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Application of water–activated carbon isotherm models to water adsorption isotherms of single-walled carbon nanotubes Pyoungchung Kim, Sandeep Agnihotri ∗ Environmental Engineering, Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN 37996-2010, USA

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 8 February 2008 Accepted 2 June 2008 Available online 15 July 2008

The objective of this study is to understand the interactions of water with novel nanocarbons by implementing semiempirical models that were developed to interpret adsorption isotherms of water in common carbonaceous adsorbents. Water adsorption isotherms were gravimetrically determined on several single-walled carbon nanotube (SWNT) and activated carbon samples. Each isotherm was ﬁtted to the Dubinin–Serpinsky (DS) equation, the Dubinin–Astakov equation, the cooperative multimolecular sorption theory, and the Do and Do equations. The applicability of these models was evaluated by high correlation coeﬃcients and the signiﬁcance of ﬁtting parameters, especially those that delineate the concentration of hydrophilic functional groups, micropore volume, and the size of water clusters. Samples were also characterized by spectroscopic and adsorption techniques, and properties complementary to those quantiﬁed by the ﬁtting parameters were extracted from the data collected. The comparison of ﬁtting parameters with sample characterization results was used as the methodology for selecting the most informative and the best-ﬁtting model. We conclude that the Do equation, as modiﬁed by Marban et al., is the most suitable semiempirical equation for predicting from experimental isotherms alone the size of molecular clusters that facilitate adsorption in SWNTs, deconvoluting the experimental isotherms into two subisotherms: adsorption onto hydrophilic groups and ﬁlling of micropores, and quantifying the concentration of hydrophilic functional groups, as well as determining the micropore volume explored by water. With the exception of the DS equation, the application of other water isotherm models to SWNTs is not computationally tractable. The ﬁndings from this research should aid studies of water adsorption in SWNTs by molecular simulation, which remains the most popular tool for understanding the microscopic behavior of water in nanocarbons. © 2008 Elsevier Inc. All rights reserved.

Keywords: Carbon nanotubes Adsorption Applications Activated carbon Surface science Water Clusters Raman spectroscopy Molecular simulation

1. Introduction The adsorption of water onto microporous carbons such as activated carbon, carbon molecular sieves, and carbon nanotubes (CNTs) is being widely studied. In particular, the adsorption of water onto carbon nanotubes may become an important issue in realizing potential applications of nanotubes for electronic devices [1], energy storage [2], and drug delivery [3]. Of the recently discovered nanocarbons, single-walled carbon nanotubes (SWNTs) are the most attractive materials. They are one-atom-thick uniform cylindrical structures of carbon that agglomerate into bundles, thus giving rise to a nanoporous structure with different adsorption sites that include internal porosity of SWNTs, interstitial wedges between adjacent SWNTs, grooves on the external surface of the bundles, and interbundle voids [4]. Theoretical studies of water adsorption onto CNTs have predicted the freezing of water inside the

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Corresponding author. Fax: +1 (865) 974 2669. E-mail address: [email protected] (S. Agnihotri).

0021-9797/$ – see front matter doi:10.1016/j.jcis.2008.06.002

© 2008

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nanotubes [5], the ﬁlling and emptying of nanotubes by sequential addition or removal of water molecules in a single-ﬁle chain [6], and effects of different microporosities [7] and surface functional groups [8] on the adsorption of water onto SWNTs. Molecular dynamics (MD) simulations of water in (n, n) SWNTs have predicted one-dimensional structures of water inside nanotubes with the net dipole moment aligned along the tube axis [9]. Some experimental studies of water–nanotube interactions have also been conducted. For example, using proton nuclear magnetic resonance (NMR), it has been suggested that at 212 K, water molecules form a rigid structure inside nanotubes that does not resemble ice [10]. NMR techniques were also used to estimate water adsorption isotherms on oxidized SWNTs [11] and reveal the importance of functional groups in clustering of water molecules around the ends and defects of SWNTs. Raman spectroscopy [12] was recently used to study the adsorption of water on closed and open-ended SWNTs and to calculate the desorption energy of water molecules from the internal volume of nanotubes. The importance of studying the adsorption of water on CNTs is also realized when one considers the practical use of these mate-

P. Kim, S. Agnihotri / Journal of Colloid and Interface Science 325 (2008) 64–73

rials as adsorbents for air and process streams where adsorption occurs in competition with water vapor present as humidity or a combustion product. Under high humidity conditions, for example, relative humidity greater than 90%, the preadsorbed water content of activated carbons can be high enough to completely saturate their capacity for organic vapors. Hence, the adsorption characteristics of water vapor are important when the removal of trace organic contaminants is considered. In spite of a tremendous effort to better understand the adsorption of water onto SWNTs, it remains ambiguous and not fully understood. SWNT nanocarbons have both micropores and mesopores [4] much like a typical activated carbon, although the differences in the pore geometry of these two types of carbon are obvious. The adsorption of water in the pores of activated carbons is known to be mediated by surface chemistry. Several semiempirical water adsorption models incorporating the role of surface chemistry can be found in the literature. Therefore, it seems reasonable to apply these models to water– nanotube experimental data to, ﬁrst, determine their applicability to a novel form of carbon, and second, extract reliable molecularscale information about interactions of water with SWNTs. To the best of our knowledge, the Dubinin–Serpinsky (DS) equation [13] remains the only water–activated carbon isotherm model that has been applied to SWNTs [11]. Several recent studies have reported water isotherms on SWNTs [14,15] without further analysis of the isotherm data by semiempirical models that are readily available. The DS equation is one of the most common equations, but is also one of the simplest water adsorption isotherm models. Several other semiempirical isotherm models have recently been developed. These models can provide more detailed and fundamentally relevant information about the behavior of water in porous carbons. Typically these models [16–22] can predict the concentration of surface functional groups, the molecular size of water clusters, and the water adsorption capacity in the micropores as well as on the surface functional groups, and also estimate equilibrium rate constants. Such models are, for example, the Dubinin–Astakov (DA) equation [16], the Talu–Meunier equation [17], the cooperative multimolecular sorption (CMMS) theory [18], and the D.D. Do equation [19] and its several modiﬁcations [20–22]. Each of these models was applied to a speciﬁc carbon adsorbent in the original study. For example, the CMMS [18] theory and the D.D. Do [19] equation revised by Lagorsse et al. [20] were ﬁtted to water adsorption isotherms measured on carbon molecular sieves. Similarly, the DA [16] equation, the D.D. Do [19] equation, and its interpretations by Zimny et al. [21] and Marban and Fuertes [22] were used to describe the data collected for water adsorption on activated carbon and activated carbon ﬁbers. The objective of this study is to understand the interactions of water with SWNT nanocarbons by implementing the semiempirical tools that were developed for adsorbents, such as activated carbons, that generally are not considered nanocarbons. This is accomplished by applying several water–carbon isotherm models whose relevance to SWNTs remains unreported in the literature. We gravimetrically measured water adsorption isotherms on several commercially available SWNTs. Each isotherm was ﬁtted to the DS equation [13], the DA equation [16], the CMMS theory [18], and the D.D. Do equation [19]. We are able to identify the D.D. Do equation, modiﬁed by Marban and Fuertes [22], as the most suitable equation for interpreting the water adsorption isotherms of SWNT with suﬃcient details. We suggest that this equation could be an appropriate model to determine from empirical data alone the concentration of surface functional groups, the average size of water clusters growing on the surface functional groups and those migrating inside the pores of nanotubes, and the limiting water adsorption capacities. Such data should be useful in supporting molecular simulation studies of water adsorption on SWNTs, which

65

Table 1 Physical characteristics of SWNT samples studied here

SWNT1 SWNT2 SWNT3 SWNT4 AC ACF10

– – – Treatede – Treatede – –

Surface area (m2 /g)

Pore volume (cm3 /g)

Totala

Micropore

Total

b

507 637 631 717 80 268 810 786

352 98 229 172 1 182 331 476

0.57 1.38 1.06 1.13 0.20 0.40 0.71 0.61

0.16 0.05 0.10 0.09 0 0.05 0.18 0.24

Pore sizec (nm)

1.52 0 .9 1 .1 – 1 .1 – 3.5d 3.1d

a

Total BET surface area. Micropore volume. c Dominant diameter from the radial breathing mode (RBM) region of Raman spectra [24,27]. b

d

Average pore size determined from standard N2 adsorption at 77 K. Samples were outgassed at 600 ◦ C for 12 h. All other samples were outgassed at 140 ◦ C. e

remains the most popular methodology for understanding the microscopic behavior of water on nanocarbons [8,23]. 2. Methodology 2.1. Sample information and characterization SWNT samples selected for this study were commercially produced and were puriﬁed by the manufacturers. The sample descriptions, morphologies, and characterization details were provided in our previous work [24,25]. Brieﬂy, the SWNT samples are labeled as SWNT1 (>95% SWNTs, from MER Corp., previously referred to as EA95); SWNT2 (>90% SWNTs, from Carbon Nanotechnologies Inc., previously labeled as CVD90); and SWNT3 and SWNT4 (70% and 80% SWNTs, from Carbon Solutions Inc., previously labeled as CS70 and CS80, respectively). The sample SWNT4 was known to contain an extremely high concentration of –COOH functional groups (source: communications with the manufacturer). Activated carbon samples were labeled as AC (Calgon activated carbon) and ACF10 (nonwoven activated carbon ﬁber, from American Kynol). The majority of experimental analyses were performed on as-received samples. However, some quantities of SWNT samples SWNT3 and SWNT4 were heated to 600 ◦ C for several hours in 10 mTorr or less vacuum to reduce the concentration of surface functional groups [26]. Prior to the water adsorption measurements by gravimetric methods, these heat-treated samples were stored under vacuum to minimize the effects of ambient conditions on the sample properties. Samples were characterized by standard N2 adsorption at 77 K (Autosorb 1-c by Quantachrome Instruments). A quantity of 20 to 30 mg of each sample was outgassed at 140 ◦ C (or 600 ◦ C for samples referred to here as heat-treated). N2 adsorption isotherms were obtained in a relative pressure, P / P 0 , range of 10−6 to 0.99, where P is actual pressure and P 0 is the saturation pressure of N2 at 77 K. For each sample, the physical properties, such as surface area, pore volumes, and pore size distributions, were extracted from the experimental N2 isotherm data by applying the appropriate algorithms built into the Autosorb 1 software. Table 1 provides a summary of the sample characterization data. For SWNTs, the typical micropore volume was found to be only a fraction of the total pore volume (0 to 25%, depending upon the sample). Activated carbons had a slightly higher fraction of microporosity (25% to 40%). Nevertheless, the differences in porosities of SWNTs and activated carbons appeared inconclusive to determine if nanocarbons offer special advantages in pore volumes when compared with traditional microporous activated carbons. The effect of heat

66

P. Kim, S. Agnihotri / Journal of Colloid and Interface Science 325 (2008) 64–73

treatment on the porosity of SWNT samples and activated carbon samples seemed insigniﬁcant; however, the sample SWNT4 exhibited a signiﬁcant increase in the surface area and micropore volume upon heat treatment. This sample was known to contain an unusually high concentration of surface functional groups. It is very likely that heat-treating this sample unblocked some pores, thus increasing the amount of adsorption, as evident from enhanced surface area and pore volume for the treated sample. Samples were characterized by Raman spectroscopy, the details of which are available in our related publications [25,27]. Brieﬂy, the spectra were obtained by a Nicolet 6700 FT-IR-Raman instrument. The excitation λ is in the near infrared region (λ = 946 nm). The instrument is ﬁtted with a liquid-N2 -cooled high-sensitivity Ge detector and was operated at a power rating of 0.06 W (less than 5% of maximum power) to minimize sample heating, which could be one of the drawbacks of a nondispersive Raman technique. Samples were prepared by grinding approximately 0.05% (w/w) adsorbent in KBr powder. Spectra were collected at 10 distinct points on the pellet. The spectra were corrected by subtracting blanks. It is known that the Raman spectrum of a carbon sample exhibits peaks at approximately 1350 cm−1 Raman shift (D peak) and 1580 cm−1 Raman shift (G peak). The intensity ratio I D / I G is commonly used to study structural disorder. Therefore, in principle, it should also be extendable to the hydrophilic component of the total surface chemistry, and if one were to follow the trends in the I D / I G ratio, then those trends should also exist in the values of the parameter that delineates the concentration of primary adsorption centers (e.g., the ﬁtting parameter S 0 in most water isotherm models, mmol/g). Here, this rationale was used in evaluating the applicability of particular water isotherm models. Representative spectra for each sample are provided in the Supplementary Information. 2.2. Water adsorption experiments The equipment used to measure the adsorption isotherms consisted of a gravimetric balance (digital recording balance DRB-200 by Thermo Cahn; limit of detection = 0.1 μg), a gas generation system, and a data acquisition system. The details of our experimental setup and its operation are provided in our previous related work [25]. Following is a brief description of the methodology. The experiments were conducted in an open system in equilibrium with the atmospheric pressure such that the vapor carrying carrier gas was continuously ﬂowing through the balance while the sample mass could be monitored in real time. The carrier gas for all experiments was ultra-high-purity (UHP) N2 at a total ﬂow rate of 200 sccm. Prior to each experiment, the balance was zeroed and recalibrated while the carrier gas was ﬂowing through the hangdown tube without the sample. This step obviates the need for the buoyancy corrections that typically need to be performed in gravimetric measurements. An adsorbent sample (3 to 5 mg) was placed on the sample pan and its initial weight was measured upon reaching equilibrium with the carrier gas. The sample was heated to 140 ◦ C for 3 h followed by cooling to the operating temperature of 20 ◦ C. Desired concentrations of water vapor, measured by a relative humidity (RH = 100 × P / P 0 ) probe, were generated by purging the carrier gas through double-distilled water using a fritted glass bubbler followed by mixing with dry gas. The water vapor carrier gas was introduced into the hangdown tube. The sample adsorbed some water, which resulted in an increase in the sample mass. Equilibrium was assumed when no increase in sample mass (<1 μg = 10 × detection limit) was observed for a continuous 30-min period. The net gain in sample mass was normalized to its dry weight, and was reported as the adsorption capacity in equilibrium with the gas-phase concentra-

tion. Isotherms were measured for 20 intermediate water vapor concentrations between 0 and 0.95P / P 0 . 2.3. Water adsorption isotherm models This paper is reporting the application of the DS equation [13], the DA equation [16], the CMMS theory [18], the D.D. Do equation [19] and its several revisions by Lagorsse et al. [20], Zimny et al. [21], and Marban and Fuertes [22] to the water adsorption isotherms collected for several SWNT samples by a high-sensitivity gravimetric method. Following is a brief description of the models and the equations, with the exception of the revisions of the D.D. Do equations, which are provided later in the manuscript. The reader is referred to the appropriate references for details regarding model development, scope, and applications. The DS equation is one of the simplest models. It assumes adsorption of one water molecule per active site, and is often ﬁtted to the lower part of the isotherm [11]. It is the equation most commonly used to estimate as a ﬁtting parameter the concentration of primary adsorption sites (i.e., hydrophilic functional groups) on the carbon surface, P P0

=

Cμ c (1 − kC μ )( S 0 + C μ )

(1)

,

where C μ (mmol/g) is the amount of adsorbed water at a speciﬁc P / P 0 ; S 0 is the concentration of primary adsorption sites (typically, 0.05 < S 0 < 5 mmol/g), which can be used to distinguish carbons with different degrees of surface oxidation; c (unitless) is the ratio of the equilibrium rate constants for adsorption and desorption of water; and k (g/mmol) is a constant related to the total amount of water adsorbed at P / P 0 = 1. Parameters S 0 , c, and k are ﬁtting parameters. The DA equation (Eq. (2)) is based on the change of Gibbs free energy, A = R T ln( P 0 / P ). It is a common model to describe the adsorption isotherms of gases and vapors. The water adsorption isotherm is usually described by two similar forms of the fundamental DA equation [28]: type I for adsorption on surface functional groups and type V for adsorption in the micropores. Such a modiﬁed DA equation [16] can be applied to interpret the total water adsorption isotherm,

C μ = S 0 exp −

A

n(I)

E H2 O(I)

+ C μs exp −

A

n(V)

E H2 O(V)

,

(2)

where E H2 O(I) and E H2 O(V) (kJ/mol), respectively, are characteristic energies related to water adsorption on functional groups and in the carbon pores; C μs is the maximum adsorption capacity of water (mmol/g); n(I) and n(V) describe the surface heterogeneity (unitless); and the deﬁnitions of other parameters are similar to those in Eq. (1). Parameters E H2 O(I) , E H2 O(V) , C μs , n(I) , n(V) , and S 0 are ﬁtting parameters. The CMMS model [18] (Eq. (3.1) or (3.2)) was originally developed by Malakhov and Volkov [29]. It has been modiﬁed by Rutherford [18] to describe the water adsorption isotherm in highly nanoporous carbon adsorbents such as carbon molecular sieves. The CMMS model assumes adsorption of one water molecule per functional group followed by adsorption of two water molecules by hydrogen bonding. This conﬁguration forms a triad of water molecules, which then allows secondary interactions to form dimers, trimers, etc. The CMMS model can describe the type IV and V water adsorption characteristics. The CMMS model,

S 0 bBET PP C μs K 0 PP 0 Cμ = P 0 P + P , 1 − K as P 1 + bL P K 0 P + w 2I sin g 0

0

(3.1)

0

is used to describe the water adsorption isotherm for samples with high concentrations of surface functional groups. It employs a

P. Kim, S. Agnihotri / Journal of Colloid and Interface Science 325 (2008) 64–73

BET-type equation to describe the adsorption contributions of the functional groups. The CMMS model, Cμ =

P P 0P 1 + bL P 0

S 0 bL

+

C μs K 0

K0

P P0

+

P P0 , w 2I sin g

(3.2)

uses a Langmuir-type equation to describe adsorption onto surface functional groups, and is therefore applied to samples with less surface oxidation, which often exhibit type V adsorption characteristics. Here w I sin g =

1 2

P

1 − K1

+

P0

1 − K1

P P0

2

+ 4K 0

P P0

, (3.3)

where K 0 and K 1 , respectively, are the equilibrium constants representing the interaction of water molecules with the functional group and with the side unit on the functional group, respectively; K as is the constant of adsorption of the side associate; and bBET and bL are the BET constant (Eq. (3.1)) and Langmuir aﬃnity constant (Eq. (3.2)), respectively. Parameters K 0 , K 1 , K as , bBET , and S 0 are ﬁtting parameters for BET-type water adsorption isotherms. Parameters K 0 , K 1 , bL , and S 0 are ﬁtting parameters for Langmuirtype water adsorption isotherms. The D.D. Do equation [19] assumes that water molecules chemically bond with the functional groups located in the mesopores and at the entrance to the micropores. The cluster of water molecules grows to the size of a pentamer (ﬁve molecules, approximate width 0.6 nm) on the functional groups. The pentamers attain suﬃcient dispersive energy to migrate into the micropores and, thus, ﬁll the micropores. The BET equation is used to describe the adsorption of water on functional groups. The overall water adsorption isotherm is deconvoluted into the two distinct isotherms: adsorption on functional groups and ﬁlling of micropores. The equation is Cμ = S0

Kf

n

i =1 i

1 + Kf

·

P i P0

n

P i =1 P 0

i + C μs

P 6 P0 6 P , K μ PP + P0 0 Kμ

(4)

where the deﬁnitions of S 0 and C μs remain unchanged; K f and K μ , respectively, are the equilibrium rate constants for the chemisorption of water on functional groups and water ﬁlling of micropore (unitless); and n is the average number of molecules in the fully developed water clusters on the surface functional groups. 3. Results and discussion 3.1. Water adsorption isotherms and modeling The adsorption and desorption isotherms of water vapor on SWNTs and activated carbon samples were measured at P / P 0 between 0 and 0.95 (Fig. 1). Samples SWNT1, SWNT2, and SWNT3 and activated carbon samples AC and ACF10 exhibited a type V characteristic. In particular, sample SWNT1 showed minimal uptake of water until P / P 0 was raised to 0.4. This characteristic is an indication of an extremely hydrophobic surface, which was also evident from the very low values of S 0 irrespective of the isotherm model used in the data modeling. These values are provided in the Supplementary Information. On the other hand, only sample SWNT4 exhibited a type IV isotherm with no sharp distinction between the adsorption on surface functional groups and the micropore ﬁlling. This indicated an extremely hydrophilic sample, which was expected from the background information available for this sample, and was quantiﬁable from the S 0 values obtained from data modeling. These values are also provided in the Supplementary Information.

67

Following here, we report data ﬁtting as a tool to extract meaningful fundamental information about the behavior of water adsorbed in carbon nanopores from experimental data alone. We performed data ﬁtting to understand water–nanotube interactions, in particular to predict water adsorption on functional groups and in the micropores using several water adsorption isotherm models available in the literature including the DS equation, the DA equation, the CMMS model, and the D.D. Do equation. We used the curve-ﬁtting toolbox provided in Matlab (version 7.0), of which the nonlinear least-squares optimizer was used to determine the values of model parameters. The Trust Region algorithm was employed as an iterative procedure for nonlinear curve ﬁtting under the boundary condition of non-negative values of zero or higher for all ﬁtting parameters. All adsorption isotherm models were ﬁtted to each of the water adsorption isotherm measured. The ﬁt to the experimental data is also presented in Fig. 1 as continuous lines. The ﬁtting parameters for each sample are provided in the Supplementary Information. The criteria to identify the most applicable model were the presence of a high correlation coeﬃcient (R 2 > 0.995) between experimental and ﬁtted isotherms and the relevance of the ﬁtting parameters, S 0 and C μs , as evaluated by other empirical methods. These parameters are common to all models, and of all parameters these are the only ﬁtting parameters that can be related to the physical properties of a sample relatively easily. Here, the trends in the values of S 0 and C μs , respectively, are compared with the sample characterization results from Raman scattering and standard N2 adsorption at 77 K. It is known that the Raman spectra of a carbon sample exhibit peaks at approximately 1350 cm−1 Raman shift (D peak) and 1580 cm−1 Raman shift (G peak). The intensity ratio I D / I G is commonly used for a qualitative estimate of the total degree of functionalization and, in principle, should be extendable to the hydrophilic component of total surface chemistry. Therefore, if one were to follow the trends in the I D / I G ratio then those trends should also exist in the values of S 0 . In our previous work, we found that this was actually the case. The reader is referred to our previous work for details on Raman scattering experiments and results [25,27]. Brieﬂy, the experiments were performed with Fourier transform (FT) Raman equipment (λexcitation = 946 nm), and the S 0 calculated from the DS equation was found to be related to the I D / I G intensity ratio in spectra regardless of the sample (Raman spectra of samples are available in the Supplementary Information). Here we are extending this comparison to all models tested. The other ﬁtting parameter, C μs , is the micropore volume from ﬁtting various models to the water adsorption data. In principle, this value should be relatable to the micropore volume by the standard N2 adsorption (77 K) technique (C μN2 ); furthermore, the former should be less than the latter because water does not ﬁll the micropores as completely as N2 [30]. All models ﬁtted very well with most SWNT and activated carbon samples with R 2 0.995. This compatibility is apparent in Fig. 1, where a near-perfect overlap between the experimental isotherms and the ﬁtted isotherms can be observed for these samples. However, the DS equation and the D.D. Do equation were found to be not as compatible as other equations to sample SWNT1 and the activated carbon sample ACF10 (Fig. 1). The adsorption data and the curve ﬁtting for samples SWNT1 and ACF10 showed R 2 ≈ 0.97 for the D.D. Do equation and R 2 ≈ 0.9 for the DS equation. In general, the DS equation is used to describe only the initial region of an isotherm (0 < P / P 0 < 0.3) [19]. Therefore, it is suggested that the DS equation may not be the most suitable model for a detailed evaluation of water adsorption in microporous carbon adsorbents. The S 0 values calculated from all models were compared to the I D / I G ratio obtained from the Raman spectra of the samples (Fig. 2a, λ = 946 nm). It was observed that the sample-to-sample

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P. Kim, S. Agnihotri / Journal of Colloid and Interface Science 325 (2008) 64–73

Fig. 1. Water vapor adsorption isotherms and ﬁts to common isotherm models for carbon nanotube samples: (a) SWNT1, (b) SWNT2, (c) SWNT3, (d) SWNT4, and activated carbon (e) AC and (f) ACF10.

trends in the S 0 values did follow those in the I D / I G ratio, corroborating the credibility of the ﬁtting methodology and supporting our hypothesis that the trends in S 0 values should be tractable from those in the surface chemistry as measured by the I D / I G ratio in a sample’s Raman spectra. However, the S 0 calculated from the CMMS theory did not follow trends closely, especially for samples SWNT4, AC, and ACF10. Furthermore, the absolute values of S 0 calculated from the DA equation were abnormally high compared to those calculated from all other models for any given sample. Therefore, based upon the criteria of quantiﬁcation of hydrophilic surface chemistry (i.e., S 0 values), DS and D.D. Do equations appeared most appropriate to both SWNTs and activated carbons. The comparison of water micropore volume, C μs , with the N2 adsorption (77 K) micropore volume suggested that the CMMS theory and the DA equation did not follow the applicability criteria

of C μs < C μN2 ) (Fig. 2b). This criterion was only fulﬁlled by the C μs calculated from the D.D. Do equation, which also followed the sample-to-sample trends when compared with the corresponding C μN2 values. It was also noticed that for sample SWNT4, C μs > C μN2 , irrespective of the isotherm model. This is because this sample has a very high concentration of surface functional groups, which would block the pores for an electrically neutral N2 molecule but allow polar H2 O molecules to grow into clusters and migrate into the internal volume of the pores. Based upon the above discussion, the D.D. Do equation was found to be successfully fulﬁlling all criteria for a water–activated carbon isotherm model to be applicable to the water–SWNT isotherms. Furthermore, this equation is also able to deconvolute an extremely hydrophilic type IV or an extremely hydrophobic type V water isotherm into two fractions: adsorption on the func-

P. Kim, S. Agnihotri / Journal of Colloid and Interface Science 325 (2008) 64–73

7

× C μs −

69

P n P0 S0 n 7 1 + n=1 K f × PP 0 n=1 n

Kf ×

,

(5)

where the deﬁnition of S 0 , C μs , K f , K μ , and n remains unchanged, is similar to the original D.D. Do equation, with the minor alteration that the clusters of water molecules adsorbed in the micropores were composed of seven molecules as opposed to ﬁve molecules [20]. The model was applied to an extremely microporous activated carbon such as carbon molecular sieves. The Zimny et al. version, Cμ = S0

bL

P P0

1 + bL

P P0

+

P m P0 C μs m P , K μ PP + P0 0 Kμ

(6)

where the deﬁnition of S 0 , C μs , and K μ remains unchanged from the parameters of the D.D. Do equation, b L is the Langmuir aﬃnity constant, and m is the number of water molecules forming the clusters migrating into the micropores, replaced the BET-type equation with a Langmuir-type equation to describe the water adsorption from functional groups, although no rational explanation was provided for this alteration [21]. Also, they introduced a new ﬁtting parameter, m, speculating as to the variability in the cluster size entering the micropores, and omitted the ﬁtting parameter n that described the variability in cluster size forming on the functional groups. The total number of ﬁtting parameters remained unchanged. This model is also expected to have limited application to extremely hydrophobic microporous carbon adsorbents. The Marban et al. version of the D.D. Do equation,

Fig. 2. (a) Trends in surface chemistry estimated from water adsorption as ﬁtting parameter, S 0 , and experimentally determined from Raman scattering of samples. (b) Trends in micropore volume calculated from water adsorption as ﬁtting parameter, C μs , and experimentally determined from standard N2 adsorption at 77 K, C μN2 . This parameter is not calculated from the DS equation. Notice that the C μs for sample SWNT4 were larger than N2 micropore volume, due most likely to an excessive concentration of hydrophilic functional groups.

tional groups and that in the micropores. Additionally, this is the only equation that can predict as ﬁtting parameters the average number of water molecules forming clusters around the functional groups (parameter n) and the critical size of a cluster penetrating into the micropores. In the present form, the size of a threedimensional water cluster entering the pores is restricted to ﬁve molecules, which relates to a 0.6-nm-wide cluster. Recently, using molecular simulations to study water adsorption inside hydrophobic nanopores, Kaneko and co-workers reported the growth of water clusters to a critical size of 0.6 nm [31], which is remarkably similar to the cluster size used in this equation. 3.2. Comparison of several versions of the D.D. Do equation The D.D. Do equation satisfactorily ﬁtted the experimental data of all SWNT samples and AC samples with R 2 > 0.997 (Fig. 1). However, for extremely hydrophobic samples, i.e., samples SWNT1 and ACF10, the R 2 values were approximately 0.97 (Fig. 1). Although these correlation coeﬃcients are suﬃciently high, they still indicate that this equation may not be most suitable for extremely hydrophobic microporous carbons, which has also been suggested by other researchers [32]. Several versions derived from the fundamental D.D. Do equation have been proposed in recent years by Lagorsse et al. [20], Zimny et al. [21], and Marban and Fuertes [22]. The Lagorsse et al. version of the D.D. Do equation,

7

Cμ =

P n P0 S0 n 7 1 + n=1 K f × PP 0 n=1 n

Kf ×

+

Kμ Kf ×

P 7 P0

1 + Kμ Kf ×

P 7 P0

Cμ = S0

Kf

n

i =1 i

1 + Kf

·

P i P0

n

P i i =1 P 0

+

P m+1 P0 C μs m+1 P , K μ PP + P0 0 Kμ

(7)

where the deﬁnition of S 0 , C μs , K f , K μ , and n remains unchanged and m is the cluster size adsorbing into the micropores (unitless, n > m), is also called a cluster-formation-induced micropore-ﬁlling (CIMF) isotherm model [22]. The CIMF model is similar to the original equation; however, this model assumed a variable size for the water clusters adsorbed in the micropores. This introduces a new ﬁtting parameter, m, into the equation in addition to the parameter n. This parameter was introduced on the assumption that the cluster size will not always be ﬁxed to a pentamer [19] or a heptamer [20], but it would depend upon the concentration of the functional groups and the pore width. The three versions of the D.D. Do equation were ﬁtted to the water adsorption isotherm data of all samples (Fig. 3). The applicability of these models was evaluated by the same criteria of goodness of ﬁt (R 2 > 0.99), relevance of the ﬁtted S 0 values to the measured I D / I G ratio in the Raman spectra of any given sample, and the comparison of micropore volume by water adsorption to that by N2 adsorption, i.e., C μs < C μN2 . The Lagorsse version of the D.D. Do equation was found to be less compatible with the extremely hydrophobic sample SWNT1 and the extremely hydrophilic sample SWNT4 with R 2 < 0.95; otherwise this equation ﬁtted well with other samples, with R 2 0.99. The Zimny version was also found to ﬁt all samples, with R 2 0.99, except for the activated carbon sample, AC. However, only the CIMF model exhibited R 2 0.995 between the experimental and ﬁtted isotherms for all samples regardless of nanotubes or activated carbons. This observation indicated that the critical size of water clusters entering into the micropore (i.e., parameter m) is an important variable that had been kept ﬁxed in equations other than the CIMF model. The comparison of S 0 values with the I D / I G ratios of the respective samples clearly indicated that the Lagorsse version and the CIMF model were more compatible than the Zimny version (Fig. 4a). Furthermore, since it was known that the sample SWNT4

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Fig. 3. Water vapor adsorption isotherms and ﬁts to the Lagorsse et al. equation [20], the Zimny et al. equation [21], and the CIMF model [22] for carbon nanotube samples (a) SWNT1, (b) SWNT2, (c) SWNT3, and (d) SWNT4, and activated carbon (e) AC and (f) ACF10.

was extremely hydrophilic, it is obvious that the S 0 values of this sample should be greater that those of other SWNT samples irrespective of the isotherm model used in its calculation. This secondary criterion was fulﬁlled by all isotherm models reported in Fig. 1. However, here only the CIMF model seems to follow this additional criterion. Upon comparing the sample micropore volumes by water and N2 , and applying the condition C μs < C μN2 , the Lagorsse version and the CIMF model were again found to be more compatible than the Zimny version (Fig. 4b). However, when the water micropore volume of the sample SWNT4 was calculated from Zimny’s version, it was found to be negligible, which is an unrealistic result, as this sample contained the same pore sizes as in sample SWNT3 but a much higher concentration of hydrophilic

functional groups that might block N2 molecules but should facilitate some water molecules entering into the micropores. Therefore, overall the CIMF model by Marban and Fuertes [22] was found to be the most applicable and most informative model to interpret the water isotherm data collected for SWNTs. 3.3. Analysis of water–SWNT isotherms by the CIMF model The ﬁt to the CIMF model and the water adsorption isotherms of SWNTs and activated carbon samples is presented in Fig. 5. The ﬁtting parameters are presented in Table 2. Also presented in Fig. 5 are the calculated isotherms for water adsorption on the surface functional groups and in the micropores. The total ﬁtted isotherm

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Table 2 Fitting parameters from the CIMF model Adsorbent

S0 (mmol/g)

C μs (cm3 /g)

Kf

Kμ

n

m

SWNT1

0.17 (0.15–0.19) 1.09 (1.03–1.16) 0.94 (0.83–1.06) 1.99 (1.86–2.12) 2.90 (2.44–3.34) 0.32 (0.1–0.5)

0.08 (0.07–0.08) 0.02 (0.01–0.02) 0.06 (0.05–0.07) 0.04 (0.04–0.05) 0.10 (0.03–0.15) 0.21 (0.20–0.22)

2 (1–3) 1 (1.0–1.1) 2 (1.4–2.8) 13 (11.7–16) 2 (1.2–2.8) 122 (12–232)

6999 (5000–9000) 70 (40–100) 1744 (1200–2200) 8 (5.8–11.6) 7 (1–14) 3099 (1773–4446)

14

12.8 (11.6–13.3) 4.6 (2.8–6.3) 10.4 (7.8–12) 3.1 (2.8–3.4) 3.2 (2.2–4.2) 9.6 (8.1–11.1)

SWNT2 SWNT3 SWNT4 AC ACF10

8 11 4 9 10

Note. The range in parentheses is the 90% conﬁdence interval. The median of this range is presented as the ﬁtting parameter.

Fig. 4. (a) Trends in surface chemistry estimated from water adsorption as ﬁtting parameter, S 0 , and experimentally determined from Raman scattering of samples. The I D / I G ratio is reproduced from Fig. 2 for clarity. (b) Trends in micropore volume calculated from water adsorption as ﬁtting parameter, C μs , and experimentally determined from standard N2 adsorption at 77 K, C μN2 . In the legend, La = ﬁt to the Lagorsse et al. version [20], Eq. (5); Zi = ﬁt to the Zimny et al. version [21], Eq. (6); and CI = ﬁt to the CIMF model by Marban and Fuertes [22], Eq. (7). Notice that the C μs for sample SWNT4 should be non zero and larger than the N2 micropore volume.

is the sum of these two individual isotherms and is found to be almost perfectly overlapping the experimental data regardless of the sample type. It is observed that the highly hydrophilic samples such as SWNT4 had a much higher fraction of water uptake by the functional groups. Similarly, extremely hydrophobic samples such as SWNT1 and ACF10 exhibited a much lower contribution of adsorption on functional groups. To further explore the accuracy of the deconvoluted isotherms, we conducted additional water adsorption experiments on samples SWNT3 and SWNT4 after reducing the concentration of their surface functional groups by heat-treating these samples in vacuum at 600 ◦ C. These additional isotherms are also presented in Fig. 5. As expected, the water uptake decreased upon heat treatment for both samples due to loss of surface functionality. Furthermore, the appearance of a type V characteristic became more obvious upon heat treatment, and most importantly, the experimental isotherms of heat-treated samples now very closely followed the micropore-ﬁlling contribution of the total isotherms of untreated samples predicted from the CIMF model. This suggests that heat treatment must have removed a large fraction of surface functional groups. Therefore, the CIMF model is most suitable for deconvoluting an experimental water– SWNT adsorption isotherm with great accuracy. In general, the curve of water adsorption by functional groups appeared to monotonically increase until approximately P / P 0 = 0.6 and then rise up sharply. This behavior corresponds with the characteristic type III isotherm and is associated with growth and accumulation of water clusters around the functional groups on

a nonporous carbon [33]. The adsorption capacity attributable to the functional groups appeared to be directly related to the hydrophilicity of the samples. The effect of hydrophilicity was also observed in the micropore-ﬁlling isotherm such that the samples with a higher degree of functionalization (i.e., higher S 0 values in Table 2) exhibited a left-hand shift in the micropore-ﬁlling isotherm. In other words, a higher degree of hydrophilicity not only caused more water uptake by the functional groups but also facilitated micropore ﬁlling at a lower vapor concentrations. The comparison of equilibrium rate constants for the majority of SWNT samples indicated a signiﬁcantly higher value of rate constants for adsorption in micropores than for adsorption on functional groups (K μ K f ), which supports the observation that at any given concentration of water vapor, adsorption in micropores is signiﬁcantly higher than that on functional groups. We also found that the ﬁtting parameters could be related to the physical and chemical properties of the samples. The number of water molecules in a cluster grown on the functional groups and of those ﬁlling the micropores (i.e., parameters n and m) were found to follow trends opposite to the I D / I G ratio in the Raman spectra of the sample (Fig. 6a). For example, the sample SWNT1 exhibited the highest n and m values of 14 and 12.8, respectively, which should correspond to a cluster 0.8 to 0.9 nm wide. This sample is known to be extremely hydrophobic, as evidenced by a very low I D / I G ratio in its Raman spectra and further supported by the lowest value of the S 0 parameter among all samples. On the other hand, for sample SWNT4 the n and m parameters were 4 and 3.1, respectively, which corresponded to a cluster size smaller than 0.6 nm, which has been reported in the literature [31]. This sample is extremely hydrophilic, as indicated from a high I D / I G ratio in its Raman spectra as well as a large value of the S 0 parameter. Therefore, we can conclude that a higher concentration of oxidation groups will result in the formation of a larger quantity of smaller clusters of water molecules on both functional groups as well as in micropores. This conclusion is not unrealistic if one were to assume that the majority of oxidation groups would exist on the pore entry as opposed to on the SWNT surface, and therefore, would constrict the pore opening, resulting in the pore appearing smaller in width. Our observation is consistent with that from molecular simulations, where the cluster size was found dependent on the hydrophobicity of the nanopores [31]. It was also noticed that the sample-to-sample trends of the I D / I G ratio and the same for the S 0 parameter were directly related. This indicated that trends in the global surface chemistry by Raman scattering experiments can indeed be extended to the hydrophilic component of the total surface chemistry estimated from data ﬁtting. Furthermore, the values of the m parameter were found to be somewhat directly related to the dominant or the

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Fig. 5. Water vapor adsorption isotherms and ﬁts to the CIMF models for carbon nanotube samples (a) SWNT1, (b) SWNT2, (c) SWNT3, and (d) SWNT4, and activated carbon (e) AC and (f) ACF10. Notice that the isotherms for samples heat treated at 600 ◦ C under vacuum (+) are lower than the original isotherms, follow type V characteristics, and more closely resemble the micropore-ﬁlling component of the total isotherm ﬁtted to CIMF model.

average pore size in the adsorbent (Fig. 6b), which is an obvious result, as wider pores should facilitate adsorption of larger clusters of water molecules so long as the concentration of the functional groups blocking the pores is not excessive. We noticed that for any given sample, the m values were also directly related to the difference in the micropore volumes by N2 and water adsorption (i.e., C μN2 − C μs ) (Fig. 6b). Larger differences in micropore volumes were observed for samples with higher m values. This is a realistic observation, as larger clusters will ﬁll the pores more incompletely than smaller clusters, thus exhibiting more deviant values of a sample’s micropore volume from water adsorption.

4. Conclusions We have applied to the water adsorption isotherms of singlewalled carbon nanotubes (SWNT) several semiempirical equations that were originally developed to interpret the adsorption isotherms of water on common carbonaceous materials. The applicability of each model was evaluated by a high correlation coeﬃcient of R 2 > 0.99, and the physical signiﬁcance of ﬁtting parameters such as the concentration of functional groups must relate to the D/G intensity ratio in the Raman spectra of the sample, the water adsorption micropore volume should be lower than that by standard N2 adsorption at 77 K, and the size of water

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Fig. 6. (a) Trends in the number of water molecules in clusters on functional groups (n) and clusters migrating into the micropores (m) as predicted from the CIMF model, and inverse trends observed in the samples’ chemistry analyzed from Raman scattering and S 0 parameter that quantiﬁes the hydrophilicity of the sample. The I D / I G ratio is reproduced from Fig. 2 for clarity. (b) Trends in values of m parameter, physical pore size from Table 1, and micropore volume remaining unﬁlled by water molecules.

clusters should be relatable to the average pore size. We conclude that the D.D. Do equation modiﬁed by Marban and Fuertes [22] is one of the most suitable equations for predicting from SWNTs’ experimental isotherms alone the size of water clusters facilitating adsorption, deconvoluting experimental isotherms into individual contributions from hydrophilic groups and ﬁlling of micropores, quantifying the concentration of hydrophilic functional groups, and determining the micropore volume. The ﬁndings from this research should be useful in supporting molecular simulation studies of water adsorption in SWNTs, which remains the most popular approach for understanding the microscopic behavior of water in nanocarbons. Supplementary material The online version of this article contains additional supplementary material. Please visit DOI: 10.1016/j.jcis.2008.06.002. References [1] Y. Saito, S. Uemura, Carbon 38 (2000) 169. [2] E. Frackowiak, F. Beguin, Carbon 40 (2002) 1775. [3] L.A. Gevorgian, K.A. Ispirian, R.K. Ispirian, Nucl. Instrum. Methods Phys. Res. Sect. B 145 (1998) 155. [4] S. Agnihotri, J.P.B. Mota, M. Rostam-Abadi, M.J. Rood, Carbon 44 (2006) 2376. [5] K. Koga, G.T. Gao, H. Tanaka, X.C. Zeng, Physica A 314 (2002) 462. [6] A. Waghe, J.C. Rasaiah, G. Hummer, J. Chem. Phys. 117 (2002) 10789. [7] A. Striolo, A.A. Chialvo, K.E. Gubbins, P.T. Cummings, J. Chem. Phys. 122 (2005) 234712.

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