2838
Langmuir 2005, 21, 2838-2846
Investigation of Activated Carbon Surface Heterogeneity by Argon and Nitrogen Low-Pressure Quasi-Equilibrium Volumetry Christophe Garnier,* Tatiana Gorner, Angelina Razafitianamaharavo, and Fre´de´ric Villie´ras Laboratoire Environnement et Mine´ ralurgie, Ecole Nationale Supe´ rieure de Ge´ ologie, Institut National Polytechnique de Lorraine, CNRS UMR 7569, 15 av. du Charmois, BP 40, 54501 Vandœuvre le` s Nancy Cedex, France Received August 17, 2004. In Final Form: November 17, 2004 Surface heterogeneity can be assessed by adsorption of different gaseous probes on solid materials. In the present study, four types of activated carbons were analyzed by classical N2 Brunauer-EmmettTeller (BET) measurements and by low-pressure quasi-equilibrium volumetry (LPQEV) (Villie´ras, F.; Michot, L. J.; Bardot, F.; Cases, J. M.; Franc¸ ois, M.; Rudzinski, W. Langmuir 1997, 13, 1104). Three methods of data evaluation were applied: (a) the Frenkel-Halsey-Hill method for estimation of fractal dimensions from BET data, (b) the Horwath-Kawazoe method to calculate the pore size distribution from LPQEV Ar and N2 adsorption isotherms, and (c) the derivative isotherm summation (DIS) method to describe the solid’s surface heterogeneity by a concept of local derivative isotherms. Similar Ar and N2 adsorption energy distributions were obtained on all carbons, which indicates the presence of mainly nonpolar surfaces. When adsorption was described by the van der Waals equation, the ratio between the interaction energy of different energetic sites with argon and nitrogen was 0.88. This value corresponded very well with a slope obtained when Ar and N2 positions of local isotherms by the DIS method were compared. This relationship has an important impact because it enables one to constrain the modeling of local isotherms. This study, besides the surface information, showed large possibilities of the DIS method for the surface analysis not only in terms of solid heterogeneity characterization but also in terms of polarity assessment.
Introduction The understanding of adsorption and desorption phenomena of organic molecules on activated carbons is necessary for describing and predicting the adsorption of organic pollutants in water treatment processes. Activated carbons are unique and versatile adsorbents extensively used to eliminate pollutants (pesticides, hydrocarbons, etc.), natural organic matter responsible for organoleptic characteristics, and the residues of organic molecules issued during ozonation in the drinking water treatment process. Industrial wastewaters can contain toxic organic molecules that are not easily degradable; therefore activated carbons adapted to the effluents2 are also applied in wastewater treatment. Activated carbons are the result of the activation process in which a primary organic raw material (wood, coconut shell, etc.) with little internal surface is oxidized in an atmosphere of air, carbon dioxide, or steam at high temperature (800-1000 °C). The elimination of most of the non-carboneous compounds results in the development of a porous structure of molecular dimensions with a large internal surface area3 that can be compared to that of sponges. The roughness of the surface, the shape and the size of the pores, the infrastructure, and the relationships between these pores influence the adsorption capacity. * Corresponding ensg.inpl-nancy.fr.
author.
E-mail:
christophe.garnier@
(1) Villie´ras, F.; Michot, L. J.; Bardot, F.; Cases, J. M.; Franc¸ ois, M.; Rudzinski, W. Langmuir 1997, 13, 1104. (2) Ba`n, A.; Scha¨fer, A.; Wendt, H. J. Appl. Electrochem. 1998, 28, 227-236. (3) Bansal, R. C.; Donnet, B. J.; Stoeckli, F. In Active carbon; Marcel Dekker: New York, 1988.
The textural description of such complex solids is not easy, and often fractal theory4,5 has been used, where fractal dimensions often allowed description of this porosity. Indeed, the microstructure of an activated carbon is relatively disordered compared with that of graphite; the activated carbon structure can be visualized as stacks of flat aromatic sheets cross-linked in a random manner. Moreover, the activation perturbs the regular arrangement of carbon atoms at the surface by creating free valences. It is likely that one part of the interactions is controlled, at least partially, by the chemical reactivity of created surfaces.3 From the textural and chemical point of view, the surface of activated carbons should then be considered as highly heterogeneous. Argon adsorption at very low pressure (LPQEV, low-pressure quasi-equilibrium volumetry)13 and the derivative isotherm summation (DIS) procedure1,7 have permitted a deeper insight into the activated carbon interactions (micropore size distribution) with phenol when it was adsorbed from water. In the case of minerals, the LPQEV method of adsorption was used to identify the different crystalline faces.1,6-12,14 (4) Hayashi, J.; Muroyama, K.; Gomes, V. G.; Watkinson, A. P. Carbon 2002, 40, 630-632. (5) Khalili, N. R.; Pan, M.; Sandi, G. Carbon 2000, 38, 573-588. (6) Balard, H. Langmuir 1997, 13, 1260. (7) Villie´ras, F.; Cases, J. M.; Franc¸ ois, M.; Michot, L. J.; Thomas, F. Langmuir 1992, 8, 1789. (8) Villie´ras, F.; Michot, L. J.; Bardot, F.; Chamerois, M.; EypertBlaison, C.; Franc¸ ois, M.; Ge´rard, G.; Cases, J. M. C. R. Geosci. 2002, 334, 597-609. (9) Michot, L. J.; Villie´ras, F.; Franc¸ ois, M.; Yvon, J.; Le Dred R.; Cases, J. M. Langmuir 1994, 10, 3765. (10) Michot, L. J.; Villie´ras, F.; Franc¸ ois, M.; Bihannic, I.; Pelletier, M.; Cases, J. M. C. R. Geosci. 2002, 334, 611-631.
10.1021/la047948h CCC: $30.25 © 2005 American Chemical Society Published on Web 02/26/2005
LPQEV of Argon and Nitrogen
Langmuir, Vol. 21, No. 7, 2005 2839
In the present work, LPQEV of argon and nitrogen was performed to assess the surface of four different activated carbons. The analysis by argon adsorption gives information about geometrical properties of the solids (micropore size distribution). The nitrogen can give specific interactions with polar surface sites; thus when compared with argon adsorption, the presence or absence of such polar surface sites8,15 can be revealed. Material and Methods Activated Carbons. The following materials were used: Filtrasorb F400 carbon provided by Chemviron (Feluy, Belgium), Maxsorb (noncommercial sample) provided by The Kansai Coke and Chemicals Co. Ltd. (Misono-cho Amagasaki, Japan), and TANACARBO 7500 and 4500 provided by TANAC S.A. (Montenegro, RS, Brazil). Prior to use, the adsorbents were gently ground in an agate mortar; the mean diameter of the obtained powders was 22.4, 41.1, 40.2, and 43.0 µm for F400, Maxsorb, Tanac 7500, and Tanac 4500, respectively, measured by a Malvern MasterSizer MS 20 device. Brunauer-Emmett-Teller (BET) Measurements. The nitrogen adsorption/desorption isotherms at 77 K were obtained by using a lab-built classical step by step volumetric setup. Prior to the experiments, the samples were outgassed at 50 °C under a residual pressure of 0.1 Pa for 18 h. Surface area and porous volume were determined using BET analysis with an error of (20 m2/g. LPQEV Measurements. Low-Pressure Argon and Nitrogen Adsorption at 77 K. High-resolution argon and nitrogen adsorption isotherms were recorded on a lab-built automatic LPQEV setup.1,7,9 The experimental conditions were as follows: the sample mass was about 0.060 g, outgassing was performed at 50 °C under a residual pressure of 0.001 Pa, and the gases were Argon N56 (purity > 99.9996%) and Nitrogen N55 (purity > 99.9995%) supplied by Alphagaz (France). In this method, a slow, constant, and continuous flow of adsorbate was introduced into the adsorption cell. From the recordings of quasi-equilibrium pressure vs time, the adsorption isotherms were derived. Method for Data Treatment. Fractal Dimensions. The fractal dimensions D were determined by applying the FHH (Frenkel-Halsey-Hill) equation to the adsorption isotherm of N2.4,5
[ ( )]
q P ) K ln qe P0
h
eq 3 assumes a higher surface coverage with gas/liquid surface tension as the controlling factor at the adsorption surface.5 Equation 2 can be used for low P, and eq 3 in the whole pressure range16 [P; P0]. When several linear portions are observed on each plot, different values of fractal dimensions can be calculated for one sample; the comparison of the D values yields valuable information on the textural properties of the solid. Horvath-Kawazoe Method. The Horvath-Kawazoe method17 (HK method) is used to estimate the size repartition of the micropores from LPQEV adsorption isotherms. This method has been developed on carboneous matters and supposes that micropores exist between graphite slits and that their filling pressure depends only on adsorbate-adsorbent interaction energy. The potential is given by eq 4, where U0 describes the adsorbent-adsorbate interaction and Pa describes the adsorbateadsorbate-adsorbent interactions.
P RT ln ) U0 + Pa P0
The potential varies with the distance (d) from the central plane. Averaging this potential over the available distance within the slit and substituting the result into eq 4 yields the general equation developed by these authors as follows:17-19
()
ln
[
]
A C P B -D )0 P0 x - d (x - d/2)3 (x - d/2)9
NaAa + NAAA A ) NAv RTσ4
(2)
h ) (D - 3)
(3)
6mc2RaRA Ra/χa + RA/χA
(7)
3mc2RaRA 2
(8)
AA )
m is the mass of an electron, c is the velocity of light, and R and χ are the polarizability and magnetic susceptibility (second and third entries in Table 1) of an adsorbent atom (subscript a) and/ or of an adsorbate molecule (subscript A). The remaining three constants (B, C, and D) are given by
Equation 2 is based on the assumption that van der Waals forces are dominant between the adsorbate and the adsorbent, while (11) Eypert-Blaison, C.; Villie´ras, F.; Michot, L. J.; Pelletier, M.; Humbert, B.; Ghanbaja, J.; Yvon, J. Clay Miner. 2002, 37, 531-542. (12) Bardot, F.; Villie´ras, F.; Michot, L. J.; Franc¸ ois, M.; Gerard, G.; Cases, J. M. J. Dispersion Sci. Technol. 1998, 19, 739-760. (13) Pre´lot, B.; Villie´ras, F.; Pelletier, M.; Ge´rard, G.; Gaboriaud, F.; Ehrhardt, J. J.; Perrone, J.; Fedoroff, M.; Jeanjean, J.; Lefe`vre, G.; Mazerolles, L.; Pastol, J. L.; Rouchaud, J. C.; Lindecker, C. J. Colloid Interface Sci. 2003, 261, 244-254. (14) Michot, L. J.; Didier, F.; Villie´ras, F.; Cases, J. M. Polish J. Chem. 1997, 71, 665. (15) Villie´ras, F.; Michot, L. J.; Bernardy, E.; Chamerois, M.; Legens, C.; Gerard, G.; Cases, J. M. Colloids Surf., A 1999, 146, 163-174.
(6)
and NAv is the Avogradro number; R and T are the gas constant and temperature, respectively. Na and NA are the number of carbon atoms of adsorbent and the number of molecules of adsorbate, respectively, per unit area of adsorbent. Aa and AA are constants given by
(1)
h ) (D - 3)/3
(5)
where A is a constant given by
Aa )
where q is the amount adsorbed at equilibrium pressure P; qe is the adsorbed amount filling micropore volume; P0 is the saturation pressure; K is a constant. When the logarithm of the adsorbed amount (q) plotted as a function of the logarithm of ln(P0/P) (FHH plot) shows a linear behavior, a fractal dimension (D) can be calculated from the slope4 (h). Two expressions can be used to derive fractal dimensions from h:
(4)
D)
B)
σ4 3
(9)
C)
σ10 9
(10)
σ4 σ10 3 3(d/2) 9(d/2)9
(11)
(16) Pfeifer, P.; Liu, K. Y. In Equilibria and dynamics of gas adsorption on heterogeneous solid surfaces; Rudzinski, W., Steele, W. A., Zgrablich, G., Eds.; Elsevier: Amsterdam, 1997. (17) Horvath, G.; Kawazoe, K. J. Chem. Eng. Jpn. 1983, 16 (6), 470475. (18) Kowalczyk, P.; Terzyk, A. P.; Gauden, P. A.; Solarz, L. Comput. Chem. 2002, 26, 125-130. (19) Terzyk, A. P.; Gauden, P. A. Colloids Surf., A 2001, 177, 57-68.
2840
Langmuir, Vol. 21, No. 7, 2005
Garnier et al.
Table 1. Parameters Applied for the Micropore Size Distribution Calculationa adsorbate parameter diameter (da and dA, nm) polarizability (R, cm3) magnetic susceptibility (χ, cm3) temperature (T, K) a
adsorbent, carbon
Ar
N2
0.34
0.336
0.300
1.02 × 10-24
1.64 × 10-24
1.46 × 10-24
13.50 × 10-29
3.21 × 10-29
2.00 × 10-29
77.5
77.5
Derivative Isotherm Summation. The data of high-resolution argon and nitrogen adsorption were treated using the DIS1,7 procedure to examine the surface energetic heterogeneity of solid samples. The total derivative adsorption isotherm on a heterogeneous surface is modeled by considering two scales of heterogeneity: in the case of crystalline minerals, the surface can be divided into i different crystal faces (patchwise distribution), each face having its own heterogeneity continuously distributed around a mean value (random distribution). The resulting adsorption isotherm can be written as follows:
θt )
Reference 19.
∑X θ
i it
i
where
σ)
(52)
1/6d
2
d ) da + dA
(12) (13)
and d is the sum of the diameters of an adsorbent atom and an adsorbate molecule. The values of the parameters used in this study are given in Table 1. From a numerical point of view, the nonlinear equation defined by eq 5 is solved by using the bisection method as proposed by Kowalczyk et al.18
)
∑X ∫ θ ()χ () d i
i
Ω i
i
(14)
where θt is the total adsorption isotherm, θit are the adsorption isotherms on the different energetic domains of the surface, Xi is its fractional contribution to θt, is the adsorption energy, Ω is the physical domain of , θi() is a “local” theoretical adsorption isotherm, and χi() is the dispersion of on the ith domain. The experimental curve is then fitted using theoretical local isotherms derived from one layer and multilayer adsorption formalisms following the procedure proposed and discussed by Villie´ras et al.1,7 The local adsorption isotherms used in that study were the Langmuir/Bragg-Williams-Temkin equation for limited adsorption and the BET/Hill equation for multilayer adsorption.7 In the case of nonsymmetrical peaks, the Dubinin-Raduskhevich equation can be used.1 Each local isotherm is characterized by three parameters: (i) the position of the peak maximum, linked
Figure 1. N2 adsorption (full points) and desorption (empty points) curves [(a) Maxsorb (diamond); (b) F400 (triangle), Tanac 4500 (circle), and Tanac 7500 (square)] and FHH plot for (c) Maxsorb, (d) F400, (e) Tanac 7500, and (f) Tanac 4500.
LPQEV of Argon and Nitrogen
Langmuir, Vol. 21, No. 7, 2005 2841 Table 2. BET and t-Plot Parametersa
activated carbons
SBET (m2/g)
Vm (m2/g)
CBET
Smicropore (m2/g)
Smeso and macropore (m2/g)
Stotal (m2/g)
Maxsorb F400 Tanac 4500 Tanac 7500
2730 1100 740 660
624 251 169 150
138 784 1267 3352
2740 1045 525 465
410 200 270 225
3150 1245 795 690
a
Estimated calculation error: (20 m2/g.
Table 3. Slopes of the Regression Lines h and Fractal Dimensions D D)3+h
h activated carbon Maxsorb F400 Tanac 4500 Tanac 7500
P/P0 P/P0 D ) 3 + 3h, P/P0 first second P/P0 first second P/P0 first range range range range range -0.49 -0.35 -0.21 -0.18
-0.08 -0.12 -0.05 -0.04
2.51 2.65 2.79 2.82
2.92 2.88 2.95 2.96
1.53 1.95 2.37 2.46
to the CBET constant, i.e., the normal interaction between the surface and an adsorbed molecule; (ii) the lateral interactions, ω, between two neighboring adsorbed molecules; and (iii) the monolayer capacity, Vm, of the local isotherm. The peak position, ln(P/P0), is proportional to the adsorption energy ∆G (-∆G ) RT ln(P/P0)). Lateral interactions are easily detected through the shape (half-height width) of the local derived isotherm. In fact, the intensity of lateral interactions must be considered as a bestfit parameter enclosing further information about the heterogeneity of the considered adsorption domain.13
Results BET Measurements and Estimation of the Fractal Dimensions Using the Fractal FHH Model. The nitrogen adsorption-desorption isotherms (Figure 1a,b) of four activated carbons were recorded at 77.5 K. The specific surface area SBET (from the BET method), monolayer volume Vm, micropore surface Smicropore, and other parameters listed in Table 2 were determined from the nitrogen adsorption/desorption data. The reported surface area SBET, micropore area Smicropore, and meso- and macropore surface Smeso and macropores (from de Boer’s tmethod) for studied carbons showed that the microporosity Smicropore and surface area SBET were very high for Maxsorb and decreased as follows: F400, Tanac 4500, Tanac 7500. The desorption hysteresis loops were very small (Figure 1a,b) which showed that the samples were only slightly mesoporous. As often observed with microporous samples, the BET monolayer was underestimated. Table 3 shows the slopes of the regression lines, h, and the fractal dimensions D of four carbons estimated from the FHH model and calculated for two ranges of relative pressures: the first range, where micropore filling was assumed to be complete, and the second range where mesoand macropore filling was supposed to be predominant. The first range of relative pressures P/P0 was equal to [0.0; 0.2], [0.0; 0.1], [0.0; 0.8], and [0.0; 0.8]; and the second range was equal to [0.2; 1.0], [0.1; 1.0], [0.8; 1.0], and [0.8; 1.0] for Maxsorb, F400, Tanac 4500, and Tanac 7500, respectively (calculated from Figure 1c-f). It can be seen that the exponent h is different from -1/3 for all samples; these cases are called nonclassical FHH isotherms. Two opposite interpretations can be used: Halsey’s hypothesis20 where the surface is planar and patchwise energetically heterogeneous, or the hypothesis in which the surface is geometrically heterogeneous (fractal) and energetically homogeneous.16 If we consider the fractal hypothesis, for h values in range [-1/3; 0], the fractal dimension may be (20) Halsey, G. D. J. Am. Chem. Soc. 1951, 73, 2693-2696.
either capillary wetting (eq 3) or van der Waals wetting (eq 2) and for values of h in range [-1; -1/3], the fractal dimension can be only calculated from eq 3 (reversible capillarity condensation). The surface of activated carbon can be characterized by only one or two (multifractal) D parameters with this method. All studied activated carbons had fractal dimensions D (Table 3) different from 2 (smooth surface) and 3 (complete volume). According to Khalili et al.,5 carbons with microporous structure have fractal dimensions of about 2.52.9. According to Choma and Jaroniec,21,22 the lower values of fractal dimensions are obtained for mesoporous carbons. In our case, Maxsorb and F400 carbons had the lowest fractal dimensions. Indeed, the organization in micropores is different with flat micropores for Maxsorb and F400 and more bulky ones for Tanac samples. The comparison of the fractal dimensions obtained from the two pressure ranges showed irregularities in pore shapes of the Maxsorb sample with flat micropores and bulky mesopores. The differences are less pronounced for F400 and negligible for Tanac samples showing similar three-dimensional geometry for micro- and mesopores. LPQEV Measurements and DIS Evaluations. Argon. Argon is an inert and nonpolar gas and will interact with adsorbent sites by van der Waals nonpolar London forces. The derivative adsorption isotherms obtained with argon are shown in Figure 2a. The argon adsorption energy distributions were very similar for all samples at high energy (low P/P0). The experimental curves become different for lower adsorption energies (higher P/P0), particularly for the Maxsorb and F400 activated carbons. Using the DIS procedure,7 argon derivative adsorption isotherms could be described by local isotherms with three peaks which represent three different adsorption sites in the case of Maxsorb carbon (Figure 2c) or four main peaks in the case of other carbons (Figure 2d-f). The local derivative isotherms reveal the geometrical heterogeneity of a solid surface. Figures 2c-f and 3c-f show the fits for derivative local isotherms. The global derivative isotherms are calculated by summation of the local models, and they are presented in Figures 2c-f and 3c-f by full lines; the numerical DIS results are shown in Table 4. The pore size distributions assessed by Ar and calculated by the HK method (Figures 2b and 4b,d,f,h) gave monomodal repartitions around 5.8 Å for all samples except the Maxsorb carbon where two modes equal to 5.8 and 7.9 Å were observed. The repartition was very narrow for Tanac 7500 and slightly wider for Tanac 4500 and showed a shoulder for F400 (Figure 4). Nitrogen. Nitrogen is a bimolecular gas and will interact with adsorbent sites by van der Waals nonpolar London forces and charge-induced dipolar Debye effects. The derivative nitrogen adsorption isotherms (Figure 3a) were very similar for all samples except for Maxsorb carbon. These derivative isotherms could be described by local isotherms with four main peaks for Maxsorb (Figure 3c) (21) Choma, J.; Jaroniec, M. Polish J. Chem. 1995, 69, 281. (22) Jaroniec, M.; Choma, J. In Equilibria and dynamics of gas adsorption on heterogeneous solid surfaces; Rudzinski, W., Steele, W. A., Zgrablich, G., Eds.; Elsevier: Amsterdam, 1997.
2842
Langmuir, Vol. 21, No. 7, 2005
Garnier et al.
Figure 2. (a) Comparison of argon adsorption derivative isotherms obtained on four activated carbons. (b) Derivative micropore size distribution calculated by the HK method on different carbons. DIS argon analysis and their local isotherms obtained on different carbons: (c) Maxsorb, (d) F400, (e) Tanac 7500, and (f) Tanac 4500. The fluctuations observed at low relative pressure for Tanac 7500 are due to some thermal instability generated by exothermal adsorption. Table 4. DIS Analysis: Argon Fit Parameters activated carbons Maxsorb
F400
Tanac 4500
Tanac 7500
peak position ln(P/P0)
Vm (cm3/g)
ω/kT lateral interaction
models
-12.41 -7.69 -2.46 -12.84 -9.00 -5.40 -2.52 -12.51 -9.12 -5.73 -2.67 -12.42 -9.03 -5.40 -2.52
51.0 416 386 33.2 82.2 48.9 46.8 50.9 75.2 39.4 48.1 58.1 48.8 33.9 24.6
0.5 -1.3 0 0.1 -0.7 -0.7 0.7 0 -1 0 0 0.1 -0.8 -0.8 0
DR BWT BET DR BWT BWT Hill DR BWT Langmuir BET DR BWT BWT BET
and five main peaks for other carbons (Figure 3d-f). Modeling parameters are presented in Table 5. The pore size distributions calculated by the HK method (Figures 3b and 4b,d,f,h) gave monomodal repartitions for all samples around 4.7 Å except for the Maxsorb carbon where two modes equal to 5.8 and 12.0 Å were observed. As observed in the case of argon adsorption, the micropore
Table 5. DIS Analysis: Nitrogen Fit Parameters activated carbons Maxsorb
F400
Tanac 4500
Tanac 7500
peak position ln(P/P0)
Vm (cm3/g)
ω/kT lateral interaction
models
-13.61 -9.16 -5.76 -2.52 -14.22 -11.73 -9.06 -4.92 -2.64 -14.22 -11.91 -8.94 -4.92 -2.40 -14.22 -12.03 -8.94 -4.92 -2.40
91.3 288 52.8 288 34.6 28.1 49.1 34.3 33.0 47.8 33.7 42.8 41.8 29.8 46.6 30.1 27.7 31.1 18.3
0.2 -1.3 0 0 -0.3 -0.3 -0.92 -1.1 0 0 -0.3 -0.92 -1.1 0 0 -0.3 -0.92 -1.1 0
DR BWT BET BET DR BWT BWT Hill BET DR BWT BWT Hill BET DR BWT BWT Hill BET
repartition was narrow for Tanac 7500 and slightly wider for Tanac 4500 and showed a shoulder for F400. Discussion In the nonclassical FHH isotherm (h * -1/3), the presence of two slopes can be interpreted as a transition
LPQEV of Argon and Nitrogen
Langmuir, Vol. 21, No. 7, 2005 2843
Figure 3. (a) Comparison of nitrogen adsorption derivative isotherms obtained on four activated carbons. (b) Derivative micropore size distribution calculated by the HK method on different carbons. DIS nitrogen analysis and their local isotherms obtained on different carbons: (c) Maxsorb, (d) F400, (e) Tanac 7500, and (f) Tanac 4500. The fluctuation observed at low relative pressure for Tanac 7500 is due to some thermal instability generated by exothermal adsorption.
from van der Waals wetting to capillarity wetting in a single pore or on a fractal surface.16 The slope changes when the capillarity forces become stronger than the adsorbent potential. The filling of the small pores, taking place before the transition, is governed by the adsorbent potential; on the other hand, the filling of large pores, occurring before the transition, is governed by capillary condensation.16 This method describes three-dimensional shape but not the repartition of the pores and the energetic heterogeneity of the micropore wall surfaces. The pore size distribution can be calculated by the HK method. However the comparison between argon and nitrogen showed discrepancies between the micropore size distributions (Figure 4b,d,f,h). The HK method failed to determine accurate and unambiguous micropore sizes. Indeed, this method does not account for the chemical heterogeneity of carbon walls. In addition, the proposed HK calculation parameters are still under discussion. Both aspects, the adsorbed quantities and energetic adsorption on local homogeneous sites on porous carbon, can be better examined by the DIS method. Energetic Considerations. The differences in the derivative isotherms and in the positions of each local isotherm (along each abscissa in Figures 2a,c-f and 3a,cf) between nitrogen and argon allowed determination of
the specific interaction of the nitrogen molecule with the surface due to its quadrupole momentum. As proposed by Villie´ras et al.,23 the comparison between argon and nitrogen derivative adsorption isotherms as a function of ln P instead of ln(P/P0) permits detection of polar interactions between nitrogen and surface sites. Argon is a monatomic gas and will share mainly London dispersion force interaction with the surface. Due to its quadrupolar inducible momentum, nitrogen shares both London dispersion and polar interactions. In the case of polar solids, different distributions should then be observed for nitrogen and argon, while for nonpolar solids, similar distributions were obtained, which was justified by Villie´ras et al.8 by the proximity of argon and nitrogen Lennard-Jones interaction potential. Comparison plots are presented in Figure 4a,c,e,g and show very similar adsorption energy distributions. The derivatives of the isotherms are superimposed in the highenergy domain (low ln P) and diverge in intensity for lower energies (high ln P), but the general shape is conserved. The fact that identical argon and nitrogen energy dis(23) Villie´ras, F.; Chamerois, M.; Bardot, F.; Michot, L. J. In Contact Angle, Wettability and Adhesion, Vol. 2; Mittal, K. L., Ed.; VSP: Utrecht, 2002; pp 435-447.
2844
Langmuir, Vol. 21, No. 7, 2005
Garnier et al.
Figure 4. Comparison of nitrogen (black points) and argon (gray points) adsorption derivative isotherms in ln P form obtained for (a) Maxsorb, (c) F400, (e) Tanac 7500, and (g) Tanac 4500. Micropore size distribution calculated by the HK method for (b) Maxsorb, (d) F400, (f) Tanac 7500, and (h) Tanac 4500.
tributions were obtained suggests that the activated carbons present mainly nonpolar surfaces. This fact reinforces the DIS modeling results for argon and nitrogen for adsorption energies (peak position) (Figure 5) as well as for adsorbed quantities (Figure 6). Correlation between Peak Positions Obtained with Nitrogen and Argon Probes. It can be observed that each nitrogen modeling requires systematically one more local isotherm (Figure 3) at low energy than the corresponding argon modeling (Figure 2). The additional nitrogen domain is probably not observed during argon adsorption, while it occurs in the multilayer adsorption
energy range, i.e., in the exponential increases of the argon derivative isotherm. Therefore this nitrogen domain will not be considered in the next comparison. Figure 5 shows the correlation between nitrogen and argon peak positions. A linear relationship was obtained with a slope equal to 0.887. The fact that a linear relationship was obtained for different samples confirms that the same adsorption energy distribution was observed with argon and nitrogen without significant polar interactions. The fact that the slope is not equal to 1 is contradictory to the hypothesis of Villie´ras et al.8 However,
LPQEV of Argon and Nitrogen
Langmuir, Vol. 21, No. 7, 2005 2845
µ12R2 + µ22R1 1 (4π0)2 r6
(19)
3 R1R2 (hν1)(hν2) 1 2 (4π )2 hν1 + hν2 r6
(20)
wD(r) ) -
wL(r) ) -
0
Figure 5. Relation between argon peak positions and nitrogen peak positions on Maxsorb (diamond), F400 (triangle), Tanac 7500 (square), and Tanac 4500 (circle).
where µ1 and µ2 are the dipole momentum of the molecules, R1 and R2 are the electronic polarizability of the molecules, 0 is the dielectric constant of vacuum, k is Boltzmann’s constant and T is the temperature, h is the Planck constant, and hν is the first ionization potential of the molecules. Thus the total van der Waals attractive interaction can be written24
wvdW(r) ) -
[
µ12µ22 1 + (µ12R2 + µ22R1) + 2 6 3kT (4π0) r
]
3R1R2 (hν1)(hν2) (21a) 2 hν1 + hν2
Figure 6. Relation between nitrogen quantity and argon quantity adsorbed on activated carbons: Maxsorb (diamond), F400 (triangle), Tanac 7500 (square), and Tanac 4500 (circle).
the obtained slope suggests that the nitrogen adsorption energy can be expressed as follows:
nN2 ) anAr + b
(15a)
The elements taken into consideration are nitrogen, argon, and carbon. Their polarizabilities are presented in Table 1, and their ionization potential energies are 15.5, 15.8, and 11.3 eV for N, Ar, and C, respectively.25-27 The nitrogen molecule, a symmetric homomolecular probe, does not possess any permanent dipolar momentum; however as it is a nonspherical probe it presents an inducible quadrupolar momentum which can give Keesom forces. In our case, the amount of polar sites can be considered as negligible because of the similitude of argon and nitrogen adsorption distributions.8 As a consequence, Keesom and Debye forces can be neglected, the London forces will then be predominant, and eq 21a gives
The relationship between peak position and interaction energy of a probe with the surface can then be written
n ) -kT ln(P*/P0) - ω/2
(15b)
aω ω + + 2kT Ar 2kT N2 1 [ln(P0N2) - a ln P0Ar] + b (16) kT
( ) ( )
Considering that lateral interactions for argon and nitrogen remain constant independently of the adsorption sites, eq 16 can be rewritten as / ) a ln P/Ar + B ln PN 2
(17)
where B is a new constant. Taking now into consideration the different intermolecular attraction forces, namely, orientation Keesom forces, induction Debye forces, and dispersion London forces, interaction energies can be written respectively: 2 2 1 µ1 µ2 1 wK(r) ) 3 (4π )2kT r6 0
[
]
3R1R2 (hν1)(hν2) 1 2 6 2 hν1 + hν2 (4π0) r
(21b)
The comparison between argon and nitrogen yields
where P* is the maximal absolute pressure of local isotherms, and ω is the effective lateral interaction between two neighboring absorbed molecules. From eqs 15a,b, it follows that / ln PN ) a ln P/Ar 2
wvdW(r) ) -
(18)
a)
wvdW N2(r) wvdW Ar(r)
)
[
]
r0C-Ar6 R2(hν2)(hν3 + hν1)
r0C-N26 R3(hν3)(hν2 + hν1)
(22)
From known values of R and ν parameters, one can obtain
R2(hν2)(hν3 + hν1) R3(hν3)(hν2 + hν1)
) 0.883
(23)
The above calculated value 0.883 corresponds very well with a slope (0.887) previously obtained when nitrogen and argon peak positions were compared (Figure 5). This suggests that in eq 23 the interatomic distances r0 are very close for these two probes. This result reinforces the validity of the method proposed by Villie´ras et al.8 for the determination of nonpolar surfaces from the comparison between argon and nitrogen adsorption distributions. This opens an experimental way to determine unknown polarizability of surface atoms of nonpolar complex solids. (24) Cappella, B.; Dietler, G. Surf. Sci. Rep. 1999, 34, 1-104. (25) Boo, J. H.; Heo, C. H.; Cho, Y. K.; Han, J.-G. J. Vac. Sci. Technol., A 2000, 18 (4), 1590-1594. (26) Inscore, F. E.; Joshi, H. K.; McElhaney, A. E.; Enemark, J. H. Inorg. Chim. Acta 2002, 331, 246-256. (27) Boyd, I. D.; Keidar, M. J. Spacecraft Rockets 2000, 37 (3), 399407.
2846
Langmuir, Vol. 21, No. 7, 2005
Garnier et al.
each site was acceptable. The observed difference is probably due to an incomplete filling of these sites by nitrogen.
Figure 7. Relation between liquid nitrogen volume and liquid argon volume compared site by site on all activated carbon samples.
Correlation between Quantity of Adsorbed Nitrogen and Argon. The perfect correlation (Figure 6) between the adsorbed N2 and Ar quantities in the monolayer for the studied activated carbons gave a slope equal to 0.84. This slope depends only on the ratio of the statistic cross sections of nitrogen and argon. It can be recalculated assuming a cross-sectional area A of 16.26 Å2 for nitrogen and 13.8 Å2 for argon molecules, using “statistic volumes” of 38.55 and 49.30 Å3 for nitrogen and argon and the formula issued from disk area and sphere volume: 4π/3(A/π)3/2. Thus the calculated value was in agreement with the graphical method within the range of 8%. If comparison of argon and nitrogen was made site by site in terms of adsorbed liquid volumes (Figure 7), a slope of about 1 (R2 ) 0.92) was obtained, confirming that our modeling in energetic terms was verified in volume terms equally. This comparison showed also that the error on
Conclusion Several methods for activated carbon characterization were examined. The fractal approach gave interesting information on surface geometry, mesoporosity, and mechanisms governing the pore filling and the transition between these mechanisms (adsorbent potential and capillary condensation). However, this method did not allow a good assessment of the different energetic sites in the case of heterogeneous surfaces. Moreover the HK method showed limits in calculating the pore size distribution from adsorption isotherms. Consequently we applied the LPQEV approach to describe adsorption in pores using two gas probes: nitrogen and argon. If adsorption was described by the van der Waals equation (eq 16), the relationship between the interaction energies of different energetic sites with each probe could be revealed. Considering the van der Waals dispersion forces, the calculated value of 0.883 corresponded very well with the slope (0.887) obtained when nitrogen and argon peak positions were compared. This result reinforces the validity of the method proposed by Villie´ras et al.23 for the determination of nonpolarity/ polarity of the surfaces from the comparison between argon and nitrogen adsorption distributions. This opens also an experimental way to determine the unknown polarizability of sites of nonpolar complex solids. Acknowledgment. This work was carried out in the framework of the European INTAS 00-505 project. LA047948H
