One-pot titration methodology for the characterization of surface acidic groups on functionalized carbon nanotubes

Carbon 96 (2016) 729e741

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Carbon journal homepage: www.elsevier.com/locate/carbon

One-pot titration methodology for the characterization of surface acidic groups on functionalized carbon nanotubes Yern Seung Kim, Chong Rae Park* Carbon Nanomaterials Design Laboratory, Global Research Laboratory, Research Institute of Advanced Materials, and Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 April 2015 Received in revised form 3 August 2015 Accepted 23 August 2015 Available online 28 August 2015

Functionalization is one of the key procedures for real applications of carbon nanotubes (CNTs) as it involves the generation of the acidic functional groups on their surfaces. In these procedures, precise elucidation of these surface acidic groups is significant for the proper utilization of the functionalized CNTs. For easy characterization of the practical acidic groups on CNTs, one-pot titration methodology is developed, breaking the boundary between the conventional indirect and direct titration methods. The practical acidic functional groups including carboxylic, lactonic, and phenolic groups were successfully computed from the acid ionization constant (pKa) distribution from the direct titration of nitric acidoxidized multi-walled CNTs by means of a one-pot titration methodology. These results were fairly identical to the results of the popular indirect titration method, showing that the developed methodology is essentially applicable for the surface characterization of acidic groups on CNTs and potentially extended to the other carbon nanomaterials. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Carbon nanotube Surface acidic group Surface characterization One-pot titration direct titration indirect titration

1. Introduction Carbon nanotube (CNT) has been recognized as one of the most fascinating materials which are potentially utilized into nextgeneration electrical and energy/environmental applications because of its unique and outstanding mechanical, electrical, optical, and thermal properties [1e4], Functionalization by oxidation is one of the key procedures leading to viable applications of CNT as this process generates desired functional groups on the surfaces [3]. These functional groups adjust the surface properties of CNT to enhance their dispersibility, adsorption properties, and reactivity levels, thereby potentially broadening the areas in which it may be applied. Among the variety of these functional groups, the surface acidic groups including carboxylic or phenolic groups are in particular importance in the various utilization of CNT due to their capability of generating surface charges and ion exchange capability by easy disprotonation [5,6]. Specifically, the repulsion forces due to the generated surface charge make CNT more readily dispersible in the aqueous/organic solvents or matrix by overcoming the strong van

* Corresponding author. E-mail address: [email protected] (C.R. Park). http://dx.doi.org/10.1016/j.carbon.2015.08.078 0008-6223/© 2015 Elsevier Ltd. All rights reserved.

der Waals interactions for processing and preparation of highperformance composites [3]. Additionally, the ion exchange capability induced from the acidic sites adjusts the adsorption properties of CNT, which makes it applicable to metal/organic adsorbents for the energy and environmental devices including secondary batteries/supercapacitors [7], pollutants filters [8], and catalyst supports [9]. The acidic functional groups can be utilized with the crosslinking agents between the CNT strands for their highperformance self-assembled structures [10]. For proper utilization of the functionalized CNT, precise elucidation of the surface functional groups including the acidic moieties is significant to correlate the surface properties of CNT and the desired performances. For this purpose, various chemical investigation techniques such as Fourier-transform infrared spectroscopy (FT-IR), temperature-programed desorption (TPD), and X-ray photoelectron spectroscopy (XPS) have been widely adopted for the surface characterization of functionalized CNT or other carbon material. Specifically, FT-IR detects the vibration energies which originate from the stretching, bending, scissoring, wagging, twisting, or rocking of chemical bonds which absorb infrared light [7,11]. Though FT-IR technique is powerful tool for qualitative classification of various functional groups, the sensitivity of the infrared absorbance is lower than that of other techniques as the carbon

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usually absorbs the entire infrared range, making the quantification of these groups unlikely. TPD utilize the different thermal stability levels of surface functional groups or physically attached moieties on the graphene layers of CNT [12]. For oxygen-containing groups, less thermally stable functional groups than graphene layers generally evolve into volatile gases such as carbon dioxide (CO2) or carbon monoxide (CO) with a thermal treatments at an elevated temperature [12,13]. Generally, TPD equipment is coupled with mass-spectrometer to differentiate the evolved gas for the further quantification of functional groups such as carboxylic acids/anhydrous, lactones, phenols, and/or quinones [12]. XPS is one of the most widely utilized and well-established techniques for the surface characterization of various materials, including metals, ceramics, polymers, and carbon materials. In an XPS analysis, the binding energies (BE) of photoelectrons emitted as a result of X-ray irradiation to the core electrons of the samples are measured. This technique is useful for the quantitative elucidation of atomic compositions of functionalized CNT and of the chemical compositions of desired atoms [14]. For example, the bonding states (including carbon single/double bonds) of carbon atoms with heteroatoms can be estimated by deconvoluting the C1s spectra, which are generally located around a BE value of 284.5 eV [8]. Though quantitative analysis of the functional groups is possible with TPD and XPS measurements, the interpretation of the spectra might be ambiguous when the deconvolution temperature (TPD) or binding energy (XPS) ranges of functional groups are similar [15]. Among the numerous characterization methods assessed thus far, the titration method is a powerful tool for elucidating populations of functional groups with acid or base characteristics on CNT surfaces. More importantly, since the titration methods provide the absolute equivalence of the acidic groups on carbon surfaces, this technique has been applied to quantitative analysis of the adsorption properties [16] or reactivity [17,18] of these acidic functional groups. For example, Carrasco-Marin et al. demonstrated the effects of acidic or basic groups on activated carbons on the adsorption properties of water [16]. In this work, the numbers of waterabsorbable sites and acidic or basic functional groups determined by titration method were correlated to investigate the number of water molecules interacting with each functional group. The results showed that ca. 3 molecules interacted with the carboxylic and lactonic groups, while ca. 1.5 molecules interacted with the phenolic and basic groups. Titration methods were also used to determine the reactivity of the acidic functional groups of CNT. Worsley et al. covalently attached octadecylamine (ODA) to carboxylic groups on singlewalled CNT to make them dispersible in tetrahydrofuran [17]. The degree of ODA loading was determined from the difference between the numbers of carboxylic groups before and after the DCC (1,3-dicyclohexylcarbodiimide) coupling amidation reaction. A similar investigation was reported for the covalent bonding of nbutylamine to carboxylic groups on multi-walled CNT (MWCNT) by means of EDAC (1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride) coupling amidation [18]. The covalent reactivity of carboxylated MWCNT was determined to range from 58 to 78% depending on the oxidation degree of the MWCNT. Titration methods for elucidation of these useful surface acidic groups of carbonaceous materials are largely categorized into the indirect and direct methods. The indirect titration method, also known as Boehm titration [19], is commonly used due to its simple principles for the identification of the practical information on the surface of various carbonaceous materials including activated carbons, carbon fibers, carbon nanotubes, and graphene oxides [17,20e28]. With this method, three major types of functional

groups (carboxylic, lactonic, phenolic groups) are determine. These are responsible for the surface properties and for the numerous applications of the carbon materials. For the classification and quantification of these functional groups, Boehm suggested three bases with different basicities (NaOH, Na2CO3, and NaHCO3) which are selectively neutralized with functional groups. Particularly it is generally assumed that NaOH reacts with all three functional groups, while Na2CO3 reacts with the carboxylic and lactonic groups, and NaHCO3 reacts only with the carboxylic group [19]. Though indirect titration provides practical information about the acidic groups of carbonaceous materials for their appropriate utilization, several limitations prevent the simple adoption of the indirect titration method. For example, experimental procedures such as reaction, filtration and titration are fairly complicated and time-consuming comparing to other surface characterization methods [23,26,27]. Specifically, a carbon sample is mixed with a reaction base for a sufficient period, followed by filtration, after which the filtrate is titrated with an acid titrant. Additionally, the filtrates are acidified to remove dissolved carbon dioxide and are then titrated with the base solution (known as the inverse or back titration method) [23]. In our previous works on indirect titration, the acidification step appeared to be completely unnecessary in a systematic study of the effects of carbon dioxide (CO2) on the titration of Boehm's reaction bases [20,21]. Nevertheless, complex experimental procedures remain and must be repeated for each reaction base, which is time-consuming and also make the indirect titration method inaccessible. Moreover, filtration steps for highly oxidized CNT individually dispersed in a reaction base [17,29] or GO with two-dimensional nanostructures [30,31] are hardly feasible or even impossible. These carbon nanomaterials can act as secondary filters and inhibit the filtration of the reaction mixture, which is an essential process in the indirect titration method. In such cases, surface characterization of carbon nanomaterials with indirect titration becomes difficult. In contrast, when using the direct titration method [32e37], the sample is simply mixed with the titrand solution and is directly titrated for the identification of the acidic or basic characteristics of carbon materials. This method is widely used for the characterization of carbons and polymers with acidic (or basic) properties under the assumption that the acid constant (pKa) values of numerous acids (or bases) are not discrete but are instead continuously distributed in a wide pKa, range expressed as the “pKa distribution function.” While the direct titration method can effectively determine the population of the strong or weak acidic groups, the practical functions of these groups for the efficient utilization of carbon materials are not commonly provided, in contrast to indirect titration. Therefore in this work, we develop a one-pot titration methodology penetrating the principles of direct and indirect titration for the simple elucidation of the surface properties of carbon nanomaterials especially for CNT. With this methodology, the pKa distribution function of the direct titration of carbon nanomaterials is converted into practical indirect titration results based on the previously developed modified HendersoneHasselbalch equation [20,21]. The validity of the developed methodology is verified with oxidized MWCNT (MWCNT). 2. Experimental 2.1. Chemicals and materials All of the chemicals used as the titrants or titrands for the titration process, including NaOH, Na2CO3, NaHCO3, and HCl, were provided by Daejung Chemicals, Korea, and the MWCNT was purchased from Hanwha Chemicals (CM250). For the functionalization

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

of the MWCNT, MWCNT (1 g) was stirred in 300 mL of 14.2 M nitric acid at 110
C for 6, 12, 24 and 48 h. After an acid treatment, the MWCNT was repeatedly filtered using a 20 mm PTFE filter (Advantec) and washed with deionized water. For the complete removal of any acidic carbon compounds (ACCs) which may be destroyed from the side-walls of the MWCNT during the acid treatment and affect the titration results were removed by washing the obtained MWCNT with 0.01 M NaOH solution until the filtrated become colorless [17]. The ACC-removed MWCNT was acidified by a 0.1 M HCl solution for reattachment of the protons to the ionized MWCNT and was then filtrated. This was followed by washing thoroughly and filtration with deionized water and then drying in a 60
C vacuum oven overnight. The nitric acid-treated MWCNT prepared for 6, 12, 24, and 48 h were denoted as N6CNT, N12CNT, N24CNT, and N48CNT, respectively.

2.2. Characterization 2.2.1. X-ray photo spectroscopy (XPS) measurement of CNT samples For the analysis of the general oxidative state of oxidized CNT, each CNT sample was investigated by XPS (AXIS-HSi, KRATOS, USA). The carbon 1s (C1s) electron binding energy spectrum was deconvoluted by a non-linear least squares curve fitting program with a linear base line and an assumption that each peak was taken as 30% Lorenzian and 70% Gaussian.

2.2.2. Indirect titration of CNT samples The indirect titration of the prepared oxidized MWCNT was conducted based on the standardized method in our earlier study [20]. This procedure consists of three steps: reaction, filtration and titration, without the need for CO2 desorption by an additional acidification process. For the reaction and filtration steps, each MWCNT sample (50 mg) was stirred in 50 mL of each 0.01 N reaction base (NaOH, Na2CO3, or NaHCO3) for 48 h (denoted reaction mixture) in HDPE bottles and then filtrated by a PTFE syringe filter (Advantec). The reaction bases before and after the reaction step are denoted as pre- and post-reaction bases. For the titration step, 10 mL of the pre- or post-reaction bases were then titrated with a 0.01 N HCl solution as a titrant using a potentiometric titrator (888 Titrando, Metrohm). In general, two inflection points appeared in each titration curve showing the CO2 effects [20]. However only the second inflection points, at which all base components (OH, CO2 3 , or HCO 3 ) are neutralized regardless of the CO2 effects, are defined as the end point of the titration curve of each reaction base; the equivalent amount of HCl at this point is regarded as that of the reaction base [20]. The titration process was repeated three times in order to determine the average equivalence of each reaction base. The numbers of carboxylic (nc), lactonic (nl), and phenolic (np) groups were determined by the following the procedures, as used done in an earlier study [20], with Equations (1.1e1.3).

731

np ¼ nFG;NaOH  nFG;Na2 CO3 ¼

eqNaOH;pre  eqNaOH;post eqNa2 CO3 ;pre  eqNa2 CO3 ;post  ; mCNT;NaOH mCNT;Na2 CO3 (1.3)

where nFG,B represents the concentrations of the functional groups [meq/g] determined from the uptake of reaction base B (B specifies NaOH, Na2CO3, and NaHCO3), eqB,pre(post) is the equivalence of the pre(post)-reaction base of B, and mCNT,B is the effective mass of the CNT (N6, N12, N24, or N48CNT) in the each post reaction base B during the titration step. For determination of the concentration of non-acidic carbonyl group from indirect titration, similar procedures were repeated with much stronger reaction base, 0.01 N sodium ethoxide (NaOEt) dissolved in ethanol [6]. 2.2.3. Direct titration of CNT samples Each CNT sample was mixed in a 0.01 N HCl solution (2 mg/mL) and agitated by bath sonication for 30 min. Next, 15 mL of the mixture was injected into an incubation titration vessel and titrated with a 0.01 N NaOH solution as a titrant at 25
C with continuous N2 purging. To achieve full equilibrium between the acid functionalities of the CNT and the titrant during the titration process, the titrant solution was dosed only when the pH variation was lower than 0.002 pH units/minute with a maximum waiting time of 20 min. The resulting titration curve (Fig. 1a for N12CNT) was converted to proton desorption isotherm, q(pH) (Fig. 1b for N12CNT), showing the concentrations of ionized functional groups on the CNT sample as a function of the pH during the titration process [33] through the application of the modified HendersoneHasselbalch (HeH) equation (Equation (s8) in Supplementary Material) developed in our previous reports [20,21] (see Supplementary Material for the detailed information). This isotherm is identical to the sodium binding isotherm [37]. Subsequently, the pKa distribution function, f(pKa) (Fig. 1c for N12CNT), indicating the population of the acidic groups in a specific pKa range, was obtained by converting the proton desorption isotherms using the equation,


vqðpHÞ f ðpKa Þy ; vpH pH¼pKa

(2)

with the application of first-order approximation [33,36]. The detailed procedures pertaining to the titration data processing are discussed in the Supplementary Material. The obtained f(pKa) was then substituted into the modified HeH equation (Equation (s8) in Supplementary Material) for the calculation of the theoretical titration curve to verify the validity of the procedures. The experimental (open black squares and red circles) and theoretical titration curves (black solid lines) shown in Fig. 1a were identical, with high precision, implying that the obtained q(pH) and f(pKa) values are practically applicable. All of the numerical calculation procedures were conducted by MATLAB 2014a.

nc ¼ nFG;NaHCO3 ¼

eqNaHCO3 ;pre  eqNaHCO3 ;post ; mCNT;NaHCO3

(1.1)

3. Results and discussion 3.1. XPS spectra of CNT samples

nl ¼ nFG;Na2 CO3  nFG;NaHCO3 eqNa2 CO3 ;pre  eqNa2 CO3 ;post eqNaHCO3 ;pre  eqNaHCO3 ;post ¼  ; mCNT;Na2 CO3 mCNT;NaHCO3 (1.2)

Before the analysis of one-pot titration and indirect titration results, XPS spectrum was preferentially analyzed for the investigation of general oxidative state of each CNT sample. The XPS measurement is widely applied for the surface characterization of various carbon materials by analysis of the binding energy spectra of core electrons exited by X-ray irradiation [38]. In the case of the

732

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

1

2

Intensity (A.U.)

3

(a) N6CNT

(c) N24CNT

Peak 1 (60.3 %) Peak 2 (22.9 %) Peak 3 (7.5 %) Peak 4 (3.6 %) Peak 5 (5.7%)

Peak 1 (53.3 %) Peak 2 (27.9 %) Peak 3 (8.8 %) Peak 4 (3.5 %) Peak 5 (6.5%)

5

4

6

(b) N12CNT

(d) N48CNT

Peak 1 (54.7 %) Peak 2 (27.5 %) Peak 3 (7.9 %) Peak 4 (4.2 %) Peak 5 (5.7%)

282

284

286

288

290

Peak 1 (51.7 %) Peak 2 (27.8 %) Peak 3 (10.2 %) Peak 4 (3.2 %) Peak 5 (7.1%)

292 282

284

286

288

290

292

Binding Energy (eV) Fig. 1. XPS C1s spectra of (a) N6CNT, (b) N12CNT, (c) N24CNT, and (d) N48CNT. Each peak was deconvoluted into 6 peaks which are C]C (peak 1), CeC (peak 2), CeO (peak 3), C]O (peak 4), O]CeO (peak 5), and pep* shakeup features (peak 6). (A colour version of this figure can be viewed online.)

CNT samples prepared in this study, each C1s binding energy spectra were resolved into the graphitic (C]C, peak 1; CeC peak 2) and oxidative carbon peaks (CeO, peak 3; C]O, peak 4; O]CeO, peak 5) with p- p* shakeup feature (peak 6) as shown in Fig. 1 [39]. The atomic composition of each peak except p-p* shakeup feature was also summarized in Fig. 1 and Table 1 for each CNT sample. As reported in the various studies, the nitric acid treatment of CNT continuously increased the oxygen functional groups as indicated by the increments in both atomic ratio of oxygen and oxidative carbon [40]. Though the above XPS spectra analysis easily shows the relative composition of the oxidative carbon species which are singly or doubly bonded with oxygen atoms, it is impossible to differentiate the acidic sites from the non-acidic ones. For example, carbon atom singly bonded with oxygen (CeO, peak 3) can be originated not only from the acidic phenols but also nonacidic ethers. Additionally, O]CeO (peak 5) group can be also divided into acidic lactone and carboxylic groups. In this point of view, more detailed analysis exhibiting the absolute equivalence of the practical acidic sites on CNT is necessary. For this purpose, the acidic characteristics of the functionalized carbonaceous materials have been usually quantified by indirect or direct titration methods. However, both methods contain their own drawbacks. Direct titration only provides the pKa distribution function simply showing the entire shape of the population of the acidic groups [32,33]. Though indirect titration quantifies the practical acidic groups, the complicated experimental procedures

make this method inaccessible [23,26,27]. Therefore in the following sections, we develop a systematic methodology for obtaining the concentrations of the practical acidic functional groups including carboxylic, lactonic, and phenolic groups which are conventionally measured by indirect titration method, by converting pKa distribution function from simple direct titration method. 3.2. Theoretical derivation of one-pot titration methodology The methodology for calculating the indirect titration results from the direct titration curves includes three steps. In the first step, the direct titration curves of oxidized CNT samples are converted into the proton desorption isotherm, q(pH), which exhibits the number of disprotonated functional groups as a function of the pH [33]. In the second step, the pKa distribution function f(pKa) is calculated from q(pH), which is discussed in detail in the experimental section and Supplementary Material. Finally, the indirect titration results are computed as a function of the concentrations of the reaction bases and the quantities of the carbon samples dissolved into the reaction bases. In this work, these procedures were initially utilized with N12CNT as a means of simplification and were then applied further to the other CNT samples in section 3.3 (N6CNT, N24CNT, and N48CNT). Following the procedures described in Section 2.2.3, the q(pH) and f(pKa) values associated with N12CNT were calculated from the

Table 1 Atomic compositions of carbon and oxygen from wide scan XPS spectra, and those of graphitic and oxidative carbon compositions from XPS C1s spectra (Fig. 1). Sample

N6CNT N12CNT N24CNT N48CNT

C1s spectrum fitting result

C/O composition (wide scan) C ratio (atomic %)

O ratio (atomic %)

Graphitic carbon (Peak 1, 2) (atomic %)

Oxidative carbon (Peak 3e5) (atomic %)

96.1 94.2 92.7 91.6

3.9 5.8 7.3 8.4

83.2 82.2 81.2 79.5

16.8 17.8 18.8 20.5

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

733

direct titration curves (Fig. 2a), as shown in Fig. 1b and c, respectively. The total equivalence of the acidic groups of N12CNT was 0.430 meq/g, as determined from the maximum value of q(pH) (qmax) or the area of f(pKa). The acidities of these functional groups were continuously distributed on the certain pKa range which can be expressed by f(pKa) [33,36]. The f(pKa) of N12CNT showed two distinct peaks around pKax5 and 10 and a small hump between them at pKax8 which may be originated from the carboxylic, phenolic, and lactonic groups, respectively, as generally demonstrated in previous reports [34,36,41]. The basic concept of the calculation of the uptake quantities of the reaction bases (NaOH, Na2CO3, and NaHCO3) from this f(pKa) value involves a simulation of a condition in which the acidic groups of the carbon materials are disprotonated. Herein, we assumed that the uptake amount of each reaction base is identical to the number of disprotonated sites of the acidic groups of carbon samples in the reaction base. In addition, further protonation or disprotonation never occurs during the filtration step. The number of disprotonated sites is simply estimated by adopting the pH value of the mixture in an equilibrium state of the reaction base and the carbon materials (denoted pHe) into a proton desorption isotherm (Fig. 1b in the case of N12CNT). This relationship is expressed as follows:

titration curves by considering the titration moieties and the titration environment, including the titrants and titrands, and thereby effectively estimating the titration behaviors of various acidic or basic elements ranging from simple monoprotic molecules to multiprotic carbon nanomaterials or polymers. The validity of the modified HeH equation was proven in our previous works, which investigated the effects of phenolic/carboxylic groups on acidic carbon compounds (ACCs) [21] or CO2 [20] on the titration behaviors of Boehm reaction bases (NaOH, Na2CO3, and NaHCO3). By applying the modified HeH equation, the computation process in this work for the calculation of the uptake amounts of the reaction bases includes the following steps: 1) a simulation of the titration curve of the mixture of the reaction base and carbon sample adopting the modified HeH equation (Fig. 2aec), 2) a numerical calculation of the pHe value of the simulated titration curve, and 3) substitution of pHe into the pH axis of the proton desorption isotherm of the carbon sample (Fig. 2c for N12CNT). The detailed derivation of the process is discussed below. For the simulation of the titration curve of the mixture of the reaction base and the acidic functional groups with the HCl titrant, the acid titrant form of the modified HeH equation was applied which was introduced in our earlier work [20] and can be expressed as

Uptake ¼ qðpHe Þ:

QHþ ðpHÞ ¼

(3)

In earlier work [32]. this pH values were experimentally measured and utilized with the proton desorption isotherms of the activated carbons for the calculation of the indirect titration results In this approach, acidified activated carbons were reacted with the reaction bases for 24 h and the pHe of each reaction base mixture was then measured before the indirect titration filtration step. The proton desorption isotherm at each pH value as determined with the direct titration method is in good agreement with the indirect titration result [32]. However, this process still requires a reaction step for each reaction base in each indirect titration condition, and the disprotonation behaviors of the acidic functional groups on the carbon surface with the reaction base have not been fully demonstrated. In this work, pHe values with different indirect titration conditions are systematically calculated from the f(pKa) value (Fig. 1a for N12CNT) via the application of the modified HendersoneHasselbalch (HeH) equation, as developed and verified in our previous reports [20,21], without any necessity of the additional experimental procedures. The modified HeH equation predicts the

(a)

2

Ref. (0.01 N HCl, 15 mL), r =0.992 2 Ref. + N CNT (15 mg), r =0.999 2

12

fC ðpHÞ ¼

X



Kb;i

;

(4.1)

QBase;titrand   ; 1 þ OH Kb;Base

(4.2)

VBase VBase   þ  ; vH2 O þ 1 OH vH2 O þ OH KW (4.3)

fHCl solvent ðpHÞ ¼ 1 þ

1=cHCl 1=cHCl     : vH2 O þ 1 OH vH2 O þ OH KW (4.4)

The above functions show the effects of the acidic functional

(c) 0.08

0.5

meq/g

0.07 0.06 0.05

0.3 0.2

4

0.04 0.03 0.02

0.1

0.01

2 0.0

QAi

fBase solvent ðpHÞ ¼ 

f (meq/g)

(meq/g)

6



1 þ OH

0.4

8

pH

X

fBase titrand ðpHÞ ¼

max=0.430

10

(4)

where

(b)

12 Ref. (0.01 N HCl, 15 mL), r =0.981 Theoretical titration curve 2 Ref. + N12CNT (15 mg), r =0.999

fC ðpHÞ þ fBase titrand ðpHÞ þ fBase solvent ðpHÞ ; fHCl solvent ðpHÞ

0.1

0.2

QOH (meq) -

0.3

0.0

2

4

6

8

pH

10

12

0.00

2

4

6

8

10

12

pKa

Fig. 2. (a) Direct titration curve of HCl titrant solutions with (red circle) and without (Ref.; black square) the agitation of the N12CNT and their theoretical counterparts (black solid lines), where QOH  is the quantity of NaOH titrant solution, (b) proton desorption isotherm (q), and (c) pKa distribution function (f(pKa)) of N12CNT. (A colour version of this figure can be viewed online.)

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Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

    QHAi ¼ mC $f  pKa;i  $ pKa;iþ1  pKa;i  ¼ cC $f pKa;i $ pKa;iþ1  pKa;i $VBase :

groups on the carbon (fC), the base titrand (fBase, titrand), the solvent of the base titrand (fBase solvent), and the solvent of the HCl titrant (fHCl solvent) on the titration curve as a function of the pH value. Here, vH2O and KW denote the molar volume and self-ionization constant of water, respectively; QHþ is the equivalent amount of Hþ ion as added from the acid titrant; A i is the conjugated base of HAi, which is the i'th component (1  i  n) of the acidic groups on the CNT when pKa ¼ pKa,i, Kb,i is the base ionization constant of the conjugated base A is the total number i (hence, pKb,i þ pKa,i ¼ pKW), QA i (equivalence) of functional groups with pKb,i, VBase is the volume of the base titrand (the reaction base in this case), cHCl is the concentration of the HCl titrant. Practical applications of Equation (4) to the titration curves of a mixture of N12CNT and the reaction bases are shown in Fig. 3. The effect of the acidic sites, HAi, on the titration curves on Equation (4.1) can be readily calculated from the pKa distribution function (Fig. 1c). Since the value of QAi is fundamentally identical to that of QHAi (equivalence of HAi), Equation (4.1) can be formulated as shown below.

fC ðpHÞ ¼

X

X QAi QHAi    : ¼ 1 þ OH Kb;i 1 þ Ka;i Hþ

where mC and cC denote the mass and concentrations of the carbon samples in the reaction base with volume VBase. For fBase titrand(pH) as described in Equation (4.2), we apply the principles of the CO2 effect on the reaction bases, as in the aforementioned earlier work [20]. In this work, Na2CO3 and NaHCO3 were considered as CO2-contaminated NaOH solutions to estimate the titration behavior of each reaction base. The theoretical equation used to obtain the corresponding titration curves is as follows:

fBase titrand ðpHÞ ¼

3

pH

12

12

10

10

8

8

6 4 2

6

12.1

4

12.0

2

11.9 0.000

0.00

0.002

0.03

0.06

0.09

0.12

NaHCO3 (rCO2=1, 0.01 N, 10 mL)

Na2CO3 + N12CNT (10 mg)

NaHCO3 + N12-CNT (10 mg)

8

6

4

11.0

8.0

10.8

2

10.6 0.000

0.00

0.002

0.03

0.06

0.09

0.12

0.002

0.03

NaOH 0.10

11

0.08

pHe

f (meq/g)

10 Ref. (0.01 N) Ref + N12CNT

0.12

Na2CO3

NaHCO3

0.5 Na2CO3

Total NaOH

NaHCO3

0.4

0.06 0.04 0.02

(1 mg,mL)

0.09

(f)

NaHCO3

12

0.06 QH+ (meq)

(e) Na2CO3

7.5 0.000

0.00

Uptake (meq/g)

NaOH

8.5

QH+ (meq)

(d)

(8)

(c) Na2CO3 (rCO2=0.5, 0.01 N, 10 mL)

QH+ (meq)

9

2 OH ðaqÞ þ CO2 ðaqÞ / CO2 3 ðaqÞ þ H2 O ðlÞ;

(b) NaOH (rCO2=0, 0.01 N, 10 mL)

(7)

In this equation, CO2 3 is assumed to be divided into an independent base component and proton binding sites, resulting in QCO2 ¼ QHCO3 . Here, it is assumed that CO2 results from the 3 3 dissolution of CO2 into the pure NaOH or Na2CO3 solution by the following reactions [20,42].

Subsequently, QHAi was obtained from the pKa distribution function f(pKa) (by combining Equation (S2) and Equation (S7.2)) via

NaOH + N12-CNT (10 mg)

QCO2 QOH 3 . þ  .  Kb;OH 1 þ OH Kb;CO2 1 þ OH 

QHCO3 þ :  . 1 þ OH Kb;HCO3

(5)

(a)

(6)

0.3 0.2

One-pot titration Indirect titration

0.1

8 0.0

0.5

rCO2

1.0

0.00

2

4

6

8 pKa

10

12

0.0

0.0

0.5

rCO2

1.0

Fig. 3. Calculated titration curve of 10 mL of the 0.01 N reaction bases: (a) NaOH, (b) Na2CO3, and (c) NaHCO3 (black dashed lines refer to the reference reaction bases and red solid lines denote the mixture with 10 mg of N12CNT). (d) pHe of the 0.01 N reaction base as a function of rCO2 , (e) proton-dissociated f(pKa) of N12CNT (cC ¼ 1 mg/mL, Alk ¼ 0.1 N), and (f) reaction base uptake quantity of N12CNT as a function of rCO2 from the one-pot titration (black solid line) method and the indirect titration (red dots) method. (A colour version of this figure can be viewed online.)

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

Therefore, QCO2 is assumed to be identical to the quantity of 3 hypothetically dissolved CO2, QCO2 (QCO2 ¼ QHCO3 ¼ QCO2 ) Addi3 tionally, NaOH can be further neutralized by HAi from the carbon sample through the following equation:

OH ðaqÞ þ HAi ðsÞ / A i ðsÞ þ H2 O ðlÞ:

(9)

The neutralization reactions (8) and (9) conserve the normality summation of the base components, which is defined as the alkalinity (Alk), which can be expressed by the following equations,

numerically obtained by solving QHþ ðpHe Þ ¼ 0 on Equation (4.11). This equation is identical to

    P cC $f pKa;i $ pKa;iþ1  pKa;i 1 þ 10pHe $Ka;i   Alk$ 1  2rCO2  qHA $cC . þ 1 þ 10pHe $KW Kb;OH þ

i h i h i Xh i h þ HCO A Alk ¼ OH þ CO2 3 3 þ i :

735

(10.1)

rCO2

rCO2

!

!

. . þ Alk 1 þ 10pHe $KW Kb;CO2 1 þ 10pHe $KW Kb;HCO3 3

1 1

þ .  ¼0 vH2 O þ 10pHe vH2 O þ 1 10pHe $KW

or

QAlk ¼ QOH þ QCO2 þ QHCO3 þ QA 3 ¼ QOH þ 2QCO2 þ QHA ;

where QAlk is the total quantity (equivalence) of the base components (QAlk ¼ Alk$VBase ) and QHA (¼QA ) denotes the equivalence of the acidic groups on a carbon sample, which is the area of mc$f(pKa). Then, Equation (7) can be reconstructed as shown below.

fBase titrand ðpHÞ ¼

(12)

(10.2)

QAlk  2QCO2  QHA QCO2 þ   . . 1 þ OH Kb;OH 1 þ OH Kb;CO2 3

QCO2 þ ;  . 1 þ OH Kb;HCO3 (7.1)

by combining Equations (4), (4.3), (4.4), (5), (6), and (7.2). Once f(pKa) is determined for a carbon sample, pHe should be a function of rCO2 , Alk, and cC, as described in Equation (13).

  pHe ¼ f rCO2 ; Alk; cC :

(13)

Here, pHe can be numerically calculated by Equation (13) or from the simulated titration curves of the mixture of the carbon sample and the reaction base. It is then substituted to the pH axis of q(pH) (Fig. 1b) for the calculation of the uptake quantity of the reaction base by the acidic functional groups. The derived one-pot titration methodology was applied to MWCNT treated with nitric acid and the results were compared to typical indirect titration results (Table 2 and S1).

Subsequently, the CO2 ratio, rCO2 , is defined as

rCO2

3.3. Practical application of one-pot titration methodology

QCO2 ¼ : QAlk

(11)

rCO2 , defined in Equation (11), is theoretically identical to Q1

NP , where QNP1 and QNP2 are QHþ at the first and second 1  QNP2

neutralization points (NPs) shown on the titration curve of the reaction base with the HCl titrant. Notably, this relationship was confirmed both theoretically and experimentally in the titration of CO2-contaminated NaOH, Na2CO3, and NaHCO3 in our recent reports showing the effects of CO2 on the titration behaviors of these reaction bases [20]. Specifically, the ideal reaction bases can be demonstrated by NaOH solutions with different rCO2 values; i.e., rCO2 is equal to 0, 0.5, and 1 for NaOH, Na2CO3 and NaHCO3, respectively. However, at atmospheric atmosphere, these ratios are never preserved, as CO2 in the air interacts with the reaction bases [20]. For a precise comparison of the indirect titration and one-pot titration results, rCO2 was measured from every pre-reaction base. Following Equation (11), Equation (7.1) can be further reconstructed as

For the easy understanding of the one-pot titration methodology, the essential procedures were preferentially adopted with the reaction mixture of 0.01 N reaction base and N12CNT (1 mg/mL). Under this condition, the normality of the acidic functional group (qmax ð0:430 meq=gÞ$cC ð1 mg=mLÞ ¼ 0:430 mN) is much lower (4.3%) than Alk (0.01 N) of the reaction bases. For the calculation of the pHe of each reaction base, the corresponding titration curve (Fig. 3aec) was calculated applying Equation (1). As shown in the insets of Fig. 3aec, the initial pH values at Q OH ¼ 0 (pHe) decreased from 12.00, 10.93, and 8.31 to 11.98, 10.81, and 7.88 for NaOH (rCO2 ¼ 0), Na2CO3 (rCO2 ¼ 0:5), and NaHCO3 (rCO2 ¼ 1), respectively. Notably, the pHe with different values of rCO2 ranging from 0 to 1 possibly observable under a laboratory condition can easily be estimated by applying our one-pot titration process, as shown by the black dashed line in Fig. 3d. The suggested methodology also provides a deeper understanding of the interaction between the reaction base and the functional groups expressed by f(pKa). This interaction can be

1 0 Alk$1  2r   q $c CO2 HA C i.  C B 1 þ OH Kb;OH C B C B fBase titrand ðpHÞ ¼ B ! CVBase ; C B rCO2 rCO2 A @ i. i. þ þ Alk      Kb;CO2 1 þ OH Kb;HCO3 1 þ OH

(7.2)

3

where qHA is mass-normalized QHA (qHA ¼ QmHAC ¼ cCQ$VHABase ) [meq/g], which is identical to the area of f(pKa). And then pHe was

demonstrated by showing how many functional groups are dissociated at a specific value of pKa when the carbon sample is agitated

736

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

in the reaction base. For this purpose, the distribution function of the proton-dissociated sites of the functional groups at pHe, which is the defined proton-dissociated f(pKa) when pKa ¼ pKa,i, was numerically calculated by applying equations (S6) and (6) in Refs. [32,33].

3 2 Ka;i Q   ½Hþ þKa;i HAi 5 4   protondissociatedf pKa;i ¼ cC $ pKa;iþ1 pKa;i $VBase

; pH¼pHe

(14.1) or

"   proton  dissociatedf pKa;i ¼ 

#   Ka;i  f pKa;i Hþ þ Ka;i

: pH¼pHe

(14.2) Fig. 3e shows the proton-dissociated f(pKa) value of N12CNT (1 mg/mL) which is assumed to be mixed into the 0.01 N NaOH (red dashed line), Na2CO3 (blue dotted line), and NaHCO3 (green dashdotted line). The original f(pKa) shown in Fig. 1c is shown as a black solid line for comparison. It is easily observed from the plot that all acidic functional groups are dissociated when N12CNT is mixed into NaOH. As rCO2 of the reaction increased, the fraction of dissociated sites clearly decreased. For Na2CO3, for which rCO2 ¼ 0:5, all acidic functional groups were dissociated in the range of 3 < pKa < 9 and were partially dissociated when pKa was greater

Total

NaOH (rCO2=0)

Na2CO3 (rCO2=0.5)

than 9. Meanwhile, the pKa limitation for the 100% dissociation decreased to pKa x5:5 while the dissociation fraction gradually decreased with pKa in the case of NaHCO3 (rCO2 ¼ 0). To the best of our knowledge, this type of systematic demonstration, showing the dissociation behaviors of the acidic functional groups in the presence of the reaction base, has rarely been reported in earlier works on pKa distribution functions, i.e., f(pKa), of various carbon materials. Typically, the fraction of acidic functional groups with strong (pKa < 7) or weak (pKa > 7) acidic strength levels are determined by the simple division of f(pKa) [34,37]. Our approach also makes it possible to estimate the indirect titration results without the need for an indirect titration process [23,28] or even the experimental measurement of the pHe of the reaction mixture [32]. The uptake amount of each reaction base from the indirect titration was obtained from the protondissociated f(pKa) area (Fig. 3e) of the corresponding reaction base, or simply from the substitution of pHe into pH axis of q(pH), as shown in Fig. 1b. In addition to ordinary reaction bases, the uptake of the reaction base with different rCO2 values can be computed as shown in Fig. 3f. This calculation with a varying value of rCO2 is practically significant, as a pure reaction base with an ideal rCO2 can never exist under an actual real condition due to the absorption or desorption of CO2 into or from the reaction bases, respectively [20]. Even in an inert condition (glove box), Na2CO3 or NaHCO3 will desorb CO2, which will lower their rCO2 values [23,43]. Nevertheless, the rCO2 values of the reaction bases used in the indirect titration experiments were maintained as the ideal values to the

Total

NaHCO3 (rCO2=1)

(a) 1 mN, 1 mg/mL

(b) 0.01 N, 20 mg/mL

0.08

0.08

0.06

0.06

f (meq/g)

f (meq/g)

(a) 0.01 N, 10 mg/mL

0.04

(b) 0.5 mN, 1 mg/mL

0.04

0.00 2

4

6

8

10

12 2

pKa

0.5

4

6

8

10

12

Na2CO3

NaHCO3

6

8

10

12 2

4

6

0.5

NaOH

8

10

12

pKa

Na2CO3

NaHCO3

0.4

0.1 mg/mL 1 mg/mL 5 mg/mL 10 mg/mL 20 mg/mL

0.2 0.1

0.0

0.5

1.0

rCO2 Fig. 4. Proton-dissociation f(pKa) of (a) 10 and (b) 20 mg/mL N12CNT in the 0.01 N reaction base. (c) Reaction base uptake quantity of N12CNT as a function of rCO2 with the variation of cC of the reaction base. (A colour version of this figure can be viewed online.)

Uptake (meq/g)

0.3

0.0

4

pKa

(c) NaOH

2

pKa

0.4

Uptake (meq/g)

NaHCO3 (rCO2=1)

0.02

0.02

(c)

Na2CO3 (rCO2=0.5)

0.10

0.10

0.00

NaOH (rCO2=0)

0.3

0.1 N 0.01N 2 mN 1 mN 0.5 mN

0.2 0.1 0.0

0.0

0.5

1.0

rCO2 Fig. 5. Proton dissociation f(pKa) of 1 mg/mL N12CNT in the reaction base with (a) Alk ¼ 1 mN and (b) 0.5 mN. (c) Reaction base uptake quantity of N12CNT as a function of rCO2 with the variation of Alk of the reaction base. (A colour version of this figure can be viewed online.)

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

greatest extent possible by minimizing their exposure to the atmosphere (rCO2 ¼ 0.04, 0.52, and 0.99 for NaOH, Na2CO3, and NaHCO3, respectively). Additionally, reaction bases with different rCO2 values (0.28, 0.76) were prepared for a more detailed comparison of the one-pot and the indirect titration results (the black solid line and the red dots in Fig. 3f, respectively). As shown in Fig. 3f, the uptake computed from the one-pot titration (black solid line) method decreased gradually from 0.430 to 0.416 meq/g as rCO2 increased from 0 (NaOH) to 0.5 (Na2CO3), followed by drastic decrease to 0.260 meq/g at rCO2 ¼ 1 (NaHCO3). This is also shown in Fig. 3e from the observation of the populations of proton-dissociated sites in each reaction base. Notably, the typical indirect titration results (red dots) also showed a similar tendency compared to the one-pot titration results (red dots on Fig. 3f) with a determination coefficient (r2) of 0.986. This similarity implies that the one-pot titration methodology is practically useful and has the potential to be an efficient alternative to the typical indirect titration procedures. The analogy can be extensively applied to reaction mixtures while varying Alk or cC, as described in Equation (7.2) or (12). Figs. 4c and 5c show the uptake of the reaction base as a function of rCO2 with various Alk and cC values, respectively; these have been typically adopted in previous indirect titration experiments on various carbon materials [18,20,44e49]. As shown in Figs. 4 and 5, the one-pot titration methodology estimated that these experimental variables significantly affect the proton dissociation behaviors of the acidic functional groups and thereby change the uptake of the reaction base. The entire proton dissociation fraction was diminished as cC increased and as Alk decreased due to the limitation of the proton dissociating capacity

of the reaction base. These tendencies were reconstructed for the representative reaction bases (NaOH, Na2CO3, and NaHCO3) to clarify the effects of cC and Alk on the uptake of each reaction base and the resultant estimations of the concentrations of the acidic functional groups shown in Fig. 6. As shown in Fig. 6a and b, the uptake amount of NaOH was mostly preserved while varying the experimental variables. Meanwhile, those of Na2CO3 and NaHCO3 are sensitive to both cC and Alk. As a result, the concentrations of the acidic functional groups estimated from the difference in the uptakes between the reaction bases (applying Equations (1.1)e(1.3)) also changed despite the fact that the nature of the acidity did not change (Fig. 6d). Indeed, the uptake amounts of all reaction bases were lowered as the normality of N12CNT reached 0.43 of that of the reaction base ([cC, Alk] ¼ [1 mg/mL, 1 mN], and [10 mg/mL, 0.1 N]) from 0.043 (see Table S1). In cases with a high normality ratio (0.43), the uptake quantities measured by means of indirect titration were 10e20% lower than those estimated with the one-pot titration methodology, possibly due to the reattachment of some protons to the acidic functional groups during the filtration procedures with the local increase in cC in the reaction mixture. In these extreme cases, the major assumption that the reaction base uptake is identical to the number of proton-dissociated sites in the reaction mixture may be partially invalid. Nevertheless, the one-pot titration approach successfully forecasted the uptake variations by the carbon concentration or via normality differences in the reaction base by monitoring the interactions between the acidic functional groups and the reaction base molecules. The effects of Alk and cC on the titration results were visualized more clearly by the construction of the three-dimensional graphics

(a)

(c)

0.5

0.4

Concentration of functional group (meq/g)

Uptake (meq/g)

0.4 0.3 0.2 NaOH Na2CO3

0.1

NaHCO3 0.0

0.005

0.010

0.015

0.3

0.2

0.1

0.005

0.010

0.015

0.4

Concentration of functional group (meq/g)

0.4 0.3 0.2 NaOH Na2CO3

0.1

NaHCO3 0

3

6

9

cC (mg/mL)

12

15

0.020

Alk (N)

(d)

0.5

Uptake (meq/g)

Carboxylic Lactonic Phenolic

0.0

0.020

Alk (N)

(b)

0.0

737

Carboxylic Lactonic Phenolic

0.3

0.2

0.1

0.0

0

3

6

9

12

15

cC (mg/mL)

Fig. 6. Reaction base uptake quantity of N12CNT as a function of (a) Alk and (b) cC and (c, d) the corresponding resultant concentrations of the acidic functional groups. (A colour version of this figure can be viewed online.)

738

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

3.4. Comparison of the one-pot and indirect titration results with nitric acid-oxidized MWCNT

Fig. 7. One-pot titration diagram of N12CNT exhibiting (a) the uptake quantity of the reaction bases and (b) the concentrations of acidic functional groups as a function of Alk and cC. (A colour version of this figure can be viewed online.)

showing the uptake quantities of the reaction bases (Fig. 7a) and the resultant concentrations of the functional groups (Fig. 7b) with various combinations of Alk and cC, as defined in the “one-pot titration diagram”. The experimental conditions under which indirect titration should be conducted can be determined from this diagram. As shown in Fig. 7b, the titration results changed remarkably with the variations of cC and Alk at the boundary, where qmax $cC =Alk is greater than 10%. At the lower boundary, the uptake of each reaction base nearly reached its maximum value; therefore, the variations in the results were relatively small. This observation implies that the experimental conditions during indirect titration should be carefully determined considering the nature of the acidity of the carbon materials to obtain reliable and reproducible results. Therefore, when conducting indirect titration, qmax should be roughly measured first from the uptake of NaOH at arbitrary cC and Alk values as a preliminary test for the determination of a valid experimental condition (qmax $cC =Alk < 10%) followed by the main procedures with the reaction bases. On the other hand, the one-pot titration methodology provides all of the titration results obtainable from both conventional indirect titration without the necessity of a series of procedures during the indirect titration process.

The one-pot titration methodology developed in this work was also applied to the surface characterization of the nitric acidoxidized MWCNT samples with various oxidation degrees (N6CNT, N12CNT, and N24CNT). Following the same calculation procedures described in the previous section, the f(pKa) (the black solid line in Fig. 8a e 8c) of these samples were computed from the q(pH) derived from the corresponding titration curves (Fig. S1). The proton desorption isotherms showed that the total number of acidic functional group (qmax) increased from 0.364 to 0.754 meq/g with longer oxidation periods (see Fig. S1). The shape of f(pKa) became more complex, and one or two additional peaks appeared in the low pKa regions, possibly due to the formation of more acidic carboxylic groups as the oxidation process continued [34]. Nevertheless, the concentrations of acidic functional groups which practically serve as carboxylic, lactonic, and phenolic groups can be readily obtained from the one-pot titration methodology. Notably, as shown in Fig. 8d, the uptake quantities of the reaction bases from the one-pot titration and indirect titration methods were identical to each other for all CNT samples. Additionally, the effects of Alk and cC on the titration results of these samples are visualized in the onepot titration diagrams shown in Fig. S2eS4. The uptake quantities shown in Figs. 3f and 8d (summarized in Table S3) were then converted to the indirect titration results, showing the practical acidic functional groups including carboxylic, lactonic, and phenolic groups (by applying Equations (1.1)e(1.3)) under specific experimental conditions. Herein, cC and Alk of the reaction bases were determined to be 1 mg/mL and 0.01 N, respectively; therefore, the qmax $cC =Alk values are lower than 10% for all samples. For a fair comparison, 2% of the uncertainties in the experimental procedures during the preparation of the samples and the reaction bases arose in the one-pot titration calculation. Specifically, cC and Alk were assumed to be between 0.98 and 1.02 mg/mL and 0.0098 and 0.0102 N, respectively. Considering the absorption and desorption behaviors of the reaction bases discussed in our previous reports, rCO2 was assumed to be in the ranges of 0e0.04, 0.5e0.54, and, 0.96e0.1 for NaOH, Na2CO3, and NaHCO3, respectively. Table 2 compares the one-pot and conventional indirect (Boehm) titration results of the prepared CNT. Significantly, the results were fairly identical within acceptable error ranges. These correspondences imply that the suggested computation methodology of one-pot titration is practically valid for estimations of indirect titration results from direct titration procedures. More importantly, the repetition of complex procedures with each reaction base during the typical indirect titration process is clearly unnecessary when utilizing the one-pot titration methodology, remarkably reducing the efforts and periods required in the determination of practical acidic functional groups. The newly developed methodology still have a potential for elucidation of the non-acidic functional groups such as carbonyl group by combining the methodology with conventional indirect titration method. For this purpose, the indirect titration of each CNT sample was conducted with sodium ethoxide (NaOEt) alcoholic solution in the principle that carbonyl group reacts with NaOEt by forming the sodium salt of a hemiacetal [6]. Since the remaining acidic groups (carboxylic, lactonic, and phenolic) on CNT sample are neutralized by the rest of NaOEt, this reaction base is regarded to react with both non-acidic carbonyl and acidic carboxylic, lactonic, and phenolic groups. Therefore, the number of carbonyl groups (ncarbonyl) can be determined by

Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

739

Fig. 8. Proton-dissociated f(pKa) of 1 mg/mL (a) N6CNT, (b) N24CNT, and (c) N48CNT in 0.01 N reaction bases. (d) Reaction base uptake quantities of N6CNT, N24CNT, and N48CNT as a function of rCO2 from the one-pot titration and indirect titration methods. (A colour version of this figure can be viewed online.)

ncarbonyl ¼ nFG;NaOEt  nFG;NaOH;onepot ¼

eqNaOEt;pre  eqNaOEt;post  nFG;NaOH;onepot ; mCNT;NaOEt

(15)

where nFG,NaOEt represents the concentrations of the functional groups [meq/g] determined from the uptake of NaOEt, eqNaOEt,pre(post) is the equivalence of the pre(post)-reaction base NaOEt, mCNT, NaOEt is the effective mass of the CNT (N6, N12, N24, or N48CNT) in the each post reaction base NaOEt during the titration step, and nFG,NaOH, one-pot is the uptakes of NaOH (Total concentrations of acidic functional groups in Table 2) determined by one-pot titration methodology. nFG,NaOEt and ncarbonyl were calculated based on Equation (15) and the results were summarized in Table 3. Furthermore, our methodology can be especially useful for highly oxidized CNT [17,29] or graphene oxides [30,31] for which filtration is difficult or impossible when using the indirect titration method. Additionally, the logic used in the one-pot titration methodology has the potential to be applied to estimate the interaction between carbon nanomaterials with a variety of acid or base environments, thus breaking the aforementioned limitation and enhancing the possible applications of the titration methodology.

Table 2 Comparison of the concentrations of acidic functional groups from the one-pot and indirect titration methods (calculations based on Figs. 2f and 8d). Sample

N6CNT

Titration method

One-pot Indirect

N12CNT

One-pot Indirect

N24CNT

One-pot Indirect

N48CNT

One-pot Indirect

Concentrations of acidic functional groups (meq/g) Carboxylic

Lactonic

Phenolic

Total

0.226 ±0.013 0.231 ±0.006 0.278 ±0.016 0.281 ±0.015 0.390 ±0.015 0.381 ±0.010 0.513 ±0.016 0.521 ±0.008

0.120 ±0.013 0.110 ±0.015 0.136 ±0.016 0.130 ±0.016 0.149 ±0.015 0.145 ±0.015 0.203 ±0.017 0.189 ±0.014

0.017 ±0.002 0.035 ±0.014 0.016 ±0.002 0.028 ±0.015 0.042 ±0.003 0.062 ±0.013 0.037 ±0.004 0.069 ±0.012

0.363 ±0.001 0.376 ±0.006 0.430 ±0.001 0.440 ±0.006 0.581 ±0.001 0.587 ±0.004 0.753 ±0.001 0.780 ±0.004

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Y.S. Kim, C.R. Park / Carbon 96 (2016) 729e741

Table 3 The concentrations of the functional groups [meq/g] determined from the uptake of NaOEt (nFG,NaOEt)and those of carbonyl groups (ncarbonyl) calculated by combining one-pot titration methodology and indirect titration method (applying Equation (15)). Sample

nFG,NaOEt (meq/g) ncarbonyl (meq/g)

N6CNT

N12CNT

N24CNT

N48CNT

0.435 ± 0.011 0.072 ± 0.011

0.590 ± 0.012 0.161 ± 0.012

0.686 ± 0.012 0.104 ± 0.012

0.902 ± 0.011 0.150 ± 0.011

4. Conclusion We develop a convenient and fundamental one-pot titration methodology for the conversion of the pKa distribution function from direct titration results to practical indirect titration results for the surface characterization of the acidic groups CNT. The developed one-pot titration methodology could ultimately break the boundary between the indirect and direct titration methods for the characterization of practical acidic functional groups and further investigations of their roles in applications of carbon nanotube and other carbon nanomaterials.

[15]

[16]

[17]

[18]

[19]

Acknowledgments This research was supported by the Mid-career Researcher Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (No. 20100029244). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.carbon.2015.08.078.

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