Thermodynamic Study of Methylene Blue Adsorption on Carbon

Article pubs.acs.org/jced

Thermodynamic Study of Methylene Blue Adsorption on Carbon Nanotubes Using Isothermal Titration Calorimetry: A Simple and Rigorous Approach Paulo F. R. Ortega,†,‡ Joaõ Paulo C. Trigueiro,†,§ Merly R. Santos,† Â ngelo M. L. Denadai,∥ Luiz Carlos A. Oliveira,† Ana Paula C. Teixeira,† Glaura G. Silva,† and Rodrigo L. Lavall*,† †

Departamento de Química - Universidade Federal de Minas Gerais. Av. Antônio Carlos, 6627 - Pampulha, CEP 31270-901, Belo Horizonte - MG, Brazil ‡ Centro Federal de Educaçaõ Tecnológica de Minas Gerais - Campus IV. Av. Ministro Olavo Drummond, 25 - São Geraldo, CEP 38180-510, Araxá - MG, Brazil § Instituto Federal de Minas Gerais - Campus Congonhas. Av. Michael Pereira de Souza, 3007 - Campinho, CEP 36415-000, Congonhas - MG, Brazil ∥ Departamento de Farmácia e Bioquímica, Universidade Federal de Juiz de Fora - Campus Governador Valadares. Av. Dr. Raimundo Monteiro de Rezende, 330 - Centro, CEP 35010177, Governador Valadares - MG, Brazil S Supporting Information *

ABSTRACT: In this article, a thermodynamic study of the methylene blue (MB) adsorption on carbon nanotubes (CNT), a known model system, was carried out by using a simple and rigorous experimental approach based on adsorption and isothermal titration calorimetry (ITC) experiments. Considering the thermodynamics of the process, the classical approach using the van’t Hoff approximation provided endothermic values for ΔadsH0 while the ITC measurements revealed that the adsorption of MB on both unmodified and acid-modified CNTs is an exothermic process. The thermodynamic parameters for the systems were obtained using the infinite dilution regime and ITC data: ΔadsH0 = −9.13 ± 0.02 kJ mol−1, ΔadsG0 = −21.18 ± 0.61 kJ mol−1, and ΔadsS0 = 40.42 ± 0.61 J K−1 mol−1 for uCNT and ΔadsH0 = −11.49 ± 0.34 kJ mol−1, ΔadsG0 = −27.88 ± 0.18 kJ mol−1, and ΔadsS0 = 54.97 ± 0.38 J K−1 mol−1 for f-CNT. The process is both enthalpically and entropically driven, having a more negative ΔadsG0 for the system based on a modified nanotube. With this work, we expect to increase the interest of researchers in the study of other solid−liquid adsorption systems using calorimetric techniques and also contribute to a more accurate characterization of the thermodynamic properties without the use of an excessive number of approximations.

1. INTRODUCTION

Concerning the adsorption process, besides the surface area and porosity, the surface chemistry of the adsorbent plays an important role in the mechanism of interaction.11 Covalent modification through acid treatments can functionalize the CNT with different groups (in different amounts) modifying the adsorption mechanism.6,11 This has been justified by the increase in the number of sites in the CNT surface for interaction with dye molecules through the oxygen available groups, for example.11 In the past, a large number of works have explored the adsorption isotherms and kinetic and thermodynamic parameters to explain the mechanism of the adsorption process of different environmental contaminants using modified and unmodified carbon nanotubes.12,24−26 However, an important and disadvantageous point related to some of those studies is

Carbon nanotubes (CNTs) have been intensively studied as important materials for several applications because of their outstanding electrical, mechanical, and thermal properties.1−3 To name a few, CNTs can be used in the preparation of polymer composites, devices for energy conversion, and sensors.1−8 In the environmental area, CNTs have also been widely investigated as highly adsorbent materials for various contaminants including dyes present in aqueous effluents from the textile, paper, pharmaceutical, and food industries.9,10 Dye wastes are pollutants of water and wastewater because they interfere with the solubility of gases and the penetration of solar radiation, leading to the destruction of aquatic biota.11,12 The surface modification (functionalization) of CNTs is a crucial step in their utilization for practical purposes.13−15 For example, the insertion of covalent or noncovalent groups/ molecules into CNTs can increase their dispersibility in liquid suspensions, their affinity for specific matrices in the solid phase, and their in vivo and in vitro biocompatibility.6,16−23 © 2017 American Chemical Society

Received: September 14, 2016 Accepted: December 28, 2016 Published: January 12, 2017 729

DOI: 10.1021/acs.jced.6b00804 J. Chem. Eng. Data 2017, 62, 729−737

Journal of Chemical & Engineering Data

Article

measurements obtained as the mean of 10 counts. The samples used in ZP experiments were unbuffered aqueous suspensions of the CNTs, at concentration of 1.0 mg mL−1, pH 6. Scanning electron microscopy (SEM) images were obtained on a Quanta 200 FEG microscope (FEI Company, USA) at 15 kV. For the measurements, the CNTs were dispersed in ethanol using an ultrasonic bath for 5 min, and the final suspension were dripped onto a silicon plate. Transmission electron microscopy (TEM) images were obtained on a Tecnai Spirit microscope (FEI Company, USA) at 120 kV in brightfield mode. The samples for TEM measurements were dispersed in ethanol PA using an ultrasonic bath for 5 min. The final suspensions were dripped onto a 300 mesh copper plate, and then they were stored in a desiccator for 24 h. The textural properties of CNTs were determined using the automated N2 adsorption/desorption analyzer at 77 K (Autosorb IQ2, Quantachrome, USA). The samples were prepared using sample port of 9 mm. Degassing was performed at 80 °C for 720 min. The isotherm data were used for the determination of the specific surface area by the Brunauer− Emmet−Teller method (BET). The same isotherms were used to determine the distribution of pores by the Barrett−Joyner− Halenda method (BJH). 2.3. Batch Equilibrium Experiments. Adsorption isotherms were obtained in triplicate by mixing solutions (20 mL) containing different concentrations of the adsorbates with 15.0 mg of the carbon nanotubes (u-CNT or f-CNT). All experiments were performed in 40 mL glass centrifuge tubes sealed with headspace screw caps. Initial concentrations were chosen in order to cover the complete isotherm adsorption behavior. The nanotubes were shaken and placed vertically in a thermostatically controlled bath in the absence of light at 298.15 K for 24 h to ensure the equilibrium state. Samples were taken from the adsorption tubes to determine the concentration of MB in the supernatants. The collected aliquots were then diluted properly to evaluate the absorbance in the UV/vis spectrometer (Cary 100, Varian, USA) at 664 nm. MB concentrations in the supernatants (equilibrium concentrations, Ce) were determined, and blank experiments were carried out using the same experimental procedure without the addition of CNTs in order to check the potential sorption of MB on the glass tubes. The amount of adsorbed MB was directly calculated from the difference between the initial and final equilibrium concentrations as follows

the approach utilized for the characterization of the adsorption process. Many researchers used the quality of experimental adjusts (mainly the correlation coefficient) for the selection of a physical−chemical model to explain their experimental results and the van’t Hoff approximation to calculate the thermodynamic parameters.12,24−29 Such procedures can provide an incorrect interpretation of the adsorption mechanism and the wrong evaluation of the thermodynamic properties of the system. In this article, we employed a more accurate approach to calculating the thermodynamic parameters of adsorption based on the infinite dilution regime and using isothermal titration calorimetry (ITC) as the main thermodynamic technique for obtaining the interaction energy of an adsorption process on a known model system: multiwalled carbon nanotubes (MWCNTs) and the cationic dye methylene blue (MB). The MWCNTs were also functionalized by acid treatment in order to evaluate the effect of surface and textural modifications, mainly considering the enthalpy changes in the evaluation of the calorimetric results. The main goal of this work is to contribute to the understanding of the mechanisms of adsorption on the solid/liquid interface based on the thermodynamic properties obtained by an alternative approach, without the use of an excessive number of approximations, employing the ITC technique.

2. EXPERIMENTAL SECTION 2.1. Materials. MWCNTs with >99% purity were obtained from Nanocyl (Belgium) with a diameter of approximately 10 nm and an average length of 1.5 μm. MB with >98% purity was purchased from Fluka (Brazil) and used without further treatment. The modified carbon nanotubes were prepared as follows. Unmodified carbon nanotubes (3.0 g, named u-CNT) were mixed with 132.0 mL of H2SO4 (Vetec, Brazil, 99%) and 44.0 mL of HNO3 (Vetec, Brazil, 99%), refluxed under stirring (420 rpm), and ultrasonicated for 3 h at 55.0 °C. The modified CNTs (named f-CNT) were washed with deionized water until pH 6 was reached, filtered over vacuum using a polytetrafluoroethylene (PTFE) membrane filter (0.45 μm), and finally dried at 100 °C for 12 h. 2.2. Characterization of Carbon Nanotubes. The thermal properties of CNTs were evaluated by thermogravimetric analysis (TGA). TGA was carried out from room temperature to 1000 °C under synthetic air flow (25 mL min−1) at a heating rate of 5 °C min−1 using a TA Instruments TGA Q5000 (USA). Fourier transform infrared (FTIR) spectroscopy was recorded on an FTIR GX spectrometric analyzer (PerkinElmer, USA) using KBr pellets. The spectra were obtained with 128 scans at a resolution of 4 cm−1 between 4000 and 400 cm−1 and were processed using the software supplied with the instrument (Spectrum software). Raman spectroscopic measurements were carried out using a Senterra Raman spectrometer from Bruker (USA) with a CCD detector equipped with an optical microscope (Olympus BX51) and a 633 nm laser. Good signal-to-noise ratios were obtained with 100 scans accumulation for each sample using a laser power of 2 mW with a 2.5 cm−1 spectral resolution. Zeta potential (ZP) values were obtained through electrophoretical mobility (EM) measurements using the Smoluchowski equation.30 The data were obtained from a Malvern Zetasizer Nano ZS instrument (Malvern Instruments, UK), and ZP values were calculated as the average of 3 independent

Γ=

⎛ C0 − Ce ⎞ ⎜ ⎟V ⎝ m ⎠

(1)

where Γ is the adsorbed amount of each MB by CNTs (mg g−1) after thermodynamic equilibrium, C0 is the initial concentration (mg mL−1), Ce is the equilibrium concentration (mg/mL), V the solution volume (mL), and m is the mass of CNTs (g). The adsorbates were dissolved in distilled water with no strict pH control. It is well reported in the literature that there is no considerable difference in the adsorption of MB on CNTs over a wide range of pH.29 2.4. Isothermal Titration Calorimetry. Calorimetric titrations were carried out at 298.15 K in duplicate with a VP-ITC microcalorimeter from Microcal after the electrical and chemical calibration. Each titration experiment consisted of 26 successive injections of an aqueous solution of methylene blue (1.5 mM) into the reaction cell loaded with 1.5 mL of aqueous 730



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suspensions (1.33 mg mL−1) of carbon nanotubes at intervals of 360 s. The first injection of 1 μL was discarded to eliminate the diffusion of material from the syringe into the calorimetric cell. Subsequent injections were performed at a constant volume of 10 μL of MB with an injection time of 2 s. The amount of CNTs in the calorimeter cell varied from 1.33 to 1.14 mg mL−1, and the concentration of the MB, from 0 to 0.214 mM. These concentrations were preprogrammed to maintain the mole ratio between CNT and MB as compatible with the isotherms obtained in the batch equilibrium experiments. The raw data were edited using Microcal Origin 7.0 software for ITC after the subtraction of blank experiments (dilution of MB in water). Figure 2. Raman spectra showing two characteristic bands of CNTs: D and G.

3. RESULTS AND DISCUSSION 3.1. Characterization of Carbon Nanotubes. The CNT samples were fully characterized to evaluate the influence of the different acid treatments on their thermal, morphological, and textural properties. This will allow a proper discussion of the adsorption process. Vibrational spectroscopy was utilized to confirm the insertion of the functional groups on the CNTs. The FTIR spectra are shown in Figure 1. The presence of bands at 3430 cm−1 can be

number of defects in the graphitic crystal structure of CNTs, including the addition of oxygenated surface groups as evidenced by the FTIR. The changes in the surface properties of CNTs after functionalization can be clearly observed by inspecting their zeta potential values. The dispersion of u-CNT showed a ZP value of 18.1 ± 3.7 mV in deionized water (pH 5). In contrast, after functionalization the CNTs become negatively charged with the ZP value of −37.6 ± 1.9 mV due to negatively charged groups at the edge and on the outermost wall of the tubes. Thermogravimetric analysis allowed the evaluation of changes in the thermal stability and inferences to be made about the extent of surface functionalization of the carbon nanotubes after acid treatment.4 Figure 3a,b shows the TGA and DTG curves for the two studied nanotubes.

Figure 1. FTIR spectra of the carbon nanotubes.

ascribed to O−H stretching vibrations due to chemisorbed water. The bands at ∼1635 cm−1 are characteristic of the CO carboxylic group stretch and are present only for f-CNT, showing the insertion of oxygenated groups with acid functionalization. The bands at ∼1385 cm−1 represent O−H bending modes, and that at ∼1115 cm−1 represents the C−O vibration of various oxygen-containing groups.31,32 Figure 2 shows the Raman spectra for different evaluated CNTs. Two regions are important for the characterization of structural damage on the surface after functionalization: the region between 1200 and 1400 cm−1 represents the disorder peak in the so-called D band, and the region between 1500 and 1660 cm−1 is due to the atoms with tangential vibrational movement that generates the graphitic band called the G band.33 The structural damage and chemical changes can be evaluate by the ratio IG/ID (ratio between the intensity of the G band and the intensity of the D band).34 The Raman spectra were normalized by taking the intensity of the D band as 100% for easy visualization of the changes in the ratio between the G and D bands. The IG/ID ratios were 0.78 and 0.50 for samples u-CNT and f-CNT, respectively. According to our results, the acid treatment affected the structure of CNTs, and the reduction of the IG/ID ratio is related to the increase in the

Figure 3. (a) TGA and (b) DTG curves of the CNTs. 731



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Figure 4. TEM images of modified and unmodified carbon nanotubes: (a) u-CNT and (b) f-CNT.

At temperatures below 120 °C, the weight loss is associated with the evaporation of the physically adsorbed water molecules. Between 120 and 400 °C, the weight loss can be attributed to decarboxylation and elimination of the hydroxyl functional groups on the surface of the nanotubes.4 In this range of temperature, the observed weight losses were on the order of 9% for f-CNT and lower than 1% for u-CNT, showing the efficiency of the functionalization process. The thermogravimetric analysis also reveals a possible fragmentation of the nanotubes with the acid procedure. The weight loss between 400 and 490 °C (small peaks on the DTG curves) observed for the f-CNT sample is related to the thermal decomposition of carbonaceous fragments (also reported as debris or fulvic acids) adsorbed on the surface of acid-oxidized carbon nanotubes.35 This step is absent in the u-CNT sample. The weight losses at temperatures above 500 °C are related to the oxidation of the carbon nanotube structure. No appreciable change in the peak of the DTG curves (∼600 °C) was observed for the studied materials. SEM and TEM were used to identify changes in the nanotube structure caused by the acid treatments. Representative TEM images of u-CNT and f-CNT are presented in Figure 4. The physical characteristics of the u-CNT and f-CNT samples, such as the length, outer diameter, and aspect ratio, were obtained from a statistical analysis of 80 nanotubes using SEM and TEM images, which are presented in Table 1. The

Figure 5. N2 adsorption/desorption isotherms and pore size distribution of the CNTs (inset).

system.36 The curves show hysteresis loops generated by the capillary condensation of the adsorbate in the mesoporous structure, with the pore sizes in the range of 5 to 55 nm for both materials and compatible with the adsorption of large molecules such as MB. The values for the specific surface area (BET area) obtained by using the BET formalism (SBET) correspond to 235 and 254 m2 g−1 for u-CNT and f-CNT, respectively. Acid functionalization could increase the SBET values because of the creation of defects in the CNT structure and the formation of new cavities between adjacent tubes in a bundle and between bundles. However, no significant difference can be considered in SBET (considering the technical error) probably due to larger amounts of fragmented carbonaceous material adsorbed on the nanotubes after the functionalization step (as detected by thermogravimetric analysis). Considering these results, it was verified that the acid treatments changed the surface of the nanotubes by adding oxygenated functional groups, with no practical change in the surface area in comparison to that of the unmodified one. 3.2. Adsorption Isotherms. The adsorption phenomenon occurs when the average equilibrium concentration of some species i is greater at the interface than at the two phases in contact. Thus, the adsorption isotherm describes how the molecules are distributed between the liquid phase and the interface when the process reaches the thermodynamic equilibrium state. The excess solute in the interface in relation to the phases in contact is defined as the adsorbed amount (Γ) of i species. Figure 6a shows the isotherms of adsorption of the MB on the CNTs at 298.15 K (Γ versus MB equilibrium

Table 1. Physical Characterization of Multiwalled Carbon Nanotubes before and after Acid Treatmenta

a

CNTs

length/μm

outer diameter/nm

aspect ratio

u-CNT f-CNT

2.9 ± 1.0 1.9 ± 0.9

8.9 ± 2.6 8.1 ± 0.7

326 234

Average values for 80 nanotubes.

values obtained for the length of the u-CNT are higher than those provided by the supplier. The data show a small decrease in length but no significant change in diameter. The acid treatment breaks the tube but does not cause substantial structural damage (related to the reduction of the number of walls) leading to a reduction in the CNT aspect ratio. An analysis of the interfacial area and pore size distribution is critical to characterizing an adsorbent material. Figure 5 shows the N2 adsorption/desorption isotherms and pore size distribution estimated using the BJH method. The N2 adsorption/desorption curves obtained for both samples can be categorized as type-IV isotherms according to the IUPAC 732



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concentration Ce). Figure 6b shows the isotherms normalized by the SBET.

Equation 2 represents the mathematical expression for the Langmuir model Ce C 1 = e + Γi Γmax ΓmaxKL

(2) −1

where Ce is the equilibrium MB concentration (mg mL ), Γ is the amount of MB adsorbed (mg g−1), KL (mL mg−1) is a Langmuir constant related to the affinity of binding sites (adsorption energy), and Γmax (mg g−1) is a Langmuir constant related to the maximum monolayer adsorption capacity, which describes the theoretical saturation capacity of the monolayer.38,40 The Freundlich model, even being empirical, is used for heterogeneous surfaces having different sites with diverse energies of adsorption and with the possibility of the formation of multilayers40 ln Γi = ln KF +

1 ln Ce n

(3) −1

where Ce and Γ were previously described and KF (mg g ) and n−1 (g mL−1) are the Freundlich constants describing the adsorption capacity and the adsorption intensity (energy distribution of the adsorption sites), respectively.41 The values obtained after these fittings are present in Table 2. The r2 values obtained for both Freundlich and Langmuir adjustments indicate, in principle, that both models are suitable for the description of the adsorption equilibrium of MB on CNTs. In fact, the Γmax values obtained by the Langmuir fit are consistent with the results observed in the adsorption isotherms, where Γmax is greater for f-CNT. The KL values indicate that the strongest interactions between MB and CNT were established at the more hydrophilic surfaces. The zeta potential results (at pH 6) showed a negative net charge for the carbon nanotubes modified by the acid treatments whereas the unmodified sample has a positive net charge. Because the MB is a cationic dye, it is natural to suggest that interactions of an electrostatic nature are mainly responsible for the increase in the MB adsorbed amount on f-CNT. Regarding the Freundlich model, it is also suitable to describe our experimental results according to the quality of the fit, and it is possible to infer the existence of different sites on the carbon nanotube surface with different energies of interaction. This was reinforced by n−1 values lower than the unity, which is related to the degree of heterogeneity of the surface.40,42 According to the reviewed literature, several researchers tend to choose between models based only on the fit parameters.12,24−29,43−45 However, the adsorption isotherms do not allow the real distinction of molecular events involved in the system and often reveal only the efficiency of the adsorptive process. Even with an excellent fit, the Langmuir model would not be appropriate in our case because adsorbents such as CNTs do not have homogeneous surfaces, especially after the functionalization process. The Langmuir model has been applied by many authors to study the adsorption of dyes on

Figure 6. (a) Isotherms for the adsorption of MB on CNTs at 298.15 K. (b) Isotherms normalized with respect to the specific surface area of CNTs.

For both evaluated CNTs, the amount of adsorbed MB increases with the increase in the equilibrium concentration and tends toward a constant saturation level of the interface. The changes on the surface of the nanotubes caused by acid treatment favor the adsorption process. For f-CNT, the highest adsorption capacity can be justified by the greatest number of functional groups per unit of area, considering the small variation in SBET compared to that of u-CNT. In this case, the influence of the functionalization procedure on the adsorption process is clear. The Langmuir and Freundlich isotherm models are the most common ones employed for the representation of the nonlinear adsorption processes in the literature.12,24−26,37 The Langmuir model assumes an ideal system where the adsorbate molecule interacts with the adsorbent surface at well-defined sites, forming a homogeneous monolayer. Each site can absorb only one molecule, and the energy involved in the adsorption of one molecule is the same for all sites in the adsorbent surface with no interaction between adjacent adsorbed molecules.38,39

Table 2. Parameters of the Freundlich and Langmuir Models Obtained at 298.15 K Freundlich adsorbent u-CNT f-CNT

−1

n /mL g

−1

0.57 ± 0.03 0.28 ± 0.01

KF/mg g

Langmuir −1

328.25 ± 4.41 264.49 ± 1.83

r

2

0.97 0.98 733

−1

Γmax/mg g

KL/mL mg−1

r2

63.53 ± 2.91 99.80 ± 2.78

0.08 ± 0.01 0.42 ± 0.10

0.98 0.99



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Values of ln K0, and consequently ΔadsG0, finally could be obtained by plotting ln(Γ/Ce) versus Γ with the extrapolation of Γ to zero.51 To obtain the ΔadsH0 values, we used calorimetric experiments. The ITC has been widely employed in the study of many molecular processes because of its high sensitivity and ability to detect small energy flows.52−54 However, the use of such a technique is little explored for adsorption studies. To our knowledge, this is the first work using ITC to evaluate the adsorption of MB on modified and unmodified carbon nanotubes. Figure 7a presents the ITC titration curves for the titration of the MB solution into the carbon nanotube suspension. The

CNTs, including the calculation of the thermodynamic parameters of adsorption.12,24,25,46−48 Yao et al. studied the adsorption of methylene blue on CNT.46 In their work, the isotherms were obtained at different temperatures, and the Langmuir constant, KL, was taken as the thermodynamic equilibrium constant for the process. Then, with the KL values at different temperatures, the thermodynamic properties were calculated by the following fundamental expressions ΔadsG 0 = −RT ln KL ln KL =

ΔadsS 0 Δ H0 − ads R RT

(4)

(5)

where KL was previously described, R is the universal gas constant, T is the equilibrium temperature of the system, ΔadsG0 is the Gibbs standard free energy of adsorption, ΔadsH0 is the standard enthalpy of adsorption, and ΔadsS0 is the standard entropy of adsorption. The values obtained by Yao and co-workers for ΔadsG0, ΔadsH0, and TΔadsS0 were −11.0 kJ mol−1, 7.29 kJ mol−1, and 64.6 J (mol K) −1 at 298.15 K, respectively.46 These data will be used as a reference in the present work. 3.3. Thermodynamic Study. Noncalorimetric approaches to the determination of the thermodynamic properties of systems involving binding or association reactions have limitations that are already known in the literature, especially van’t Hoff analysis.49,50 For this reason, in the present work we performed the calculation of the thermodynamic properties using a different and rigorous approach. ΔadsG0 is calculated from the thermodynamic relationship51 ΔadsG 0 = −RT ln K 0

(6)

0

where K is the equilibrium constant of the adsorption process. The constant K0 for the adsorption process can be obtained sol by considering that at thermodynamic equilibrium μint i = μi int/sol 0 int/sol int and μi = μi + RT ln ai , where μi is the chemical potential of the i species (in our case, the MB) adsorbed at the CNT−solution interface; μsol i is the chemical potential of the i species in solution (at equilibrium); μ0i is the chemical potential of the i species under standard conditions; and aint/sol is the i activity of i species (in solution or at the CNT−solution interface). After some manipulation of the equations, we have ⎛ γ int C int ⎞ ⎛ a int ⎞ ln K 0 = ln⎜⎜ isol ⎟⎟ = ln⎜⎜ isol isol ⎟⎟ ⎝ ai ⎠ ⎝ γi Ci ⎠

Figure 7. Standards enthalpies of (a) injection and (b) adsorption as a function of the system composition at 298.15 K.

ordinate axis represents the enthalpy changes due to the MB injection (ΔinjH0 in kJ mol−1 of titrant), and the abscissa axis is the corresponding composition of the system (MB/CNT concentration ratio). Figure 7b shows the ΔadsH0 values (obtained by the difference between the ΔinjH0 for MB titration in the presence of CNTs and the ΔinjH0 for MB titration in water) as a function of the system composition. According to our data, the dilution of MB in water is an endothermic process. This could be due to the breakdown and desolvation of higher-order dye aggregates upon dilution. On the other hand, in the presence of carbon nanotubes the MB titration curves assume exothermic values (with ΔinjH0 values gradually approaching zero) due to the adsorption process. uCNT has a less negative profile and f-CNT is the more negative one. We assume the experimental quantity, ΔadsH0, to be a result of different contributions at the molecular level (eq 9):54

(7)

where Cint is the concentration of the adsorbed MB at the i CNT−solution interface (mg g−1), Csol i is the concentration of the MB in solution at equilibrium (mg mL−1), γint i is the activity coefficient of the adsorbed MB, and γsol is the activity i coefficient of the MB in solution at equilibrium. Concerning the fact that adsorption occurs on a solid phase, where the behavior of the adsorbate is similar to that of the solid, γint i was taken as a unit. As the concentration of the solute approaches zero, the activity coefficient γsol i also was considered to be unity, and eq 7 was reduced to the following form: ⎡ ⎛ Γ ⎞⎤ ⎛ a int ⎞ ⎛ C int ⎞ ln K 0 = ln⎜⎜ isol ⎟⎟ = ln⎜⎜ isol ⎟⎟ = lim ⎢ln⎜ ⎟⎥ ⎝ ai ⎠ ⎝ Ci ⎠ Γ→ 0⎢⎣ ⎝ Ce ⎠⎥⎦

(8) 734



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ΔadsH 0 = Δdeh H 0 MB − H2O + Δdeh H 0CNT − H2O

Table 3. Thermodynamic Properties of MB Adsorption on the CNTs Obtained by ITC at 298.15 K

+ Δint H 0 H2O − H2O + Δint H 0 MB − MB(CNT) + Δint H

0 MB − CNT

(9)

The left-hand side in the equation is the quantity that is experimentally available using ITC, and the right-hand side is a decomposition (or a model) of its five possible contributions. ΔdehH0MB−H2O and ΔdehH0CNT−H2O are the standard enthalpies of dehydration for the MB and the CNT, respectively (both endothermic). Exothermic ΔintH0H2O−H2O is related to the interaction between water molecules released from the desolvation process. ΔintH0MB−MB(CNT) (exothermic or endothermic) describes the interaction energy between MB molecules adsorbed at adjacent sites on the CNTs surface, and exothermic ΔintH0MB−CNT gives the intensity of the enthalpic interactions between the MB molecules and the carbon nanotube surface. These interactions between the MB molecules and the surface of the carbon nanotubes have contributions of a hydrophobic nature, π-stacking interactions, electrostatic forces, and hydrogen bonds. Naturally, ΔdehH0CNT−H2O, ΔintH0MB−MB(CNT), and ΔintH0MB−CNT differ from one CNT to another. For the discussion that follows, it is important to emphasize that ITC measurements do not allow the quantification of the values of each proposed ΔH0 (right side of eq 9), and we use this model in a qualitative way. Furthermore, throughout the titration, there are no changes in the enthalpic contribution of each interaction described in eq 9. However, it is possible to observe variations in the number of each of those interactions. After a comparison between f-CNT and u-CNT, it is easy to verify the highest negative ΔadsH0 values throughout the entire [MB]/CCNT range for f-CNT. This can be explained by the greatest extent of functionalization of this nanotube and practically the same SBET. The more hydrophilic surface implies more negative values for ΔintH0MB−CNT due to the insertion of functional groups, in agreement with the zeta potential data. The contribution ΔintH0H2O−H2O must also be more negative in the case of the f-CNT sample due to the release of a larger number of hydration water molecules. It should be mentioned that the effect of the pore size distribution was not considered in our discussion because our data showed a small number of micropores and a wide distribution of the mesopores for all assessed nanotubes. In addition, the pores of all CNTs are larger than the molecular dimensions of the MB molecule (1.43 nm × 0.61 nm × 0.4 nm).55 For the thermodynamic characterization of the system, the values of ln K0 and ΔadsG0 were obtained by taking into account the infinite dilution regime. In this case, parameters ΔadsH0 and ΔadsS0 must be obtained for the same boundary condition. By using eq 10, we can calculate ΔadsS0 by considering the ΔadsH0 value acquired by ITC after the extrapolation of the curves at [MB]/CCNT equal to zero (infinite dilution regime). Table 3 shows the values of the thermodynamic properties obtained using this approach. ΔadsG 0 = ΔadsH 0 − T ΔadsS 0

adsorbent

ΔadsG0/kJ mol−1

ΔadsH0/kJ mol−1

ΔadsS0/J K−1 mol−1

u-CNT f-CNT

−21.18 ± 0.61 −27.88 ± 0.18

−9.13 ± 0.02 −11.49 ± 0.34

40.42 ± 0.61 54.97 ± 0.38

while the ITC measurements proved that the adsorption of the MB on modified and unmodified CNTs is an exothermic process. The use of ITC allows us to obtain results with great realism and avoids the use of many approximations in the description of the system. The data in Table 3 also show that the MB adsorption process is spontaneous, with ΔadsG0 becoming more negative with the increase in the degree of functionalization of the nanotubes. There is an increase in the system entropy in all cases mainly due to the increase in the configurational entropy of water molecules that are desorbed and released into the bulk solution. Because f-CNT is less hydrophobic and consequently more hydrated, the ΔadsS0 value for f-CNT is still greater than that for u-CNT. Finally, the thermodynamic parameters obtained by infinite dilution are independent of the nature of the system once it is not necessary to impose any interaction model. In addition, as a consequence of the low concentrations of the adsorbate, we can disregard MB−MB interactions and other competition effects at the surface of CNT in our approach. For comparison, in the Supporting Information we add the results of the fit by applying the classical model to the ITC data. The results obtained by nonlinear regression (Wiseman isotherm) were inadequate for our system probably because this approach considers that the binding occurs through only one step where the ligands bind to the receptors which contain one set of degenerate sites. However, the physicochemical characterization presented in this work showed the presence of very heterogeneous material which must have different sites with different energies.

4. CONCLUSIONS According to the data and discussion presented in this work, it is possible to affirm that the quality of the fit cannot justify the choice of a model to represent the physical meaning of a system. Such an approach tends to be a source of errors in the thermodynamic characterization of the process. In the present case, the Langmuir fits cannot be used to model the system due to nonuniformity of the carbon nanotubes surface. Together with the van’t Hoff fits, the utilization of both approaches gives inconsistent information about the adsorption process, especially ΔadsH0. The use of the microcalorimetry technique provides more detailed information about the enthalpy changes throughout all extension of the adsorption experiment with great accuracy and without the use of many approximations. Therefore, we demonstrate that the adsorption of MB on CNT is an exothermic process and that the use of a simple technique such as ITC, combined with other experimental techniques, allows an appropriate thermodynamic evaluation of the adsorption process. Through suitable considerations, it is possible to model the system in a most convenient way to extract more accurate information about adsorption mechanisms at the molecular level.

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(10)

There are discrepancies between the results presented in Table 3 (ITC-based approach) and those obtained by Yao and co-workers.46 The use of the Langmuir model together with the van’t Hoff approximation gives endothermic ΔadsH0 values

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00804. 735



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Article

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Thermodynamic parameters obtained by the adapted Wiseman isotherm: related methodology, data, and results and discussion. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +55 (31) 34097550. Fax: +55 (31) 34095711. ORCID

Rodrigo L. Lavall: 0000-0003-1975-1827 Funding

The authors are grateful to Fundaçaõ de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG: APQ-02273-14), ́ Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq: DT-310175/2014-3, 458487/2014-7; MCT/ CNPq-NANO: 550321/2012-8 - Brazil) and Financiadora de Estudos e Projetos (FINEP/CT-INFRA 01/2013, 0633/13) for financial support. P.F.R.O. and J.P.C.T. thankfully acknowledge the scholarships received from CNPq. This work is a collaborative research project with members of Rede Mineira ́ de Quimica (RQ-MG) supported by FAPEMIG (project CEX RED-0010-14). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the Centro de Microscopia/UFMG for the provided images.

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