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Surface Structure of Carbonaceous Materials L. E. Cascarini de Torre and E. J. Bottani" Instituto de Investigaciones Fisicoquimicas Tebricas y Aplicadas (INIFTA), C.C. 16 SUC.4, RA-1900 La Plata, Argentina Received June 1, 1994. In Final Form: September 28, 1994@ Nitrogen adsorption, at 80.2K, on a series of amorphous carbonaceous materials is studied. To verify the hypothesis that all these materials share similar surface characteristics, two structures generated following different approaches are employed. GCEMC and CEMC computer simulations are performed to calculate nitrogen adsorption isotherms and the corresponding heats of adsorption. Simulation results are compared with experimental data obtained in our laboratory and from the literature. The agreement between the simulations and experimental results is quite good confirming the amorphous nature of the surface of these materials.
Introduction The problem of surface heterogeneity has deserved a great amount of work.lf2 Nevertheless it remains almost unresolved. The heterogeneous nature of real solids is strongly dependent on either their mode of formation or modifying treatments (chemical or thermal). Carbonaceous materials that are technologicallyimportant because of their structural and surface properties314 present strongly heterogeneous surfaces. In addition, the study of amorphous carbon films is permanently growing due to their possible applications as coating materials5s6and as adsorbents.' Several papers have been published where surface heterogeneity has been introduced and the behavior of the adsorbed phase was studied.8-12 According to Bakaev's ideal3 actual surfaces should be described as amorphous rather than ideal surfaces with defects. Amorphous surfaces could be modeled in different ways. One approach, Bernal's model, describes the structure of an amorphous solid as a dense random packing of hard spheres. This model has proved to be successful in reproducing the main features exhibited by heterogeneous surfaces, particularly in the case of oxides.14 In this paper two structures are employed to describe these materials. The first one, AC, was calculated by Frauenheim et al.15 using a semiempirical molecular dynamic density functional (MD-DF) approach. MD-DF has been successfully tested on the physical properties of bulk crystalline material such as bulk moduli, lattice Abstract published in Advance ACS Abstracts, December 1, 1994. (1)Rudzinski,W.; Everett, D. H.AdsorptionofGases on Heterogeneous Surfaces; Academic Press: New York, 1992. (2)Jaroniec, M.;Madey, R. Physical Adsorption on Heterogeneous Solids. Studies in physical and theoretical chemistry; Elsevier: Amsterdam, 1988. (3)Bansal, R. C.; Donnet, J. B.; Stoeckli, F. Active Carbon; Marcel Dekker: New York, 1988. (4)Wigmaus, T. Carbon 1989,27,13. (5) Angus, J. C.; Hayman, C. C. Science 1988,241,913. (6)Carrot, P.J. M.; Sing, K. S. W.; Raistrick, J. H. Colloids Surf. 1986,21,9. (7)Leboda, R.Mater. Chem. Phys. 1992,31,243. (8) Bojan, M.;Steele,W. A. Su$. Sci. 1988,199,L395. (9)Boian, M.:Steele. W. A. Langmuir 1989.5 . 625. (10)Bakaev, V.; Steele, W. A. LGngmuir 1992;8, 1372. (11)Bakaev, V.;Steele, W. A. Langmuir 1992,8, 1379. (12)Bottani, E. J.An. Asoc. Quim. Argent. 1989,77,217. (13)Bakaev, V.Su$. Sci. 1968,198,571. (14)Bakaev, V.;Chelnokova, 0. V. Surf. Sci. 1989,215,521. (15)Frauenheim, Th.; Blandeck, P.; Stephan, U.; Jungnickel, G. Phys. Rev. B 1993,48, 4823. @
constants, and electronic density of states. This model optimizes the energy of a cluster taking into account its electronic and atomic structures. The second amorphous structure, BC, was generated accordingto Bernal's model. Our main goal is to test the ability of both structures to reproduce physisorption experimental data. We present the results of GCEMC and CEMC computer simulations of nonspherical rigid physisorbed nitrogen on both model surfaces. Experimental data from different authors together with our results are compared with the simulated isotherms and heats of adsorption.
Experimental Section Nitrogen adsorption isotherms at 80.2 K were obtained employing conventional adsorption volumetry. Pressures were determined using an absolute capacitance manometer and temperature was measured with a digital thermometer with a Pt-100(DIN)sensor head previously calibrated againstan oxygen vapor pressure thermometer. The maximumexperimentalerror, determined according to standard methods, was 0.3% in the adsorbed volume; more details concerning the experimental technique have been published e1sewhere.I6 A series of 13 samplesof nonporous carbonaceousmaterialswas studied. This series, that includes carbon fibers, synthetic graphites, mesocarbon microbeads, carbon blacks, and cokes, represents a wide variety of carbonaceousmaterials. The samples were chosen to fulfill two main characteristics: to be nonporous and nongraphitized. In all cases the absence of porosity was tested in several ways: "t"method, COZadsorption isotherms were obtained at 273.2 K and finally by performing adsorption and desorption points at different pressures. BET specific surface areas ranged from 2 to 100 m2.g-I. These values were determined using 0.162 nm2 for nitrogen cross-sectionalarea and the slopes of straight lines were determined in the standard range ofrelativepressures. All samples that have been characteri~edl~ by means of X-ray diffraction and Raman microprobe spectrometryl8 showed different degrees oforganization. Almost all samples show anX-ray spectrum correspondingto turbostratic materials. The interlayer spacing is currently employed to determine the degree of graphitization of these materia1s.Ig The values obtained17for the samples studied here range among 0.3368nm (best graphitized sample) to 0.4nm (mineralcarbon). These values should be compared with the values corresponding to ideal graphite (0.3354nm) and ideal turbostratic material (0.344nm). (16)Bottani, E. J.;Llanos, J. L.;Cascarini de Torre, L. E. Carbon 1989,27,531. (17)Cuesta-Seijo,A. Research Work, Department of Physical and Analytical Chemistry,University of Oviedo, Oviedo, Spain, 1992. (18)Delhaye, M.; Dhamelincourt, P. J.Raman Spectrosc. 1975,3, 33. (19)Vogel, W.; Hoseman, R. Carbon 1979,17,41.
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Surface and Potential Models As was mentioned above, two approaches were employed to generate the solids used in the simulations. The AC structure contained 50% of sp3 bonded atoms a n a density close to 3 g ~ m - ~The . semiempirical molecular dynamic density functional approach was employed15to optimize a cluster of 64 carbon atoms. The final solid used in the simulations was obtained by replication of the original cluster in such a way that the simulation box area was 10.22 nm2 and the number of carbon atoms was 2500. The BC solid was generated following Bernal's formalism.14 In this case the area of the simulation box was 12.68 nmz and the number of spheres contained in the simulation cell was 1000. In Bernal's model, as used by Bakaev,14the spheres that are randomly packed represent the anions ofthe oxide. To simulate a n amorphous carbon structure, we have defined the diameter of each sphere to be 0.308 nm, twice the C-C bond length in diamond. In this way each sphere contains five carbon atoms constituting a regular tetrahedron with one carbon atom in its center. This model was adopted to obtain a solid with an apparent density similar to actual carbonaceous materials. Gas-solid interaction was calculated assuming a sum of site-site energies, where each nitrogen atom interacts with a carbon atom in the solid. This interaction is modeled with a Lennard-Jones 12-6 function. The parameters employed in the simulations were cg$k = 34.65 K and a,, = 0.336 nm. It must be noted that this cgsis 10% larger than the currently accepted value for a nitrogengraphite system, but it is well-known that Lorentz combining rules are not always obeyed and significant deviations have been found.z0 A detailed experimental study is under development to obtain the necessary data to confirm the validity ofthese parameters through a virial analysis of high-temperature experimental isotherms. The interaction between nitrogen molecules was modeled as in a previous paperz1via a 12-6 Lennard-Jones function with c"Ik = 36.4 K and UNN = 0.332 nm. Quadrupolar interaction was approximated by placing a positive charge, 12.98 x C, a t the symmetry center of the molecule and two negative charges, 6.49 x C, located on each nitrogen atom.
Results and Discussion A detailed description of the Monte Carlo algorithm (GCEMC and CEMC) employed in this paper has been published elsewhere.21It must be noted that to obtain all the simulated points, 2 x lo6 trials (this includes displacements, creation, and destruction of molecules) were employed, the exceptions to this are the first points of each run that were calculated from 4 x lo6 trials to avoid any dependence of the results on the starting configuration. The correctness of the length of the simulation run was checked in all the runs in the same way as in a previous paper.21 In all cases the acceptance ratios were -50% for translation or orientational movements and 1-5% for creation or destruction of molecules. Periodic boundary conditions were applied in t h e m plane and a reflecting hard wall was placed a t -10 adsorbate molecular diameters above the uppermost surface atom. The gas phase in equilibrium with the solid was always considered as ideal and no corrections were applied to convert equilibrium pressure into chemical potential. (20)Steele, W. A. J.Phys. Chem. 1978,82,817. (21)Bottani, E.J.; Bakaev, V. A. Langmuir 1994, 10,1550.
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GCEMC and CEMC simulations were performed a t 80.2 and 77.5 K to compare with the available experimental data. All the experimental adsorption isotherms of nitrogen can be represented by a single curve if they are plotted as surface coverage versus the equilibrium pressure. Hereinafter the BET monolayer capacity is adopted as reference to determine the surface coverage. In Figure 1 the experimental average adsorption isotherm is shown together with the simulated ones. It must be pointed out that all the experimental points were fitted to a single curve for the sake of clarity. Figure 2 shows the low pressure region; in this case, some experimental points corresponding to a nongraphitized carbon black are included together with the average line. The bars drawn on the solid line indicate the region enclosing all experimental points. It can be seen in both figures that the agreement between simulated and experimental isotherms is quite good. It can also be observed that there are some minor differences between the simulated isotherms due to statistical errors. The BET model appliedto the simulated isotherms gives surface areas of 9.30 nm2 for AC solid and 12.15 nm2 for BC. The geometrical areas of the simulation boxes could be considered as the limiting values for the surface of
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Surface Structure of Carbonaceous Materials 20
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Langmuir, Vol. 11, No. 1, 1995 223
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both solids if they were completely flat. In consequence the BET areas obtained seem to be quite reasonable. In view of these results it could be said that both model surfaces are equally able to reproduce the adsorption isotherms. Now it must be shown that these model surfaces also produce heat of adsorption versus surface coverage profiles that are similar to the corresponding ones to actual surfaces. CEMC simulations were carried out at 77.5 Kto compare the heats of adsorption with experimental results. Data previously published by other authors were taken to perform this comparison. The differential heats of adsorption were obtained by Beebe et al.22,23 calorimetrically for three samples of different carbon blacks; the other set of experimental heats was obtained by Grahamz4for samples of amorphous carbon and diamond dust. In Figure 3 experimental and simulation results are compared. The error bars included in this figure are estimates of the experimental errors, not published by the authors, based on a standard error analysis. The agreement, as in the case of the isotherms, is good. I t must be noted that the experimental points do not fall on a unique curve. It could be due to different facts, the most obvious being the experimental errors involved in the determination of experimental heats of adsorption. The second reason that could produce such a dispersion of the experimental points is the different origin of the samples studied. In any case it could be considered that our simulation results can reproduce the main features of the heat of adsorption versus surface coverage profiles. The small discrepancies between the simulations and the experiments could be removed if a better set of interaction parameters is obtained. Adsorption on heterogeneous surfaces is characterized by multilayer formation rather than a layer by layer growth of the adsorbed film. In our simulations it is possible to calculate the density profile of the adsorbed film a t different equilibrium pressures. Figure 4c displays the obtained profiles for the adsorption of nitrogen on a perfect graphite surface. These profiles show a clear layerby-layer adsorption with a sharp minima between each layer. These profiles can be compared with the ones
Figure 4. Density profiles of the adsorbed phase at different surface coverages: (a,top) amorphous carbon, average number of adsorbed molecules 29.59,113.35,and 122.91;(b, middle) bernal surface, average number of adsorbed molecules 61.60, 107.5,and 142.56;(c,bottom) perfect graphite surface, average number of adsorbed molecules 43.75,51.38,and 90.12.
(22) Beebe, A.; Biscoe, J.; Smith, W. R.; Wendell, C. B. J . Chem.SOC. 1947, 69,95. (23)Beebe, A.; Millard, B.; Cynarsky,J. J . A m . Chem. SOC.1983,75, 839. (24) Graham, D. J . Phys. Chem. 1960,64,1089.
included in parts a and b of Figure 4 that have been determined for both model structures a t different surface coverages. It must be noted that there is not a clear distinction between different layers and that even a t low
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224 Langmuir, Vol. 11, No. 1, 1995 pressures there is a significant amount of molecules that are in higher layers than in the first.
Conclusions The main conclusion that can be derived from the present study is that both model surfaces (AC and BC) can account for the main characteristics of amorphous carbonaceous materials. The simulated adsorption isotherms and heats of adsorption are in good agreement with the experimental results. Since Bernal's model is quite modest in computer requirements, it will be adopted in future studies. I t could be argued that this model does not provide a correct chemical picture of these materials. This problem does not seem to be a serious one in view of the success of the generated solid in reproducing the experimental results. The gas-solid interaction potential
parameters employed in this paper need further validation. This task will be performed by means of a virial analysis of high temperature (low surface coverage) experimental isotherms.
Acknowledgment. We are indebted withV. A. Bakaev who kindly provided the computer code to generate a Bernal solid and for helpful discussions at the very beginning of this work. We must also acknowledge Dr. Frauenheim for providing us with the amorphous carbon structure. Both authors are researchers of the Comisi6n de Investigaciones Cientificas de la Provincia de Buenos Aires. This research project is partially supported by CONICET, CIC, and UNLP. LA940432L
