Thermodynamics and Kinetics of Carbon Dioxide Adsorption on HiPco

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Thermodynamics and Kinetics of Carbon Dioxide Adsorption on HiPco Nanotubes Justin Petucci, Brice Adam Russell, Shree Banjara, Aldo D Migone, and Maria Mercedes Calbi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06156 • Publication Date (Web): 14 Aug 2018 Downloaded from http://pubs.acs.org on August 17, 2018

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The Journal of Physical Chemistry

Thermodynamics and Kinetics of Carbon Dioxide Adsorption on HiPco Nanotubes Justin Petucci,a Brice A. Russell,b Shree Banjara,b Aldo D. Migone,b and M. Mercedes Calbi *a a

Department of Physics and Astronomy, University of Denver, Denver, CO 80208, USA

b

Department of Physics, Southern Illinois University, Carbondale, IL 62901-4401, USA

*To whom correspondence should be addressed. E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT. We present the results of a combined experimental and computational study of CO2 adsorption on purified HiPco nanotubes. Isotherms were measured at six temperatures between 147 and 207 K, below the bulk triple point for CO2. Unlike the case of other adsorbates on HiPco nanotube bundles, adsorption isotherms at corresponding temperatures do not reveal the presence of any resolvable substeps. The isosteric heat values derived from the measured isotherms are lower than the latent heat of sublimation for most of the loadings, with the exception of a narrow range at very low coverage. Results from Grand Canonical Monte Carlo simulations show that this is due to the much larger contribution of the CO2-CO2 interactions (owing mostly to the presence of the electrostatic component) that greatly exceeds the size of the gas-surface interaction as the coverage increases beyond the monolayer. Measurements of the kinetics of adsorption show that the equilibration time increases with sorbent loading, which is typical of systems with relatively larger adsorbate-adsorbate interactions.


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INTRODUCTION The study of the adsorption of carbon dioxide on different, new, sorbents is a topic that continues to attract a great deal of interest and attention. CO2 sorbed systems are of interest both from a fundamental as well as from a practical perspective. From a practical point of view, CO2 sorbed systems are intensively investigated because adsorption can be used to achieve the capture and separation of CO2 in various industrial applications.1-3 From a fundamental perspective, CO2 adsorption phenomena are particularly interesting because carbon dioxide has a relatively strong electrical quadrupole moment.4 As a result, there are cases in which the van der Waals forces between the CO2 and the sorbent are either weaker or are of the same order as those between the interactions between the CO2 gas molecules themselves. This competition between sorbate-sorbent and sorbate-sorbate interactions of similar magnitude leads to sorbed systems of unique characteristics.4, 5 The investigation presented here is mostly focused on the exploration of these fundamental characteristics of carbon dioxide adsorption. In this work we report on a low-temperature adsorption isotherm study of CO2 on bundles of as-produced HiPco nanotubes. As explained below, the adsorption behavior of several gases has been investigated on this material, and by focusing on this sorbent we are able to identify and contrast the particular properties of carbon dioxide as a sorbate. The six isotherms that we measured span a 60 K interval between 146.7 K and 206.7 K; all isotherms are below the bulk triple point of 216.6 K. We measured both the equilibrium adsorption properties (upload capacity, effective specific surface area, isosteric heat of adsorption), as well as the kinetics of adsorption for this system. In addition, we performed Grand Canonical Monte Carlo (GCMC) simulations of the equilibrium adsorptive properties of CO2 by modeling the external surface of a bundle as an infinite array of parallel tubes (we offer justification for this model choice in the


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next section). We also calculated the isosteric heat of adsorption as a function of coverage and compared it with the experimental results. Analysis of the energy per molecule, the separate contributions of each kind of interaction to the isosteric heat, and the configuration of the CO2 molecules as loading increases provide crucial information to interpret the experimental results. Gas adsorption on bundles of close-ended single-wall carbon nanotubes has been extensively studied ever since methods for the production of this material in sufficiently large amounts to make volumetric and gravimetric adsorption studies possible were developed. The HiPCO process is the most effective method for producing single-wall nanotubes of high initial purity; this is why most of the studies of gases adsorbed on closed single-wall nanotubes are conducted on nanotubes produced through this process. The interest in studying adsorption on bundles of nanotubes stems, in part, from the fact that these adsorbed systems provide a possible way of producing one-dimensional matter in the laboratory (specifically, lines of single atoms adsorbed in the grooves of a nanotube bundle). Numerous experimental studies and computer simulations have been performed for a variety of rare gases and simple molecular adsorbates on carbon nanotubes (mainly H2, but also N2, CH4, CF4, and some light hydrocarbons).6-9 The availability of information on the sorption characteristics of this wide range of sorbates on carbon nanotubes provides a stimulus for studying how CO2 behaves on the same sorbent as the results obtained for CO2 can be contrasted with those obtained for them. For all these sorbates mentioned before, the strength of the nanotube-sorbate interaction is greater than that of the sorbate-sorbate interaction. For bundles of close-ended nanotubes (i.e. nanotubes for which their interior space is inaccessible to adsorption) monolayer isotherms for these sorbates generally display two substeps.6,

7

These substeps

correspond to adsorption on the two different groups of sites that are present on the external


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surface of these close-ended nanotube bundles: the grooves (which are spaces on the convex valleys, between two adjacent nanotubes, on the outer surface of the bundle); and, the external sites (that correspond to adsorption on the individual surface of a single nanotube, located at the periphery of the bundle). The binding energy of these various adsorbates on the grooves is greater than the binding energy for the same adsorbate on the surface of planar graphite, while the binding energy on the external sites is lower than that on graphite.6-8 Another characteristic that is common to the sorbates listed above is that the isosteric heat of adsorption has a monotonic dependence on the coverage (or sorbent loading): this quantity decreases as the coverage or loading increases, having its highest value at the lowest coverages. 6-8 As the pressure along the isotherm approaches the saturated vapor pressure for the isotherm temperature, the isosteric heat of adsorption decreases to a limiting value equal to the latent heat for the corresponding bulk phase transition (either liquid-vapor, or solid-vapor, depending on the temperature range involved). As shown by the measurements of Bienfait et al.7 and also the results presented here, none of the characteristics of the isotherms or the isosteric heat present in those other sorbates are shared by the films of CO2 on bundles of close-ended carbon nanotubes. Before summarizing previous results for CO2 on closed-ended nanotubes, it is instructive to review the characteristics of the adsorption on CO2 on exfoliated graphite. At temperatures below 104 K, CO2 does not form an adsorbed film on graphite (i.e. this sorbate behaves as a nonwetting fluid on the surface of graphite).10, 11 This is because the free energy for the formation of a CO2 film on the graphite surface is less favorable than that for the formation of crystallites of bulk solid CO2.10 The constraint to form a two dimensional film imposed on the CO2 molecules by the adsorbing surface prevents the molecules from adopting orientations that would maximize the molecular interaction energy; this results in a higher free energy for the film than for the bulk


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solid CO2 at and below 104 K. Above this temperature, a one-layer-thick CO2 film can grow on the graphite surface; this film is said to be entropically stabilized.10 The value of the isosteric heat of adsorption for this one layer thick film is lower than the corresponding bulk latent heat of sublimation for CO2. There have been previous studies of the adsorption behavior of CO2 on carbon nanotubes, both single- and multi-walled. In a recent study of adsorption of multi-walled nanotubes Khalili et al. reported on CO2 adsorption isotherms measured between 298 and 318 K, and provided values for the isosteric heat of adsorption as a function of sorbent loading which approached 125 K at high loadings.12 In a computer simulation and adsorption isotherm study Rahimi et al. report on the adsorption of CO2 on arrays of 3D vertically aligned double-walled carbon nanotubes; the experimentally determined isosteric heat of adsorption varies sinusoidally about a value of 200 meV as a function of loading.13 There have been reports on the displacement by Xe of CO2 adsorbed on single-walled nanotube bundles;14 and on the vibrational behavior of CO2 adsorbed on single-walled nanotubes.15 Recent reports also exist on the behavior of CO2 on single-walled carbon nanohorns a sorbent closely related to single-walled nanotubes.16, 17 Two studies, by Bienfait et al.7, and by Cinke et al.18, are closest in scope to this investigation. Both of these reports involve the measurement of adsorption isotherms on single-walled carbon nanotubes samples performed at several temperatures, and in both cases the isosteric heat of adsorption is determined from the isotherm data. The Bienfait et al. study was performed at low temperatures. Unfortunately, the results for CO2 were not extensively discussed; only a single adsorption isotherm (at 124 K) was shown in that report.7 The characteristics of the CO2 isotherm, however, are different from those of all the other sorbates that were included in the study (H2, O2, Ar, D2 and CH4). The specific surface area measured with CO2 was much smaller


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(roughly one half) of that measured with the other sorbates.7 The isosteric heat was presented as a function of sorbent loading. For CO2 this quantity was an increasing function of loading, approaching at high loadings the value of the bulk heat of sublimation. By contrast, for all the other sorbates they studied, the isosteric heat was a monotonically decreasing function of loading.7 The Cinke et al. study consisted of isotherms measured gravimetrically at four temperatures, between 273 K and 473 K. Inexplicably, the isosteric heat determined from the adsorption data for CO2 in this work was determined to be 24 meV.18 Such a value would make this quantity smaller than the isosteric heat for every rare gas adsorbate on graphite except for 4

He and 3He. The reported isosteric heat value is inconsistent with the significant amount of CO2

adsorbed at 273 K (and higher temperatures), for pressures well below one atmosphere. If the isosteric heat were in fact 24 meV, there would be essentially no CO2 adsorbed at these pressures and temperatures. It is possible that there was an error made in the computation of the isosteric heat from the data, or may be a typo in the reported value. The need for studying the adsorption isotherms of CO2 on nanotubes is amply justified by both the paucity of results available, and by the disagreement in the values for the isosteric heat reported in the literature for this system. 7, 18

METHODS A. Experimental. All adsorption isotherms were measured in a specially-built apparatus that allows for the performance of isotherms between 20 and 300 K. The apparatus has been described in detail elsewhere.19 The sample consisted of 0.1106 g of HiPco purified single-walled carbon nanotubes (SWNT). The sample was subjected only to mild heating under vacuum, so the spaces at the interior of the nanotubes are not accessible for adsorption (any tubes that may have


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been chemically opened as a result of the purification process will have the entrance to their interior blocked by functional groups that cannot be removed by the mild heating under vacuum used here). The reported diameter of HiPco nanotubes is 0.8-1.2 nm. Adsorption only takes place on the external surfaces of the bundles. The gas used was research grade CO2 purchased from Airgas (reported purity above 99.999%). It was used without any further purification. B. Computational. We performed GCMC simulations to explore the equilibrium adsorptive behavior of CO2 on the external surface of a carbon nanotube bundle. The model sorbent is in contact with a gas reservoir at a fixed temperature and pressure, and the simulation provides the average number of adsorbed molecules at equilibrium under those thermodynamic conditions. By performing a series of runs for increasing values of the pressure at a given temperature, we are able to generate adsorption isotherms for the system investigated. In this work, we used a modified version of the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)20 to perform the simulation in the grand canonical ensemble. Each point of the adsorption isotherm is calculated using a GCMC run of 2-4 109 steps to bring the system into equilibrium and to calculate averages. Every MC step is comprised of a trial creation, destruction, displacement, or rotation move with attempt probabilities of 0.3, 0.3, 0.2, 0.2, respectively. In addition to this, the maximum rotation and displacement steps were dynamically adjusted during the equilibration phase to achieve a move acceptance value of 50%. We model the sorbent surface as the exterior of an infinite array of parallel SWNT, of the same diameter (1.356 nm), arranged on a single plane (xy plane in the simulations). The wall-to-wall separation between the tubes is 0.32 nm. The simulation cell includes three nanotubes, spanning a distance of 50.29 Å along the x-axis. This cell width is large enough to accurately account for the longer range of the CO2-CO2 interactions. Along the direction of the axis of the tubes (y-


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axis), the cell extends for a length of 20 σgg. Periodic boundary conditions are applied along both the x- and y- directions. The height of the cell (along the z-axis, pointing away from the plane of the tubes) is set to be 100 Å. After exploring different models for the nanotube bundles (that included various bundle and tube sizes), we chose this configuration because it provided the most cost effective solution to reproduce and help understand the experimental results. As explained in the Results section, the unique characteristics of the gas-gas interaction for CO2 in combination with its particular competition with the gas-surface interaction made the simulation results much more sensitive to the choice of the bundle model than is the case for the adsorption simulation of other adsorbates. We represent the CO2-CO2 interaction with the Harris-Young potential,21 which models CO2 as a rigid molecule with three Lennard-Jones (LJ) sites and three point charges centered at each atom. The LJ parameters and the charge values are listed on Table 1. The bond length between the C and O atoms is 1.161 Å. The charge values are set to reproduce the quadrupole moment value of 4.3 10-26 esu.21 We add up the electrostatic interaction between the charges in two different molecules to account for the quadrupole-quadrupole molecular interaction. We calculate the gas-surface interaction by adding up the contributions of the C-CO2 LJ interaction from all the carbon atoms in the tubes. As we have done before, we consider a continuous approximation for the tube walls, characterized by a carbon density of 0.38 Å-2. With the LJ parameters for the carbon atoms in the nanotube of σCC=3.4 Å and εCC=28 K, the corresponding σC-gas and εC-gas LJ parameters are calculated by using the Lorentz-Berthelot semi-empirical combining rules considering the parameters in Table 1 for each of the atoms in the CO2 molecule.


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atom

σgg (Å)

εgg (K)

Q/e

C O

2.785 3.064

28.999 82.997

0.6645 -0.3323

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Table 1. Lennard-Jones parameters and atomic charges for the gas-gas interaction.

RESULTS I. Experimental: Isotherms. We measured six adsorption isotherms for CO2 on the HiPco nanotube bundles. The temperatures selected were 146.7 K, 158.7 K. 173.7 K, 183.7 K, 196.3 K and 206.7 K; all below the bulk triple point temperature for carbon dioxide. Isotherms measured at two of these temperatures (146.7 and 158.7) span a full range of film loadings, eventually reaching saturation. The remaining four isotherms cover only a portion of this range of loadings. The data are displayed, in a semi-logarithmic plot, in Figure 1. The nearly vertical step that is present at high loadings for the two lowest temperature isotherms corresponds to the isotherms reaching the corresponding values of the saturated vapor pressure for these two temperatures, where the loading increases at fixed pressure. As can be clearly seen from the data displayed in Fig. 1, there are no discernible substeps present in any of the isotherms. In each case a smooth curve, always convex towards the pressure axis, grows with loading until saturation is reached.


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20

Amount adsorbed (in thousands of cc-Torr)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


146.66 K

18

158.66 K

16

173.66 K 183.66 K

14

196.34

12

206.66

10 8 6 4 2 0 -8

-6

-4

-2

0

2

4

Ln P (pressure in Torr)

Figure 1. Experimental isotherms measured at several temperatures (1 cc-Torr at 273 K = 3. 54 x 1016 molecules). We note that adsorption isotherms for other simple atomic or molecular gases on this same type of nanotubes, at corresponding temperatures, yield isotherms which have two substeps in the monolayer range.6, 7 The likely explanation for the difference between the results with carbon dioxide and those obtained with other sorbates is the fact that in the CO2 case, the ratio of the gas-surface to gas-gas interaction is much smaller than the same ratio for the other gases . When gas-surface interactions are relatively stronger, adsorption on the two groups of sites present on the outside surface of the bundles (external sites and grooves) appear as distinct substeps, and are easily resolvable in the data. Since the sorbent-sorbate interaction is relatively much smaller in the CO2 case, differences between the adsorption sites do not translate into isotherm substeps in that case. We explicitly show that this is indeed the case in Section IV where we discuss the simulation results and the contributions from each kind of interaction.


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We note that the single 124 K isotherm shown in the work of Bienfait et al. displays a single, small substep at loadings corresponding to the middle of the monolayer.7 Possible explanations for the difference between the results for the data of Bienfait et al. at 124 K and that shown in Fig. 1 are: that our measurements were conducted at higher temperatures, which tends to smear out any existing features; or, the fact that freezing of the CO2 in the dosing line is not uncommon, and when it occurs it would appear as a substep in the adsorption data. II. Experimental: Specific Surface Area. The specific surface area for the HiPco nanotube sample can be estimated from the adsorption isotherms by evaluating the monolayer capacity of the sorbent. We then multiply this number of molecules adsorbed by the area per adsorbed molecule and divide the result by the mass of sample. We determined the monolayer capacity using the point B method.22 The result is shown in Figure 2. In this linear plot, the amount adsorbed is presented as a function of the fractional pressure relative to the saturated vapor pressure. Using a value for the specific area per molecule for CO2 of 15.2 Ǻ2/molecule,10, 11 and dividing the absolute area obtained for the nanotube sample by its mass, we obtain a specific surface area of 306 m2/g for the purified HiPco sample. This value is slightly more than half of what we have determined on the same type of closed carbon nanotube samples using other gases; for example, we determined the specific surface area of this same sample through the application of the Point B method to an Xe isotherm, and we obtained an area of 608 m2/g.23 This result is consistent with what was observed for the specific surface area measurements conducted by Bienfait et al.7 These much smaller values of the surface area found by adsorbing CO2 suggests that a great deal of care should be taken when determining specific surface areas with CO2 for cases in which sorbent-sorbate interaction is relatively weak, because the estimates for the sample area obtained


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from measurements under these conditions clearly appear to be just a lower limit for this quantity, at best. Amount Adsorbed (cc-Torr)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


point B

P/P0

Figure 2. Linear plot of the adsorption isotherm at 158.66 K. The pressures on the horizontal axis have been scaled by the saturated vapor pressure corresponding to this temperature, P0. The point B is determined as the lower limit at which the linear segment drawn through the data points above P/P0 ~ 0.1 separates from the isotherm data. This point determines the location of the monolayer. III. Experimental: Isosteric Heat of Adsorption. When adsorption isotherms for a system are available at various temperatures, the isosteric heat of adsorption (which is the amount of heat released when a molecule adsorbs on the sorbent at fixed value of the sorbent loading) can be determined from the isotherm data. The isosteric heat in terms of the adsorption data is given by:24

qst = −k B

∂ ln P ∂ (1/T) N

(1)

€


13


In this expression qst is the isosteric heat, kB is Boltzmann’s constant, P is the value of the pressure, T the temperature, and N the fixed value of the loading for which the isosteric heat is being determined. 310

150 K - 200 K

300

Isosteric Heat (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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290 280 270 260 250 240 230 0

4000

8000

12000

16000

20000

Amount Adsorbed (cc-Torr)

Figure 3. Loading dependence of the isosteric heat of adsorption. The uncertainty in the values of the isosteric heat presented here is ±2%. The horizontal black segment at loadings above 15,000 cc-Torr corresponds to the bulk latent heat of sublimation (Ref. 10).

In practice, in order to determine the isosteric heat of adsorption for a given value of the sorbent loading we first determine, for each isotherm, the value of ln P for the selected fixed value of the loading. Then we plot these values of ln P for the fixed value of the loading, as a function of the inverse of the isotherm temperatures. The slope of the resulting straight line is directly proportional to the isosteric heat. The sorbent loading dependence of the isosteric heat can be determined by repeating the process just described above for a number of different values of the sorbent loading, N. Such data is presented in Figure 3. Figure 3 displays a non-monotonic behavior in the dependence of the isosteric heat on loading. The parallel dark bar slightly below the data at the highest coverage is the value corresponding to


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the latent heat of sublimation for carbon dioxide (which is the proper bulk value to which the data should be compared with, as all the isotherms were measured below the bulk triple point). The small fluctuations in the isosteric heat values (± 5 meV) are the result of the numerical analysis and cannot be attributed to true energy heterogeneity in the system. One possible way to derive a smoother isosteric heat curve involves fitting the isotherms with a virial-type of equation before performing the calculations.25 We note that for all the loadings corresponding to the film (between 1000 to 15000 cc-Torr), the corresponding isosteric heat values are lower than the bulk heat of sublimation. This behavior agrees well with the data of Bienfait et al.7 in the region where the two sets of data can be compared. Bienfait et al.’s data for the isosteric heat starts at what would correspond to a loading of approximately 5000 cc-Torr in our Figure 3; there is no isosteric heat data presented for lower loadings. The high values of the isosteric heat obtained in the present work at very low coverage (below 1000 cc-Torr, about 10% of the monolayer coverage) are very likely due to adsorption of CO2 on a few impurities or inside wider interstitial channels due to stacking defects of the bundles. By contrast, the value cited by Cinke et al.18 is off by about an order of magnitude with respect to our data (and also with respect to data presented in Bienfait et al.).7 Barring some possible calculation mistake (as we have already speculated above) in Cinke et al.’s work, we have no other way to account for this difference. IV. Computational: Equilibrium Simulations Results. We present in Figure 4 a set of adsorption isotherms obtained from the simulations. In addition to the ones in the same range of the experimental measurements (150 K to 200 K), we also show an isotherm at a lower temperature to better identify adsorption features that might be smoothed out by temperature effects. As we observed in the experimental isotherms, sub-steps are practically non-existent, and


15


hardly visible only at the lowest temperatures. This minor difference with respect to the experimental isotherms is indeed expected, as the model surface used in the simulations is perfectly homogeneous. Even in that case, the steps span a very narrow pressure range, pointing to the lack of clearly defined adsorption sites. 400

100 K 150 K

300

〈N〉

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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175 K 200 K

200

100

0 -10

-5

0

5

ln P (P in Torr)

Figure 4. Adsorption isotherms from the simulations. The dotted lines indicate the coverage at which the three main configurations (groove, monolayer, bilayer) can be resolved at low temperature. A look at the molecular configurations along the 100 K isotherm (Figure 5) indicates that the sub-step hinted in the 150 K isotherm at around N~200 corresponds to the formation of the monolayer. The other two dotted lines indicate the coverages corresponding to the filling of the grooves (N~30) and the development of a bilayer (N~380). However, these features are not discernible in any of the higher temperature simulated isotherms, in agreement with the experimental findings in the 150 K – 200 K temperature range.


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N=34

N=207

N=378

Figure 5. Cross section of the low temperature (T=100 K) configurations corresponding to the coverages indicated with the dotted lines in Figure 4.

Similarly, the absence of distinguishable adsorption sites with characteristic energies is also evident in the dependence of the isosteric heat with coverage. We calculate the isosteric heat from the simulations as: qst = k B T −

∂U ∂ N

T ,V

(2)

where U is the total potential energy and the brackets indicate an ensemble average. In Figure € 6, we show the isosteric heat values as a function of the number of adsorbed molecules, for each

simulated isotherm. In order to understand this dependence, we also show in Figure 7, the energy per molecule as a function of coverage at the lowest temperature. At low coverage (when there are roughly 10 to 30 molecules adsorbed in the grooves), it is possible to recognize a region of nearly uniform isosteric heat only at the lowest temperature (T=100 K). At higher temperatures, in this same low coverage range, the isosteric heat decreases steadily indicating a dominance of entropic effects. The first vertical dotted line at N~ 35 indicates the coverage at which the groove


17


is fully filled and most of the molecules start to change their orientation to lie perpendicularly to the groove and on the outer surface of the adjacent tubes. This produces a drastic reduction in the strength of the gas-surface interaction (as can be seen in Fig. 7) that is most notable at the lowest temperature. 260 100 K 150 K

240

qst (meV)

175 K 200 K 220

200

180 0

100

200

300

400

〈N〉

Figure 6. Isosteric heat of adsorption corresponding to the simulated isotherms. The dotted lines indicate the filling of the groove at low coverage (N~35) and the monolayer completion (N~200). As discussed in the text, the decreasing trend observed at the highest loadings for the three higher temperatures (T > 150 K) is an artifact of the simulations for CO2 adsorption. 0

-50 utotal

〈U〉/〈N〉 (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ugg-LJ

-100

ugg-Coul ugs-LJ

-150

-200

-250 0

100

200

300

400

〈N〉


18

Page 19 of 30

Figure 7. Energy per molecule as a function of coverage at 100 K; the total energy (blue line) is the sum of the gas-surface (green) and the gas-gas (red and black) contributions. As the coverage increases, the gas-surface interaction keeps getting weaker as expected but the corresponding increase of the total gas-gas interaction for CO2 (the Lennard-Jones and the electrostatic components combined) overcomes this reduction causing the overall isosteric heat to increase as the monolayer phase develops. This is in striking contrast to what has been observed for many other adsorbates where the increase in the molecular interaction energy is typically not enough to make up for the loss of the gas-surface interaction. The difference for CO2 results from the contribution of the quadrupole-quadrupole interaction, which is not present for the other gases (see Fig. 7): while the magnitude of the Lennard-Jones contribution is comparable to that of other adsorbates of similar size, the electrostatic energy is almost as large as the LJ energy, giving rise to gas-gas interaction energies that are roughly twice as large as those for other adsorbates. 250

200

qst (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


150

100

50

0

qtotal

0

100

qgg-LJ

200

qgg-Coul

300

qgs-LJ

400

〈N〉

Figure 8. Individual contributions to the total isosteric heat at 100 K (blue curve) originated from each kind of interaction (green, red, and black, full lines); the increasing trend of the total


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isosteric heat (blue curve) contrasts with the decreasing function (dotted curve) that would be obtained if there were no electrostatic interactions. The distinctive effect of the quadrupole-quadrupole interaction on the isosteric heat dependence with coverage is clearly demonstrated in Fig. 8 where we show the separate contributions to the isosteric heat originated from each kind of interaction, at 100 K. The dotted line, that does not include the contribution from the quadrupole-quadrupole interactions, follows the decreasing trend characteristic of simple LJ gases with no electrostatic interactions. After monolayer completion the isosteric heat keeps increasing, slowly approaching the bulk value as a second layer forms. In the simulation, this can only be seen at the lowest temperature (see Fig. 6). For higher temperatures it becomes increasingly more difficult to ensure that the system is at equilibrium for the higher coverage phases, since the interaction energy values strongly depend on the relative orientation of the molecules. Slight deviations in orientation (due to thermal effects and/or variations in the external potential) produce relatively large changes in energy, making it much harder for the system to reach the equilibrium configurations (and hence energies) at high coverages. Once again, this is not the case for other adsorbates that only interact through LJ potentials. Therefore, we consider the final decrease in isosteric heat for the higher temperature curves to be an artifact of the simulations, indicating a clear limitation of this approach for simulating CO2 adsorption under these specific conditions. We want to emphasize that this difficulty does not occur when we use this same approach to simulate LJ gases (with no electrostatic interactions), or even when simulating CO2 at lower coverage. We have used the same molecule-molecule interactions in additional CO2 simulations, and we were able to reproduce the correct bulk phase as well as the monolayer phase on graphite with no trouble. These results, which provide an internal consistency test, rule out problems with the potential


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used resulting from the choices made for the values of the parameters. Indeed, a top view of the monolayer configuration (Figure 9) reveals the typical T-shape orientations of the twodimensional phase of CO2. N=207

Figure 9. Top view (xy plane) of the monolayer phase at T=100 K. The vertical lines indicate the location of the grooves between two tubes. Comparing the simulations (see the curve for 100 K in Fig. 6) with the isosteric heat values obtained in the experiments, we find overall good agreement. While it is not possible to determine an exact correspondence between the experimental and simulation loading scales, we can estimate that N~210 in the simulations corresponds to about 6500 cc-Torr for the experiments. This is based on the fact that the molecular configurations from the simulations show the completion of the monolayer at about N~210 (see Figs. 5 and 9) while the experimental surface area determination (Fig. 2) suggests that monolayer completion happens at about 6500


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cc-Torr. The isosteric heat values in the simulations increase from the initial stages of monolayer formation (N~100 in Fig. 6) to the bulk value. The experimental results for these loadings do essentially the same. In addition, the measurements of Bienfait et al. are also in agreement with this trend. The experiments reported here find a value of about 250-255 meV at the monolayer coverage (this value is slightly below the isosteric heat value on graphite at 120 K, 262 meV). The isosteric heat value from the simulations at monolayer coverage for T=100 K is 250 meV. Bienfait et al. report a value of 230 meV at 124 K. Overall, this constitutes rather good quantitative agreement between simulations and experiments near monolayer loading. Moreover, the value at the bilayer coverage in the simulations, 260 meV, also agrees with the experimental value found in our measurements (Figure 3) if we use the monolayer coverage to be approximately 6500 cc-Torr as determined by the point-B method. At low coverage, as the grooves are being filled (N < 30), the isosteric heat values found in the simulations decrease with loading (Fig. 6). The values measured experimentally at the lowest loading are also a decreasing function of loading (see Fig. 3). The main difference between the simulations and the experimental results is that the values of the isosteric heat measured at very low loadings (less than 1000 cc-Torr) are much higher than those obtained in the simulations. It is very likely that in the low coverage region the CO2 molecules are adsorbing on the small number of impurities that are present in the sample and/or in the few, wider, interstitial channels that may be present in the sample (as a result of stacking defects in the bundles). Either one of these alternatives (or both) will lead to the high isosteric heat values measured in the experiments. The sorbent in the simulation is perfect, and there are no impurities present; this accounts for the differences observed in this loading region.


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V. Experimental: Adsorption Kinetics. We have also investigated how the adsorbed system equilibrates after a dose of gas is added to the sample cell that contains the nanotubes, for each point along the adsorption isotherms. After a dose of gas is added to the experimental cell the sorbent loading will increase, and the pressure in the experimental cell will decrease, as equilibrium is approached. At every instant the amount of gas adsorbed on the nanotubes can be determined from the pressure at that same instant (just using the expressions employed to determine the equilibrium values).9, 26 We define the fractional pressure change, ΔP(t)/Peq, as:

ΔP(t) P(t) − Peq = Peq Peq

(3)

Here, P(t) is the value of the pressure inside the sample cell a time t after the last dose of gas

€ the pressure in the cell once equilibrium has been reached. was added; Peq is the value of In Figure 10 we show the fractional pressure change as a function of the time elapsed after the gas was dosed into the cell, for selected points along the 174 K isotherm. The numbers indicate which point along the isotherm is being plotted (e.g. #1 would correspond to the first point along the isotherm, the one with the lowest pressure and loading, #2 would be the immediate higher loading, etc.; the higher the number, the higher the equilibrium loading of the sorbent). All the curves, except the lowest one, have been displaced upwards for the sake of clarity. In this graph, equilibrium corresponds to the curve becoming parallel to the time elapsed axis.


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Frac%onal Pressure Change


0.05

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Fract # 3 Fract # 5 Fract. # 7 Fract # 10

0.04 0.03 0.02 0.01 0 0

50000

100000

150000

200000

Time (s)

Figure 10. Fractional pressure change inside the sample cell as the system approaches equilibrium, after a dose of gas is added. It is clear that, as the equilibrium loading value increases, a greater amount of time is required in order to establish equilibrium for CO2 adsorbed on the outer surface of the bundles of purified HiPco nanotubes. This is not the case for many other adsorbates. For small spherical adsorbates with no significant electrical multipoles (e.g. Ne, Ar, CH4) adsorbed either on planar graphite or on closed ended nanotubes we have found that the time needed to reach equilibrium decreases as the loading and the pressure inside the sample cell increases.26 The behavior measured here for CO2 is opposite to those observed for small spherical adsorbates. On the other hand, the behavior of linear hydrocarbons (methane, ethane, propane, butane and pentane) on bundles of closedended carbon nanotubes is a non-monotonic function of molecular length.9 For ethane and methane the behavior is similar to that of small spherical adsorbates: the time to equilibrium decreases as the loading and pressure increase. By contrast, for propane, butane and pentane the equilibration times in the monolayer increase as the coverage increases, just as we have seen here for CO2.9 For the linear hydrocarbons the equilibration times at correspondingly similar temperatures increases very markedly with increasing hydrocarbon length.9 For CO2 on bundles of close-ended nanotubes it is likely that both the linear nature of the molecule, as well as the


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strong intermolecular interaction (relative to the gas-surface interaction) both play a role in determining the adsorption kinetics for this system.27

CONCLUSIONS The adsorption of CO2 on the external surface of SWNT bundles presents several distinctive features when compared to the adsorption behavior of other adsorbates on the same sorbent. At corresponding temperatures, the CO2 isotherms are considerably smoother, with very small or non-existent evidence of sub-steps in them. This is due to the combination of two effects: 1) the linear nature of the molecule that leads to a gas-surface energy broadening caused by the orientational freedom of the molecules, and 2) the relatively much larger magnitude of the gasgas interaction for CO2, a direct consequence of the added quadrupole-quadrupole interactions. This drastically reduces the sensitivity of the CO2 molecules to the adsorption energy inhomogeneity of the external potential provided by the tubes, giving rise to featureless isotherms for CO2. A simulated isotherm at a much lower temperature, however, does reveal a very narrow plateau corresponding to the monolayer formation. This feature is rapidly washed out as the temperature increases. Also in contrast to most simple LJ gases, the isosteric heat for CO2 on the surface of bundles of closed SWNTs increases with coverage after monolayer completion, indicating once again the dominant effect of the gas-gas interactions. The simulations clearly show that this behavior is the result of the additional contribution of the quadrupole-quadrupole electrostatic interaction between the CO2 molecules. This behavior is also consistent with the observation that the isosteric heat values measured for monolayer CO2 on graphite are lower than the bulk heat of transition values. For most of the studied LJ gases (Ne, Ar, Xe, H2, O2, Kr, CH4, CF4), the


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adsorption potential on the outside of nanotube bundles always produces isosteric heats at the monolayer coverage that are higher than the bulk values.6, 7, 22 Experimentally, we observed that the adsorption equilibration times for CO2 on the bundles of closed SWNTs increase with increasing loading. This behavior is similar to those observed for longer alkanes (propane, butane and pentane) both on graphite and on SWNT.9 Trends observed from our previous adsorption kinetics simulations for other gases allow us to conclude that the experimentally measured increase in equilibration time with coverage can be attributed to the presence of stronger molecular interactions, combined with their notable enhancement with coverage as molecules adopt orientations that tend to favor the optimization of the quadrupolequadrupole interaction.27 ACKNOWLEDGMENT We acknowledge the support provided by the National Science Foundation through Grant DMR-1006428. REFERENCES (1) White, C. M.; Strazisar, B. R.; Granite, E. J.; Hoffman, J. S.; Pennline, H. W. Separation and Capture of CO2 from Large Stationary Sources and Sequestration in Geological FormationsCoalbeds and Deep Saline Aquifers. J. Air Waste Manag. Assoc. 2003, 53, 645-715. (2) Aaron, D.; Tsouris, C. Separation of CO2 from Flue Gas: A Review. Sep. Sci. Technol. 2005, 40, 321-348. (3) Lackner, K. S. A Guide to Sequestration. Science 2003, 300, 1677-1678.


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(4) Steele, W. A. Monolayers of Linear Molecules Adsorbed on the Graphite Basal Plane: Structures and Intermolecular Interactions. Langmuir 1996, 12, 145-153. (5) Steele, W. A. Molecular Interactions for Physical Adsorption. Chem. Rev. 1993, 93, 23552378. (6) Migone, A. D. In Adsorption by Carbons; Bottani, E. J., Tascon, J. M. D., Eds.; Elsevier B. V.: Amsterdam, 2008; pp 403-430. (7) Bienfait, M.; Zeppenfeld, P.; Dupont-Pavlovsky, N.; Muris, M.; Johnson, M. R.; Wilson, T.; DePies, M.; Vilches, O. E. Thermodynamics and Structure of Hydrogen, Methane, Argon, Oxygen, and Carbon Dioxide Adsorbed on Single-Walled Carbon Nanotube Bundles. Phys. Rev. B 2004, 70, 035410-1-10. (8) Rawat, D. S.; Furuhashi, T.; Migone, A. D. Adsorption Characteristics of Linear Alkanes Adsorbed on Purified HiPco Single-Walled Carbon Nanotubes. J. Phys. Chem. C 2010, 114 20173-20177. (9) Rawat, D. S.; Migone, A. D. Non-Monotonic Kinetics of Alkane Adsorption on SingleWalled Carbon Nanotubes. J. Phys. Chem. C 2012, 116, 975-979. (10) Terlain, A.; Larher, Y. Phase Diagrams of Films of Linear Molecules with Large Quadrupole Moments (CO2, N2O, C2N2) Adsorbed on Graphite. Surf. Sci. 1983, 125, 304-311. (11) Morishige, K. The Structure of a Monolayer of Carbon Dioxide Adsorbed on Graphite. Mol. Phys. 1993, 78, 1203-1209.


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(12) Khalili, S.; Goreyshi, A. A.; Jahanshahi, M. Carbon Dioxide Captured by Multiwalled Carbon Nanotube and Activated Charcoal: A Comparative Study. Chem. Ind. & Chem. Eng. Quart. 2013, 19, 153-164. (13) Rahimi, M.; Singh, J. K.; Babu, D. J.; Schneider, J.; Muller-Plathe, F. Understanding Carbon Dioxide Adsorption in Carbon Nanotube Arrays: Simulation and Adsorption Measurements. J. Phys. Chem. C 2013, 117, 13492-13501. (14) Matranga, C.; Cheng, L.; Bockrath, B.; Johnson, J. K. Displacement of CO2 by Xe in Single-Walled Carbon Nanotube Bundles. Phys. Rev. B 2004, 70, 165416 1-7. (15) Yim, W.-L.; Byl, O.; Yates, J. T., Jr.; Johnson, J. K. Vibrational Behavior of Adsorbed CO2 on Single-Walled Carbon Nanotubes. J. Chem. Phys. 2004, 120, 5377-5386. (16) Krungleviciute, V.; Migone, A. D.; Yudasaka, M.; Iijima, S. CO2 Adsorption on Dahlialike Carbon Nanohorns: Isosteric Heat and Surface Area Measurements. J. Phys. Chem. C 2011, 116, 306-310. (17) Krungleviciute, V.; Ziegler, C. A.; Banjara, S. R.; Yudasaka, M.; Iijima, S.; Migone, A. D. Neon and CO2 Adsorption on Open Carbon Nanohorns. Langmuir 2013, 29, 9388-9397. (18) Cinke, M.; Li, J.; Bauschlicher, C. W., Jr.; Ricca, A.; Meyyapan, M. CO2 Adsorption in Single-Walled Carbon Nanotubes. Chem. Phys. Lett. 2003, 376, 761-766. (19) Krungleviciute, V.; Calbi, M. M.; Wagner, J.; Migone, A. D.; Yudasaka, M.; Iijima, S. Probing the Structure of Carbon Nanohorn Aggregates by Adsorbing Gases of Different Sizes. J. Phys. Chem. C 2008, 112, 5742-5746.


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(20) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1-19. (21) Harris, J. G.; Yung, K. H. Carbon Dioxide's Liquid-Vapor Coexistence Curve and Critical Properties as Predicted by a Simple Molecular Model. J. Phys. Chem. 1995, 99, 12021-12024. (22) Emmett, P. H.; Brunauer, S. The Use of Low Temperature Van der Waals Isotherms in Determining the Surface Area of Iron Synthetic Ammonia Catalysts. J. Am. Chem. Soc. 1937, 59, 1553-1564. (23) Rawat, D. S.; Heroux, L.; Krungleviciute, V.; Migone, A. D. Adsorption of Xenon on Purified HiPco Single Walled Carbon Nanotubes. Langmuir 2006, 22, 234-238. (24) Bruch, L. W.; Cole, M. W.; Zaremba, E. Physical Adsorption: Forces and Phenomena; Oxford Science Publications: New York, 1997. (25) Czepirski, L.; Jagiello, J. Virial-Type Thermal Equation of Gas-Solid Adsorption. Chem. Eng. Sci. 1989, 44, 797-801. (26) Rawat, D. S.; Calbi, M. M.; Migone, A. D. Equilibration Time: Kinetics of Gas Adsorption on Closed- and Open-Ended Single-Walled Carbon Nanotubes. J. Phys. Chem. C 2007, 111, 12980-12986. (27) Burde, J. T.; Calbi, M. M. Adsorption Dynamics of Polyatomic Molecules on Planar Surfaces. Phys. Chem. Chem. Phys. 2017, 19, 30715-30725.


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Thermodynamics and Kinetics of Carbon Dioxide Adsorption on HiPco

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