Influence of Carboxylation on Structural and Mechanical Properties of

Article pubs.acs.org/JPCC

Influence of Carboxylation on Structural and Mechanical Properties of Carbon Nanotubes: Composite Reinforcement and Toxicity Reduction Perspectives Karolina Z. Milowska* Photonics and Optoelectronics Group, Department of Physics and Center for NanoScience (CeNS), Ludwig-Maximilians-Universität München, Amalienstraße 54, 80799 Munich, Germany Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 Munich, Germany ABSTRACT: Carboxylation of carbon nanotubes (CNTs) is an important process that is applied routinely for various applications, in particular for biomedical usage and the manufacturing of next-generation composite materials. This study investigates the influence of carboxylation on the structural and mechanical properties of CNTs. Ab initio calculations were performed within the density functional theory framework for metallic and semiconducting single- and multiwalled CNTs, imperfect and carboxylated at various concentrations, including disorder. The morphologies were analyzed, the stabilities of the carboxylated CNTs were determined, relevant electronic properties were evaluated, and elastic moduli were calculated (Young’s, shear, and bulk moduli, as well as Poisson’s ratio). The properties of grafted (COOH, OH, O) and imperfect (vacancy defects) CNTs were compared with those of carboxylated CNTs. In particular, both the structural and elastic properties were found to exhibit significant differences between COOH-grafted and carboxylated systems, with the dependence of the Young’s modulus on the concentration of functional groups or vacancies being the most striking. Experimental observations showing that small concentrations of COOH groups improve the strength of CNTs in comparison to that of defected CNTs are explained. The critical concentration above which the carboxylation of CNTs leads to significant structural changes of the nanotubes was determined. These changes were found to result in a significant decrease of the Young’s modulus, making the CNTs unsuitable as composite reinforcements. Moreover, mechanisms governing the toxicity reduction of carboxylated CNTs are explained.

1. INTRODUCTION After their discovery in 1991,1 carbon nanotubes quickly became considered to be ideal candidates for reinforcement in composite materials, mostly because of their unique characteristics, such as high stiffness, high aspect ratios, and low densities. New composite materials created by adding carbon nanotubes (CNTs) to various materials such as alloys, polymers, and metals are expected to have enhanced mechanical strengths, electrical and thermal conductivities, and chemical stabilities in comparison to their base constituents. Unfortunately, pure CNTs are not soluble in water or organic solvents and have a tendency to aggregate. This sharply limits their usage in industrial applications. Chemical functionalization of CNTs allows for improved bonding of the CNTs into the composite matrix and their debundling2,3 but can decrease their stiffness.4−6 Among different types of chemical modifications, carboxylation is the most common and effective procedure.7,8 It is an important process that is applied routinely for several purposes, not only for increasing the dispersibility of nanotubes in composites. Carboxylation is used for nanotube purification and as a first step of target functionalization.9,10 COOH groups allow for the coupling of other molecules through the creation of amide and ester bonds. This enables the formation of © 2015 American Chemical Society

building blocks for various applications, including chemical, biological, and medical sensing; drug delivery; and catalysis.11−15 Carboxylated CNTs have been successfully used for water filtration,16 anticancer therapy,17 and the removal and inactivation of viruses and bacteria.18 Moreover, carboxylation minimizes the negative effects of using pure CNTs on humans and the environment.13,19 To facilitate a full understanding of the influence of carboxylation on the structural and mechanical properties of CNTs, a theoretical study seems to be s prerequisite. Nearly all theoretical studies of carboxylated CNTs4,20−25 present a picture that is not consistent with experimental observations.3,19,26−30 Many people have falsely believed that the common oxidizing acid functionalization treatment yields CNTs with COOH groups added to the sidewall and that the carboxylation and grafting processes lead to similar property changes. Nevertheless, carboxylation is usually carried out by treating CNTs with oxidizing inorganic acids, such as HNO3 and H 2 SO 4 , alone or in combination with peroxide.9,16,19,26−28,31,32 The carbon atom in the COOH linkage Received: August 28, 2015 Revised: October 17, 2015 Published: October 26, 2015 26734

DOI: 10.1021/acs.jpcc.5b08402 J. Phys. Chem. C 2015, 119, 26734−26746

Article

The Journal of Physical Chemistry C

Figure 1. (a) Schematic views of all types of nanotubes studied: (i) (9,0), (ii) (8,2), (iii) (5,5), (iv) (14,0), and (v) (5,0)@(14,0). (b) Structural representations of all surface modifications considered: (i) vacancy defects, (ii) carboxylation, (iii) COOH grafting, (iv) hydroxylation, (v) epoxidation, (vi) simultaneous epoxidation and carboxylation, (vii) simultaneous hydroxylation and carboxylation, and (viii) simultaneous epoxidation and hydroxylation. (c) Transverse (d1) and longitudinal (d2) distances between the two carbon atoms from two carboxylic groups used for disorder analysis. Both the cross-sectional and side views of the local arrangements of functional groups or defects are presented for each system.

In this article, we consider grafted (COOH, OH, O), imperfect (vacancy defects), and carboxylated CNTs and compare their structural and mechanical properties. We analyze their morphologies, determine the stabilities of carboxylated CNTs, and analyze their elastic properties with respect to the concentrations and mutual orientations of functional groups or vacancies. Moreover, we consider metallic and semiconducting, chiral and achiral, single-walled and multiwalled nanotubes (SWNTs and MWNTs, respectively) that are imperfect and carboxylated at various concentrations, including disorder. Through this systematic study, we were able to (i) observe the emergence of morphology changes caused by functionalization, (ii) determine how the properties of the functionalized

is one of the CNT backbone carbons. This requires one of the sidewall carbon atoms to have three new bonds to oxygen atoms, leaving only one bond to another sidewall carbon, which means that a surface group and a vacancy in the CNT wall are present simultaneously. For each COOH group created, three bonds in the CNT wall are broken. This introduces major damage to the wall that affects structural, electronic, and mechanical properties and has even been shown to lead to spontaneous degradation.19 Aside from radicals, however, none of the simple adsorbates functionalizing pristine CNTs, including COOH as adducts, have been shown to cause such damage to nanotube structure. 26735


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All presented results are based on calculations of the groundstate total energy, not including vibrational dynamical contributions to the free energy. Therefore, we performed a very careful search through configuration space to optimize the geometries of all functionalized systems that guaranteed the energetically most favorable configurations. In comparisons of the stabilities and morphologies of various structures, we always refer to the systems characterized by the equilibrium geometry. In the present article, we follow the convention of other authors and measure the concentrations of functional groups as the number of groups N per number of carbon atoms in the supercell, NC, which is equal to 72, 56, 60, 112, and 152 for (9,0), (8,2), (5,5), (14,0), and (5,0)@(14,0) CNTs, respectively. To facilitate comparisons between different CNTs, we also express the percentage concentrations of functional groups as C = (N/NC) × 100%. The morphology changes are described in terms of changes in the lattice constant along the tube axis l, the radius of the tube r, and the coefficient of variation of the radius CV. l and r take on the values that minimize the total energy of the functionalized or defected systems with the optimized positions of all atoms in the supercell (i.e., with reduced forces acting on the atoms). Because the cross sections of the functionalized CNTs in the plane perpendicular to the CNT symmetry axis were no longer circular (see Figure 1), the average radius of the nanotube had to be calculated. The average radius was determined as a geometrical average of distances between the axis of the tube and the carbon atom positions that formed the lateral surface of CNTs after functionalization. In other words, the C atoms incorporated into the carboxyl groups were omitted in the calculation of the radius of the carboxylated nanotube. One should remember that the carboxylation of a CNT simultaneously introduces a surface group and a vacancy defect in the nanotube wall; therefore, not only the cross section but also the cylindrical shape of the CNT is changed. To quantitatively describe the total shape change, a coefficient of variation of the radius was used. This CV is defined as the ratio of the standard deviation in the CNT radius to the mean CNT radius (calculated as the arithmetic average). The stability of the functionalized structures can be quantitatively described in terms of the adsorption energy,6,41,42 sometimes called the binding energy,20,21,43 packing energy,23 or reaction energy.44 The adsorption energy per group, Eads/N, was calculated as

systems evolve with the concentration and aggregation pattern of functional groups/defects, and (iii) evaluate the critical density of adsorbed molecules above which CNTs are unsuitable for use as composite reinforcements.

2. METHODS AND COMPUTATIONAL DETAILS The presented studies of the structural and elastic properties of carboxylated CNTs were carried out with in the framework of spin-polarized density functional theory (DFT)33,34 as realized in the SIESTA package.35,36 The generalized gradient approximation of the exchange-correlation functional in the Perdew−Burke−Ernzerhof (PBE)37 parametrization was applied to all systems. Valence electrons were represented with double-ζ numerical basis sets of orbitals localized on atoms, with polarization functions also included. The influence of core electrons was taken into account within the pseudopotential formalism. The norm-conserving Troullier−Martins nonlocal pseudopotentials38 used in our studies were cast in Kleinman− Bylander separable form.39 The kinetic cutoff for real-space integrals was set at 350 Ry. The Brillouin zone was sampled in the 1 × 1 × 10 Monkhorst and Pack scheme.40 During all calculations, the self-consistent field (SCF) cycle was iterated until the total energy changed by less than 10−5 eV/atom. The convergence criterion for the density matrix was set to 10−4. The structural optimization was conducted using the conjugate gradient algorithm to achieve residual forces acting on the atoms of less than 0.01 eV/Å. Calculations were performed within the supercell scheme with a lateral separation between nanotubes of 30 Å, which is large enough to eliminate completely spurious interactions between neighboring cells. To explore the influence of carboxylation on all types of CNTs, we considered four different SWNTs, namely, (9,0), (8,2), (5,5), and (14,0), and one example of MWNTs, namely, nominally double-walled nanotubes (DWNTs) of the form (5,0)@(14,0) (see Figure 1a). All of these CNTs were considered as both (i) defected (vacancy defects) and (ii) carboxylated (see panels i and ii, respectively, of Figure 1b). For the sake of comparison with previous works, (9,0) CNTs grafted with COOH groups [Figure 1b(iii)] were prepared. All systems were examined at various concentrations reaching up to 4.6 × 1014 COOH groups or vacancies per square centimeter of CNT surface. Moreover, functionalizations with hydroxyl (OH) and epoxy (O) groups and their combinations with carboxylated (9,0) CNTs [Figure 1b(iv− viii)] were studied. The molecules at various concentrations were attached to the sidewalls of the CNTs and distributed around the exterior surface of the CNTs as homogeneously and symmetrically as possible. Nonetheless, systems used for carboxyl group aggregation studies (on the lateral surface of the CNTs) had those groups placed randomly. Two examples of such systems, namely, supercells containing (9,0) CNTs with exactly two carboxyl groups per two primitive unit cells and two carboxyl groups per four primitive unit cells, are shown in panels i and ii, respectively, of Figure 1c. The effect of disorder was analyzed by changing the orientation and distance between the two functional groups on the lateral surface of the nanotubes. To quantify aggregation preferences, two distances were introduced to describe the distances between the C atoms from the carboxyl groups, across the tube (transverse, d1) and along the tube (longitudinal, d2). These distances were measured with respect to periodic boundary conditions. For clarity, d1 and d2 are indicated in panels i and ii, respectively, of Figure 1c.

Eads/ N =

1 [ECNT + groups − (ECNT + NEgroup) + Ecorr] N (1)

with Ecorr = ECNT + ghost − ECNT + Eghost + groups − NEgroup

(2)

where ECNT+groups is the total energy of the functionalized CNT with the optimized unit cell lengths and atomic geometry, Egroup is the total energy of one functionalizing group, and ECNT is the total energy of a nanotube with vacancy defects in the carboxylated case or a pristine nanotube for the other systems. The number of vacancy defects is equal to the number of COOH groups in the carboxylated system. The vacancy defects are introduced in the positions of C atoms in the pristine nanotube that belong to COOH groups after carboxylation. Ecorr is correction due to basis-set superposition error (BSSE) resulting from use of the numerical code with the localized basis.45,46 Eghost+groups and ECNT+ghost are Kohn−Sham 26736


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Table 1. Equilibrium Lattice Constants, Radii, Coefficients of Variation of the Radii, Adsorption Energies per Molecule, and Elastic Properties of (9,0) CNTs Functionalized with Two Groups on Opposite Sides of the Lateral Surface of the Tubes, Giving the Maximum Transverse Distance between Them

a

COOH grafting is denoted by superscript g.

where Δr describes the change in the average radius of the functionalized CNT caused by the applied strain ε. The shear modulus (G) and bulk modulus (K) (which can easily be derived from eq 3 and eq 4) are given by

energies of the functionalized system with the functional groups and CNTs, respectively, replaced by their ghosts36 and all atoms fixed in the optimized positions. The BSSE correction to the adsorption energy originates mostly from the calculation of the total energy of a functional group, Egroup. This energy, when calculated with the basis functions connected to a few atoms, differs considerably from the energy calculated using the full basis of the whole functionalized system. However, unlike in systems where the interaction is physical, this correction is rather small in systems where the interaction occurs through chemical bonding.6,42,46,47 To determine the elastic properties, eight different stress tensors with only one nonzero component along the symmetry axis of the nanotube were constrained for each studied system. The structures were optimized at the required stress. The obtained strain components were less than 1% for all structures. Therefore, the most interesting quantity, namely, the Young’s modulus, could be determined as a constant of proportionality between the magnitude of nonzero stress σii and the components of strain εii Y=

σii , εii

εii =

Δl l

Δr l r Δl

Y 2(1 + η)

(5)

K=

Y 3(1 − 2η)

(6)

to complete the set of elastic constants calculated in this work.

3. RESULTS AND DISCUSSION 3.A. Influence of Functionalization on the Structure. Covalent functionalization induces local and global changes in the morphologies of functionalized CNTs through the formation of strong bonds between the adsorbates and the nanotube backbone. All adsorbates induce rehybridization of the CC bonds in the vicinity of the attachment from sp2 to sp3. Radicals, in comparison to nonradical functional groups, cause stronger deformation of the CNT backbone structure. They can induce characteristic heptagon/pentagon defects and substitutional doping depending on their concentration around the nanotube.6,42 However, it is the carboxylation process that simultaneously introduces the surface group and the vacancy into the nanotube backbone. Pulling out the carbon atom from the nanotube backbone, leaving only one bond to another sidewall carbon and breaking three bonds in the CNT wall for each COOH group, leads to a significant deterioration of the CNT structure. Therefore, carboxylation results in more changes in morphology than other types of covalent functionalizations of CNTs. The structural parameters for other possible types of surface modifications of (9,0) CNTs resulting from acid treatment7,9,19,27−29 are gathered in Table 1. The longitudinal lattice constants, tube radii, and coefficients of variation of the radius as functions of the concentration of COOH groups/vacancies are depicted in Figure 2. The longitudinal lattice constants and radii of CNTs grafted with COOH groups increase slightly with increasing number of adsorbates, but even for a concentration of 12.5%, they are close to the values for pure CNTs. The maximum absolute percentage changes in l and r for (9,0) CNTs grafted with COOH groups are equal to 0.22% and 0.45%, respectively. Functionalization with OH groups has a comparably small influence on nanotube structure. The maximum absolute percentage changes in l and r of (9,0) CNTs functionalized with hydroxyl groups at concentrations of up to 12.5% are equal to 0.26% and 0.41%, respectively. Greater changes in r and l are induced by epoxy groups because of the creation of two bonds with the nanotube backbone per functional group.

(3)

where Δl is the elongation in the direction of the symmetry axis. This definition does not take into account the BSSE correction. The elastic properties were determined on the basis of the total energy of the whole functionalized system where the bases are identical (up to atomic positions). In particular, the stress tensor σ is the positive derivative of the total energy with respect to the strain tensor ε. Therefore, the BSSE correction becomes negligible when one calculates the elastic properties.6,46 The SIESTA code calculates the stress tensor with respect to the volume of the whole supercell, so to obtain the elastic modulus in SI units, we also had to calculate the CNT volume. The volume of a CNT was calculated as the volume of a hollow cylinder using the relation V0 = 2πrlt, where the thickness t was chosen as twice the van der Waals radius of the C atom (equal to 0.34 nm).48−55 The volume of functional groups on the lateral surface of the tube was neglected. Double-walled nanotubes were treated as two nested SWNTs. The interactions between tubes are mainly due to van der Waals forces, which are rather weak in comparison to the covalent bonds between neighboring C atoms.53,56 Hence, the volume of the system was calculated as the sum of the volumes of two hollow cylinders corresponding to the inner and outer tubes. The Poisson ratio was obtained as η=−

G=

(4) 26737


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These changes are similar to the changes caused by radicals. Nevertheless, the changes in morphology are more pronounced for the defected and carboxylated systems than for other types of functionalization. As one can see in Figure 2a,b, both l and r change rather strongly with the concentration of vacancy defects and functional groups. The maximum absolute percentage changes of l and r for CNTs with vacancy defects are equal to 10.99% and 5.09%, respectively. The simultaneous presence of COOH groups with vacancy defects reduces the maximum absolute percentage change of l to 6.20% and increases the maximum absolute percentage change of r to 7.52%. Starting from a 5.6% concentration of vacancy defects, the relative changes in l for carboxylated (9,0) CNTs are smaller than for defected (9,0) CNTs. CNTs with vacancy defects have fewer C atoms and more broken bonds than carboxylated CNTs for the same amount of vacancies/functional groups. Therefore, the impact on the longitudinal lattice constant is higher for the defected case than for the carboxylated case. The opposite trend in nanotube radius can be understood in terms of the effective tensile strain induced by the presence of COOH groups. Adsorbates that bind strongly to the CNT surfaces stretch out the tube in the direction perpendicular to the tube axis, changing the cross section of the CNT.6,42,57 Also, the distribution and orientation of groups on the nanotube backbone is of importance in morphology changes. The effects of disorder and aggregation preferences were analyzed by changing the orientation and the transverse and longitudinal distances between the two functional groups on the lateral surface of tube. The structural parameters for 12 different configurations of COOH groups on the lateral surface of (9,0) CNTs are gathered in Table 2. In each case, the system was fully relaxed. As a consequence, Table 2 presents the energetically most favorable orientations of both COOH groups on the surface of tube for a given pair of distances (d1, d2). When the transverse distance d1 between the two carbon atoms from the two COOH groups increases, one can observe a greater reduction in both the tube radius r and the lattice constant l. The trend is opposite for the longitudinal distance d2. In other words, a homogeneous distribution of functional groups over the lateral surface of a nanotube leads to a greater reduction in r and l in comparison to the same parameters for pure nanotubes. In general, the relative changes in the longitudinal lattice constants induced by the presence of vacancy defects and carboxylation decrease with increasing tube radius and number of walls. For carboxylated CNTs, one can observe the same

Figure 2. (a) Equilibrium lattice constant (l) along the nanotube symmetry axis, (b) average radius, and (c) coefficient of radius variation for (9,0), (8,2), (5,5), (14,0), and (5,0)@(14,0) nanotubes as a function of the concentration of COOH groups/vacancies.

Table 2. Structural and Elastic Properties for All Studied Configurations of Two COOH Groups Functionalizing (9,0) CNTs

a

Configurations 5, 6, and 8 represent the three cases in which groups are present on the same ring of the tube. 26738


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COOH groups in Figure 3. Generally, the adsorption energy decreases with increasing longitudinal distance between the

trend with increasing chiral angle. The relative changes in the radii of defected and carboxylated CNTs are greater for the (5,0)@(14,0) system than for the (14,0) system and also are more enhanced for smaller tubes. The two parameters r and l are not sufficient to describe the shape changes induced by carboxylation. The cross sections of the functionalized CNTs in the plane perpendicular to the CNT symmetry axis are no longer circular because of stretching induced by the functional groups. Breaking bonds in the defected and carboxylated case results in the appearance of 5−7 defects and local narrowing of the tube. The coefficient of variation in the radius, which is a standardized measure of the dispersion of a CNT radius distribution, was chosen to quantitatively describe the changes in nanotube shape. Generally, adsorbates that bind to a nanotube’s lateral surface with one bond induce smaller changes in shape (smaller CV) than those that create two bonds, such as epoxy group (see Table 1). The CV of a (9,0) CNT functionalized with two OH groups (with the maximum d1 value) is 31.8% less than the CV of a CNT functionalized with two epoxy groups and half that of a carboxylated CNT. Interestingly, simulatenous carboxylation and epoxidation leads to even greater deformation (larger CV). Wang et al.58,59 also observed evident local radial distortion leading to a change in tube shape from circular to oval for COOH groups adsorbed on Stone−Wales (SW) defects and vacancies in (10,0) CNTs. As one can see in Figure 2c, the grafted and carboxylated systems exhibit completely different trends in CV. The coefficient of variation is rather constant for (9,0) CNTs grafted with COOH groups, whereas for defected and carboxylated tubes, it strongly increases with increasing concentration of vacancy defects and COOH groups. For higher concentrations (C ≥ 11.1%), carboxylated nanotubes show smaller CV values than CNTs with vacancy defects. The positions of the groups are crucial for the deformation of the nanotubes (see Table 2). By changing the configuration of the functional groups over the tube surface, one can change the CV by even as much as 38.2% (see Table 2). The circular shape of the cross section of the pure nanotube is mostly altered for carboxylated CNTs with COOH groups localized as close as possible to each other (minimum value of d1) and as far as possible from each other (maximum value of d1). Interestingly, when the second COOH group is placed in the middle of those two positions (d1 = 7.087 Å), the shape deformation is the smallest. The dependence of CV on the chirality of the nanotube can be also observed. For achiral tubes, the deformation is larger than for chiral tubes. As expected, the relative changes in CV for carboxylated CNTs decrease with increasing nanotube radius and number of walls. 3.B. Stability and Disorder Analysis. Before we turn to a discussion of the elastic properties, we need to analyze the functional aggregation preferences, the stability of the studied systems, and their relation to the changes in the electronic properties of the systems. First, the aggregation trend was checked. For this purpose, nine different orientations of two carboxyl groups on (9,0) CNTs were studied, including three with the two groups on the same ring. In addition to those nine configurations with different transverse distances (d1) between groups, another three configurations with different longitudinal distances (d2) between the COOH groups were analyzed. The adsorption energies for all considered configurations are gathered in Table 2 and plotted as a function of the distance between the two

Figure 3. Adsorption energy per molecule of the carboxylated (9,0) CNTs as a function of distance between the two COOH groups. Red crosses indicate the three cases in which groups were present on the same ring of the tube.

groups or transversal distance on the same ring of the tube. This makes the presence of a second COOH group close to the first one less probable. Surprisingly, there is an optimal transversal distance between functional groups placed on different rings that does not characterize clustered nor isolated COOH groups. Eads/N as a function of d1 follows the already presented trend in CV (square symbols without red crosses in Figure 3). The most stable system is the system in which second group forms an angle of ca. 90° with the first group when projected onto a plane perpendicular to the tube axis. The observed trends for carboxylated CNTs are again different from those observed for COOH-grafted CNTs. Saidi24 found that the aggregation of COOH adducts on the lateral surface of pure CNTs is thermodynamically favorable. The presence of topological defects also favors the clustering of COOH groups on the nanotube surface. Wang et al.58 showed that the adsorption of two COOH groups on the same Stone−Wales defect leads to a more energetically stable structure. However, both systems studied by Saidi and Wang et al. assumed no reduction in the number of C atoms in the nanotube wall during COOH adsorption, which is not fulfilled for carboxylated CNTs. Creation of second COOH group in the vicinity of the first will lead to a severe weakening of the nanotube wall by pulling out another C atom from that part of wall. The adsorption energies (per adsorbed molecule) for grafted and carboxylated CNTs are shown in Figure 4. The carboxyl groups bind to the surface of the CNTs regardless of the type of functionalization (i.e., the adsorption energy is negative for both grafted and carboxylated CNTs). However, grafted and carboxylated CNTs follow different trends and can easily be distinguished. Clearly, grafted CNTs are less stable than carboxylated CNTs. Defects act as nucleation centers and enhance their catalytic performance. Wang et al.58,59 also showed that the binding of COOH groups to SW defects on nanotubes is stronger than their binding to pure nanotubes. Later, Al-Aqtash et al.60 compared the binding of carboxyl groups to SW and vacancy defects and showed that carboxylation is more energetically favorable. As can be seen in Figure 4a, the adsorption energy per functional group for a grafted CNT generally remains nearly constant with increasing number of functional groups. This 26739


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additional presence of the next group in the odd case (2n + 1). Steric effects are complemented here by electronic effects. It can be also observed from Figure 4a that the stability of a carboxylated CNT decreases with decreasing chiral angle and number of walls. The chirality dependence can be understood in terms of the different orientations of CC bonds along tube axis in (9,0), (8,2), and (5,5) CNTs. Therefore, the vacancies and functional groups that provide an effective tensile strain have different impacts on the structures of these three nanotubes. Finally, an electronic structure analysis based on the differential charge-density (DRHO) distribution was carried out to facilitate a deep understanding of the differences between grafted and carboxylated CNTs. We showed previously42 that grafting functional groups to the lateral surface of a nanotube leads to the redistribution of electronic charge. An analogous process can be observed in carboxylated CNTs. From the DRHO distribution shown in Figure 4b, the changes in electronic structure after grafting and carboxylation of CNTs can be understood. In both cases, there is a charge transfer between the nanotubes and the functional groups. One can clearly see areas of additional negative charge in the middle of the bond between the functional group and the nanotube. The charge rearrangement is more pronounced in carboxylated CNTs than in grafted CNTs. In carboxylated CNTs, at concentrations of ≤5.6%, the spread of the negative charge outside the tube and the delocalization are slightly greater than in grafted CNTs. This effect is more pronounced for carboxylated CNTs with even numbers of COOH groups at higher concentrations, whereas for carboxylated CNTs with odd numbers of COOH groups (C > 5.6%), the electron delocalization and charge transfer are comparable to those in grafted CNTs. Charge transfer from COOH groups to the surface of defected tubes was also observed by Wang et al.59 and Al-Aqtash et al.,60 whereas Girao et al.16 reported electron transfer from the tube to the COOH group. Having determined the morphologies and stabilities of functionalized CNTs, we are in a position to analyze their elastic moduli. 3.C. Elastic Properties of Pure CNTs. As a starting point for further investigations of the elastic properties of carboxylated CNTs, these quantities are presented here for pure CNTs. The chiral angles, radii, elastic moduli, and Poisson’s ratios of (9,0), (8,2), (5,5), (14,0), and (5,0)@(14,0) CNTs are gathered in Table 3. All calculated values for the pure CNTs are in good agreement with experimental findings and previous theoretical works. Comparing three tubes with similar radius, namely, (9,0), (8,2), and (5,5), one can see that an armchair nanotube has a Young’s modulus that is only 9 GPa higher than that of a zigzag nanotube and only 53 GPa higher than that of a chiral one. A s imilar trend can be observed in the shear modulus and the opposite trend in the bulk modulus and Poisson’s ratio. Starting from tubes with diameters greater then 5 Å, the Young’s modulus seems to be almost insensitive to the diameter of the CNT and the number of walls.6 The differences are more pronounced in shear modulus (increase with increasing radius and number of walls), bulk modulus, and Poisson’s ratio (again, opposite trend to shear modulus). 3.D. Elastic Properties of Carboxylated CNT. After discussing the elastic properties of pure CNTs, we now focus on the elastic properties of carboxylated CNTs. Fully understanding the influence of the carboxylation of CNTs on

Figure 4. (a) Adsorption energies per molecule of COOH-grafted (9,0) CNTs and carboxylated (9,0), (8,2), (5,5), (14,0), and (5,0) @(14,0) CNTs as a function of the concentration of COOH groups. Dashed, dotted, and solid frames indicate different relative trends between the grafted and caboxylated cases. Ball-and-stick models of all marked cases are presented above and below the frames for grafted and carboxylated CNTs, respectively. (b) Differences between the valence pseudocharge density and the superposition of the atomic valence pseudocharge densities (DRHO) for grafted (top) and carboxylated (bottom) (9,0) CNTs in the plane perpendicular to the nanotube axis. Concentrations of functional groups: (i) 5.6%, (ii) 11.1%, and (iii) 12.5%.

trend is also obeyed for carboxylated CNTs, with COOH group concentrations of ≤5.6%. For higher concentrations, an interesting phenomenon can be observed, namely, an odd− even relationship between the number of COOH groups and the stability of these systems. The presence of a COOH group is always related to the presence of a vacancy defect in the lateral surface of the carboxylated tube. The number of defects (vacancies and pentagon/heptagon rings, resulting from surface reconstruction after a C atom has been pulled out of the surface) therefore increases with increasing concentration of functional groupss. The functional groups and vacancies are homogeneously and symmetrically distributed over the nanotube surface, which is energetically preferred. However, carboxylated tubes with even numbers of functional groups are more stable than those with odd numbers of groups. The cross section of a carboxylated CNT containing eight functional groups is more regular than that of a carboxylated CNT containing nine functional groups (see the cross sections of the CNTs below the dotted and solid frames in Figure 4a). One can observe the same trend for six and seven functional groups (see Figure 2c). The preferred alignment (perpendicular to the tube axis, opposite to the grafted case) of the planes of even numbers (2n) of COOH groups is disturbed by the 26740


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Table 3. Structural and Elastica Properties of Pure (9,0), (8,2), (5,5), (14,0), and (5,0)@(14,0) CNTs: Chiral Angle (θ); Nanotube Radius (r); Young’s (Y), Bulk (K), and Shear (G) Moduli; and Poisson’s Ratio (η)

a

Elastic properties are compared to available experimental and other theoretical values. If necessary, elastic properties were recalculated in SI units using twice the van der Waals radius of the C atom (0.34 nm) as the nanotube thickness. bY0 set to 1.06 TPa (pure graphene),62 according to the formula from ref 63. cResults for (5,5)@(10,10). dYoung’s modulus calculated according to the formula derived by Govindjee and Sackmann61 for MWNTs using the parameters from this work and Y0 = 1 TPa. eResults for DWNTs with radii of (2.3 Å)@(5.5 Å).

can be also created later during nanocomposite or device preparation, or they can be deliberately to obtain desired functionalities.97,98 According to our findings, increasing the number of vacancy defects up to a concentration of 8.3% leads to a monotonic reduction of the Young’s modulus. A similar trend was reported by Haskins et al. 98 For higher concentrations of vacancies, the structure of the nanotube is substantially changed. The considered (9,0) CNT is a relatively small nanotube with high curvature. The number of carbon atoms constituting the tube backbone is severely reduced, and therefore, systems with odd and even numbers of vacancy defects start to behave differently. The Young’s moduli of (9,0) nanotubes with seven and nine vacancy defects are noticeably higher than those with six and eight defects, respectively. This trend is related to surface reconstructions. Larger tubes are less influenced by the presence of vacancy defects; hence, their Young’s moduli are higher. Similar observations were noted by Sammalkorpi et al.97 and Wong.99 The Young’s modulus of DWNTs is slightly smaller than that of SWNTs. Comparing tubes with different chiral angles [(9,0), (8,2), and (5,5)], one can see that the position of vacancy the defect in the nanotube backbone and the related reconstruction of dangling bonds have a noticeable influence on Young’s modulus values of the corresponding tubes. This occurs because the Young’s modulus of carbon nanotubes is related to sp2 bonds. A uniaxial load

their elastic properties also requires the consideration of CNTs with vacancy defects as well as CNTs grafted with oxygenbearing groups. We start with a presentation of the results for the Young’s moduli of carboxylated, grafted, and defected CNTs as functions of the concentration of COOH groups/vacancies. This quantity measures the stiffness of a material and is crucial for all potential applications of CNTs. In Figure 5, we show the Young’s moduli of (9,0), (8,2), (5,5), (14,0), and (5,0)@(14,0) nanotubes. For all considered types of surface modifications, the Young’s modulus decreases with increasing density of defects/functional groups. However, for grafted CNTs, the trend is noticeably less pronounced than for defected or carboxylated CNTs. For (9,0) CNTs grafted up to 12.5%, the Young’s modulus decreases by 13.78%, whereas defected and carboxylated CNTs exhibit reductions in the Young’s modulus of 56.98%, and 60.71%, respectively. This is consistent with the already described relative tendencies of the structural and electronic properties of grafted and carboxylated CNTs. The results presented here for CNTs grafted with COOH groups are in good agreement with previous findings.23,25 Nevertheless, more interesting are surface modifications that can be experimentally observed, namely, vacancy defects and carboxylation. Vacancy-related defects can easily appear in nanotubes during growth and purification processes.16,96 They 26741


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Figure 5. Young’s moduli of (9,0), (8,2), (5,5), (14,0), and (5,0)@(14,0) nanotubes as functions of the concentration of COOH groups/ vacancies. Right axis: Percentage change in the Young’s modulus relative to that of pristine (9,0) CNTs (Y0(9,0) = 1.018 TPa). The critical concetration is indicated by a red arrow.

functionalization (i.e., ozone treatment or aryl sulfonation) improves the biodegradation of CNTs. COOH groups cause forming of active sites providing points of attack for further oxidative degradation. It minimizes potential long-term side effects of CNT usage for selective drug targeting of cancer cells and drug delivery. Indeed, we have shown that the critical concentration of functional groups marking the onset of CNT degradation is not observed for OH- or COOH-grafted CNTs. This is the most striking result, which distinguishes the properties of the commonly used model of carboxylated CNTs (COOH-grafted CNTs) from truly carboxylated CNTs. The exact value of the critical density of COOH groups depends strongly on nanotube radius and metallic/semiconducting character of the carboxylated tube. Yang et al.104 observed the selective removal of small metallic SWNTs treated with nitric and sulfuric acids, whereas semiconducting tubes remained intact. For SWNTs with diameters smaller than 1.1 nm, metallic tubes were found to be more degradated than semiconducting tubes. This result can be explained in terms of the higher degree of reactivity of metallic tubes. Therefore, the value of critical density for (9,0) CNTs presented here will be higher for semiconducting and larger tubes. To properly model the influence of carboxylation on the mechanical properties of CNTs, the effect of disorder on the stiffness of these nanotubes must be analyzed. The Young’s modulus of carboxylated (9,0) CNTs for different distances between the two COOH groups are collected in Table 2. The Young’s modulus can be changed by 9.16% by changing the transversal distance between functional groups. The standard deviation of the Young’s modulus of carboxylated CNTs at a 2.8% concentration of functional groups is equal to 0.027 TPa. The statistical spreads of Young’s modulus corresponding to different arrangements of defects and functional groups on lateral surface of tubes experimentally observed are expected62 to increase with increasing concentration of functional groups. The Young’s moduli of carboxylated CNTs with different chiral angles, diameters, and numbers of walls follow the same trends as the Young’s moduli of defected CNTs. However, the differences in Young’s modulus for carboxylated CNTs are less pronounced. One can observe greater changes comparing

applied in the direction of the tube’s symmetry axis spreads symmetrically on the defect region in zigzag nanotubes, whereas in armchair CNTs, it spreads unevenly on the respective bonds. Also, Agrawal et al.73 reported smaller Young’s moduli of armchair compared to zigzag nanotubes. Experimental data82,84,85,100−102 confirmed the reduction of the Young’s modulus due to the presence of defects. Small SWNTs have been found to be extremely sensitive to the presence of vacancies.100 Arc-grown MWNTs, containing very few defects, have Young’s moduli comparable to those of individual defect-free SWNTs. The Young’s moduli of catalytic MWNTs, which contain many more defects, vary depending on their structure. Those, which have a highly defective structure, have a very low modulus. The qualitative relation between the Young’s modulus and the disorder in the atomic structure of the walls observed experimentally by Salvetat et al.100 is similar to the trend depicted in Figure 5. Carboxylation, as well as the presence of vacancy defects, leads to a significant reduction in Young’s modulus. For small concentrations, the additional presence of COOH groups with vacancies stabilizes the system and improves its stiffness. However, at concentrations of COOH groups above 5.6%, the Young’s modulus of a carboxylated CNT becomes smaller than that of the corresponding defected system. Surprisingly, the presence of COOH groups above vacancy defects does not diminish the tube’s degradation but does hamper the surface reconstruction. This result confirms experimental observations3,5,8,19,29 that carboxylation at some point leads to the deterioration of CNTs. Moreover, if the concentration of highly carboxylated CNTs in a composite matrix is sufficient, they will form large agglomerates,9,103 thus making strong carboxylation useless for solving the bundling problem of pure CNTs. It should be emphasized that the results presented in this work perfectly describe those trends. One can clearly see in Figure 5 that there is a critical density of COOH groups above which their use as a reinforcement in composites is no longer advantageous. On the other hand, concentrations of carboxylic groups above this critical density should start to reduce the toxicity of CNTs. Liu et al.19 showed that the biodurability of SWNTs depends on surface functionalization. In particular, carboxylation, in contrast to other types of 26742


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intertube links. A similar effect was observed102 for carboxylated CNTs because of better connections between tube and matrix and therefore more homogeneous distribution of nanotubes inside composite. The shear moduli of defected and carboxylated CNTs are sensitive to the chirality, nanotube size, and number of walls and follows the same trends as the Young’s modulus. Carboxylation in comparsion to epoxydation, hydroxylation, and their combinations also has a greater impact on the shear modulus than the Young’s modulus (see Table 1). We complete the discussion of the elastic moduli with the bulk modulus and Poisson’s ratio. The bulk moduli of COOH- and OH-grafted SWNT behave similarly to other elastic moduli and decrease with growing concentration of functionalizing molecules. The percentage reduction in the bulk modulus for this type of surface modification is greater than the reductions in the shear and Young’s moduli. For (9,0) CNTs grafted up to 12.5%, the bulk modulus decreases by 19.33% and by 20.49% for COOH and OH groups, respectively. However, the dependence of the bulk modulus on the concentration of functional groups/vacancies for defected and carboxylated cases is nonmonotonic. This quantity is very sensitive to structural changes in the nanotube backbone structure induced by CNT irradiation/oxidation, in particular, to the relative positions of vacancies/functional groups and differences in surface reconstructions (see Table 2). The bulk modulus, which measures the resistance of the system to uniform compression, shows that the orientation of defects has a large impact on the load distribution in carboxylated CNTs. For the highest considered concentrations of vacancies/ functional groups, the bulk modulus is reduced by 73.72% and 54.41% for defected and carboxylated tubes, respectively. The last elastic property that was taken into consideration is the Poisson’s ratio. The Poisson’s ratio, which describes how easily the system is deformed in the direction perpendicular to the applied load, exhibits clear dependencies on neither the type of functionalizing molecules nor the concentration of vacancies/functional groups. For all studied types of surface modifications, it always varies between values 0.15 and 0.28.

CNTs functionalized with different oxygen-bearing groups (see Table 1). As expected, all considered systems that contain COOH groups and vacancies are less stiff than those without COOH groups and vacancies. Simultaneous carboxylation and epoxidation, as well as carboxylation itself, leads to the highest reduction in Young’s modulus among the systems presented in Table 1. Surprisingly, the Young’s modulus of epoxidated CNTs is slightly higher than that of hydroxylated CNTs. It is known62 that the mechanical properties of carbonbased systems are strongly related to their electronic properties. Therefore, the differences in the Young’s moduli of hydroxylated and epoxidated CNTs should be correlated with changes in the electronic properties between those systems. The charge density distributions (RHO) of epoxidated CNTs are more similar to those of pure CNTs than to those of hydroxylated CNTs. The shear modulus as a function of the concentration of COOH groups/vacancies, depicted in Figure 6, is very

Figure 6. Shear moduli of (9,0), (8,2), (5,5), (14,0), and (5,0)@(14,0) nanotubes as functions of the concentration of COOH groups/ vacancies. Right axis: Percentage change in the shear modulus relative to that of pristine (9,0) CNTs.

4. CONCLUSIONS This article presents direct evidence that COOH-grafted CNTs can not be used as a model of carboxylated CNTs. Both the structural and elastic properties differ significantly between grafted and truly carboxylated CNTs. By studying morphological and related electrical property changes induced by the carboxylation of CNTs with different diameters, numbers of walls, and metallic and semiconducting characters, we explain the experimental observations showing that small concentrations of COOH groups improves the strength of CNTs in comparison to that of defected CNTs, whereas higher concentrations lead to tube degradation. We determined the critical concentration above which the simultaneous presence of COOH groups and vacancy defects will lead to significant changes in the structure of the nanotube, resulting in a significant decrease in the Young’s modulus, making the CNT unsuitable as reinforcement in composites. Moreover, we show the governing mechanisms of reduction of CNT toxicity in the case of carboxylation. These studies shed light on physical processes governing the carboxylation of CNTs and also provide valuable quantitative predictions that are of importance for design of novel composite materials, environmental and medical usage of CNTs.

similar to the Young’s modulus (Figure 5). Generally, the shear modulus drops in value with increasing density of functional groups/vacancies, which is in agreement with experimental observations.89,105 For (9,0) CNTs grafted up to 12.5%, the shear modulus decreases by 12.12%, whereas defected and carboxylated CNTs exhibit reduction in shear modulus equal to 53.42%, and 68.22%, respectively. The difference between grafted and carboxylated systems is even more conspicuous in shear modulus than in Young’s modulus. However, the critical density of COOH groups is less visible. A glance on Figure 6 shows that above 5.6% concentration the simultaneous presence of COOH groups and vacancies leads to reduction of shear modulus in comparison to the sole presence of vacancy related defects. This observation is in good agreement with experimental findings. It was shown by Kis et al.106 that lowdose irradiation improves the mechanical properties of CNT bundles, whereas high-dose irradiation results in the deterioration of mechanical properties. Small amounts of defects should enhance the shear modulus through the creation of 26743


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author acknowledges funding from the European Commission through the FP7-NMP programme (Project UNION, Grant 310250). Prof. Jacek A. Majewski is kindly acknowledged for assistance with the YASARA program. We also thank PL-Grid Infrastructure and Interdisciplinary Centre for Mathematical and Computational Modeling of University of Warsaw (Grants G47-5 and G54-8) for providing computer facilities.

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