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Abstract

The surface heterogeneity of the multiwalled carbon nanotubes is investigated on the basis of adsorption isotherms from dilute aqueous phenol solutions at various temperatures. The Dubinin–Astakhov isotherm connected with the non-symmetrical distribution function of adsorption energies has been applied to describe adsorption equilibrium. Theoretical isosteric heats of adsorption connected with the Dubinin–Astakhov isotherm have been estimated as well. It is known that the decrease of the isosteric heat of adsorption with adsorbate loading is characteristic for the energetically heterogeneous surfaces. Theoretical description of kinetics is based on the Statistical Rate Theory of Interfacial Transport. The Statistical Rate Theory approach links the rate of transport between two phases with the difference in the chemical potentials of the molecules in these phases. Theoretical studies were verified successfully using the literature experimental adsorption data.

Keywords

Multiwalled carbon nanotubes phenol surface heterogeneity heat of adsorption kinetics

Introduction

Adsorption at solid/solution interfaces plays essential role in a variety of technological processes applied in the protection of the environment. Multiwalled carbon nanotubes (MWCNTs) can be used for effective removal of aromatic organic compounds like phenol, nitrophenols, chlorophenols, etc., from contaminated water (Arasteh et al., 2010; Li et al., 2013; Liao et al., 2008; Pan and Zhang, 2014; Podkościelny et al., 2014; Shen et al., 2009; Tóth et al., 2012; Wiśniewski et al., 2012; Wu et al., 2012; Yang and Xing, 2010; Yang et al., 2016).

Due to strong van der Waals interactions, MWCNTs adhere to each other and form bundles as can be seen by TEM images. The interstitial channel space between the tubes within the bundles can be regarded as pores. Generally adsorption can occur (Shen et al., 2009; Sheng et al., 2010) on the external surfaces of the nanotubes, in the interstitial channels between nanotubes, in the hollow space inside nanotubes, and on the grooves present on the periphery of a nanotube bundle. So, the overall adsorption of phenols contains the contributions from the adsorption on the graphene surface and because of pore filling. Surface defects also play a key role in the properties of the surface (Lehman et al., 2011). Chemical heterogeneity of the nanotubes is associated with the presence of oxygen functional groups, traces of metal catalyst, and amorphous carbon. Above-mentioned heterogeneity of the surface generates the exceptional adsorption properties of MWCNTs.

Sorptive properties of MWCNTs can be modified by chemical oxidation using HNO₃, H₂O₂, KMnO₄, etc. After oxidization, the carbon nanotubes became more hydrophilic and have more functional groups on the surface. The increase of pore volume and the BET surface area are observed. It is attributed to removal of amorphous carbon, traces of metal catalyst, and hemispherical caps on the nanotubes (Shen et al., 2009; Sheng et al., 2010).

The main objective of the article is to investigate the surface heterogeneity of MWCNTs when placed in contact with dilute aqueous phenols solutions. The Dubinin–Astakhov (DA) isotherm connected with the non-symmetrical distribution function of adsorption energies has been applied to describe adsorption equilibrium. Theoretical isosteric heats of adsorption connected with the (DA) isotherm have been estimated as well. During adsorption at the solid/solution interface, a solid and a solution are usually brought into contact for a limited period of time. Theoretical description of kinetics is based on the Statistical Rate Theory (SRT) of Interfacial Transport (Azizian and Bashiri, 2008; Podkościelny and Nieszporek, 2011; Rudziński and Płaziński, 2008a, 2008b, Azizian et al. 2008; Rudziński et al., 2005; Ward et al., 1982). The SRT approach links the rate of transport between two phases with the difference in the chemical potentials of the molecules in these phases.

Theoretical studies were tested using the literature experimental adsorption data (Sheng et al., 2010). They included the data of phenol adsorption from aqueous solution on as-prepared and oxidized MWCNTs.

Theory

Adsorption equilibrium

The fundamental expression of the integral equation approach describing single-solute adsorption from dilute aqueous solutions on heterogeneous solids has the following form (Jaroniec and Madey, 1988):

θ_{t} (c) = \int θ_{L} (c, ɛ) χ (ɛ) d ɛ

(1)

where

θ_{t} (c)

is the overall adsorption isotherm,

θ_{t} (c)

= N_t/M, where N_t is the absolute adsorbed amount of solute, and M is the monolayer adsorption capacity,

θ_{L} (c, ɛ)

is the local isotherm,

χ (ɛ)

is the normalized adsorption energy distribution function, and c is the equilibrium solute concentration.

Use of so-called non-symmetrical function in the condensation approximation (CA) and Langmuir isotherm (as the local isotherm) results in well-known DA isotherm in the form (Crittenden et al., 1999; Dobruskin, 1998; Podkościelny and László, 2007; Yang and Xing, 2010; Yang et al., 2008, 2016):

θ_{t} (c) = \exp {- [\frac{kT}{E} \ln (\frac{c_{s}}{c})]^{r}}

(2)

where E is the characteristic energy of adsorption, r is the heterogeneity parameter, T is the temperature, c_s is the saturation concentration at temperature T, and k is the Boltzmann constant.

For special values of the parameter r, the (DA) isotherm is reduced to the following isotherms: the Dubinin–Radushkevich (DR) isotherm for r = 2 and the Freundlich (F) for r = 1.

Adsorption model based on the DA equation has been successfully used to describe the adsorption of simple aromatic compounds from aqueous solutions on MWCNTs (Pan and Zhang, 2014; Wu et al., 2012; Yang and Xing, 2010; Yang et al., 2008).

Heat effects of adsorption

The proper analysis regarding the heat effects accompanying the adsorption phenomenon provides additional information on the analyzed adsorption systems (Nieszporek et al., 2009; Podkościelny and Nieszporek, 2011; Podkościelny et al., 2014). The elementary equation which enables to obtain expressions for isosteric heats of adsorption q_st has the following form:

q_{st} = - k (\frac{\partial \ln c}{\partial (1 / T)})_{N_{t}}

(3)

The method to receive the theoretical expressions for $q_{st}$ is the transformation of the adequate isotherm equation for $\ln c$ and its differentiation over $(1 / T)$ . We therefore rewrite isotherm (2) as follows:

\frac{kT}{E} \ln c = - (- \ln θ_{t})^{\frac{1}{r}} + \frac{kT}{E} \ln c_{s}

(4)

Combination of equation (3) and isotherm (4) leads to the expression that defines isosteric heat of adsorption q_st:

q_{st} = q_{st, 0} + E (- \ln θ_{t})^{\frac{1}{r}}

(5)

where

q_{st, 0} = - k (\frac{\partial \ln c_{s}}{\partial (1 / T)})_{N_{t}}

(6)

The parameter $q_{st, 0}$ is frequently called as “non-configurational” isosteric heat and it shifts the heat curves on the ordinate axis.

You may notice that the equation specifying the isosteric heat of adsorption (equation (5)), and the adsorption isotherm (equation (2)) both use the same parameters, which is a great advantage of this calculation.

Kinetics of adsorption (SRT theory)

In the publications on the theoretical description of the experimental kinetic isotherms in most cases, the authors use known expressions, for example, Lagergren, pseudo-second-order equation, etc. A relatively new theory is SRT of Interfacial Transport (Ward et al., 1982). This theory was successfully used to describe kinetics of many different experimental adsorption systems in the liquid/solid phase (Azizian and Bashiri, 2008; Azizian et al., 2008; Podkościelny and Nieszporek, 2011; Rudziński and Płaziński, 2008a, 2008b).

The SRT is based on the assumption that the chemical potentials of the adsorbed molecules $μ_{s}$ and molecules in the bulk phase $μ_{b}$ are the most fundamental quantities determining the qualities of adsorption kinetics. Ward et al. have developed the following rate expression (Ward et al., 1982):

\frac{d θ}{d t} = K'_{ls} [\exp {\frac{μ_{b} - μ_{s}}{kT}} - \exp {\frac{μ_{s} - μ_{b}}{kT}}]

(7)

where

K_{ls}^{'}

describes the exchange rate between the liquid and adsorbed state at equilibrium.

The amount of adsorbate in the bulk phase strongly prevails over the adsorbed amount, so after the system is isolated and equilibrated, the adsorbate concentration in the solution, c, does not change much, $c_{eq} = c$ . Therefore, the chemical potential of the adsorbed phase $μ_{s}$ can be calculated by using isotherm equation (4):

\frac{μ_{s}}{kT} = \frac{μ_{b, 0}}{kT} - \frac{E}{kT} (- \ln θ_{t})^{\frac{1}{r}} + \ln c_{s}

(8)

The chemical potential of bulk phase $μ_{b}$ has the following well-known form:

\frac{μ_{b}}{kT} = \frac{μ_{b, 0}}{kT} + \ln c

(9)

Therefore, the expression specifying rate of adsorption can be obtained by using equations (7) to (9) (Rudziński et al., 2005):

\frac{d θ_{t}}{d t} = K'_{ls} {c \exp [\frac{E}{kT} (- \ln θ_{t})^{\frac{1}{r}}] \frac{1}{c_{s}} - \frac{1}{c} \exp [- \frac{E}{kT} (- \ln θ_{t})^{\frac{1}{r}}] c_{s}}

(10)

The actual adsorbate concentration, c, can be calculated based on the following equation (Rudziński and Płaziński, 2008b):

c = c^{0} - \frac{m_{ads} M θ_{t}}{V}

(11)

where c⁰ is the initial adsorbate concentration in the bulk phase, V is the volume of solution, and m_ads is the mass of adsorbent.

The obtained SRT kinetic equation (10) by using equilibrium (DA) isotherm (2) ensures the consistency of theoretical studies.

Results and discussion

Our theoretical studies were tested using experimental adsorption data taken from literature. They included the data of phenol adsorption from aqueous solution on as-prepared and oxidized MWCNTs reported by Sheng et al. (2010). The concise porosity characteristics of adsorbents are included in Table 1 (Sheng et al., 2010). Abbreviations CNT and CNTox mean as-prepared and oxidized MWCNTs, respectively. The increase of the S_BET surface area and pore volume were observed after oxidation by HNO₃. It is connected with removal of large amount of metal catalysts as well as amorphous carbon. It could be seen and confirmed on TEM images. The FTIR spectrum of the oxidized MWCNTs indicated that the acid treatment process introduced many functional groups on the MWCNTs surface such as carboxylic, lactonic, and hydroxyl. The major acidity was caused by carboxylic groups as could be seen from results of Boehm titration (Sheng et al., 2010).

Table 1.

The basic characteristics of the MWCNTs surface (Sheng et al., 2010).

MWCNTs	S_BET (m²/g)	V_t (cm³/g)		C (%)	H (%)	pH_pzc
MWCNTs	S_BET (m²/g)	Micropore vol. t-plot method	2–100 nm pore vol. BJH method	C (%)	H (%)	pH_pzc
CNT	72	0.008	0.41	93	0.26	∼5.5
CNTox	121	0.0004	0.49	90	0.19	<5.0

Equilibrium adsorption

The adsorption isotherms of phenol from aqueous solutions on as-prepared (CNT) and oxidized MWCNTs at 298 K, 318 K, and 338 K are presented in Figure 1(a) and (b), respectively. The symbols denote the experimental data (Sheng et al., 2010), whereas the lines are theoretical isotherms estimated from DA equation (2). It can be seen that the adjustments of DA to the experimental isotherms are very good. The results of calculations for equation (2) are summarized in Table 2. The table includes the values M of monolayer capacity, E/kT values, and the heterogeneity parameter r. The quality of the fit of equation (2) to the experimental data is described by the following Error function (residual sum of squares): $Error = \sum (\exp - theor)^{2}$ . Generally, increasing solution temperature decreases the adsorption capacity M, indicating that the adsorption process is exothermic. The best uptake of phenol was observed at 298 K both in the case of adsorption on the original and oxidized MWCNTs. In our article, the parameters r reach quite big values. Typically r ranges from 1.5 to 6–7 (Inglezakis, 2007; Pan and Zhang, 2014; Stoeckli et al., 1994). In many studies on the adsorption of phenols on carbon materials, the value of r equal to 4 was assumed (Fernandez et al., 2003; Hugi-Cleary et al., 2005; László et al., 2006; Podkościelny and László, 2007; Terzyk, 2003, 2004). Parameter r value depends on solute-adsorbent interactions, solute size, and pore size distribution (Pan and Zhang, 2014).

Figure 1.

The adsorption isotherms of phenol from aqueous solutions on as-prepared (a) and oxidized (b) MWCNTs at various temperatures. The symbols are the measured values of isotherms (Sheng et al., 2010) and the lines are the theoretical isotherms calculated from (DA) equation.

Table 2.

Parameters characterizing adsorption of phenol from aqueous solutions on as-prepared (CNT) and oxidized (CNTox) MWCNTs (Sheng et al., 2010) obtained from the (DA) equation (2).

T (K)	M (mg/g)	E/kT	r	Error
CNT
298	15.48	8.029	4.78	0.3500
318	14.38	8.181	5.77	0.7354
338	11.26	8.696	5.35	0.6806
CNTox
298	11.32	7.853	5.14	0.2035
318	10.63	7.912	5.72	0.4893
338	10.25	8.340	4.94	0.4063

The adsorption mechanism of phenol is complex. The driving forces are “π-π” electron-donor-acceptor interactions between aromatic molecules and the polarizable graphene sheets of MWCNTs (Chen et al., 2008; Pan and Xing, 2008; Podkościelny et al., 2014; Shen et al., 2009; Sheng et al., 2010). Both electron-donator and electron-acceptor groups on benzene ring can increase the adsorption on MWCNTs. The –OH group as a strong electron-donating group makes the benzene ring(s) electron rich, thus allowing the compound to interact strongly with the (electron-depleted) surfaces of carbon nanotubes.

After oxidization, hydrophilic oxygen-containing groups, including carboxylic, lactonic, and hydroxyl groups were introduced into the surface of MWCNTs. The addition of these groups results in a more negatively charged MWCNT surface due to deprotonation of carboxylic groups at the equilibrium adsorption (near neutral pH = 6.5). At this pH, adsorption of water is more favorable relative to the adsorption of simple aromatic compounds. Therefore, water is preferentially sorbed by the oxygen-containing surface groups (Tóth et al., 2012). The adsorbed water molecules can act as nuclei for the formation of larger H-bonded water clusters. As a result, the associated water can prevent migration of the phenol molecules to the hydrophobic parts of the surface and effectively reduce their uptake. Carboxylic groups on the surfaces of oxidized MWCNTs can act as electron withdrawing groups localizing electron from π system of MWCNTs, and in consequence—weakening the π–π interaction between aromatic ring of phenol and carbon nanotubes. Many studies show that oxygen functional groups decrease the adsorption of organic compounds on carbon materials such as activated carbons, carbon fibers, and MWCNTs.

Calorimetry

The next stage of our studies is analyzing heat effects accompanying adsorption of phenol on MWCNTs (Nieszporek et al., 2009; Podkościelny and Nieszporek, 2011; Podkościelny et al., 2014). Unfortunately, the experimental heats of adsorption were inaccessible for the analyzed adsorption systems, so we could calculate the theoretical ones only. From the theoretical analysis of the experimental equilibrium adsorption isotherms by DA equation (2), we obtained the quantities E/kT and r. These parameters can just be used to calculate the theoretical isosteric heats of adsorption q_st in terms of equation (5). Thus the occurrence of common parameters is the significant advantage of both equations.

Figure 2(a) and (b) presents the theoretical isosteric heats of adsorption of phenol from aqueous solutions estimated based on equation (5). The calculations were carried out by using the parameters included in Table 2.

Figure 2.

Theoretical isosteric heats of phenol adsorption from aqueous solutions on as-prepared (a) and oxidized (b) MWCNTs, calculated based on equation (5). The calculations were performed by using the parameters included in Table 2.

In all analyzed systems, the isosteric heats of adsorption decrease with the increasing surface coverage. The sharp decrease of the isosteric heat at low surface coverage followed by a slower drop at higher coverage is observed. It is known, the decrease of the isosteric heat of adsorption with adsorbate loading is characteristic for the energetically heterogeneous surfaces. The correctness of adjustment of (DA) equation (2) to the experimental adsorption isotherms is confirmed by the regular temperature dependence of the theoretical isosteric heats of adsorption for a given adsorption system (Figure 2(a) and (b)).

Kinetics of adsorption

Important issue of our research is theoretical description of adsorption kinetics. Figure 3 presents the comparisons of the experimental kinetic isotherms for the systems studied (Sheng et al., 2010) with the theoretical isotherms (lines) calculated from the SRT equation (10) at 298 K.

Figure 3.

Comparison of the experimental kinetic isotherms for phenol adsorption from aqueous solutions on as-prepared and oxidized MWCNTs (Sheng et al., 2010) with the theoretical isotherms (lines) calculated from the SRT equation (10). The values of the obtained best-fit parameters are included in Table 3.

The values of obtained parameters are included in Table 3. The table presents the monolayer capacity M values, the rate constants

K_{ls}^{'}

, E/kT, and heterogeneity parameter r values. Besides, the technical parameters of the investigated adsorption systems, such as mass of adsorbent m_ads, initial sorbate concentration c⁰, and volume of solution V are included too.

Table 3.

Values of parameters used while fitting kinetic experimental data (Sheng et al., 2010) presented in Figure 3 by SRT equation (10).

T (K)	V (dm³)	m_ads (g)	c⁰ (mg/dm³)	$K'_{ls}$	M (mg/g)	E/kT	r	Error
CNT
298	0.1	0.2	50	0.00125867	10.71	15.186	3.28	0.5928
CNTox
298	0.1	0.2	50	0.00346388	10.14	14.361	3.11	0.3539

The difference in adsorption kinetics between as-prepared and oxidized MWCNTs may be due to the changes in the surface chemistry of MWCNTs after HNO₃ oxidization, which was discussed in “Equilibrium adsorption” section.

The agreement between the theoretical kinetic isotherms and the experimental ones is good for all analyzed systems, which emphasizes the utility of the SRT model for the description of kinetics of phenols adsorption on MWCNTs surfaces. The result of the lower adsorption for HNO₃-oxidized MWCNTs indicates that surface chemical properties, rather than specific surface areas or pore volume, are important factors to determine the adsorption of MWCNTs.

Originally, the kinetics for systems studied was described in terms of pseudo-second-order (PSO) model. It should be noted that a theoretical interpretation for (PSO) model based on SRT has been derived (Rudziński and Płaziński, 2006), which indicates the universal character of this theory.

Conclusions

The concise theoretical description of the phenol adsorption from aqueous solutions on MWCNTs has been presented. The (DA) isotherm equation has been applied to investigate the effect of the surface heterogeneity. The perfect adjustments of (DA) isotherm to the experimental data have been obtained. Then, theoretical isosteric heats of adsorption connected with the (DA) model have been estimated. For the all analyzed systems, the isosteric heats decrease with the increasing surface coverage. Correctness of fitting of (DA) isotherm to the experimental data is confirmed by the regular temperature dependence of the theoretical isosteric heats of adsorption for a given adsorption system.

The final step in our research was theoretical description of adsorption kinetics based on the SRT of Interfacial Transport. The chemical potential of the adsorbed phase μ_s was determined in terms of the DA isotherm. The agreement between the theoretical kinetic isotherms and experimental ones was good for all analyzed systems. Therefore, the utility of the SRT model for the description of kinetics of phenols adsorption on the MWCNTs surfaces has been confirmed. We can conclude that greatest advantage of the model of calculations is the set of common parameters occurring in each type of equations concerning adsorption equilibrium, heat effects, and kinetics of adsorption.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Adsorption of phenol from aqueous solutions on original and oxidized multiwalled carbon nanotubes

Abstract

Keywords

Introduction

Theory

Adsorption equilibrium

Heat effects of adsorption

Kinetics of adsorption (SRT theory)

Results and discussion

Equilibrium adsorption

Calorimetry

Kinetics of adsorption

Conclusions

Footnotes

Declaration of Conflicting Interests

Funding

References