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Langmuir 2008, 24, 5746-5754
Regioselective Competitive Adsorption of Water and Organic Vapor Mixtures on Pristine Single-Walled Carbon Nanotube Bundles Sandeep Agnihotri,*,† Pyoungchung Kim,† Yijing Zheng,† José P. B. Mota,‡ and Liangcheng Yang† EnVironmental Engineering, Department of CiVil and EnVironmental Engineering, UniVersity of Tennessee, KnoxVille, Tennessee, and Requimte/CQFB, Departamento de Química, Faculdade de Ciências e Tecnologia, UniVersidade NoVa de Lisboa, 2829-516, Caparica, Portugal ReceiVed NoVember 19, 2007. ReVised Manuscript ReceiVed January 19, 2008 Sequential adsorption of water and organic vapor mixtures onto single-walled carbon nanotube (SWNT) bundles is studied experimentally and by grand canonical Monte Carlo (GCMC) simulation to elucidate the distinct interactions between select adsorbates and the nanoporous structure of SWNTs. Experimental adsorption isotherms on SWNT bundles for hexane, methyl ethyl ketone, cyclohexane, and toluene individually mixed in carrier gases that were nearly saturated with water vapor are compared with the GCMC-simulated isotherms for hexane, as a representative organic, on the external surface of the heterogeneous SWNT bundles. From the nearly perfect overlap between the experimental and simulated isotherms, it is concluded that until near saturation only the internal pore volume of pristine SWNT bundles fills with water. The adsorption of water vapor on the peripheral surface of the bundles remains insignificant, if not negligible, in comparison to the adsorption of water in the internal volume of the bundles. This is in contrast with the adsorption of pure hexane, which exhibits appreciable adsorption both inside the bundles and on their external surface. It is also suggested that during competitive adsorption, water molecules take precedence over small nonpolar and polar organic molecules for adsorption inside SWNTs and leave unoccupied the hydrophobic external surface of the bundles for other more compatible adsorbates.
Introduction Water is ubiquitous. It is known to compete with other adsorbates for adsorption sites. It is also expected to interact with any nanomaterial either released into the environment or simply stored under normal laboratory conditions. Researchers have been investigating the adsorption of water on single-walled carbon nanotubes (SWNTs) to develop biological applications and to explore their environmental interactions. Several studies have addressed interesting water-related phenomena, such as the freezing of water inside the nanotubes,1 reduced hydrogen bonding of supercritical water confined in carbon nanospaces,2,3 filling and emptying of nanotubes by sequential addition or removal of a single-file chain of water molecules,4 gating mechanisms of water transport in nanotubes,5 effects of different microporosities6 and degrees of surface functionality7 on water uptake by nanotubes, characteristics of water adsorption on the structural defects of hydrophilic SWNTs,8 water selectivity on chemically modified nanotubes,9 and estimation of adsorption isotherms by Raman scattering10 and by nuclear magnetic resonance techniques.11,12 In general, the adsorption of water on carbon materials is fundamentally different from that of simpler fluids, such as * To whom correspondence should be addressed. Phone:+1 (865) 9747728. Fax: +1 (865) 974-2669. Email:
[email protected]. † University of Tennessee. ‡ Universidade Nova de Lisboa.
(1) Koga, K.; Gao, G. T.; Tanaka, H.; Zeng, X. C. Physica A 2002, 314, 462. (2) Gordillo, M. C.; Marti, J. Chem. Phys. Lett. 2000, 329, 341. (3) Gordillo, M. C.; Marti, J. Chem. Phys. Lett. 2001, 341, 250. (4) Waghe, A.; Rasaiah, J. C.; Hummer, G. J. Chem. Phys. 2002, 117, 10789. (5) Beckstein, O.; Biggin, P. C.; Sansom, M. S. P. J. Phys. Chem. B 2001, 12902. (6) Striolo, A.; Chialvo, A. A.; Gubbins, K. E.; Cummings, P. T. J. Chem. Phys. 2005, 122, 234712. (7) Striolo, A.; Chialvo, A. A.; Cummings, P. T.; Gubbins, K. E. J. Chem. Phys. 2006, 124, 074710. (8) Ellison, M. D.; Good, A. P.; Kinnaman, C. S.; Padgett, N. E. J. Phys. Chem. B 2005, 109, 10640.
nitrogen, carbon dioxide or hydrocarbons. The major differences arise from water being a highly polar molecule, which leads to a fluid-fluid interaction stronger than the fluid-solid interaction. Water adsorption on carbon can be best summarized as a clustering process in which the adsorption is initiated by hydrophilic surface functional groups. Adsorbed water molecules become nucleation sites for clusters of water molecules to grow and migrate into the carbon pores, thus giving rise to pore-filling mechanisms similar to capillary condensation.13,14 One fundamental difference between SWNTs and other carbon materials, such as activated carbon, is in the heterogeneity of the material. SWNTs exist in bundles of nonuniformly distributed diameters (Figure 1), which are relatively less complicated to model than the disordered porous structure of most activated carbons. The tube-size distribution of SWNTs can be determined from Raman scattering of samples, as opposed to from the more traditional standard gas adsorption techniques; however, such as a size-distribution cannot discriminate between open- and closedend nanotubes. In previous studies from our group, we exploited this very fact and developed a relatively simple integrated experimental and molecular simulation methodology for representing the heterogeneity of SWNT bundles for adsorption.15,16 Our methodology distinguishes and quantifies with great accuracy the adsorption of small probe molecules, such as nitrogen or (9) Vermisoglou, E. C.; Georgakilas, V.; Kouvelos, E.; Pilatos, G.; Viras, K.; Romanos, G.; Kanellopoulos, N. K. Microporous Mesoporous Mater. 2007, 99, 98. (10) Sharma, S. C.; Singh, D.; Li, Y. J. Raman Spectrosc. 2005, 36, 755. (11) Mao, S. H.; Kleinhammes, A.; Wu, Y. Chem. Phys. Lett. 2006, 421, 513. (12) Sekhaneh, W.; Kotech, M.; Dettal-Weglikowska, U.; Wiebren, S. V. Chem. Phys. Lett. 2006, 428, 143. (13) Dubinin, M. M.; Serpinsky, V. V. Carbon 1981, 19, 402. (14) Brennan, J. K.; Bandosz, T. J.; Thomson, K. T.; Gubbins, K. E. Colloids Surf., A 2001, 187, 539. (15) Agnihotri, S.; Mota, J. P. B.; Rostam-Abadi, M.; Rood, M. J. Langmuir 2005, 21, 89. (16) Agnihotri, S.; Zheng, Y.; Mota, J. P. B.; Ivanov, I.; Kim, P. C. J. Phys. Chem. C 2007, 111, 13747.
10.1021/la7036197 CCC: $40.75 2008 American Chemical Society Published on Web 04/30/2008
H2O, Organic Vapor Mixtures on SWNT Bundles
Figure 1. Pictorial representation of a typical heterogeneous SWNT bundle and its different adsorption sites: (1) intratube (endohedral), (2) interstitial channel, (3) external grooves, (4) external surface. The dotted line depicts the peripheral surface of the bundles over which hexane adsorption was probed here by GCMC simulation.
hexane, inside the SWNT bundles and on their peripheral surface,15–17 as well as estimates the adsorptive contributions from any impurities present in samples,18 all of which remain indistinguishable from experimentation or simulation alone. Using grand canonical Monte Carlo (GCMC) simulations, we found that the internal pore volume of SWNT bundles with 9 to 15.2 Å wide tubes is almost saturated with hexane at a relative pressure P/Po ) 10-2 (P is the actual pressure and Po is the saturation pressure of the vapor adsorbate at system temperature). Furthermore, the external surface of the bundles (depicted by the dotted line in Figure 1) behaves much like a planar carbon surface after a monolayer of the adsorbate is formed. Most importantly, the adsorption on the peripheral surface increases drastically between10-4 < P/Po < 0.9, and it is this general characteristic that imparts the mesoporosity that is typically observed in SWNT samples.15,16 Molecular simulation is the most common tool for understanding adsorption of water on SWNTs.1–7 There are a few experimental studies,9–12 and even fewer joint experimental and theoretical studies reported in the literature.8 Experimental studies are often limited in describing how adsorption takes place at the microscopic level. Similarly, theoretical studies are challenged in accurately describing the heterogeneous structure of the adsorbent and representing the surface chemistry of the carbon. It is imperative to incorporate the surface chemistry in the adsorbent model (for example, as representative charges for oxygenated functional groups7,8,19–21) because otherwise, the predicted water adsorption could be negligible until nearsaturation conditions are reached,22 which would be an unrealistic adsorption scenario. In principle, our GCMC characterization of SWNT bundle heterogeneity can be extended to water-SWNT systems if the local density and the location of the charged sites are known. However, these parameters are difficult to determine experimentally to aid computations and may not be readily transferable to other polar adsorbates. In this manuscript, we are reporting an indirect method that can circumvent several experimental and computational com(17) Agnihotri, S.; Mota, J. P. B.; Rostam-Abadi, M.; Rood, M. J. J. Phys. Chem. B 2006, 110, 7640. (18) Agnihotri, S.; Mota, J. P. B.; Rostam-Abadi, M.; Rood, M. J. Carbon 2006, 44, 2376. (19) Muller, E. A.; Rull, L. F.; Vega, L. F.; Gubbins, K. E. J. Phys. Chem. 1996, 100, 1189. (20) Jorge, M.; Schumacher, C.; Seaton, N. A. Langmuir 2002, 18, 9296. (21) Slasli, A. M.; Jorge, M.; Stoeckli, F.; Seaton, N. A. Carbon 2004, 42, 1947. (22) Zhao, X. C. Phys. ReV. B: Condens. Matter Mater. Phys. 2007, 76, 041402.
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Figure 2. Raman spectra of SWNT samples from multiple excitation energies. The ratio of the peak intensities at 1350 cm-1 (D peak) and 1550 cm-1 (G peak) is much smaller for sample EA95 than for sample CVD80. The spectra for EA95 are shifted upward for clarity.
plexities encountered in developing a better understanding of adsorption of water in SWNTs. We carried out sequential adsorption of water and organics onto purified samples by gravimetric methods. We also performed GCMC simulations of hexane, as a representative organic, on heterogeneous bundles of SWNTs. The diameter distribution selected for simulation was determined from the Raman spectra of the sample. The hexane molecule was modeled as a flexible chain of pseudoatoms.23 The results reveal the mechanisms of adsorption of organics onto the external surface of the bundles and the restriction of water to the internal pore volume of the bundles only, thus leaving unoccupied the external surface of the SWNT bundles for adsorption of more compatible adsorbates, such as organics.
Methodology Samples. The SWNT samples were manufactured by electric-arc and high-pressure catalytic cracking of carbon monoxide and contained 95–98 wt % (EA95) and 80 wt % SWNTs (CVD80). The details of sample morphology and characterization by standard N2 adsorption (77 K) are provided in our previous work.16,24 The diameter distribution for each SWNT sample was determined from the radial breathing mode (RBM) region of the Raman spectra obtained at λ ) 532, 633, and 785 nm (Table 1). The ID/IG ratio in the Raman spectra, which indicates the degree of structural defects and surface functionalization, was much lower for sample EA95 than for sample CVD80, regardless of the excitation energy (Figure 2). This indicated the presence of more pristine and relatively defectfree SWNTs in the sample EA95. Simulation. A simulation strategy for detailed modeling of heterogeneous SWNT bundles using N2 at 77 K as the probe adsorbate was developed by our group15 and was thoroughly validated in our most recent study.16 Here, we are presenting an application of the overall methodology to calculate only the external component of the adsorption isotherm, extension of the simulation procedure to efficiently handle flexible chain molecules such as hexane, and incorporation of a more detailed diameter distribution obtained from multiple excitation energies in the Raman experiments because a single excitation energy might be insufficient to explore all tube sizes. A brief description of our integrated experimental-simulation strategy for modeling heterogeneous SWNT bundles is presented below. GCMC calculations are to be carried out in three steps. First, the heterogeneous bundle (Figure 1) is imagined to be deconvoluted into several homogeneous bundles with diameters the same as those (23) Martin, G. M.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (24) Agnihotri, S.; Rostam-Abadi, M.; Rood, M. J. Carbon 2004, 42, 2699.
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Agnihotri et al. Table 1. SWNT Samples Analyzed in the Present Worka λ ) 532 nm
sample identifierb
2
sample description
EA95
electric arc, 0% metal
CVD80
HiPco, 12% Fe coated with carbon
λ ) 633 nm
λ ) 785 nm
Sp (m /g)
D (Å)
wD
D (Å)
wD
D (Å)
wD
156
13.7
0.76
12.5
0.39
11.5
0.15
15.4
0.24
9.2
0.39
13.0 14.3 8.0
0.32 0.28 0.09
14.0 15.2 9.0
0.34 0.51 0.42
15.6
0.61
8.4 9.2 10.9 12.3
0.16 0.35 0.22 0.17
10.2 10.7 11.1 11.8
0.21 0.17 0.11 0.10
437
a Diameter (D) and distribution (wD) of SWNTs used in GCMC simulations were obtained by Raman scattering. Diameters were determined by Raman scattering at three different excitation energies. The scattering experiments at λ ) 785 nm were performed on individually dispersed SWNTs in 10% surfactant solution in nanopure water, and D was calculated from ωRBM ) 12.5 + 223.5/D (nm). Scattering experiments at λ ) 633 and 532 nm were performed on solid nanotubes. D was determined from ωRBM ) 10.0 + 234.0/D. Sp is the specific external surface area of the sample; its definition is provided in the caption of Figure 3. bNumerals denote the wt % of SWNTs in the sample, as provided by the manufacturer. Our previous GCMC modeling15,17,18 was based on a narrowwer diamter distribution obtained from Raman scattering at λ ) 785 nm only.
Figure 3. Example of a simulation box for GCMC study of adsorption on the external surface (including groove sites) of a homogeneous SWNT bundle. The external surface area (Sp) of the bundle is defined as the area of the plane boundaries of the prism with vertices on the center of the outermost shell of the nanotubes; this corresponds to the area of the top face of the simulation box. This area can be converted to a corrugated area,S′P, which takes into account the curvature of the tubes, using the conversion formula S′P ) Sp(π/2 - θ)/cos θ, where cos θ ) (D + ∆s)/(D + σsf). D is the tube diameter, ∆s ) 3.4 Å is the intertube distance, and σsf is the collision diameter for sorbate–carbon interaction. To determine the fluid-solid interaction, each pseudoatom of an adsorbate molecule was mapped onto the hatched area, and its interaction with the five nearest nanotubes (darker tubes) was computed.
comprising the discrete approximation of the tube-diameter distribution of the sample (Table 1). Second, each homogeneous bundle is further deconvoluted into two regions: (i) the internal volume comprising the endohedral volume and interstitial channels, and (ii) the external surface and grooves of the outermost SWNTs. Only the external adsorption was modeled in this work. Third, upon calculating the GCMC external adsorption isotherms for the relevant homogeneous bundles, they are weight-averaged according to the tubediameter distribution obtained from the relative peak intensity at each RBM frequency (wD in Table 1): s qsim )
1 nλ
s ∑ ∑ wλ,Dqsim,D λ
D
∑ wλ,D ) 1
(1)
D
s This provides the theoretical isotherm, qsim , incorporated with s sample-specific heterogeneity. In eq 1, qsim,D(P/Po) is the adsorption isotherm for the external surface of a homogeneous bundle of tube diameter D expressed as a function of relative pressure P/Po; Σλ denotes the summation over nλ excitation energies probed in Raman scattering experiments; wλ,D is the tube-diameter distribution obtained
at a particular excitation, λ, which is estimated from the ratio of the peak heights in the RBM region of the corresponding Raman spectrum. s It should be noted that in our simulation methodology, qsim is determined as the amount adsorbed per unit of external surface area of the bundles (either mmol/m2 or mg/m2). However, for comparison s with any experimental data, qsim must be scaled by the total external surface area of the SWNT bundles specific to a sample, Sp (m2/g), to express the external isotherm per unit mass of sample (mmol/g or mg/g). This requires the estimation of Sp. A method for estimating this structural parameter was developed in our previous work.15 Briefly, plotting the experimental total adsorption isotherm, qexp, s versus qsim yields a curve whose slope of the linear asymptote at high loading is the value of Sp. The calculated values of Sp (for samples EA95 and CVD80) based on N2 adsorption simulation and experiments at 77 K are listed in Table 1. Here, GCMC simulations of hexane adsorption were carried out for the values of D listed in Table 1 at 298.15 K and relative pressures (P/Po) similar to the experimental ones for comparative purposes. The intertube distance for all simulations was fixed at ∆s ) 3.4 Å to mimic SWNTs adhering to each other by van der Waals forces to form bundles. Figure 3 shows an example of a simulation box for external adsorption. The faces of the box implement periodic boundary conditions, except for the top face, which is a reflecting wall, and the bottom face, which is blocked by the outermost shell of nanotubes in the bundle. The actual length of the simulation box is a function of the imposed sorbate pressure; however, in every case, it is an integer multiple of D + ∆s. To determine the solid–fluid interaction potential during simulation, each pseudoatom of a hexane molecule is mapped onto the hatched area of the box and interacts with five nearest nanotubes: three on the outermost shell and two on the second shell. Including farther nanotubes had minimum impact on the total solid–fluid interaction potential. The effect of making the outermost shell of nanotubes accessible for internal adsorption was explored but no change in the external adsorption was observed. Therefore, to reduce the computation time, the nanotubes were not made part of the simulation box (see Figure 3), and molecules were not allowed to adsorb inside them. The force field adopted for hexane was the transferable potential for phase equilibria (TraPPE),23 which is based on a united-atom model in which each CH3 or CH2 group is treated as a single interaction site. The interaction between the carbon atoms of a nanotube and each pseudoatom of a hexane molecule was modeled using the Lennard–Jones potential, uij(r) ) 4εij[(σij/r)12 - (σij/r)6] (r is the intermolecular distance), as was the nonbonded interaction between the pseudoatoms on different hexane molecules or pseudoatoms within a hexane molecule that were separated by more than three bonds. The well depths, εi/kB (kB is Boltzmann constant), and the collision diameters, σi, are listed in Table 2. The cross-terms
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Langmuir, Vol. 24, No. 11, 2008 5749
Table 2. Lennard-Jones Potential Parameters pseudoatom
ε/kB (K)
σ (Å)
C (SWNT) CH3 CH2
28 98 46
3.40 3.75 3.95
are obtained using the standard Lorenz–Berthelot combining rules: εij ) √εiεj and σij ) (σi + σj)/2. At 298.15 K, the nanotubes can be approximated as smooth, structureless nanocylinders. For a fluid interaction site located at a nearest distance, δ, from the central axis of a nanotube, an effective potential, Usf(δ), was developed by integrating the LJ solid–fluid potential, usf, over the positions of all wall atoms in a nanotube of infinite length:
Usf(δ) ) 4FsR
∫0π usf(r) dθ dz
r2 ) R2 + δ2 - 2δR cosθ (2)
where R ) D/2 is the pore radius, z is the distance along the cylinder axis, θ is the radial angle, and Fs ) 0.382 Å2 is the atomic surface density of the pore wall. By integrating over z and θ, eq 2 is reduced to a one-dimensional potential, which depends on δ only:
Usf(δ) )
{
π2Fsεsfσsf2
( ) ]} ( ) ]}
63 R - δ δ2 δ -10 9 9 1+ F - , - , 1; 32 σsf R 2 2 R δ2 R-δ δ -4 3 3 3 1+ F - , - , 1; (3) σsf R 2 2 R
{
(
) [ ( ) [
where F(R, β, γ; δ) is the hypergeometric function. To speed up the calculation of Usf, eq 3 was tabulated on a grid with 31 knots equally spaced in δ2. During simulations, Usf was reconstructed from the tabulated information using the cubic Hermite polynomial interpolation. Adjacent pseudoatoms of a hexane molecule were connected by a rigid bond length of 1.54 Å; the harmonic bond-bending potential, Ubend(θ), along three successive pseudoatoms was governed by Ubend ) kθ(θ - θ0)2/2 with force constant kθ/kB ) 62,000 K rad-2 and equilibrium bending angle θ0 ) 114°. The dihedral torsion potential, Utors(φ), along four successive pseudoatoms was modeled as Utors ) c1[1 + cos φ] + c2[1 - cos(2φ)] + c3[1 + cos(3φ)] with c1/kB ) 355.03 K, c2/kB ) -68.19 K, and c3/kB ) 791.32 K. The application of standard techniques of molecule insertion or deletion of larger molecules to systems in which molecules fit very tightly in the pores, resulted in very low acceptance rates of those steps that were needed to correctly sample the ensemble. Furthermore, even for a simple geometry, such as that of the corrugated external surface of a SWNT bundle, not all portions of its accessible space were equally favorable; there exist preferred regions in which adsorbate molecules are localized. This information can be incorporated into a simulation if the insertions are not attempted randomly throughout the volume and are rather performed such that the molecules are inserted preferentially into the most favorable locations of the simulation box. This provides a substantial improvement in the efficiency of the simulations. To enhance the sampling of configurational space and increase the acceptance rate of the molecule insertion or removal step, we resorted to configurational-bias sampling techniques.25–28 In the configurational-bias method, a flexible molecule is grown atom-by-atom toward energetically favorable conformations, leading to a scheme that is orders of magnitude more efficient than the traditional method of random growth. The implementation of the configurational-bias method is presented in detail in the Supporting Information file. (25) Siepmann, J. I. Mol. Phys. 1990, 70, 1145. (26) Siepmann, J. I.; Frenkel, D. Mol. Phys. 1992, 75, 59. (27) Frenkel, D.; Mooij, GCAM.; Smit, B. J. Phys. Condens. Matter 1992, 4, 3053. (28) Depablo, J. J.; Laso, M.; Suter, U. W. J. Chem. Phys. 1992, 96, 6157.
Figure 4. GCMC hexane adsorption isotherms at 298.15 K on the external surface of homogeneous SWNT bundles with diameters of 9.0, 12.5, and 15.6 Å.
In addition to the usual trial step of molecule insertion/deletion where the acceptance rate is enhanced by resorting to configurationalbias techniques, three additional types of Monte Carlo (MC) moves involving only individual molecules were necessary to sample the internal configuration of the simulation box: translation, rotation about the center of mass, and configurational-bias partial regrowth to change the internal conformation of the molecule. Each run was equilibrated for 2 × 104 MC cycles, followed by an equal number of MC cycles for the production period. Each cycle consisted of 0.8N attempts to translate a randomly selected molecule, 0.2N trial rotations, 0.2N attempts to change the conformation of a molecule using configurational-bias partial regrowth, and max (20, 0.2N) molecule insertion/deletion steps. Here, N is the number of molecules in the simulation box at the beginning of each cycle. The maximum displacement for translation and angle for rotation were adjusted during the equilibration phase to give a 50% acceptance rate. Standard deviations of the ensemble averages were computed by breaking the production run into five blocks. Experiments. Experiments were performed using a high-sensitivity gravimetric analyzer (detection limit ) 0.1 µg). It is worth noting that the adsorption of organic vapors and water vapor mixtures, as attempted here, qualifies as a multicomponent competitive adsorption experiment. In the first trial of the experiments, the amount adsorbed for each component was determined from the material balance between the total gravimetric adsorption and the unadsorbed vapor; the latter was estimated from an online monitoring of the outlet concentration of vapors in a particular adsorption step. This approach was tested; however, it was concluded that in order to obtain meaningful results, the outlet concentration profile would have to be measured with at least 0.1% accuracy, which was not achievable due to instrumentation limits (see the Supporting Information). Therefore, sequential adsorption was
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Figure 5. Snapshots of hexane adsorbed on the external surface of 9 Å (left) and 12.21 Å (right) SWNT bundles at 298.15 K andP/Po ) 10-5 (a), 10-4 (b), 10-3 (c), 10-2 (d), and 10-1 (e). CH3 and CH2 pseudoatoms are shown in red and cyan, respectively. Po ) 0.2 bar.
selected as an appropriate alternative technique. Details of our experimental setup, schematic, and standard operating procedure are provided in the Supporting Information. The following is a brief description of the methodology with emphasis on the sequential method. Experiments were carried out in an open configuration in which the vapor carrying gas (200 sccm of ultrahigh purity N2) was continuously flowing through the measuring chamber during each adsorption experiment. The measurements were made on 2 to 3 mg sample loadings. Prior to testing, the sample was dried and then cooled to the operating temperature inside the balance. All experiments were performed under isothermal conditions at 298.15 K. Each adsorption experiment was carried out in two equilibration stages: one with the humidified carrier gas and a subsequent one in which the organic vapor was continuously supplied to the humidified carrier gas in a controlled manner. After measuring the dry weight of the sample, water vapor at 90 ( 1% relative humidity (RH ) 100P/Po, where Po ) 0.0317 bar is the saturation vapor pressure of water) was introduced into the carrier gas. The sample was allowed to adsorb as much water as possible. Equilibrium was assumed when the mass increase was
