Adsorption Equilibria of Light Organics on Single-Walled Carbon

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Adsorption Equilibria of Light Organics on Single-Walled Carbon Nanotube Heterogeneous Bundles: Thermodynamical Aspects Fernando J. A. L. Cruz,† Isabel A. A. C. Esteves,† Sandeep Agnihotri,‡ and Jos
e P. B. Mota*,† †

Requimte/CQFB, Dept. Química, Faculdade de Ci^encias e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre 2829-516, Caparica, Portugal ‡ Environmental Engineering, Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, Tennessee 37996-2010, United States

bS Supporting Information ABSTRACT: Single-component adsorption equilibria of five different hydrocarbons (CH4, C2H6, C2H4, C3H8, and C3H6) on a high-purity sample of single-walled carbon nanotube heterogeneous bundles were measured using a static gravimetric method. The physicochemical properties and morphology of the bundles were thoroughly characterized to obtain information about the tube diameter distribution; the latter is shown to be well approximated by a Gaussian function with a mean diameter of 14.1 ( 1.4 Å. The adsorption measurements were performed at room temperature (T ≈ 300 K) and pressures from 2
10-3 up to 80 bar corresponding to reduced temperatures, T/Tc, from 0.81 to 1.59 and relative pressures, p/p0, in the range 1.4
10-5 to 0.89, where Tc and p0 are, respectively, the critical temperature and saturation vapor pressure of the adsorptive fluid. The excess adsorption isotherms exhibit an overall type-II shape, except that of supercritical CH4 which is type-I; none of the isotherms yield a hysteresis loop at the studied temperature. Henry constants, H, determined in the low-pressure region, show that the adsorbate's affinity for the solid increases with the number of carbon atoms in the molecule and decreases with the presence of an unsatured chemical bond: H(C3H8) > H(C3H6) > H(C2H6) > H(C2H4) > H(CH4). The comparison of the experimental Henry constants to theoretical values obtained by molecular simulation of specific sites of the bundle shows that the experimental values lie between the simulated values for adsorption on the external surface of the bundle and those for intrabundle confinement.

1. INTRODUCTION Natural gas (NG) is a fluid mixture composed mainly of methane (70-90 wt %) and other light hydrocarbons, such as ethane (5-15 wt %) and propane ( qex (C3H8; C3H6), but the reverse trend is observed when the loading is measured on a mass basis. In addition to other information, Table 2 lists the normal liquid densities of the condensed adsorptives, Fm, at the experimental temperature, which decrease almost linearly with the molecular weight. Thus, expressing the adsorption isotherms as the mass of adsorbate per amount of adsorbent, as done in Figure 5, is nearly equivalent to measuring the adsorbate loading by volume of adsorbed fluid or by the total number of carbons atoms in the adsorbate, since for the fluids under study the molecular weight is nearly proportional to the adsorbate’s chain length. If the adsorbate molecules differ only in their degree of unsaturation (i.e., alkane vs alkene), an interesting observation can be extracted from Figure 5; that is, at the same absolute pressure, the alkane is always more adsorbed than the corresponding alkene. A similar finding was observed before for the pair ethane/ethylene (p < 3 bar), using molecular simulation techniques and addressing only intratubular confinement.45 This is mostly due to the enhanced dispersive interactions of the alkane molecule compared to its unsaturated analogue: the CH3 (sp3) group is energetically more attracted by the carbon atoms of a nanotube than the CH2 (sp2) group, whereas the CH2 (sp3) and CH (sp2) are more or less similarly attracted. For example, in the TraPPE force field,46,47 which works well for hydrocarbons, the Lennard-Jones energy parameter, ε/kB (ε is the potential well depth, and kB is the Boltzmann constant), for CH3 (sp3) is 98 K, whereas that for CH2 (sp2) is 13 K lower. Propane [CH3(sp3); CH2(sp3);CH3(sp3)] and propylene [CH2(sp2)dCH(sp2); CH3(sp3)] differ in two pseudoatoms; the summed energy parameter for propane’s CH3(sp3);CH2(sp3) group is 98 þ 46 = 144 K, whereas that for propylene’s CH2(sp2)dCH(sp2) group is 85 þ 47 = 132 K, which is 12 K lower than its saturated counterpart. As pressure is progressively increased, more and more adsorbate molecules are packed inside the nanotubes until the entire pore volume is full of liquid-like condensate. The external 2626

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The Journal of Physical Chemistry C

Figure 7. Superimposition of propane's experimental adsorption equilibrium data (symbols) over the saturation capacities of the SWCNT bundles for the same adsorptive. The capacity of the internal pore volume, VnFm, and the BET monolayer capacity of the external surface, SBET/am, are converted into excess quantities using the scaling factor (1 - Fg/Fm). The vertical dashed line locates the relative pressure at which complete filling of the external monolayer occurs.

grooves, which behave like wedge-shaped pores (Figure 1), have a much higher attractive potential than the external rounded surfaces but a smaller saturation capacity. Molecular simulation studies have shown that at ambient temperature the internal pore volume and the external grooves fill at a much faster rate than the external surface of the bundles.34 Furthermore, the fitting of the BET equation to molecular simulation data for the external surface of the bundles gives positive values of c around 2 (eq 1);35 in this case, the BET equation results in a curve having the general shape of a type-III isotherm for which monolayer completion occurs at a large value of (p/p0). Thus, the steep initial portion of the isotherms shown in Figure 6 is attributed mainly to pore filling, whereas the subsequent linear branch represents adsorption on the external surface until monolayer completion, after which the concave tail becomes more noticeable. The slope of the linear segments (plateaus) of the isotherms recorded in Figure 6 decreases with increasing adsorbate molecular weight. Table 1 indicates the maximum adsorption capacity of the internal pore volume of the bundles, determined from the value of Vn multiplied by the normal liquid density of the condensed adsorptive, Fm, and the monolayer capacity of the external surface, calculated from the value of SBET divided by the molecular area of the adsorbate, am. If VnFm and SBET/an are to be compared with experimental data, it is convenient to plot them against pressure as excess quantities; in order to do so, their values must be scaled by 1 - (Fg/Fm). More interesting, however, is to superimpose over Figure 6 a plot of (VnFm þ SBET/am)(1 - Fg/Fm) vs p/p0 for each adsorptive, since this makes it possible to estimate the pressure at which complete filling of the external monolayer occurs. This procedure is illustrated in Figure 7 for propane. 3.2. Henry’s Law. From the experimental data recorded in Figures 5 and 6, we have also determined the corresponding Henry constants, H, from the intercepts of polynomial fittings of low-pressure plots of ln(q/p) vs p, which derive from the truncated virial isotherm equation.48 The results thus obtained are shown in Figure 5, from which the following general trend can be established: H(C3H8) > H(C3H6) > H(C2H6) > H(C2H4) > H(CH4). It is clear that the adsorbate’s (energetic) affinity for the solid is essentially governed by two independent

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Figure 8. Logarithmic plot of the Henry constant, H, for alkanes (b) and alkenes (O), as a function of the number of carbon atoms in the adsorbate molecule, NC. Simulation data were obtained by GCMC simulations,35 considering an average individual nanotube diameter of d = 14.15 Å, and represent Henry constants for intrabundle confinement (I), for adsorption onto groove sites (G), and for adsorption onto the external surface (ES) (see text for details). Lines are exponential growth fittings of data with eq 3.

factors: (i) it increases with the molecular weight/number of carbon atoms of the adsorbate, and (ii) it decreases with the existence of an unsaturated chemical bond, because the alkenes always exhibit lower H-values than their alkane analogues. We have previously addressed these issues via grand canonical Monte Carlo simulations,35 using an idealized SWCNT bundle model composed of homogeneous nanotubes with tube diameter d = 14.15 Å, a value which is very close to the mean diameter obtained by fitting a Gaussian distribution to the Raman spectra of the solid sample employed in the experiments (cf. Materials and Adsorbent Characterization). This previous simulation work probed independently the internal volume of the bundle (intrabundle confinement) and the external adsorption sites, including grooves and external rounded surfaces. These latter simulation results are indicated in Figure 8, along with the experimental values determined in the present work. It can be observed that both the experimental and simulated Henry constants increase with the number of carbon atoms, NC, in the adsorbate molecule, and can be accurately estimated from an exponential growth function: H ¼ R expðβNC Þ

ð3Þ

The experimental Henry constants (R = 0.1603 mol 3 kg-1 3 bar-1, β = 1.0169) lie in a region between pure intrabundle confinement and localized adsorption onto the external surfaces of the bundle. The differences between the experimental H constants and their simulated counterparts, for intrabundle confinement, are more of an experimental origin than the result of employing an inadequate force field for the solid-fluid interactions. The C3 fluids require carefully measured adsorption data at much lower pressure than the C2 molecules in order to permit the Henry’s law constant to be determined directly from the extrapolation to zero-adsorbed phase concentration of a virial plot of ln(q/p) vs q. Methane, which is the lightest molecule, has the least steep isotherm near the origin and thus is the most accurate to extrapolate to zero-loading conditions; its Henry constant determined from the low-pressure experimental data is 2627

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The Journal of Physical Chemistry C almost identical to the value calculated from the intrabundle simulations. The experimental H constants for the other adsorbates approach the simulated values for the groove sites and external surfaces, and the agreement increases with the number of carbon atoms in the adsorbate molecule. Overall, the results validate our previous finding that, at very low pressure, intrabundle adsorption is (energetically) favored over adsorption onto the external surface of the bundle.34,35 On the other hand, Table 2 shows that the internal pore volume of the bundles has about the same saturation capacity as the external monolayer; thus, the contribution of the external surface to the global adsorption isotherm is not negligible except at very low pressure, a region where, for energetical arguments, molecules are essentially intrabundle adsorbed. Furthermore, the local slope of the adsorption isotherm for the internal pore volume of the bundle decreases with pressure (type-I isotherm), whereas that for the external surface shows the opposite trend (type-III isotherm). Thus, as we move along the global adsorption isotherm, its local slope moves away from the value for the internal pore volume of the bundles and approaches the value for external adsorption. Because of the limited low-pressure range explored in the experiments, it is therefore possible that the slopes extracted from the extrapolation of the experimental data for the larger molecules are the result of combining a damped slope for intrabundle confinement with the slope for external adsorption.

4. CONCLUSIONS The adsorption equilibria of CH4, C2H6, C2H4, C3H8, and C3H6 onto SWCNT heterogeneous bundles were measured using a closed-loop gravimetry technique. The isotherms exhibit an overall type-II shape in the IUPAC classification, except that of methane whose shape is similar to a type-I isotherm (Figures 5 and 6). Using geometrical concepts of bundle morphology and previously determined physicochemical parameters of the solid sample, the global excess adsorption isotherms can provide information regarding the amounts of fluid adsorbed on the external surfaces and confined in the intrabundle volume: the methodology was exemplified for propane (Figure 7), and the corresponding adsorbed quantities individually accessed for intrabundle and external surface adsorption (Table 1). Adsorption trends were interpreted in terms of the molecular nature of the adsorbate itself, highlighting the fact that, under the same pressure conditions, the length of the carbon backbone and the presence of a π bond in the molecule, respectively, increase or decrease the amount of fluid adsorbed in the solid phase. The Henry constants, H, determined from extrapolation of low-pressure experimental data by a virial-type polynomial expression, evidenced that methane adsorption is the less energetically favored adsorbate. From the analysis of the obtained results, it is observed that H increases monotonically with the number of carbon atoms of the adsorptive molecule (Figure 8), and, for fluids with identical carbon content, H decreases with the existence of an unsaturated chemical bond. ’ ASSOCIATED CONTENT

bS

Supporting Information. Tables showing the experimental data sets and information on helium picnometry. This material is available free of charge via the Internet at http://pubs. acs.org.

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’ AUTHOR INFORMATION Corresponding Author

*Phone: þ35 1212948385. Fax: (þ351) 212 948 550. E-mail: [email protected].

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