Langmuir 2000, 16, 1343-1348
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Physisorption of Simple Gases on C60 Fullerene A. Martı´nez-Alonso and J. M. D. Tasco´n Instituto Nacional del Carbo´ n, CSIC, Apartado 73, 33080 Oviedo, Spain
E. J. Bottani* Instituto de Investigaciones Fisicoquı´micas Teo´ ricas y Aplicadas (INIFTA)sUNLPsCICsCONICET, Casilla de Correo 16, Sucursal 4, (1900) La Plata, Argentina Received July 22, 1999. In Final Form: October 4, 1999 Experimental adsorption isotherms of nitrogen and argon at 77.4 K and carbon dioxide at 273.2 K on C60 fullerene have been obtained to characterize the surface of this material. Grand Canonical Monte Carlo computer simulations of nitrogen physisorption have been performed that reproduce the experimental isotherm. Adsorption energy distribution functions calculated from the experimental isotherms of the studied gases are compared with the results obtained from the simulations and with experimental data obtained with other materials such as polycrystalline diamond and two carbon blacks (Vulcan 3-G and Vulcan 9). From the simulations the distributions of adsorbed molecules with respect to their gas-solid energies are discussed. Microdensity profiles are employed to calculate the local adsorption isotherms. Three adsorption sites have been identified, and the isosteric heat of adsorption at zero coverage has been calculated.
Introduction Pseudospherical carbon structures known as fullerenes have attracted a great deal of attention in recent years since their first discovery in the gas phase1 and further preparation in macroscopic amounts.2 In this new class of solids, exemplified by C60, carbon atoms cluster into closed cages, each of which constitutes a single molecule. In the solid state, these molecules arrange in turn into different crystalline structures, e.g., a face-centered cubic one in the case of C60. The solid-state features of this new type of material seem to be firmly established as are many of their physical and chemical properties.3 However, their surface properties are considerably less known, especially as concerns their adsorption properties. With the aim to characterize the porous texture of these solids, Ismail and Rodgers4 first reported gas (Kr, N2, O2 and CO2) adsorption measurements on C60, although at the time these measurements were made sufficiently pure fullerenes were difficult to obtain. Kaneko et al.5 studied the adsorption of N2 and O2 on C60 and agreed with Ismail and Rodgers in finding evidence for the presence of micropores in these solids. Abraham et al.6 determined by gas chromatography the gas-solid partition coefficients of 22 gases and vapors on C60; it was shown that this fullerene is weakly polarizable, which is not unexpected for a closed-cage alkene. * To whom correspondence may be addressed. E-mail: ebottani@ inifta.unlp.edu.ar. FAX: 54-221-425-4642. TEL: 54-221-425-7430. (1) Kroto, H. W.; Heath, J. R.; O′Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (2) Kra¨tschmer, W.; Fostiropoulos, K.; Huffman, D. R. Chem. Phys. Lett. 1990, 170, 167. (3) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. In Science of Fullerenes and Carbon Nanotubes; Academic Press: New York, 1996. (4) Ismail, I. M. K.; Rodgers, S. L. Carbon 1992, 30, 229. (5) Kaneko, K.; Ishii, C.; Arai, T.; Suematsu, H. J. Phys. Chem. 1993, 97, 6764. (6) Abraham, M. H.; Du, C. M.; Grate, J. W.; McGill, R. A.; Shuely, W. J. J. Chem. Soc., Chem. Commun. 1993, 1863.
Following a different experimental approach, Folman et al.7-9 have used infrared spectroscopy to study CO physical adsorption on C60 embedded in alkali halides and C60 high-area films; these results confirm earlier predictions from calculations of adsorption potentials suggesting that adsorption sites are most probably voids between C60 molecules and sites on top of C60 molecules. It is interesting to note that their results obtained for CO with a different technique are consistent with the results reported in this work. More recently, Kra¨tschmer et al.10 have compared the behavior of C60 and other crystallographically defined forms of carbon as adsorbents for Kr at 77 K. It was found that at low pressures the fullerene behaves similarly to a graphitized carbon black and very differently from polycrystalline diamond. Accordingly, these authors proposed that Kr is adsorbed on C60 and graphite by the same mechanism in this range of surface coverage and that the adsorption of Kr on C60 crystals with perfectly developed facets can be expected to be very similar to that on the basal plane of graphite. Papirer et al.11 have studied the adsorption of a series of n-alkanes on C60, graphite, and carbon black samples by means of inverse gas chromatography. These authors have reported the adsorption energy distribution function obtained for n-hexane and n-heptane that we will discuss later on. This paper focuses on physical adsorption of nitrogen on high-purity C60. For comparative purposes, the adsorption of N2 at 77.4 K was measured on this and other carbon solids under identical conditions. C60 was also used as a sorbent for Ar (77.4 K) and CO2 (273.2 K). (7) Folman, M.; Lubezky, A.; Chechelnitsky, L. Preoc. 3rd International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis by Solids, Torun, Poland 1998, p 204. (8) Fastow, M.; Kozirovski, Y.; Folman, M. Surf. Sci. 1995, 331-333, 121. (9) Folman, M.; Fastow, M.; Kozirovski, Y. Langmuir 1997, 13, 1118. (10) Kra¨tschmer, W.; Rathousky´, J.; Zukal, A. Carbon 1999, 37, 301. (11) Papirer, E.; Brendle, E.; Ozil, F.; Balard, H. Carbon 1999, 37, 1265.
10.1021/la990978d CCC: $19.00 © 2000 American Chemical Society Published on Web 11/24/1999
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Figure 1. Nitrogen adsorption isotherms at 77.4 K: (b) C60; (O) Vulcan 3-G; (]) Vulcan 9; (3) polycrystalline diamond.
The paper is organized as follows: after the presentation of technical details concerning the experimental method, simulation algorithm, and the characterization of the sample employed, the adsorption energy distribution functions are discussed. Then the energy profile and the isosteric heat of adsorption are presented. The density profiles as a function of the distance to the surface are shown and connected to the energy distributions obtained from the simulations. The adsorption isotherm is decomposed in the local isotherms, and a description of how adsorption progresses is discussed. Finally the BET surface areas obtained from the local and full isotherms are discussed as well as nitrogen cross sectional area. Experimental and Simulation Details The experimental adsorption isotherms have been obtained with automatic equipment (NOVA 1200 Quantachrome). Figure 1 shows the experimental nitrogen adsorption isotherms on the materials studied at 77.4 K. All the samples are nonporous, and their BET surface areas are 0.3 m2/g (C60), 71.3 m2/g (Vulcan 3-G, graphitized carbon black), 143.6 m2/g (Vulcan 9, nongraphitized carbon black), and 0.11 m2/g (polycrystalline diamond). CO2 (273.2 K) and Ar (77.4 K) isotherms do not exhibit any unusual feature, which is why they are not shown. The C60 sample (manufactured by Dynamic Enterprises Ltd., Berkshire, UK) employed in this work has been obtained by electric arc vaporization with graphite electrodes and has been purified by recrystallization until a 99.9% purity was achieved; finally the sample has been heated under vacuum at ca. 473 K to remove volatiles, packed, and stored in the dark at room temperature. The sample was employed as received, and to determine the adsorption isotherms it was outgassed at 383.2 K overnight. This temperature has been selected to avoid any alteration of the C60 structure or sublimation of the solid during the outgassing process. To characterize the structure of the solid employed in this work the X-ray diffractogram which is shown in Figure 2 was obtained in a Siemens D5000 powder diffractometer, using Cu KR radiation (λ ) 0.15408 nm) at 40 kV and 20 mA and scan rate 0.025° 2θ/3 s. The sample was finely ground in an agate mortar and packed into a glass holder. Peaks appearing in the diffractogram are in good agreement with previous reports12,13 for cubic C60. The signal/ noise ratio in the diffractogram is typical for a highly (12) Stephens, P. W.; Mihaly, L.; Lee, P. L.; Whetten, R. L.; Huang, S. M.; Kaner, R.; Diederich, F.; Holczer, K. Nature 1991, 351, 632. (13) McCready, D. E.; Alnajjar, M. S. Powder Diffr. 1994, 9, 93.
Martı´nez-Alonso et al.
crystalline solid. The degree of crystallinity was ascertained by calculating the average crystallite size by applying the Debye-Scherrer equation to the three main diffraction peaks, corresponding to the (111), (220), and (311) planes, taking a value of K ) 0.9 and calculating the experimental broadening (β) as β ) x (B2 - b2), where B is the measured fwhm and b the instrumental broadening. The values obtained for the crystallite size are D111 ) 265 ( 27 nm, D220 ) 50.6 ( 0.1 nm, and D311 ) 44.8 ( 0.1 nm. This indicates that C60 crystallites have grown longer in the direction perpendicular to the (111) plane than in those perpendicular to the other two planes under consideration. Further characterization of the solid C60 was conducted by scanning electron microscopy (SEM) using a Zeiss DSM942 scanning electron microscope. Samples of as received particles of C60 were covered with a thin gold coating before the measurements were made. Figure 3a shows a typical SEM micrograph where individual crystals group into macles. The crystals exhibit polyhedral shapes with roughly hexagonal features as expected for a face-centered cubic (fcc) structure. The surfaces of the polyhedra look flat, but at higher magnification (Figure 3b) it can be seen that irregularities appear at these surfaces. Grand Canonical Monte Carlo (GCMC) simulations have been performed using the algorithm described elsewhere.14 Basically, in a GCMC simulation the chemical potential is fixed while the number of adsorbed molecules fluctuates and the average of some property, F, is given by ∞
〈F〉µVT )
(N!)VN zN ∫ds F(s) exp[-βU(s)] ∑ N)0 QµVT
(1)
where V is the system volume, N is the number of adsorbed molecules, U(s) is the potential energy, z ) exp(βµ)/Λ3 is the activity, Λ ) h2/(2πmkBT)1/2, s is the set of coordinates, and QµVT is the grand canonical partition function. The solid has a fcc structure, and the molecular structure of each C60 has been taken into account. The area of the simulation cell is 8.63 nm2, which contains 56 C60 units or 3360 carbon atoms. The simulated structure has a lattice parameter equal to 1.417 nm and a density of 1.76 g/cm3, which agrees very well with both the experimental (1.82 g/cm3) and literature3 values (1.72 g/cm3). To calculate the gas-solid energy, each C60 molecule is considered as a collection of 60 spherical Lennard-Jones interaction sites located on each carbon atom of the molecule. The nitrogen molecule is modeled as two spherical Lennard-Jones interaction sites. The interaction parameters employed in the simulations are NC ) 38.1 K, σNC ) 0.336 nm and NN ) 36.4 K, σNN ) 0.332 nm. NC is the N-C(C60) well depth and has been fitted to reproduce the experimental isotherm. It can be noted that it differs in less than 10% with the value obtained for nitrogen adsorption on amorphous carbons.16 Lateral interactions have been calculated as in ref 14 including the quadrupolar interaction. Nitrogen quadrupole moment (1.5 × 10-26 esu) has been simulated by placing a positive electric charge at the molecular mass center and negative charges at each nitrogen atom center. Periodic boundary conditions have been applied in x and y directions and a reflection plane (14) Bottani, E. J.; Bakaev, V. A. Langmuir 1994, 10, 1550. (15) Cascarini de Torre, L. E.; Bottani, E. J. Colloids Surf., A 1996, 116 (3), 285. (16) Cascarini de Torre, L. E.; Flores, E. S.; Llanos, J. L.; Bottani, E. J. Langmuir 1995, 11, 4742. Bojan, M. J.; Steele, W. A. Langmuir 1987, 3, 1123.
Physisorption of Simple Gases on C60 Fullerene
Langmuir, Vol. 16, No. 3, 2000 1345
Figure 2. X-ray diffractogram of the C60 sample.
Each simulation point was calculated using 5 × 108 movement/creation/destruction attempts except for the first point were 1.5 × 109 attempts have been employed. Each equilibrated configuration has been stored to be processed at the end of the simulation. The adsorption energy distribution functions have been calculated from the experimental isotherms following the procedure described elsewhere (see for example ref 15). The method is based on the general adsorption isotherm equation which, in the patchwise approximation, takes the form
∫UU
V(p) ) Vm
θL(p,U) F(U) dU
max
min
(2)
where p is the equilibrium pressure, U is the adsorption energy, Umax and Umin are the integration limits, Vm is the monolayer capacity, θL(p,U) is the local adsorption isotherm, and F(U) is the distribution function. The problem of solving this equation by the least-squares method is equivalent to finding the absolute minimum of an i-dimensional hypersurface, where i is the number of adjustable parameters included in the local isotherm and the distribution function. This is accomplished by minimizing the deviation given by s
χ2 )
[V(pi) - Vc(pi)]2 ∑ i)1
(3)
where χ2 is the deviation, V(pi) and VC(pi) are the experimental and calculated adsorbed volumes at equilibrium pressure pi, and s is the number of experimental points. Results and Discussion Figure 3. SEM micrographs of C60 sample: (a, top) polyhedral crystals and (b, bottom) crystal detail showing a flat surface.
has been placed in the z direction at different distances to optimize the sampling process. Usual creationdestruction and movement (translation and rotation) attempts have been performed in such a way that the acceptance ratios were 1-4% and 40-60%, respectively.
Nitrogen adsorption isotherms on the materials studied when expressed as coverage vs relative pressure are coincident except at the low-pressure region as could be expected since this region of the isotherm is the most sensitive to surface characteristics. It must be mentioned that Ismail et al.4 have found that nitrogen adsorption isotherm was fully reversible while oxygen adsorption
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Figure 4. Nitrogen adsorption energy distribution functions at 77.4 K: (s) C60; (‚‚‚) polycrystalline diamond; (- - -) Vulcan 3-G; (-‚-) Vulcan 9.
Figure 5. Experimental (0) and simulated (O) nitrogen adsorption isotherms at 77.4 K. Nm ) 75.5 molecules.
al.5
isotherm showed an open hysteresis loop. Kaneko et found that oxygen adsorption isotherms were fully reversible and nitrogen adsorption isotherm was of type I. In this work, all the isotherms are fully reversible and no traces of hysteresis loop have been observed and in the particular case of nitrogen adsorption the isotherm is of type II. From the experimental isotherms the adsorption energies distribution functions, shown in Figure 4, have been calculated. C60 heterogeneity degree inferred from these results is similar to the one obtained for polycrystalline diamond. The most probable adsorption potential of both distributions is almost the same as well as the width of the distributions. Moreover the difference with respect to the carbon blacks is larger for the nongraphitized one as could be expected. To obtain more information about nitrogen adsorption on C60, GCMC computer simulations have been performed. To check gas-solid and gas-gas interaction parameters the complete adsorption isotherm has been obtained and compared with the experimental one. In Figure 5 both the simulated and experimental isotherms of nitrogen on C60 at 77.4 K are shown. It can be seen that the agreement is excellent up to relative pressures close to 0.5. The observed deviations at higher relative pressures are indicating that lateral interactions should be better described for high densities of the adsorbed film. This problem has been previously discussed for nitrogen adsorption on the graphite basal plane.14 The simulated
Figure 6. Total average energy for nitrogen adsorbed on C60 at 77.4 K. ∆Hvap ) 5.6 kJ/mol.
Figure 7. Model surface topographic map. X and Y units are arbitrary, and Z units are in angstroms.
adsorption isotherm, like the experimental one, is fully reversible over the whole pressure range studied. The total potential energy of the adsorbed molecules as a function of the surface coverage, see Figure 6, corresponds to the profiles obtained for heterogeneous surfaces. The potential energy tends to the vaporization enthalpy of liquid nitrogen in the multilayer regime as could be expected. The isosteric heat extrapolated at zero coverage calculated from the Henry’s law constant is 15.4 ( 0.1 kJ/mol, which is larger than the accepted value for graphite (10.4 kJ/mol) (see for example ref 16). Unfortunately we are not aware of any experimental measurement of nitrogen heat of adsorption on C60 to which to compare the value quoted here. The energy profiles together with the value of the isosteric heat are indicating that the surface of C60 presents some features that need to be known to explain its adsorption properties and to fully characterize its surface. Figure 7 shows a map of the simulation box obtained by sweeping the surface with a nitrogen molecule and plotting the distance to the surface for which the gassolid energy is minimum at each point of an arbitrary 50 × 50 mesh in which the surface has been divided. The position of each C60 molecule is clearly seen on the map and three different regions could be identified. The first region (A) is the space between four C60 molecules, the second (B) is between two C60 molecules, and the third one (C) is on top of the C60 molecules. Nevertheless it
Physisorption of Simple Gases on C60 Fullerene
Figure 8. Gas-solid energy map obtained for solid C60 unit cell. X and Y units are arbitrary, and energy is expressed in K.
Figure 9. Adsorption energy distribution function, F(U), obtained from the experimental isotherm (- - -) compared with the gas-solid energy histogram obtained for the model surface (s).
must be mentioned that this map does not show the exact depth of the first region due to the algorithm employed in its calculation. A similar procedure has been employed to obtain the energy map shown in Figure 8. In this map just the unit cell of the solid has been considered to make more evident the three regions mentioned above. As could be expected, the minimum energy is achieved in the region defined by four C60 units. This map can be very easily converted into a histogram. In Figure 9 the histogram obtained from the energy map is compared with the adsorption energy distribution function obtained from the experimental isotherm. It must be noticed that the experimental distribution function smoothly covers all the features exhibited by the histogram obtained for our model solid and that the areas of both curves are almost equivalent (the difference is less than 10%). It must be pointed out that the experimental distribution function was forced to a Gaussian; having employed a more complicated distribution, a better agreement in the shape of both distributions could be obtained. The deconvolution of the histogram produces three peaks located at -13.8 ( 0.3, -9.04 ( 0.08, and -5.00 ( 0.05 kJ/mol that can be assigned to the three adsorption regions mentioned above. As was mentioned in the Introduction, Papirer et al.11 have determined the adsorption energy distribution function for n-hexane at 273 K and n-heptane at 302 K using inverse gas chromatography. The distribution functions that they have reported are very similar to our energy histogram (Figure 9). In fact both curves can be
Langmuir, Vol. 16, No. 3, 2000 1347
Figure 10. Density profiles of the adsorbed phase calculated for 〈Nad〉 ) 1.51 (s) and 〈Nad〉 ) 139.1 (- - -). σ ) 0.332 nm. F(Z) is the adsorbed phase density calculated at a distance Z from the surface.
brought into coincidence just by shifting the energy axis, which seems reasonable if the difference in the heats of adsorption of the adsorbates is taken into account. If their curve is shifted by 15.3 kJ/mol, the three peaks observed in their distribution (see Figure 4 and Table 4 in ref 11) are located at -5.0, -9.1, and -13.9 kJ/mol, which are exactly the positions of the peaks of our distribution. It is also interesting to note that the ratios of the peaks amplitudes are almost the same as ours. In fact, normalizing the peak amplitudes of Papirer’s distribution with the amplitude of the smaller peak gives new amplitudes equal to 3.3, 1.5, and 1. Doing the same with our results, the corrected amplitudes give 3.5, 1.6, and 1. In their analysis, Papirer et al.11 assigned the peak located at the lowest energy to the adsorption on top of the C60 molecules (sites C) in agreement with our results. We do not agree with Papirer’s assignment of the other two peaks to adsorption on oxygenated surface sites. Moreover those peaks could be assigned to sites A and B since the alkane molecules could be adsorbed on the surface in an orientation other than flat, especially if the very small value reported by Papirer et al. for the BET C parameter is considered (C ) 9 for n-heptane). It is evident that the answer to this question needs a precise determination of the state of the alkane molecules in the adsorbed film with special attention to the cross-sectional area of the adsorbate. The density profiles of the adsorbed film as a function of the distance to the surface obtained at different surface coverage indicate how the adsorption progresses. In Figure 10 the profiles obtained at two surface coverages (0.02 and 1.84) are shown as examples of the general behavior. It must be pointed out that the top of a C60 molecule, or what is equivalent, the surface “plane” is located at Z/σ ≈ 4.2, where Z is the distance to the surface and σ ) σNN. At the lowest coverage adsorption mainly takes place on top of the C60 molecules, and at higher coverage two peaks grow at Z/σ < 4.2. Moreover these peaks cease to grow at a certain pressure meaning that a saturation is reached, thus suggesting that both peaks correspond to the adsorption on a finite volume. To confirm that this volume corresponds to the free volume between the fullerene molecules, a simple calculation was made. From the density of the material and the volume of a C60 molecule considered as spherical, it is possible to calculate the free volume remaining under the surface plane and that is accessible to the gas molecules. This volume amounts to 0.930 nm3 or its equivalent 16 molecules assuming the
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surface coverage. In previous studies of the adsorption of simple gases on graphite and amorphous carbons, it has been found a large variation of the cross-sectional area of the adsorbate with the surface coverage and a constant value was achieved after at least two or three layers were completed.17
Figure 11. Nitrogen local adsorption isotherms calculated for molecules adsorbed at Z/σ < 4.5 (O) and Z/σ g 4.5 (3)
liquid state for the adsorbate. Direct integration of the density profiles gives the number of molecules adsorbed between the limits taken. The integration performed on a series of profiles obtained from different runs and at different pressures gives an average value of 16.4 if the upper integration limit is set at Z/σ ) 3.9-4.0. Given the uncertainty in the definition of the peak boundary it could be said that the agreement is quite good and could be considered as a proof of the origin of these peaks. It must be pointed out that the inner volume corresponds to the octahedral cavities of the structure since the tetrahedral ones are not accessible to the adsorbate molecules.3,5 The local adsorption isotherms depicted in Figure 11, calculated by direct integration of the density profiles, clearly show that adsorption begins on top of the C60 molecules and that adsorption in the inner volume of the crystal structure is detected at larger pressures. The saturation limit attained by the isotherm at Z/σ < 4.5 is slightly larger than the value obtained quoted above due to the uncertainty in the definition of density peak limits. The BET area obtained from the local isotherm corresponding to the inner region is 3.28 and 11.63 nm2 for the full isotherm while the geometric area of the simulation box is 8.03 nm2. The difference between the geometric area of the simulation box and the BET area obtained from the full isotherm can be ascribed to the surface of the voids (3.6 nm2). This value differs in less than 10% with respect to the one obtained from the local isotherm (3.28 nm2). Moreover the voids have a surface area that is ca. 28% of the total, which can explain why even though the voids present the most energetic adsorption sites, they are not appreciably covered at very low pressures because they represent a small portion of the surface. The cross-sectional area of nitrogen employed in this paper has been obtained from the simulation results. From the equilibrated configurations it is possible to determine the cross-sectional area averaged over all the configurations and molecules. The obtained value is 0.154 ( 0.001 nm2 and it must be noted that it is independent of the
Conclusions The adsorption isotherms of nitrogen, argon, and carbon dioxide obtained on the C60 sample employed in this work do not show any trace of hysteresis. Nitrogen isotherms are clearly of type II. Previous results suggesting the presence of microporosity could be due to imperfect samples in the sense of their purity or their crystallinity degree. Now that purification and crystallization procedures are better than in the past, the agreement found between the data reported in this work and Papirer’s results is not unexpected. The surface of crystalline C60 fullerene presents a heterogeneity degree comparable to polycrystalline diamond as can be inferred from the adsorption energy distribution function obtained from the experimental adsorption isotherm. It has been shown that ca. 28% of the surface area of this material originated in the intermolecular void space. The number of adsorbed molecules that could be accommodated in the inner free volume is consistent with the number obtained from the density profiles. At low pressures adsorption begins on top of the fullerene molecules and then it continues by filling the void spaces as was shown with the density profiles and local adsorption isotherms. The total energy of the adsorbed phase exhibits behavior typical for a heterogeneous surface. Three types of adsorption sites have been clearly identified; the most energetic sites are located between four C60 molecules (A), followed by sites located between two fullerene molecules (B), and finally sites located on top of the C60 molecules (C). The isosteric heat of adsorption at zero coverage has been determined for the first time, and the obtained value is larger than the accepted value for graphite. The contribution of adsorption sites A and B seems to constitute the origin of the higher isosteric heat value. Nitrogen cross-sectional area is independent of the surface coverage, and the value is within the limits of accepted values. The BET method produces reasonable values for the areas of the inner and full surfaces, and both values are in agreement with the simulation cell geometric area. Acknowledgment. E.J.B. is Associate Professor of the Engineering Faculty of the National University of La Plata (UNLP) and Researcher to the Comisio´n de Investigaciones Cientı´ficas de la Provincia de Buenos Aires (CIC). The research project is financed by Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas (CONICET)CIC and UNLP on the Argentinean side and by CICYT (project MAT96-0430) on the Spanish side. LA990978D (17) Cascarini de Torre, L. E.; Bottani, E. J.; Steele, W. A. Langmuir 1996, 12, 1399.
