rev. B 1994, 50, 6006.


Figure 7. (a) SAXS spectra of sample APETA in air, in hexane vapor, and in liquid hexane. The APETA-hexane vapor curve is identical to that of the APETA-air sample at low q, but at q g 0.1 Å-1, it joins that of the liquid hexane. This shows that hexane in the micropores is in the liquid state. (b) SAXS spectra of sample APETB in air, in hexane vapor, and in liquid hexane.

area SXhex of carbon in contact with the hexane (Table 4). In all three samples, it is notable that the values of the constant b in eq 6 are smaller than for the carbon-air specimens. This observation indicates that the structure contributing to atomic disorder is partly penetrated by the hexane molecules, that is, the walls of the pores are not smooth but contain shallow cavities in which the hexane molecules nest, an effect called captation.34 A corollary of the decrease in b in the presence of hexane is that the range of q over which eq 6 applies is narrower than in the carbon-air spectra (Figure 8a). Those parts of the carbon matrix into which the hexane molecules cannot nest have a higher contrast, and the signal at high q accordingly increases. The striking result of these measurements, shown in Table 4, is that in samples APETW and APETA, SX is equal to SXhex within experimental error. It follows immediately that in these samples the difference between any of the adsorption-derived surfaces and SX cannot be attributed to permanently closed pores. For APETB, on the other hand, SXhex is intermediate between SX and the adsorption surface listed in Table 2, but each of the ratios SBET/SXhex or SDR/SXhex adopts the same value as in the other two samples. In this case, it is reasonable to attribute the differences, at least in part, to inaccessible pores. Indeed, their presence is likely, in view both of the LPH in the adsorption curve of this sample (34) Pa´szli, I.; La´szlo´, K. Prog. Colloid Polym. Sci. 2001, 117, 51.

Langmuir, Vol. 20, No. 4, 2004 1327

Figure 8. (a) I(q)q4 vs q4 for samples APETA-air (upper curve) and APETA-hexane (lower curve). Straight lines are fits to the regions displaying Porod behavior. The intercept at the origin is the Porod constant K. Note the smaller slope and earlier deviation from linearity in APETA-hexane. (b) Structure factor S(q) ) I(q)/P(q) calculated for sample APETB in air and in liquid hexane, where P(q) is given by eq 2.

(Figure 2) and of the low value of FHe. These observations confirm the deformable structure of this sample. The presence of hexane molecules in one pore can close neighboring pores in a random way, a phenomenon that also can happen during nitrogen adsorption. Direct evidence for such local mechanical deformation is found in the change of the structure factor S(q) when hexane is added (Figure 8b). The resulting value of L, the interBSU distance, increases from about 19 Å in the dry sample to 27 Å in the presence of hexane (Table 4). Such local swelling is consistent with the existence of LPH. In samples W and A, however, the corresponding variation of L is small and of the order of the experimental error. An independent measure of the minimum characteristic distance in the sample, wmin, is determined by the ratio Vtot/SXhex, assuming that the Gurvitsch rule holds. This is very often the case when the adsorption isotherm is of type I. Deviation from the Gurvitsch rule may arise when a molecular sieve effect occurs. The pore then has a width of less than two molecular diameters.4 For slit geometry, the width wmin is equal to 2Vtot/SXhex. From the data given in Table 4, this yields the values wmin ) 5.1, 4.7, and 5.4 Å in samples APETW, APETA, and APETB, respectively. These results are larger than the calculated critical molecular size of hexane, 4.0 Å.35 Empirical limiting sizes, indicating the smallest slit size into which a hexane molecule can be fitted, range between 4.3 and 4.9 Å.4,36 (35) Webster, C. E.; Drago, R. S.; Zerner, M. C. J. Am. Chem. Soc. 1998, 120, 5509. (36) Breck, D. W. In Zeolite Molecular Sieves; Wiley: New York, 1974; p 636.

1328


The foregoing evidence thus tends to show that there is a single layer of hexane between the slit walls. On the other hand, the slit widths derived entirely from adsorption data (listed in Table 2) range from 8.4 to 11.0 Å. When the carbon samples are in contact with liquid hexane, the electronic contrast is reduced by a factor of about 4. Inspection of Figure 7 reveals that the shape of the response remains unchanged, except at the highest and at the smallest q values. In the first case, the change in shape is due to the molecular sieve effect discussed earlier. In the latter case, the curvature observed in the carbonair spectrum vanishes and simple power-law behavior is recovered. This implies that distortion of the spectrum due to multiple scattering is negligible, except at the lowest values of q. In view of the differences in surface chemistry and adsorption properties, the similarity of the SAXS spectra from the carbon-air samples, which is illustrated by the similarity of all the parameters deduced purely from SAXS, may seem surprising. Differences among these samples in their X-ray specific surface area stem essentially from the differences in density and in pore volume, which are determined by an independent technique. The nanoporous regions, which are preferentially destroyed in the BP acid reaction, have a higher true density than other regions with small inaccessible voids. It seems likely that these differences are the result of the formation of nanobubbles during carbonization, which can generate ordering of the atoms in their immediate vicinity. It may be recalled that the starting polymer, PET, is a thermoplastic, with a glass transition temperature at 80 °C. Endothermic melting occurs at 259 °C, and exothermic decomposition at about 400 °C.37 Since the pyrolysis takes place in the fluid state, the volatile degradation products form bubbles, the smallest of which may freeze in the matrix during vitrification. 4. Conclusion Surface functionalization of activated carbon by exposure to nitric acid modifies the chemistry of the solid material, to a degree that depends on the severity of the treatment. XPS reveals a moderate increase in the surface oxygen content, from 6 to 9 at. %, and a much larger enhancement to 21 at. % for acid treatment at ambient or elevated temperature, respectively. The significant difference in the surface chemistry influences mainly the finer structure. The SEM micrographs of all three samples reveal an alternating pattern with a characteristic size of about 1 µm, and the carbons display an apparent surface fractal dimension of Ds ) 2.4 in the wave vector range 0.001-0.02 Å-1. (37) Polymer Data Handbook; Mark, J. E., Ed.; Oxford University Press: New York, 1999.

La´ szlo´ et al.

The control sample, which was in contact only with water but not with acid, displays a micrometer scale layered structure under SEM. It is strongly microporous with a BET and a DR surface area of 1156 and 1352 m2/g, respectively. Ninety-six percent of its pores contribute to the 0.48 cm3/g micropore volume. The polydisperse pore size distribution shows a dominant peak at 8.4 Å. The average width of the slit-shaped pores derived from the DR plot is 8.4 Å, and the minimum slit width available either for nitrogen or hexane is 5.1 Å from the X-ray and pore volume data. The control sample is composed of randomly packed turbostratic basic structural units with an average separation L of 19.6 Å. The X-ray derived surface area SX, measured both in air and in hexane, is about 2000 m2/g. The SEM images of the room temperature treated sample show a more pronounced steplike surface structure than the control. Both the adsorption-derived surface areas (BET, 1114 m2/g; DR, 1293 m2/g) and the X-ray-derived surface areas (ca. 2000 m2/g) are practically unchanged. The marginally smaller micropore volume (0.46 cm3/g) amounts to the same fraction of the total porosity. In the HK pore size distribution, in addition to the main peak around 8 Å, a second peak appears at 10 Å, but the average and the minimum slit widths as well as the separation of the basic structural units are virtually unaffected. The severe damage caused by the boiling acid reveals an underlying fiberlike structure in the SEM image with a typical diameter of 1 µm. A drastic loss of about 75% in all the measured surface areas is observed. Two new peaks appearing at 15.6 and 18.7 Å in the semiempirical HK pore size distribution correspond to a doubling of some of the interlayer distances, as is also revealed by the increase in the average slit width to 11 Å. The weakening of the pore walls is sensed by several indicators: low helium density, pronounced low-pressure hysteresis, and the swelling of the separation between basic structural units when hexane is introduced (from 18.9 to 27.2 Å). The greater hydrophilic character also may contribute to this effect. The minimum slit width expands from 3.3 Å in air to 5.4 Å in hexane. Acknowledgment. Access to the 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 as well as to J. F. Be´rar, K. Kosik, and D. Djurado for their invaluable assistance and helpful discussions. This research was supported by the National Research Fund (OTKA, Grant No. T 025581) and the National Research and Development Programs (NKFP 3/043/2001). LA035954S

Morphological Investigation of Chemically Treated Poly(ethylene

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