Water at Curved Carbon Surface: Mechanisms of Adsorption

Article pubs.acs.org/JPCC

Water at Curved Carbon Surface: Mechanisms of Adsorption Revealed by First Calorimetric Study Sylwester Furmaniak,† Marek Wiśniewski,†,‡ Karolina Werengowska-Ciećwierz,† Artur P. Terzyk,*,† Kenji Hata,§ Piotr A. Gauden,† Piotr Kowalczyk,∥ and Mirosław Szybowicz⊥ †

Physicochemistry of Carbon Materials Research Group, Faculty of Chemistry, Nicolaus Copernicus University in Toruń, 7 Gagarin Street, 87-100 Toruń, Poland ‡ INVEST-TECH R&D Center, 32-34 Plaska Street, 87-100 Toruń, Poland § Nanotube Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan ∥ School of Engineering and Information Technology, Murdoch University, Murdoch, Western Australia 6150, Australia ⊥ Chair of Optical Spectroscopy, Faculty of Technical Physics, Poznań University of Technology, Piotrowo 3, 60-965 Poznań, Poland S Supporting Information *

ABSTRACT: Water adsorption isotherms and calorimetrically measured enthalpy of this process are reported for a series of modified chemically single and multiwalled nanotubes. On the basis of calorimetric measurements, entropy of adsorption is calculated and discussed. Next the data are described using popular models of adsorption, and finally a new approach for simultaneous description of water adsorption and enthalpy of this process is discussed. On the basis of the results of this model, four different possible mechanisms of water adsorption in nanotubes are proposed.

1. INTRODUCTION Although theoretical and experimental studies on behavior of water confined in pores of different geometries have been widely reported,1−11 the studies reporting (measured simultaneously) adsorption isotherms and the enthalpy of water adsorption on nanotubes have been reported relatively rarely. Experimental results of water adsorption on nanotubes usually reveal the isotherms of type V following the IUPAC classification.12 The description of adsorption data using theoretical models proposed by Do and Do13 (DD), Dubinin and Serpinski14 (DS), and others leads to the conclusion that each isotherm has two points of inflection, dividing the data into three regions: water uptake on primary adsorption sites, simultaneous water adsorption by capillary condensation (and on functional groups), and pore saturation.12 It is assumed that the first point of inflection occurs after saturation of hydrophilic functional groups, and further increase in water vapor concentration results migration of water clusters into the pores and the initiation of capillary condensation process. It is important to point out that the initial shape of water adsorption isotherm in nanotubes cannot be necessarily determined only by the interactions with oxygen surface groups. Wang et al.15 © 2015 American Chemical Society

showed that in narrow nanotubes the temperature change in the shape of water adsorption isotherms can be caused by the temperature-dependent hydrophilic−hydrophobic transition. Their results prove that the “hydrophobicity” should not be considered as an absolute property, but it also depends on the structure of confined water, and this is a fundamental statement. Authors of ref 12 also showed that the relative pressure, at which inflection on isotherm occurs, is inversely related to the ID/IG ratio (the intensities of “disordered” and “graphitic” carbons detected from Raman spectroscopy). In their opinion increasing the ID/IG value also reflects increasing hydrophilicity. They additionally observed the similarity of trends in the values of the DD model parameter a0 and the p/p0 at inflection on water adsorption isotherm. Similar conclusions were given in the paper by Kim and Agnihorti,16 reporting the applicability of DS and different modifications of the DD equation for data of water adsorption on carbon nanotubes. The same group17 calculated the isosteric enthalpy of water Received: December 12, 2014 Revised: January 12, 2015 Published: January 13, 2015 2703

DOI: 10.1021/jp512383g J. Phys. Chem. C 2015, 119, 2703−2715

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The Journal of Physical Chemistry C

CVD) method. Briefly, ethylene was used as the carbon source with a ppm level of water on Fe/alumina catalysts to grow vertical aligned SWNT forests with a diameter of around 3.0 nm and with carbon purity above 99%.22−26 (b) A0-o Series. Commercial, high-purity, open, single-walled nanotubes from Nanostructured & Amorphous Materials, Inc. (Houston, TX, USA) were investigated (labeled as A0-o). They were hydrothermally oxidized in concentrated 30% H2O2 at temperatures 453 and 473 K (for details see ref 27). The labeling of the samples is A0-o-XXX where XXX denotes the temperature in K. (c) B_MWNT Series. Multiwalled carbon nanotubes (Baytubes C150HP) were purchased from Bayer Material Science (Germany) and used without further purification. Nanotube samples were oxidized in concentrated nitric acid for 2 and 7 h at 398 K (for details see ref 28). Obtained materials are denoted B_MWNT_xh, where x means the duration of the process in hours. The pristine sample (B_MWNT_0 h) was used as a reference. Table 1 collects the basic characteristics of all the considered nanotube samples, and Figure 1 shows selected SEM/TEM images.

adsorption, and the values in the range 46−58 kJ/mol were obtained. It was concluded that the heat of adsorption is inversely related to the size of water clusters, and the parameters responsible for concentration of surface functional groups are related to the total oxygen content. Considering the possible centers of water molecules interactions with surface oxygen groups, Picaud et al.18 (using MD simulation) showed that the crucial types of interactions during water adsorption are water−water and water−surface carboxylic groups (the energy of interactions is about −38 kJ/mol; two hydrogen bonds are formed). Larger density of carboxylic groups leads to the preferring of water−carboxylic groups interactions over water−water ones. In contrast, water− surface hydroxyls interactions seem to be relatively weak. The DFT calculations performed by Oubal et al.19 suggest the possibility of water chemisorption on carbon surface defective sites, leading to the creation of “ketone-like” structures playing as adsorption centers for subsequent water molecules. GCMC simulation results obtained by Striolo et al.20 suggest the values of the enthalpy of water adsorption inside nanotubes in the range 10−60 kJ/mol and the progressive rise in the enthalpy with increasing equilibrium pressure of water. These authors also calculated (from the GCMC simulation results) the values of the isosteric enthalpy of water adsorption on a series of carbon nanotubes.21 It was noticed that with the decrease in tube diameter the enthalpy of adsorption at small fillings becomes little exothermic than for wider nanotubes. Hyperbolic-like shapes of curves were recorded. From this short introduction one can conclude that, to our knowledge, the calorimetric results of water adsorption on carbon nanotubes have not been recorded yet, and this is the first report showing (determined simultaneously) adsorption and calorimetric data. We consider the effect of surface nature of nanotubes and the influence of chemical oxidation of carbon nanotubes on the calorimetric enthalpy of adsorption. To do this, two series of chemically modified single- and multiwalled nanotubes are studied. Additionally we report the data measured for vertically aligned carbon nanotube forest. Measured data are applied for the calculation of differential entropy of adsorption, for discussion on adsorption mechanism, and for checking the applicability of different popular and recently applied models for simultaneous description of water isotherm and enthalpy of adsorption. Simultaneous description of adsorption (and related enthalpy) is necessary because it is well-known that adsorption isotherm, as a measure of the changes in chemical potential of gas during conversion from gaseous to adsorbed phase, is a Legendre transform of enthalpy and entropy. This is why sometimes single adsorption isotherm can be successfully described by different, even contradictory, models. It means that satisfactory description of isotherms (with omission of enthalpy) is a necessary (but not sufficient) condition of the applicability of a model. Finally, a new approach making possible the simultaneous description of water isotherm and enthalpy data measured for adsorption on nanotubes is introduced and discussed. All reported data make possible the formulation of the mechanism of adsorption on curved carbon surface.

Table 1. Basic Characteristics of All Studied Nanotube Samples: BET Surface Area (SBET) Calculated from LowTemperature Nitrogen Adsorption, Oxygen Content from Elemental Analysis, and ID/IG from Raman Analysis

2. MATERIALS AND METHODS 2.1. Carbon Nanotubes. We used three types of carbon nanotubes. (a) CNF. The single-walled carbon nanotubes were synthesized by water-assisted CVD (so-called supergrowth

sample

BET surface area SBET, m2/g

oxygen content {O}, %

ID/IG

CNF A0-o A0-o-453 A0-o-473 B_MWNT_0h B_MWNT_2h B_MWNT_7h

1092.0 554.0 550.3 466.2 198.4 242.4 264.5

2.32 6.38 5.86 6.11 0.29 6.21 10.34

0.140 0.031 0.020 0.017 2.100 2.270 2.410

Figure 1. SEM/TEM images of studied nanotubes. 2704


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The Journal of Physical Chemistry C 2.2. Applied Measurement Techniques. In order to characterize the structure of pristine and oxidized carbon nanotube samples, N2 adsorption isotherms at 77 K were measured using ASAP 2010 (Micromeritics) sorption apparatus. High-resolution transmission electron microscopy (HRTEM) images were taken using a transmission electron microscope F20X-TWIN (FEI-Tecnai) operated at 200 kV. The chemical composition of samples was characterized by the elemental analyzer Vario Macro CHN (ELEMENTAR Analysensysteme GmbH, Germany). The nonpolarized Raman scattering spectra of carbon structures were investigated in the spectral range of 100−3600 cm−1. Raman spectra were recorded in the backscattering geometry using inVia Renishaw micro-Raman system. As an excitation light we used the near-infrared laser operating at 785 nm. The laser beam was tightly focused on the sample surface through a Leica 50x LWD microscope objective (LWD-long working distance) with numerical aperture (NA) equal to 0.5, leading to a laser beam diameter of about 2 μm. To prevent any damage to the sample, an excitation power was fixed at 1 mW. The position of the microscope objective with respect to the sample was piezoelectrically controlled (XY position). The reference position (level 0) was assumed for the laser spot focused on the surface of the sample. The inVia Raman spectrometer allowed for recording of the Raman spectra with spatial resolution of about 2 μm and spectral resolution about 2 cm−1. To increase the signal-to-noise ratio, accumulation of Raman spectra was made 50 times. Water adsorption isotherms were measured volumetrically at 298 K, and differential enthalpy of adsorption (qdiff) was determined at the same temperature using a Tian−Calvet isothermal microcalorimeter described in detail previously.28−31 2.3. Theoretical Models. Similar to other authors12,15,16 to describe water adsorption isotherms, we used the DD model in the generalized form proposed by Neitsch et al.32 The authors assumed that the number of water molecules forming clusters filling pores is the best fit parameter. The equation of isotherm, using this approach, may be written as33 N

a=

a0K f ∑i = 1 ihi N

1 + K f ∑i = 1 hi

+

multilayer. The GDW adsorption isotherm equation may be written in the form30 a=

(2)

where am is the concentration of primary adsorption sites, KL and c are the equilibrium constants connected with adsorption on primary and secondary centers, respectively, and w is the parameter determining the ratio of molecules bound to the primary centers and converted into secondary ones. We also proposed the so-called multisite GDW (MSGDW) model.30 This approach takes into account the presence of different types of primary centers on adsorbent surface, i.e., surface heterogeneity. This modification makes it possible to generate different shapes of observed experimentally adsorption enthalpy curves (not only monotonic but also steplike or wavelike); see ref 30. The effects connected with heterogeneity in MSGDW approach are visible only for low loadings (usually in a submonolayer region of isotherm), while the analysis of enthalpy curves related to H2O adsorption on considered in this work nanotube samples (see below) suggests that effects related to heterogeneity appear in some cases not only in monolayer region but also at higher loadings. Thus, in this study we propose to take into account not only heterogeneity of the primary sites but also the heterogeneity of the secondary ones. So this approach may be called “double heterogeneous GDW” (dh-GDW) model. Similarly as in the MSGDW in the first step adsorption takes place on Nprim types of primary sites (concentration of each type is denoted as am,i). Molecules bound to these centers may create Nsec types of secondary sites. These assumptions together with other characteristics of original GDW model30 make it possible to formulate the dh-GDW adsorption isotherm equation as ⎛ Nprim a K h ⎞⎛ m,i L ,i ⎟⎜1 + a = ⎜⎜ ∑ ⎟⎜ 1 K h + L , i ⎝ i=1 ⎠⎝

Nsec

∑ j=1

⎞ cjwh j ⎟ 1 − cjh ⎟⎠

(3)

where KL,i and cj are the equilibrium constants related to adsorption on ith type of primary and jth type of secondary centers, respectively, and wj is the parameter determining what part of H2O molecules adsorbed on all the kinds of primary sites converts into the jth kind of secondary ones. Since the dh-GDW model (similar to its precursors, i.e., the GDW and MSGDW approaches) has strong thermodynamic basis,30 it is possible to generate the isosteric enthalpy of adsorption formula related to this equation. It requires defining the relations describing the temperature dependence of adsorption isotherm parameters. As previously,30 we assume that am,i and wj parameters are temperature-independent, while the equilibrium constants decrease with the rise in T according to the basic thermodynamic formulas (for details see ref 30 and references therein):

aμsKμhm 1 + Kμhm

amKLh 1 − c(1 − w)h 1 + KLh 1 − ch

(1)

where a is adsorption amount, h is relative H2O pressure (equal to p/ps where p and ps are the equilibrium and the saturation vapor pressure at given temperature, respectively), a0 is the concentration of surface active groups, aμs is the saturation concentration of water in pores, K f and K μ are the chemisorption and micropore equilibrium constants, respectively, N is the maximal size of vertical complex forming by H2O molecules bound to the surface centers, and m is the (average) size of water clusters in pores. Previously, in our group another theoretical approach for modeling of water adsorption was proposed. This model, called generalized D’Arcy and Watt (GDW) equation,30 was successfully used for description of water sorption isotherms on materials of different origin.30,34−36 It is especially useful in the case of isotherms of the II or III type of IUPAC classification. The GDW model similarly assumes a two-step mechanism of adsorption process.30 At the first step, water molecules are bound by primary adsorption sites of surface. H2O molecules bounded to these centers become the secondary ones allowing adsorption of next molecules in

⎡ Q prim, i − L ⎤ ⎥ KL , i = K L0, i exp⎢ RT ⎣ ⎦

(4)

⎡ Q sec, j − L ⎤ ⎥ cj = c j0 exp⎢ ⎦ ⎣ RT

(5)

K0L,i

c0j

where and are almost temperature independent preexponential factors, Qprim,i and Qsec,j are the enthalpy values of adsorption on ith kind of primary sites and jth kind of 2705


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The Journal of Physical Chemistry C secondary ones, respectively, L is enthalpy of water condensation, and R is the universal gas constant. Using the differential calculus and combining eqs 3−5, the following expression describing the isosteric adsorption enthalpy (qst) is derived (for general method of derivation see, for example, refs 30 and 37): ⎧⎛ Nprim ⎞⎛ ⎪ am , iKL , i ⎟⎜1 + q = ⎨⎜⎜ ∑ Q ⎪⎝ i = 1 (1 + KL , ih)2 prim, i⎟⎠⎜⎝ ⎩ st

Nsec

∑ j=1

used the well-known relation between differential and isosteric enthalpy of adsorption:39 qdiff = qst − RT

In addition, we defined the goodness of enthalpy fit (similarly as in eqs 8 and 9):

⎞ cjwh j ⎟ 1 − cjh ⎟⎠

DCq = 1 − ηq

Nsec

∑ j=1

NP

ηq =

qdiff − L p − R ln + R T ps

NP

diff diff 2 ∑i = 1q (qexp, − qtheo ̅ ) i

DC = 1 −

(12)

ηiz ηq

(13)

For each system we checked different combination of the primary and secondary numbers (Nprim = 2 or 3 and Nsec = 1 or 2) and the smallest values giving satisfactory fit quality were chosen.

(6)

The change in the values of differential entropy of adsorption (ΔSdiff) was calculated taking into account the vapor at saturated vapor pressure (ps) as the reference state and the expression describing the Gibbs free enthalpy: ΔS diff = −

diff diff 2 ∑i = 1q (qexp, ) − qtheo, i i

Notation in eq 12 is analogical as in eq 9. The global parameter representing the goodness of fit of both adsorption and enthalpy was defined as (geometric mean)

⎞ cjwh j ⎟ 1 − cjh ⎟⎠

⎫ ⎛ Nprim a K h ⎞ Nsec cjwj ⎪ m,i L ,i ⎟∑ ⎬ + ⎜⎜ ∑ ⎟ 2 ⎝ i = 1 1 + KL , ih ⎠ j = 1 (1 − cjh) ⎪ ⎭

(11)

where

⎫ ⎛ Nprim a K h ⎞ Nsec cjwj ⎪ m,i L ,i ⎜ ⎟ Q sec, j⎬ + ⎜∑ ∑ 2 ⎟ ⎪ ⎝ i = 1 1 + KL , ih ⎠ j = 1 (1 − cjh) ⎭ ⎧⎛ Nprim ⎪ am , iKL , i ⎞⎛ ⎟⎜1 + ⎨⎜⎜ ∑ ⎪⎝ i = 1 (1 + KL , ih)2 ⎟⎠⎜⎝ ⎩

(10)

3. RESULTS AND DISCUSSION Figure 2 collects low-temperature nitrogen adsorption data on studied nanotube samples. One can see that all adsorption

(7)

where L is the enthalpy of water condensation at measurement temperature (−43.96 kJ/mol). 2.4. Experimental Data Fitting. During the fitting of experimental data by theoretical equations we use the genetic algorithm proposed by Storn and Price.38 This procedure was previously successfully applied for description of different data sets (see, for example, refs 30 and 34−37). First we fitted only adsorption isotherms by DD and GDW models, as it is usually done in different papers reporting water adsorption results. The best fit parameters are a0, Kf, N, aμs, Kμ, and m (DD) and am, KL, c, and w (GDW). In the case of DD model one additional constrain equation was necessary according to the mechanism assumed by this approach (the size of vertical complex should be larger than the number of molecules forming clusters): N + 1 ≥ [m] (where [m] denotes the largest integer number not lower than m). The goodness of fit of each isotherm was estimated using the determination coefficient: DCiz = 1 − ηiz

(8) Figure 2. Comparison of N2 adsorption−desorption isotherms (at T = 77 K) on all the considered nanotube samples. The subsequent curves are shifted by 1550 (CNF), 1350 (A0-o), 1150 (A0-o-453), 950 (A0-o-473), 450 (B_MWNT_0h), 150 (B_MWNT_2h), and 0 (B_MWNT_7h) units, respectively.

where NP

ηiz =

∑i = 1iz (aexp, i − a theo, i)2 NP

2 ∑i = 1iz (aexp, i − aexp ̅ )

(9)

aexp,i and atheo,i are experimental and theoretically predicted values of adsorption amount for the ith point of isotherm, ae̅ xp is the average experimental adsorption amount, and NPiz is the number of points. Next we fitted simultaneously the isotherms and related enthalpy of adsorption by the dh-GDW-model (eqs 3 and 6). To do this, it is necessary to define the relation between experimentally measured differential enthalpy of adsorption (qdiff) and theoretically calculated isosteric enthalpy value. We

isotherms are of type IV of IUPAC classification; thus, they are typical for mesoporous solids. The results collected in Table 1 show that the BET surface area is the largest for CNF, and it is almost 2 times larger than for A0-o samples and almost 4 times larger than for B_MWNT materials. Two effects can be visible if the influence of oxidation is discussed; namely, for A0-o samples the decrease in BET surface area value is seen with the rise in oxidation temperature (especially visible for tubes A0-o-473). In contrast, for B_MWNT we see the progressive 2706


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Figure 3. Comparison of experimental H2O adsorption isotherms (at T = 298 K) and related differential enthalpy of adsorption for all the considered carbon nanotubes samples.

Figure 4. Comparison of differential enthalpy of adsorption for all the considered systems plotted as the function of relative pressure in logarithmic scale. The dashed line represents enthalpy of water condensation.

Adsorption isotherms and calorimetrically determined enthalpy of adsorption values are collected in Figure 3. All water adsorption isotherms are of type II following IUPAC classification. At low loadings adsorption increases in the order: B_MWNT_0h < B_MWNT_2h < A0-o = A0-o-453 < A0-o-473 < B_MWNT_7h = CNF. One can see that there is no relation between water adsorption at low pressure and the value of BET surface area. Moreover, also the oxygen content is not crucial in the adsorption abilities toward water. CNF and B_MWNT_7h adsorb the largest amount of water. As it will be shown below, adsorption properties toward water are determined by the concentration of surface primary adsorption

development of surface area with the rise in oxidation degree. Thus, it can be expected that in the case of A0-o single-walled nanotubes during a gentle hydrothermal oxidation process, with the rise in oxidation temperature we observe only purification of nanotubes (Table 1), while for B_MWNT, oxidation (with strong oxidizing agent) causes the appearance of surface defects and development of specific surface area is observed. At the same time in the case of B_MWNT tubes one can observe the linear dependence between ID/IG and oxygen content, meaning that the introduction of oxygen destroys graphitic surface of nanotubes. For A0 tubes, however, this ratio decreases, but at the same time the oxygen content is almost constant. 2707


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Figure 5. Comparison of the changes in differential entropy of adsorption for all systems (eq 7). The dashed line represents the ΔS = 0 (it means that the adsorbed phase has the entropy of liquid).

centers obtained from the fitting of the dh-GDW model introduced in this study. 3.1. Enthalpy and Entropy of Adsorption. In Figure 3 one can observe interesting effects if the differential heat of adsorption is considered. For all studied systems the plots start from relatively low values; however, for one system (CNF) enthalpy starts from extremely low values close to zero. The similarities in shapes of enthalpy can be strongly pronounced if we consider the plots of enthalpy as a function of logarithm of relative pressure (Figure 4). Generally the shapes of heat of adsorption plotted in this way are similar to those reported from GCMC simulations.20,21 For all the systems at low pressures the rise in enthalpy value is seen (it remains constant and very small for CNF) up to the specific value. Considering the behavior at larger pressures, enthalpy plots are divided into two groups. For two nanotubes the heat of adsorption decreases after reaching a maximum (B_MWNT_7h and B_MWNT_2h), and for the remaining systems it increases. For the both groups the decrease (down) and/or increase (up) to the heat of water condensation is recorded. The decrease is observed for multiwalled and strongly oxidized nanotubes. Thus, in our opinion the plot of the heat of adsorption for CNF suggests that water molecules are accumulated in nanotubes and the enthalpy of this process is very small. Thus, in this case, the entropic term dominates, and since the adsorption process is spontaneous, water molecules increase their entropy in comparison to the vapor. This may suggest the breaking of hydrogen bonds present in vapor and adsorption of isolated water molecules. Since with the rise in pressure the number of water molecules in tube channels increases, they finally condense. CNF is composed of very long nanotubes of millimeter length;22−26 therefore, it is necessary to increase the pressure remarkably to observe condensation. Extremely low heat of adsorption observed for this case can be additionally powered by well documented hydrophobic nature of carbon nanotubes40 and even superhydrophobic nature of CNF, proved many times,41,42 and this property leads to the socalled “Lotus effect” and self-cleaning properties of nanotube forests. In contrast, for the remaining nanotubes enthalpy of adsorption is larger (if absolute values are considered) and the rise in enthalpy at small pressures is caused by filling of internal tube channels. The decrease observed after filling of channels can be caused by adsorption on active sites and partial water condensation in surface cracks and slits produced by oxidation of multiwalled nanotubes. This is why in this case the enthalpy

of water adsorption is larger than the enthalpy of condensation. In contrast, since in the case of single walled nanotubes the amount of disordered carbon is smaller (see Table 1), the enthalpy rises up to the enthalpy of condensation because only surface clusters of water around groups are created. The detailed analysis of proposed mechanisms will be given below. Suggested mechanisms can be confirmed by analysis of the changes in differential entropy of adsorption shown in Figure 5. For all the nanotubes at low adsorption values we observe entropy higher than for saturated vapor. For CNF this entropy does not reach the entropy of liquid water, and the adsorbed phase resembles overheated liquid. In contrast to A0, as well as B_MWNT nanotubes at higher loadings, the entropy of adsorbed phase is close to the liquid. 3.2. Fitting of Experimental Data Using Water Adsorption Models: A New Concept. Figure S1 in Supporting Information presents the results of H2O adsorption isotherms (on all considered samples) fitting by the DD model (eq 1, blue lines) and Table S1 in Supporting Information collects obtained values of the best-fit parameters. The quality of the fit seems to be satisfactory (high values (>0.99) of determination coefficients). However, in at least two cases (i.e., samples A0-o-453 and A0-o-473) the DD model predicts a different type of isotherm (i.e., type III) than that observed experimentally (i.e., type II). Moreover, analyzing the values of m parameter listed in Table S1 in Supporting Information, one can see that for five systems these values are relatively high (in the range 40.00−136.3). Since this parameter is interpreted as the (average) size of water clusters filling the pores, obtained values seem to be unphysical. In addition, in some cases also other parameters connected with the second term in DD model (i.e., aμs and Kμ) have extremely high values. Figure S1 in Supporting Information may be helpful in explanation of observed unphysical values of these parameters (m, aμs, and Kμ). This figure additionally presents the contributions of both terms of eq 1 to the total isotherm. As one can see, the second term usually contributes significantly to the total adsorption only for high values of pressure. This term according to its mathematical form generates the sigmoid shape of isotherm. However, the final plateau is observed for the pressures above the highest experimentally observed values (vertical dashed lines). So during the fitting the obtained unphysical values of some parameters in DD model are the consequence of the fact that studied isotherms do not belong to the IV or V types 2708


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Figure 6. Results of the fitting of H2O adsorption isotherms on all the considered nanotube samples by the GDW model (eq 2).

refs 13 30, and 33). So if the H2O adsorption isotherms on carbon nanotubes represent the II type, a simplified variant of DD model (eq 14) may be used to fit the data instead full eq 1. On the other hand, as one can see in Figure 6 the GDW model excellently describes all the considered isotherms. Moreover obtained values of the best fit parameters (see Table S3 in Supporting Information) do not exceed the limits resulting from their physical meaning. So in the case of the II type of isotherms, description the GDW model seems to be more useful than the DD one. The expression of GDW equation is simpler, and this equation contains smaller number of the best-fit parameters (4 vs 6). Finally, in Figures 7−9 we show the results of the simultaneous fit of both H2O adsorption isotherms and related enthalpy of adsorption by the dh-GDW model (eqs 3 and 6). Table 2 collects the obtained values of the best-fit parameters (in this table parameters connected with different types of sites are arranged according to decreasing values of KL,i or cj constants). As one can see, the fitting quality is very good and even some nuances detected on the adsorption heat are very well captured by the model. Obtained sets of parameters reflect the differences in the shapes of both curves (a = f(h) and

(which are typically generated by the DD model), but they are of the II type. Since the contributions of the second term in eq 1 are not high (and the values of best-fit parameters connected with them often are unphysical), we decided to check the applicability of simplified variant of DD model without the above-mentioned term in the form N

a=

a0K f ∑i = 1 ihi N

1 + K f ∑i = 1 hi

(14)

Figure S2 in Supporting Information presents the comparison of the experimental isotherms fitting by the full DD model (eq 1) and its simplified version (eq 14), and Table S2 in Supporting Information collects the obtained values of the bestfit parameters. As one can see, both approaches (with the exception of those for the B_MWNT_0h system) give similar fit quality. In the case of eq 14 parameter N (maximal size of vertical complex) quite often reaches its upper limit. This is probably caused by the lack of experimental points for the values of relative pressure very close to 1.0 (i.e., in the range where the N parameter influences the shape of isotherm; see 2709


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qdiff = f(a)). The sums of concentrations of primary centers (∑am,i) and connected with them KL,i constants correspond to the shape of isotherms in the low-pressure region (Langmuirian part). There are two exceptions: the second kind of primary sites for CNF sample and the third kind of these sites for B_MWNT_2h nanotubes. The constants (KL,2 and KL,3) for these centers have values below 1. Therefore, adsorption on those sites has the linear character (reduction of Langmuir equation (see eq S2 in Supporting Information) to the linear Henry’s isotherm) and they are not totally saturated even at high relative pressures. On the other hand, the parameters wj and cj are responsible for the shape of isotherms at higher relative pressures. It is also worth noticing that the dh-GDW model correctly predicts the peaks observed on differential enthalpy of adsorption (Figures 7−9). Since the energy of adsorption on different types of sites (both primary and the secondary ones) is constant, observed changes in qdiff values are the consequence of the difference in contribution of adsorption on individual centers to the total value at different loadings. The contribution of the given site to the total energy (at the given loading) is proportional to the increment in adsorption on this site. The measure of this increment is the derivative of adsorption (on the given center) with respect to relative pressure (dai/dh). Thus, the weights at which the energy of adsorption on individual sites contributes to the total value are equal to the ratio of derivatives of adsorption on each center and of total adsorption: (dai/dh)/(da/dh). So in order to interpret the adsorption mechanism predicted by the dh-GDW model in Figures 10−12, we compare the differential enthalpy of adsorption on all the considered samples with the ratios of derivates of adsorption on individual sites ((dai/dh)/(da/dh)).

Figure 7. Results of simultaneous fitting of H2O adsorption isotherm on CNF sample and related enthalpy adsorption by the dh-GDW model (eqs 3 and 6): points, experimental data; lines, theoretical predictions.

Figure 8. As in Figure 7 but for raw and oxidized A0-o samples. 2710


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Figure 9. As in Figures 7 and 8 but for raw and oxidized B_MWNT samples.

Table 2. Values of the Best-Fit Parameters Obtained from the Simultaneous Fitting of Water Adsorption Isotherms and Related Enthalpy by the dh-GDW Model (Eqs 3 and 6) on All the Studied Carbon Nanotubes Samples Nprim

Nsec

am,i, mmol/g

KL,i

CNF

2

1

A0-o

3

2

A0-o-453

3

2

A0-o-473

3

2

B_MWNT_0h

2

2

B_MWNT_2h

3

1

B_MWNT_7h

3

1

0.9451 5.570 0.1111 0.02712 0.3545 0.1432 0.02168 0.3901 0.1652 0.01053 0.3901 0.02118 0.1050 0.01338 0.09718 0.9223 0.02233 0.03836 1.072

48.23 0.4658 3470 55.60 13.73 6368 82.46 24.47 5697 922.4 70.39 31.75 3.650 1574 57.67 0.8136 1673 444.7 9.233

sample

cj

Qprim,i, kJ/mol

Qsec,j, kJ/mol

DCiz

DCq

0.1618

wj

1.032

30.67

0.9906

0.9978

6.047 × 10−3 2.852

1.065 0.9099

101.3 33.12

0.9993

0.9903

0.03005 2.474

1.161 1.009

98.75 31.54

0.9963

0.9942

0.4145 2.063

1.148 0.9876

56.46 24.33

0.9956

0.9976

0.2441 0.1767 2.748

1.192 0.9826 0.8187

40.95 92.28 46.96

0.9810

0.9947

0.9998

0.9568

3.308

0.6809

2.753 ∼0 13.90 134.6 ∼0 6.395 117.6 ∼0 4.990 142.4 8.342 ∼0 22.58 30.59 62.02 52.89 0.6181 111.2 57.63

47.87

0.9999

0.9693

The mathematical formalism of derivatives calculations is described in Supporting Information. In the case of CNF nanotubes (Figure 10) at low loadings, enthalpy of adsorption is very small. This is connected with adsorption on low-energy primary sites (P1; see Table 2). Next (according to increase in adsorption amounts) the contribution of secondary sites rises, and it is connected with the increase in adsorption enthalpy up to a value related to this type of center. The next figure (Figure 11) presents the data for A0-o samples. Since the curves (adsorption isotherms and related enthalpy) for these nano-

tubes present similar behavior, the dh-GDW model reveals similar mechanism of the process. There are three types of primary sites. The first and third ones have small energy (110 kJ/mol). At very low loadings adsorption on first type of centers dominates and low qdiff values are observed. Next the contribution of the second ones increases, and this is responsible for the observed peaks (the location of these peaks corresponds to the location of maxima on the derivates ratio for this type of sites). Then total energy is 2711


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mainly affected by the contribution from the third (low-energy) centers and enthalpy of adsorption decreases. Finally, the contributions from the secondary sites are revealed (qdiff increases). Since the qdiff values in multilayer adsorption region are not constant, its correct description requires the presence of at least two types of secondary sites with different energies. Increasing contribution from the site having higher energy is responsible for the rise in adsorption enthalpy observed at high loadings. Finally, Figure 12 compares the results for B_MWNT

Figure 10. Comparison of differential enthalpy of H2O adsorption on CNF sample (the experimental and theoretically predicted by the dh-GDW values are shown as points and dashed line, respectively) and ratios of derivative of adsorption on each kind of sites with respect to the relative pressure (dai/dh) to derivative of total adsorption (da/dh). The data are presented as solid lines (Pi and Sj denote the curves connected with adsorption on ith kind of primary centers and jth kind of secondary centers, respectively). The gray vertical dashed line represents the location of maximum on the curve connected with the second type of primary sites.

Figure 12. As in Figures 10 and 11 but for B_MWNT nanotubes.

nanotubes. In the case of B_MWNT_0h sample enthalpy maximum is observed for adsorption amounts originating from multilayer region. Thus, this peak is related to maximum on contributions connected with one of the secondary sites (having higher energy), while the differences in energy of primary centers are responsible for inconstant plot of enthalpy for low loadings. For the other two samples (B_MWNT_2h and B_MWNT_7h) the observed peaks are associated (similarly as for A0-o nanotubes) with the heterogeneity of primary sites. In the case of B_MWNT_2h its location corresponds with maximal contribution of second type of primary sites. This picture is slightly more complicated for

Figure 11. As in Figure 10 but for A0-o nanotubes. The gray vertical dashed lines represent the location of maxima on the individual curves. 2712


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Figure 13. Schematic representation of the successive stages of water adsorption on different kinds of considered nanotubes samples: (A) adsorption inside nanotube channels, (B) adsorption on oxygen-containing groups located at nanotube entrances, (C) adsorption on external surfaces of nanotubes (CI, low-energetic centers; CII, high-energetic centers; CIII, surface defects); D, multilayer adsorption.

A0-o-453, and A0-o-473); (3) raw multiwalled nanotubes, case 3 (B_MWNT_0h); (4) oxidized multiwalled nanotubes, case 4 (B_MWNT_2h and B_MWNT_7h). Figure 13 and Figures S3−S6 in Supporting Information show the differences in the postulated mechanisms of adsorption. Generally, the first step is adsorption on low energetic centers located inside nanotubes (A stage), and this explains the experimentally observed low values of adsorption enthalpy. The only exception is the sample B_MWNT_0h (case 3) which is closed-ended, and the internal space is inaccessible for water. In this case adsorption starts on low-energy centers located on external surfaces of nanotubes, CI (the role of these centers can be played by, for example, hydroxyl groups and/or surface defects), and on surface structural defects, CIII. Next stages are different for different nanotubes. The comparison of adsorption enthalpy for case 1 (mechanically opened nanotubes) and case 2 (single walled Amor nanotubes) shows that for the latter case one can observe the presence of a peak in the range of low coverages. Adsorption on oxygencontaining groups located at nanotube entrances (stage B) is probably responsible for the presence of this peak. This stage is absent for the case of adsorption on CNF, because the mechanical opening of nanotube forests (shearing) does not create surface oxygen functionalities. Next common stage for these nanotubes (case 1 and case 2) is the adsorption on external surfaces, where also because of low enthalpy one can postulate the presence of low-energy centers (CI stage). In contrast, for oxidized multiwalled nanotubes (case 4) also opened but having relatively larger diameter, the presence of the peak caused by interaction of water with groups located at pore entrances is not seen. This effect can be explained by the similar energy of water interaction with groups located at pore entrances and at arbitrary different positions. In this case the surface carboxylic groups play the role of high-energy centers (CII), and this is related to high adsorption enthalpy value. In

B_MWNT_7h nanotubes. Here, the presence and location of maximum on enthalpy are connected not only with high contributions from the high-energy primary sites but also with reduction in contribution from the first ones having low energy. The values of some parameters collected in Table 2 are also related to the properties of considered samples and/or to the changes in properties of nanotubes in series. For example, energies of adsorption on all the primary sites of CNF sample are close to 0. This independently confirms its hydrophobic nature. In the case of A0-o series (raw an oxidized nanotubes) concentration of primary centers and energies connected with them are similar for all the samples because these nanotubes have similar oxygen content (see Table 1) and H2O adsorption isotherms on them have similar shape. The opposite situation occurs for B_MWNT series. Here oxidation of nanotubes is connected with the rise in oxygen content and the appearance of significant differences in shapes of isotherms. This is reflected in systematic changes in dh-GDW model parameters. For the nanotubes in this series (B_MWNT_0h, B_MWNT_2h, and B_MWNT_7h) the total concentration of primary sites (∑am,i) increases. The energy of adsorption connected with the most energetic primary centers (i.e., the second ones) also rises. It is also interesting that oxidation of multiwalled nanotubes not only increases the concentration and energy of primary sites but also causes the increase in the concentration of creating secondary centers (which is reflected by the rise in wj parameter). This may be explained by the fact that a lot of oxygen-containing surface groups are able to form hydrogen bonds with more than one adsorbed water molecule. From Figures 10−12 and from the analysis of entropy of adsorption, it can be seen that similarities are observed in the mechanisms of water adsorption on all studied nanotubes. Taking into account the results of our study, nanotubes can be divided into four groups: (1) carbon nanotube forest, case 1 (CNF sample); (2) single-walled nanotubes, case 2 (A0-o, 2713


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The Journal of Physical Chemistry C this case adsorption can also occur on structural defects (CIII) created after nitric acid treatment. The last common stage for all cases is the polymolecular adsorption (D).

measurements of pore size and pore size distribution. J. Phys. Chem. C 2014, 118, 8474−8480. (6) Yamashita, K.; Daiguji, H. Molecular simulations of water adsorbed on mesoporous silica thin films. J. Phys. Chem. C 2013, 117, 2084−2095. (7) Striolo, A.; Gubbins, K. E.; Chialvo, A. A.; Cummings, P. T. Simulated water adsorption isotherms in carbon nanopores. Mol. Phys. 2004, 102, 243−251. (8) Hantal, G.; Picaud, S.; Hoang, P. N. M.; Voloshin, V. P.; Medvedev, N. N.; Jedlovszky, P. Water adsorption isotherms on porous onionlike carbonaceous particles. Simulations with the grand canonical Monte Carlo method. J. Chem. Phys. 2010, 133, 144702. (9) Horikawa, T.; Sakao, N.; Do, D. D. Effects of temperature on water adsorption on controlled microporous and mesoporous carbonaceous solids. Carbon 2013, 56, 183−192. (10) Gauden, P. A.; Terzyk, A. P.; Pieńkowski, R.; Furmaniak, S.; Wesołowski, R. P.; Kowalczyk, P. Molecular dynamics of zigzag single walled carbon nanotube immersion in water. Phys. Chem. Chem. Phys. 2011, 13, 5621−5629. (11) Ohba, T.; Taira, S.; Hata, K.; Kanoh, H. Mechanism of sequential water transportation by water loading and release in singlewalled carbon nanotubes. J. Phys. Chem. Lett. 2013, 4, 1211−1215. (12) Kim, P.; Zheng, Y.; Agnihotri, S. Adsorption equilibrium and kinetics of water vapor in carbon nanotubes and its comparison with activated carbon. Ind. Eng. Chem. Res. 2008, 47, 3170−3178. (13) Do, D. D.; Do, H. D. A model for water adsorption in activated carbon. Carbon 2000, 38, 767−773. (14) Dubinin, M. M.; Serpinsky, V. V. Isotherm equation for water vapor adsorption by microporous carbonaceous adsorbents. Carbon 1981, 19, 402−403. (15) Wang, H.-J.; Xi, X.-K.; Kleinhammes, A.; Wu, Y. Temperatureinduced hydrophobic-hydrophilic transition observed by water adsorption. Science 2008, 322, 80−83. (16) Kim, P.; Agnihotri, S. Application of water-activated carbon isotherm models to water adsorption isotherms of single-walled carbon nanotubes. J. Colloid Interface Sci. 2008, 325, 64−73. (17) Kim, P.; Meyer, H. M.; Agnihotri, S. Effect of surface oxygen and temperature on external and micropore adsorption of water in single-walled carbon nanotubes by gravimetric and spectroscopic experiments. J. Phys. Chem. C 2009, 113, 12109−12117. (18) Picaud, S.; Collignon, B.; Hoang, P. N. M.; Rayez, J.-C. Adsorption of water molecules on partially oxidized graphite surfaces: a molecular dynamics study of the competition between OH and COOH sites. Phys. Chem. Chem. Phys. 2008, 10, 6998−7009. (19) Oubal, M.; Picaud, S.; Rayez, M.-T.; Rayez, J.-C. Interaction of water molecules with defective carbonaceous clusters: an ab initio study. Surf. Sci. 2010, 604, 1666−1673. (20) Striolo, A.; Gubbins, K. E.; Gruszkiewicz, M. S.; Cole, D. R.; Simonson, J. M.; Chialvo, A. A.; Cummings, P. T.; Burchell, T. D.; More, K. L. Effect of temperature on the adsorption of water in porous carbons. Langmuir 2005, 21, 9457−9467. (21) Striolo, A.; Chialvo, A. A.; Gubbins, K. E.; Cummings, P. T. Water in carbon nanotubes: adsorption isotherms and thermodynamic properties from molecular simulation. J. Chem. Phys. 2005, 122, 234712. (22) Chen, G.; Futaba, D. N.; Kimura, H.; Sakurai, S.; Yumura, M.; Hata, K. Absence of an ideal single-walled carbon nanotube forest structure for thermal and electrical conductivities. ACS Nano 2013, 7, 10218−10224. (23) Sakurai, S.; Inaguma, M.; Futaba, D. N.; Yumura, M.; Hata, K. Diameter and density control of single-walled carbon nanotube forests by modulating Ostwald ripening through decoupling the catalyst formation and growth processes. Small 2013, 9, 3584−3592. (24) Chiang, W.-H.; Futaba, D. N.; Yumura, M.; Hata, K. Direct wall number control of carbon nanotube forests from engineered iron catalysts. J. Nanosci. Nanotechnol. 2013, 13, 2745−2751. (25) Xu, M.; Futaba, D. N.; Yumura, M.; Hata, K. Alignment control of carbon nanotube forest from random to nearly perfectly aligned by utilizing the crowding effect. ACS Nano 2012, 6, 5837−5844.

4. CONCLUSIONS The DD model is hardly applicable for description of water adsorption isotherms of II type, as revealed by the systems studied in this paper. In contrast the GDW model leads to satisfactorily results; moreover, it is mathematically simpler. To obtain satisfactory description of all observed shapes of water adsorption isotherms and especially calorimetrically measured enthalpy of adsorption, the dh-GDW should be applied. All studied systems show the heterogeneity of primarily adsorption centers and additionally the heterogeneity of secondary centers. Obtained sets of parameters of dh-GDW model reflect the experimental differences in the shapes of isotherms and enthalpy of water adsorption on different nanotubes. Obtained parameter values qualitatively correspond to the changes of content of surface oxygen in a given series of nanotubes. The ratio ID/IG is in fact linearly correlated with the content of oxygen for one studied series of multiwalled nanotubes (B_MWNT). For single-walled nanotubes A0 this correlation is not observed. In this case this ratio changes but the oxygen content almost remains constant. On the basis of the results of this paper, four general mechanisms of water adsorption on nanotubes are proposed. The dh-GDW model analysis is a very helpful tool for determination of this mechanism.

■

ASSOCIATED CONTENT

S Supporting Information *

Calculations of derivatives of adsorption on the individual sites; values of the best-fit parameters obtained from the fitting of water adsorption isotherms by the full (Table S1) and simplified (Table S2) DD model and by the GDW model (Table S3); results of the fitting of H2O adsorption isotherms on all the considered nanotube samples by the full (Figure S1) and simplified (Figure S2) DD model; suggested mechanism of adsorption for cases 1−4 (Figures S3−S6). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. URL: http://www.chem.umk. pl/∼aterzyk/. Phone: (+48) (56) 611-43-71. Fax: (+48) (56) 654-24-77. Notes

The authors declare no competing financial interest.

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REFERENCES

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