Keywords

1 Introduction

Removal of toxic molecules and ions of heavy metals from environment is an urgent technological requirement of human civilization. One of the most promising methods of such kind of removal is adsorption of toxic molecules by artificial adsorbents [1, 2]. The search for new adsorbent materials which can allow economically efficient schemes of such removal is a topical research task [1, 3].

Materials based on carbon nanostructured materials, in particular carbon nanotubes (CNTs), are considered as very promising candidates for such application [1, 2, 4, 5]. Among other adsorbent materials, the CNTs are characterized by a number of advantages, most notably large surface area and generally high adsorption capability of carbon surface for many toxic compounds [1, 3].

Carbon nanotubes (CNTs) are intensively studied at present time as promising materials for gas sensors [6,7,8,9,10]. Specific properties of CNT-based materials allow elaboration of efficient gas sensors with sensitivity in the ppb region [6, 11, 12] and with several additional advantages, such as low dimensions, fast response, good reversibility at ambient temperature, and low power consumption.

Computational studies of adsorptions of various molecules on the surfaces of carbon nanostructures, in particular CNTs and graphene, have become a powerful tool for quantitative description of adsorption characteristics of real carbon nanomaterials [13]. Computational approaches in the studies of adsorption of toxic molecules and anions on the CNT surface have been recognized as having high predictive power. Since computational modeling can predict several important physical and chemical properties of the sensor materials, the computations themselves can evaluate the prospects for removal of toxic molecules from the environment, as well as for elaboration of novel gas sensors [14,15,16,17]. Adsorption of several types of molecules of industrially important toxic gases on the B- or N-CNTs was treated so far in the density functional theory (DFT)-based electronic structure calculations. In particular, such studies were reported for carbon monoxide (CO) [18,19,20], nitrogen dioxide (NO2) [18, 19], chlorine (Cl2) [20], formaldehyde (HCOH) [17], methanol (CH3OH), and ammonia (NH3) [19, 21].

Hydrogen halide gases HX (X = F, Cl, Br) are widely used in the industry as reagents (see [22]) and also are produced as byproducts in many industrial applications (see [23,24,25,26]). At the same time, these gases are very toxic and harmful for biological organisms even at low concentrations [22, 27]. Majority of electrochemical gas sensors of hydrogen halides available on the market are relatively expensive and their detection limit usually does not exceed the ppm level [28]. Elaboration of novel, more efficient, and sensitive sensors of hydrogen halide gases is an important present-day task.

Compounds of hexavalent ions of heavy metals M(VI), in particular Cr(VI), are widely spread industrial pollutants, and at the same time, they are very harmful to living bodies [29,30,31]. Therefore, there is a strong technological need to remove such compounds from industrial waste as well as from the environment [32, 33]. The properties of CNTs as adsorption materials for Cr(VI) compounds have been studied over the last decade [4, 32, 34,35,36,37,38] and it was found that these materials are very promising for the efficient removal of Cr(VI) compounds from the environment [2, 32, 35,36,37].

However, despite of a large volume of accumulated experimental data, there is a considerable lack of understanding of Cr(VI)-on-CNTs adsorption mechanisms at the single-molecule level. In particular, the peculiarities of chemical bonding between the most common types of Cr(VI) anions and the CNT surface still remain unclear.

Adsorption models developed in the mentioned above research papers usually employ analogies with adsorption of molecules on a carbon surface without explicit consideration of specific CNT structures. However, it is well-known that carbon surface of CNTs (particularly low-diameter ones) may be significantly curved, and this feature determines their distinctive adsorption properties [39].

Chromium is the 21st most abundant element in the earth’s crust [40], and its valance state can range from −2 to +6, but it is generally found as trivalent Cr(III) and hexavalent chromium Cr(VI) in natural environments.

Trivalent chromium occurs naturally in many vegetables, fruits, meat, grains and is often added to vitamins as a dietary supplement, whereas Cr(VI) most often produced by industrial processes and mining of chromium ore, is an indicator of the environmental contamination. The main industries that contribute to water pollution by Cr(VI) are leather production, mining, electroplating, textile dyeing, metal finishing, wood manufacturing, nuclear power plants, electrical and electronic equipment manufacturing, catalysis [41,42,43,44,45,46]. For this reason, hexavalent chromium is among very common environmental pollutants.

Most of the Cr(III) compounds are sparingly soluble in water, whereas the majority of Cr(VI) compounds are highly soluble. In addition, Cr(III) is several times less toxic than Cr(VI) [47]. The tolerance limit for Cr(VI) for discharge into inland surface waters is 0.1 mg/L and 0.05 mg/L in potable water.

The effect of hexavalent chromium on humans can occur not only due to use of contaminated water but also by inhalation of contaminated air and the contact of evaporation with the skin. Hexavalent chromium, Cr(VI), are dangerous to humans at all ways of interaction, even with short-term impact. The above determine the relevance for investigation of the adsorption mechanisms of chromium-containing anions, first of all those containing Cr(VI), and shows the need to study these mechanisms both in gas and water environments. Chromium(VI) generally exists in monomeric (HCrO4 − and CrO4 2−) or biomeric state (Cr2O7 2−) [48]. The dependency of concentration of these species on the pH and concentration of Cr(VI) solution are presented in Figs. 21.1 and 21.2, respectively.

Fig. 21.1
figure 1

Distribution of Cr(VI) species as a function of pH [48]

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Fig. 21.2
figure 2

Fraction of HCrO4 − and Cr2O7 2− at pH 4 as a function of total Cr(VI) concentration [48]

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It is evident (Fig. 21.2) that CrO4 2− predominates above pH 6.5 and HCrO4 − dominates in the pH range of 1–6.5.

The above description shows the need to study the mechanisms of adsorption on the surface of carbon materials of such molecular chromium groups as CrO4 2−, HCrO4 −, and Cr2O7 2−.

Besides Cr(VI)-containing ions, the DFT-based calculations provide an opportunity to study the adsorption mechanisms of molecules with other hexavalent ions Mo(VI) and W(VI). These ions are isovalent to Cr(VI), which, however, does not determine the identity of the adsorption characteristics of corresponding molecules and anions on the surfaces of various carbon nanostructured materials.

2 Fundamentals of the Structural and Electronic Properties of Carbon Nanotubes

It is well-known that the first observation of the structure of multi-walled carbon nanotubes was in 1991 [49]; however, there are a number of works in which the evidence is provided for an earlier discovery of the CNTs. In 1976, it was clearly shown the existence of hollow carbon fibers of nanometer diameters [50]. In 1987, the US patent [51] was issued for the production of discrete cylindrical carbon fibers with a constant diameter in the range of 3.5–70 nm and a length that is 102 times greater than the diameter. In 1991, the multiwalled carbon nanotubes contained in arc discharge were registered and investigated [49]. Methods for the synthesis of the single-walled carbon nanotubes were also described [52, 53].

Carbon nanotubes have a hollow cylindrical structure with a diameter of 1 to several 10s of nanometers and a length of up to hundreds of micrometers, consisting of one or more hexa-honalnyh graphite planes (graphene sheets) rolled into a tube and ending generally hemispherical surface, which can be seen as half fullerene molecule [53]. For example, СNT(10,10) ends with a half-fullerene C240. The CNT can also have open ends after oxidation [54]. Depending on the number of graphene layers, the nanotubes can be single-walled (SWCNT) or multiwalled (MWCNT). The ideal SWCNT can be represented as a graphene sheet (hexagonal layer of carbon atoms) rolled up into the cylinder without the presence of any seams.

Since the microscopic structure of SWCNT is closely related to graphene, the tubes are usually denoted in terms of graphene lattice vectors, it can be obtained geometrically by curling strips of graphene. The geometry of the SWCNT is completely determined by a pair of indices (n,m) indicating the relative position C h = na 1 + ma 2 pair of atoms of graphene strips, which, upon the tube formation of, are superimposed on each other (a 1 and a 2 are the basis vectors of the hexagonal layer).

This chiral vector C h defines the circumference of the tube. The diameter d t of the nanotube can thus be calculated from:

$$ {d}_t=\left|{C}_h\right|/\pi $$
(21.1)

The chiral vector C h uniquely defines a particular (n,m) of the tube, as well as its chiral angle θ, which is the angle between C h and a 1.

Nanotubes of the (n,n) type (θ = 30°) are called armchair tubes, because they exhibit an armchair pattern along the circumference. Such tubes display carbon-carbon bonds perpendicular to the nanotube axis. Both zigzag and armchair nanotubes are achiral tubes, in contrast with general (n,m ≠ n ≠ 0) chiral ones (Fig. 21.3).

Fig. 21.3
figure 3

Atomic structures of (12,0) zigzag, (6,6) armchair, and (6,4) chiral nanotubes [55]

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The geometry of the graphene lattice and the chiral vector determine not only the diameter of the CNT but also the unit cell and its number of carbon atoms. The smallest graphene lattice vector T perpendicular to C h defines the translational period t along the tube axis. The lattice vector T can also be expressed in terms of the basis vectors a 1 and a 2 as T = t 1 a 1 + t 2 a 2. Using C h,·T = 0, the expressions for t 1 and t 2 are represented by:

$$ {t}_1=\left(2m+n\right)/{N}_R,\kern1em {t}_2=-\left(2n+m\right)/{N}_R $$
(21.2)

where N R is the greatest common divisor of (2m + n) and (2n + m). The number of carbon atoms per unit cell N C can also be expressed as a function of n and m:

$$ {N}_C=4\left({n}^2+ nm+{m}^2\right)/{N}_R $$
(21.3)

As in the case of bulk crystalline solids, in CNTs, the appearance of “native” defects, which are formed in the places of the transformation of a part of hexagonal cycles into five- and seven-circular cycles with the formation of rings of nanotubes, may occur. Defects can also be external: introduced accidentally due to the manufacturing process or which are specially incorporated to modify the properties of the nanotubes. The appearance of defects in CNT leads to the bend of the tube, the change of the chirality vector and its diameter, the change in the relation with adjacent tubes in the beam, and, consequently, the change in the properties of the CNTs.

Carbon nanotubes are known for their special electronic properties due to the nature of the bonds of the electron orbitals of carbon atoms in the structure of the tubes. The orbitals (s, p x, p y) combine to form in-plane σ (bonding or occupied) and σ∗ (antibonding or unoccupied) orbitals. The lateral interaction with neighboring p z orbitals (labeled the ppπ interaction) creates delocalized π (bonding) and π∗ (antibonding) orbitals. In analogy, the σ bonds in the nanotube form a hexagonal network which strongly connects the carbon atoms in the cylinder wall of the CNT. The π bonds are perpendicular to the surface of the nanotube and are responsible for the weak interaction between SWNTs in a bundle, similar to the weak interaction between carbon layers of pure graphite [56].

The energy levels associated with the inplane σ bonds are known to be far away from the Fermi energy in graphite and thus do not play a key role in its electronic properties. In contrast, the bonding and antibonding π-bands cross the Fermi level at the high-symmetry points in the Brillouin zone of graphene [57].

The electronic structures of undoped single-walled CNT(3,3) and CNT(5,5) were calculated relatively long ago, and these low-diameter CNTs may be considered now as objects which are well-studied by various calculation methods [58,59,60].

The electronic structures of the low-diameter (i.e., with low values of m and n) B- or N-doped CNT(n,m) are also well-studied. In particular, such calculations were reported for the B(N)-doped metallic-type CNT(5,5) [61,62,63] and also for semiconductor-type B(N)-CNT(5,7) [64] and N-CNT(6,0) [65] and for many other B(N)-doped CNTs with higher values of (n,m). The electronic structures of B(N)-doped graphene sheets were studied recently within a molecular cluster approach by the DFT-based methods (see [66, 67]).

As it was found, doping of CNTs with the B or N impurities enhances their ability to absorb gaseous molecules [14, 15, 68]. This finding has roused an intense interest on the boron- and nitrogen-doped CNTs (B-CNTs and N-CNTs) as promising materials for gas sensors [14, 68, 69].

It is known that CNT(n,m) for which n − m = 3l with l an integer (including armchair-type CNTs for which m = n) is characterized by the metallic-type electronic band-structure, whereas all other CNTs with n − m = 3l ±− 1 are semiconductors [55]. Principle of operation of a CNT-based gas sensor is based on measurements of resistance of the working material. So, as the working material is a mixture of CNTs with dispersed (m,n), just the metallic-type CNTs should form conductivity properties of the mixture rather than semiconductor ones. Therefore, studies of armchair-type CNTs obviously should have higher priority.

It should be noted that the majority of modern synthesis procedures of CNTs allow to produce only mixes of CNTs with high dispersion of index (m,n) (see [70] and references therein). Technologies of synthesis of CNTs monodisperse by (m,n) index (or procedures of selection of already synthesized CNTs by their structure) appeared only in the recent years and still are very complicated and expensive (see [71] and references therein). Sensing materials of existing CNT-based gas sensors are in fact “mixes” of CNTs with high dispersion of (m,n) index as these materials were produced by “conventional” synthesis methods without preliminary selection by the CNT structure (see [8, 18, 72]). Therefore, it is obvious that studies of a set of CNTs with various (m,n) indexes are desirable for prediction of properties of real working materials of the CNT-based gas sensors. However, studies of such a set require extensive computing resources and make analysis of results very complicated. So, researchers generally limit themselves to consideration of gaseous adsorption of the CNTs with some single case of (m,n) index [14, 17]) or graphene [18] reasonably regarding such limitation as being sufficient for adequate prediction of the physical properties of real gas sensing materials.

3 Modelling of Adsorption Properties of the CNT Surface by the DFT-Based Electronic Structure Calculations: A Brief Description of Computational Approach

3.1 Construction of CNT Clusters

The lengths of CNTs in mixtures may vary from several micrometers to hundreds of micrometers, and their diameters vary from nanometers to tens of nanometers [34]. Commercially available mixtures of carbon nanotubes consist mainly of MWCNTs with average diameters of 5 nm. The present-day computational capabilities are insufficient to perform a first-principle calculation for the full-length carbon nanotubes as well as for the entire variety of the nanotube structures.

The CNT(3,3) and CNT(5,5) are the narrowest possible nanotubes, with diameters of ∼0.4 and ∼0.7 nm, respectively. However, such nanotubes are convenient objects of calculations, since their clusters will have sufficient length for modeling of molecular adsorption even with relatively small number of atoms. A single-layered graphene sheet is commonly used to model the surface of large-diameter CNTs (with correspondingly, low surface curvature). Consideration of both low-diameter CNTs and graphene is a widely spread approach in prediction of the adsorption properties of real CNT mixtures by computational studies [73,74,75].

The CNTs and graphene were modeled in our calculations as molecular clusters. For calculations of adsorption of hydrogen halide molecules HX, the clusters of CNT(3,3) comprised 78 carbon atoms (or in other words, 13 C6 “rings” along the nanotube axis) were taken. To compensate the effects of dangling C–C bonds, 12 outermost C atoms of the clusters were replaced by the H atoms providing C66H12 formula of the cluster. Such replacement is a widely used approach in computational modeling of CNTs within molecular cluster approach [69, 76, 77]. To model the B or N impurities, one carbon atom from the central 6 “ring” of the cluster was substituted by the boron or nitrogen atom.

It should also be noted that the lengths of real CNTs usually exceed their diameters by several orders of magnitude. So, a “section” of the CNT modeled in a cluster must be long enough to provide a negligible influence of side surfaces on the central region of the section where the B(N) impurities and adsorbed HX molecules are adsorbed. To examine this property, we performed supplementary geometry-optimized calculations of undoped CNT(3,3), CNT(5,5), and graphene clusters. According to the supplementary calculations, addition of two extra carbon “rings” to both sides of CNT(3,3) and CNT(5,5) clusters only slightly (within 0.8% of magnitude) changes the C-C distances in the central regions of clusters. Analogous weak changes in the core region were observed when two extra carbon “strips” were added to the opposite sides of graphene cluster. The following characteristic size parameters of undoped CNT(3,3) cluster were obtained in geometry-optimized calculations: distance along the nanotube axis between outermost C6 “rings” was 12.3 Å, distance between edging H6 “rings” (clusterlength) was 14.1 Å, and averaged distance between “contralateral” C nuclei of the central C6 “ring” (cluster diameter) was 4.2 Å. Analogously, the length and diameter of the undoped CNT(5,5) cluster were obtained as 14.2 and 7.0 Å, respectively. Characteristic dimension of undoped graphene cluster (the longest internuclear distances between the H nuclei located on the opposite sides) was obtained as ∼11.74 × 13.6 Å, respectively.

Since molecular anions of M(VI) metals have sizes larger than the hydrogen halide molecules HX, molecular clusters of larger sizes were needed to calculate molecular anions adsorption simulations than for hydrogen halide. Therefore, for the calculation of adsorption of M(VI) molecular anions the clusters of CNT(3,3) comprising 23 C6 “rings” of armchair CNT(3,3) was used. The dangling C–C bonds in the cluster were capped with H atoms, resulting in C126H12 formula (see Fig. 21.4a).

Fig. 21.4
figure 4

Undoped clusters with optimized geometry: CNT(3,3) (a), CNT(5,5) (b), and graphene sheet (c)

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Clusters with the formulas C210H20 and C266H46, respectively, were constructed to model a CNT(5,5) and graphene (see Fig. 21.4b, c, respectively). Approximate lengths of both CNT clusters were 26.5 Å. The dimensions of GR cluster were 24.1 × 30.8 Å.

Clusters of all undoped carbon nanostructures used in calculations were electrically neutral, while additional charges equal to −1e and +1e were assigned to clusters describing the B- and N-doped clusters, respectively. By using such additional charges, we have modeled a very common situation when an “additional” electron introduced into a real CNT by the N C impurity is compensated by an additional charge +1e of defect created somewhere far from the N C site (such compensating defects were not modeled explicitly in our calculations). Correspondingly, additional compensating defects can supply one “missing” electron in the B C case. Taking into account the −2e charge of “free” M(VI)O4 2− anion, additional −2e charges were assigned to the clusters of undoped adsorbent and chromate anion. So, additional charges of −3e or −1e were assigned to the B- or N-doped clusters, respectively. All systems were treated as closed-shell, that is, with no unpaired electrons.

Characteristic size parameters of undoped CNT(3,3) cluster used in calculations of adsorption of M(VI) anions were the following: distance along the nanotube axis between the outermost C6 rings was ∼24.7 Å, distance between outermost H6 rings (cluster length) was ∼26.5 Å, mean distance between “contralateral” C nuclei of the central C6 ring (cluster diameter) was ∼4.21 Å. Analogously, the length and diameter of undoped CNT(5,5) cluster were ∼26.5 and ∼6.84 Å, respectively. Characteristic dimension of undoped GR cluster (the maximal internuclear distances between the H nuclei located on the opposite sides of the sheet) was ∼24.1 × 30.8 Å. It should be noted that the lengths of real CNTs usually exceed their diameters by several orders of magnitude. So, a “section” of the CNT modeled in a cluster must be long enough to guarantee a negligible influence of side surfaces on the central region of the section where the B(N) impurities and adsorbed M(VI)O4 2− anion are situated. To examine this property, we have performed supplementary geometry optimization calculations of undoped CNT(3,3), CNT(5,5), and GR clusters. As the calculations showed, removal of the two outermost carbon rings from both edges of CNT(3,3) and CNT(5,5) clusters (or the two outermost carbon “strips” from GR cluster) changes the C-C distances in the central regions of clusters within 0.3%. Such slight changes ensure a negligible influence of the cluster edges on the calculated adsorption geometries. Consequently, the selected sizes of clusters were considered optimal, as larger clusters require more CPU time.

To complement these edge cases of the CNT surface curvatures by an intermediate one, we have additionally considered a fragment of the hexa-layered multiwalled carbon nanotube which can be denoted using formal rules as MWCNT(17,17)@(21,21)@(25,25)@(29,29)@(33,33)@(37,37) and will be mentioned in the following text as MWCNT. The outer diameter of such MWCNT is ∼5.1 nm, which corresponds to an average tube diameter in commercially available mixtures of CNTs [34].

As it was found for the low-diameter CNTs [74], the nanotube fragments of at least 30 Å length can guarantee a sufficiently weak influence of the edges on the central part. However, construction of MWCNT cluster of such length would require 6800 carbon atoms. Such a number is too large for efficient DFT-based calculations of adsorption geometries, inasmuch as up to a 100s of combinations of adsorbents and adsorbates that have to be considered in our studies. For this reason, we have constructed a conical section of MWCNT which comprises a hexagonal part of the nanotube outer surface (for construction of the cluster, see Fig. 21.5). This part has transverse dimension of 29.0 Å, and the distance between inner and outer walls of MWCNT is 15.2 Å. All dangling C–C bonds of MWCNT cluster were capped by placement of H atoms providing a C546H126 formula.

Fig. 21.5
figure 5

(a) Scheme of selection of MWCNT cluster from six-walled carbon nanotube (edge atoms of the cluster are marked by red shadows); (b) structure of selected MWCNT cluster given in two projections

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During geometry optimization calculations, the H atoms of MWCNT cluster were fixed (frozen). As our geometry optimizations showed, the structure of MWCNT cluster was not stable without such freezing, that is, the carbon sheets constituting the conical part of the multiwalled tube moved apart. Normally, coaxial structure of MWCNTs prevents such decomposition. The freezing of the edge hydrogen atoms was applied in studies of molecular adsorption on the outer layer of MWCNT of 2 nm diameter [78]. Such freezing obviously provides some limitations to geometric optimization of the whole cluster. However, it leaves the atomic positions in the cluster core to be optimized thus providing (as it was also shown in [78]) an adequate treatment of molecular adsorption properties.

As a result, it was found that geometry optimization of undoped MWCNT cluster resulted in a little bulging of the outer carbon layers of the cluster (several deeper layers were also bulged but to a lower extent). However, despite the bulging, the cluster preserved the curvature of the outer surface (after optimization, corresponding curvature radius decreased only by 10%). This feature shows that freezing of outer atoms provides a reasonable approximation in modeling of adsorption on medium-diameter MWCNT. An analogous approach to model the medium-diameter MWCNT has been successfully applied in [73].

3.2 Calculation Method, Basis Sets, and Other Computational Parameters

The geometry-optimized calculations were performed with use of Gaussian 09 [79] software package within density functional theory (DFT) level with B3LYP nonlocal correlation functional [80, 81]. The calculations used a basis set of 6-31G, which is typical for computational studies of adsorption of molecules (hydrogen halide) on the surface of CNT in recent years [69]. However, other base sets were used to calculate the molecular anions, since the heavy metals contained in the molecular anions are beyond the range that can be calculated using the base set of 6-31G. The basic set of cc-pVDZ was used for Cr and O atoms [82]. The atoms Mo and W are represented by the basis set of cc-pVDZ-PP with pseudo-potentials [83, 84]. Such combination of basis sets is generally utilized in computational studies of adsorption of molecules with d-metals on the CNT surfaces [85, 86]. All other settings were Gaussian 09 defaults, that is, no additional keywords were specified. Effects of water solvent on the studied adsorption properties were considered within the polarizable continuum model (PCM) [87].

As starting geometry, the HX (X = F, Cl, Br) molecules were put at 1.5 Å distance from the CNT surface in the vicinity of the B(N) atom, and the HAX bond was initially oriented parallel to the CNT axis. In the geometry optimization studies, several starting positions of M(VI)O4 2− (M(VI) = Cr, Mo, W) anions with respect to the carbon surface were considered for each adsorption case. In all cases, the anions were initially put in such a way that the shortest C/B/N-O distance lied between 1.5 and 2.2 Å. Using such initial geometry, we ensure binding of the anion particularly to the dopant atoms, not at just some other site of the doped CNT or graphene sheet.

Excited electronic states of CrO4 2− anions in “free” and in adsorbed configurations were studied by the time-dependent DFT method (TD-DFT) method. In these calculations, the two-level ONIOM-2 approach in treatment of interatomic interactions was used [88]. The “adsorbent +CrO4 2− anion” system with optimized geometry was divided into two regions, the quantum mechanical (QM) and the molecular mechanical (MM). The QM region comprised the atoms of CrO4 2− anion, while the MM region comprised all atoms of the adsorbent molecule (C and H) (see Fig. 21.6). The electronic embedding was used in order to take into account electrostatic interaction between the QM and MM regions, i.e., the atoms of the QM region were treated by TD-DFT calculations, while the atoms of the MM region were treated as partial charges contributing to the quantum-mechanical Hamiltonian. Successful applications of the ONIOM approach to calculations of the excited states of molecules are reviewed in [89]. The TD-DFT is a well-established method for treatment of the excited states of tetrahedral oxyanions of d 0 metals (see [90] and references therein). The TD-DFT calculations of the singlet excited states of CrO4 2− anions (QM region) were carried out in a single-point (no geometry optimization) calculation with the previously optimized geometry. The B3LYP exchange-correlation functional was used and only single excitations were taken into account. The same basis sets as for the geometry optimization calculations were used. Energies and oscillator strengths of electronic transitions from the ground to 50 lowest energy excited states were obtained.

Fig. 21.6
figure 6

Geometry-optimized structures of СNT(3,3) with adsorbed on the surface of CrO4 2− anion are considered in the approximation of quantum mechanics (the region is painted blue), and СNT(3,3) is considered in the approximation of molecular mechanics (the region is painted with pink color)

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4 Electronic Structure and Sensing Properties of Carbon Nanotubes with Adsorbed Hydrogen Halide Molecules HX (X = F, Cl, Br)

The results of geometry-optimized calculations of the electronic structure of carbon nanotubes (СNTs) and graphene (GR) with adsorbed HX (X = F, Cl, Br) are presented in this section. The influence of boron and nitrogen impurities on the formation and character of chemical bonds between carbon materials the molecules of halogen halides is analyzed.

The binding energies, E b, were obtained as the difference of the calculated total energies using expression: E b = E CNT-B(N)-HX – E CNT-B(N) – E HX.

The calculated E b value should be negative in a stable adsorption configuration. The charge states of HX (X = F, Cl, Br) adsorbates are obtained as an algebraic sum of calculated Mulliken charges of H and X atoms. Negative value of charge of the adsorbate molecule means transfer of negative electronic charge from the CNT to the molecule.

The calculated binding energies, charges on the HX adsorbate molecules (X = F, Cl, Br) and the optimized geometry of the internuclear distances of CNT(3,3), CNT(5,5) and graphene are presented in Table 21.1.

Table 21.1 Calculated binding energies, charges of adsorbate molecules HX (X = F, Cl, Br) and internuclear distances for undoped configurations
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As Table 21.1 shows, our calculations provide relatively low values of binding energies between adsorbed HX (X = F, Cl, Br) molecules and undoped clusters: they range from −0.07 to −0.19 eV. Internuclear distances in adsorbed molecules R H–X are only slightly changed with respect to corresponding distances in free molecules (the difference does not exceed 1.5%). For all considered cases of adsorption on undoped clusters, the “axis” of HX molecule is settled practically perpendicular to the carbon surface. The shortest R C–H distance exceeds 2 Å for all studied HX cases.

For all adsorption configurations, calculations indicate lower binding energies and higher (R C–H)min distances for undoped graphene clusters in comparison with CNT(3,3) and CNT(5,5) (see Table 21.1). Values of E b obtained for undoped CNT(3,3) and CNT(5,5) fall into the region of binding energies typical for hydrogen bonds (0.1–0.6 eV [91]) but are close to its lower limit. The E b value in GR-HCl and GR-HBr cases are even slightly below this lower limit and fall into the region of the van der Waals bonds (0.01–0.1 eV, see [92]). Relatively low values of E b and slight changes of internuclear distances in adsorbed molecules indicate the absence of covalent bonding between HX (X = F, Cl, Br) adsorbates and undoped carbon nanotubes.

Calculations also give low values for charges or HX molecules adsorbed on undoped clusters: they are in the −0.02 to −0.07 e range (see Table 21.1).

The calculated binding energies, charges on the HX adsorbate molecules (X = F, Cl, Br), and the optimized geometry of the internuclear distances of B-doped CNT(3,3), CNT(5,5), and graphene are shown in Table 21.2. In general, calculations show a completely different situation with respect to the adsorption of HX molecules on the surface of boron-doped carbon nanotubes in comparison with undoped nanostructures.

Table 21.2 Calculated binding energies, charges of adsorbate molecules HX (X = F, Cl, Br), and internuclear distances for the B-doped configurations
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Calculations reveal far different situation for adsorption of HX molecules on the B-doped CNTs. In this case, the binding energies with adsorbate molecules range from −0.36 to −2.53 eV (see Table 21.2), and they are generally higher by an order of magnitude than corresponding energies of adsorption on undoped clusters. The E b values for CNT(3,3) and CNT(5,5) definitely fall into the region of hydrogen bonds (0.1–0.6 eV, Ref. 202) or are slightly above this region [−0.87 eV, for CNT(3,3)-B-HCl], while the −2.13 eV value observed in CNT(3,3)-B-HBr case is typical for covalent bonds [93].

For CNT(5,5), all adsorption cases reveal lower binding energies relatively to CNT(3,3) (compare corresponding rows in Table 21.2). The B-doped graphene clusters reveal binding energies typical for covalent bonds (ranging from −2.53 for GR-B-HF to −2.38 for GR-B-HCl, see Table 21.2).

As Table 21.2 shows, in each case of HX adsorption on the B-doped CNT(3,3) and CNT(5,5), the H atom of the adsorbate is located closer to one of the atoms of the nanotube, than to the impurity atom B, that is, (R C–H)min < (R B–H)min. In the CNT(3,3)-B-HBr case, the (R C–H)min distance is even almost twice shorter than the (R B–H)min distance. So, it is arguable that C and H atoms create chemical bonds in all studied cases of adsorption on the B-doped CNT(3,3) and CNT(5,5) clusters. For the B-doped graphene, on contrary (R C–H)min > (R B–H)min and the H atoms of the adsorbates create chemical bonds with the B dopants.

The most significant elongations of the H–X distances are obtained for CNT(3,3)-B-HBr and CNT(3,3)-B-HCl cases (∼53% and ∼93%, respectively). In contrast, adsorption of HX molecules on the B-doped graphene clusters, despite high binding energies, does not lead to significant changes of internuclear distances in the adsorbates (the relative change does not exceed 12.5%).

The calculated binding energies, charges on the HX molecules (X = F, Cl, Br), and the optimized geometry of the internuclear distances of N-doped CNT(3,3), CNT(5,5), and graphene are presented in Table 21.2.

In general, calculations show a situation similar to the case of adsorption of HX molecules on the surface of undoped clusters.

For all studied adsorptions cases, calculations give relatively low values of the binding energies (do not exceed −0.41 eV; see Table 21.3), small adsorbate charges (do not exceed |0.05| e), slight changes if internuclear distances in adsorbates (do not exceed 2.5%), and relatively high internuclear distances between the adsorbates and nanotubes (above 2 Å). Although for some cases (CNT(3,3)-N-HF, CNT(5,5)-N-HF, GR-N-HF, and CNT(5,5)-N-HBr) the values of E b can be formally attributed to the energy range of weak hydrogen bonds (see above), the rest of the adsorption cases reveal binding energies typical for van der Waals’ interaction (0.01–0.1 eV range of binding energies [92]), that is, physisorption.

Table 21.3 Calculated binding energies, charges of adsorbate molecules HX (X = F, Cl, Br), and internuclear distances for N-doped configurations
Full size table

Results of the study of the system “HX molecule (X = F, Cl, Br), adsorbed on the surface of undoped, B-, and N-doped CNT(3,3), CNT(5,5), and graphene” allow the following conclusions. The calculated binding energies and charges on adsorbates reveal the mechanism of physisorption of HX molecules on undoped graphene and undoped CNTs and on N-doped materials. Therefore, undoped, B-, and N-doped carbon nanotubes are less attractive to elaboration of sensors of hydrogen halide gases.

Materials based on the B-doped CNTs are perspective for sensing of HCl and HBr hydrogen halides as the molecules are chemisorbed on the nanotube surfaces.

5 Electronic Structure of Carbon Nanotubes with Adsorbed Molecular Anions of Hexavalent Metals and Perspectives for Removal of Toxic M(VI) Metals by Carbon Nanomaterials

This section presents calculation results and corresponding analysis for the electronic structure of single- and multiwalled carbon nanotubes and graphene with adsorbed anions of M(VI) metals. The influence of impurities (boron and nitrogen) and oxygen- and ammonia-containing functional groups on the formation of the interatomic bonds between carbon materials and the anions is analyzed in view of potential application of carbon nanomaterials for removal of M(VI) metals from air and water media.

The binding energies E b of anions to adsorbents, both in vacuo and in aqua, were obtained as the difference of the calculated total energies using expression:

$$ {E}_{\mathrm{b}}={E}_{\mathrm{ads}-\mathrm{anion}}-{E}_{\mathrm{ads}}-{E}_{\mathrm{anion}}, $$
(21.4)

where E ads-anion are total energies of the optimized adsorption system “adsorbent with anion,” E ads are total energies of the optimized adsorbent, and E anion are total energies of optimized anions calculated within the same approximations.

Clusters of all undoped carbon nanostructures in calculations were electrically neutral, while additional charges equal to –1e and +1e were assigned to clusters describing the B- and N-doped clusters, respectively. Taking into account the −2e charge of “free” MVIO4 2− (MVI = Cr, Mo, W) anion, additional −2e charges were assigned to the clusters of undoped adsorbent and chromate anion. Consequently, additional charges of −3e or −1e were assigned to the B- or N-doped clusters, respectively.

Differences in charge density on the MVIO4 2− (MVI = Cr, Mo, W), Cr2O7 2−, and HCrO4 − anions (in respect to the isolated anion) in adsorbed state were defined as Δq = −2e – q (Δq = −e – q for HCrO4 −), where q is an algebraic sum of charge states of all atoms of anion (calculated in adsorbed configuration using Mulliken population analysis). If the calculated value of Δq is negative, the electronic charge is transferred from the anion to the adsorbent.

5.1 Adsorption of M(VI)O4 2− (M(VI) = Cr, Mo, W) Anions on Undoped and B(N)-Doped CNTs

Single adsorption configurations were found in each case (see Fig. 21.7), except for the adsorption on undoped graphene.

Fig. 21.7
figure 7

Geometry-optimized structures of CrO4 2− anions adsorbed on CNT(3,3) and CNT(5,5) in vacuo (only central parts of the clusters are shown)

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In all cases, the binding energies are negative and fall within −0.5 to −7.2 eV range (Table 21.4). Such E b values are typical for the chemisorption mechanism of adsorption [93].

Table 21.4 Binding energies E b (eV), charge differences Δq (e) of M(VI)O4 2− (M(VI) = Cr, Mo, W) anions adsorbed on undoped and B(N)-doped carbon nanostructures, and the shortest internuclear distances R min between anions and adsorbents (Å) calculated in vacuo
Full size table

All three anions, CrO4 2−, MoO4 2−, and WO4 2−, have very similar dependencies of both E b, and Δq on type of doping and type of the adsorbent structure. This feature is quite expected since Cr, Mo, and W metals are isoelectronic and the valence properties of M(VI)O4 2− anions are determined by interplaying 3d (4d or 5d) orbitals of the M(VI) cation and 2p orbitals of the oxygen ligands. At that, the cationic d orbitals are localized at the central core of the anion, so creation of the chemical bonds to outer atoms is determined mainly by the oxygen 2p orbitals which have very common energy and spatial structure for all three M(VI)O4 2−anions [90].

Two stable configurations (GR-1 and GR-2) were found for the case of the adsorption of MVIO4 2− (MVI = Cr, Mo, W) molecules on graphene sheet (Fig. 21.8).

Fig. 21.8
figure 8

Geometry-optimized structures of CrO4 2− anions adsorbed on graphene in vacuo (only central parts of the clusters are shown)

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So, our results indicate that one would expect quite similar absorption characteristics for the three anions and also for other types of adsorbents; for this reason we have limited the set of anions to only CrO4 2− in studies of adsorption on the functionalized carbon nanostructures.

The optimized geometries of CrO4 2− adsorbed on pristine and doped graphene (Fig. 21.8) illustrate typical peculiarities of adsorption configurations.

As Fig. 21.8 shows, in configuration 1 (such kind of atomic configuration is the most common among all adsorption cases), the chemical bond between the O atom of the anion and C atom of the adsorbent is created (the internuclear distance R C–O min is 1.47 Å which is a typical value for C–O covalent bonding [94]).

In configuration 2 (see Fig. 21.8), three O atoms are located at approximately equal distance from the carbon surface, that is, one of the faces of the CrO4 2− tetrahedron is parallel to the graphene surface. In this configuration, each of the three O atoms is located about 2.80 Å above the center of C6 “honeycomb” of graphene surface, and all three O atoms have approximately the same local surrounding. Within this accuracy, the structure is characterized by the C3 symmetry axis perpendicular to the graphene plane and containing one C atom of the adsorbent, the Cr atom, and the “upper” O atom of the CrO4 2− anion.

In the GR-B-CrO4 2− case, one O atom of the anion creates a covalent bond to the boron dopant of the adsorbent (Fig. 21.8), and such kind of bonding is common for all cases of adsorption on the B-doped adsorbents. The situation is different for the N-doped adsorbents: one O atom of the anion can create bond either with N atom or with C atom which is the nearest neighbor to N (see Fig. 21.7 and 21.8). Creation of covalent O-C bonds is observed for adsorption of CrO4 2− and MoO4 2− on CNT(3,3)-N and CNT(5,5)-N and for WO4 2− on CNT(3,3)-N. The O-N covalent bonds are created in all other adsorption cases on the N-doped adsorbents. As Table 21.4 shows, creation of O-N bonds provides the highest absolute values of binding energies.

The calculated oscillator strengths of CrO4 2− anions are given in Fig. 21.9. As can be seen from the figure, calculations predict appearance of additional red bands of optical absorption of CrO4 2− anions after on N-doped CNT. Such an appearance can be related to the fact that adsorption of CrO4 2− on the N-doped CNT is accompanied by significant distortions of the anion nuclei. When considering distances and angles for adsorption on carbon nanostructures (see Table 21.5), one can see that the most significant distortions of the CrO4 2− geometry are observed for adsorption on nitrogen-doped structures in comparison with undoped and B-doped configurations.

Fig. 21.9
figure 9

Top plot: calculated energies of electronic transitions from the ground (1A1) to the low-energy excited states of free CrO4 2− anions (blue bars); energies of the same transitions calculated with another basis sets [90] (green bars) and determined experimentally (red triangles); experimental absorption spectrum of chromate anion in aqueous solution (black solid line) [95]. Other plots: oscillator strengths of electronic transitions of CrO4 2− anions adsorbed on the surface of carbon nanostructures calculated with (black circles) and without (red triangles) account of influence from the adsorbents

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Table 21.5 Characteristic parameters of distortions of adsorbed CrO4 2− anions
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Since our results reveal the chemisorptions mechanisms, they indicate that the CNT-based materials can efficiently adsorb CrO4 2−, MoO4 2−, and WO4 2− anions in gaseous media, i.e., from air atmosphere. However, the situation is quite different for adsorption in water.

The binding energies (E b) and the charge difference (Δq) for the adsorbed configurations of M(VI)O4 2− on the surface of undoped, boron-nitrogen-doped, carbon nanostructures calculated in aqua are shown in Fig. 21.10.

As Fig. 21.10 shows, much lower absolute values of binding energies are observed for all studied combinations relatively to corresponding cases in vacuo. The E b values of all adsorption cases on MWCNT cluster and graphene are positive indicating that adsorption of M(VI)O4 2− anions by such adsorbents is energetically unfavorable. Positive are also the energies of adsorption cases on all undoped adsorbents. Only the B- and N-doped CNT(3,3) and CNT(5,5) reveal negative E b values and these values are below −2 eV for adsorption of CrO4 2− and MoO4 2− on CNT(3,3). All three anions reveal no stable adsorption configurations in aqua on undoped graphene, i.e., geometry optimization was not convergent.

Fig. 21.10
figure 10

Dependencies of binding energies E b on adsorbent type and type of doping calculated in aqua

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From these results, we can conclude that undoped CNTs could be less-efficient materials for adsorption of M(VI)O4 2− anions in water. The efficiency can be improved if the materials would contain a valuable amount of low-diameter CNTs, or they would be doped by aliovalent impurities like B or N. Both ways of improvement are expensive and hardly realizable for massive production of CNT mixtures [96, 97]. So, another mechanism should be proposed to explain a substantial uptake of Cr(VI) anions by CNT-based materials from water solutions observed in experiments [36, 38, 98, 99]. These mechanisms are examined in the following subsection.

5.2 Adsorption of CrO4 2− Anions on Functionalized CNTs

It is believed that one of the most efficient ways for enhancement of the adsorption capability of CNTs with respect to Cr(VI) compounds is functionalization of the CNT-based materials by the oxygen-containing surface functional groups (OSG) [2, 4, 34, 35]. In such functionalization, mixes of CNTs are treated by acids, for instance, by HNO3 [34, 35] and then filtered, washed out, and dried up. As a result, various OSGs are created on the CNTs surfaces (a schematic explanation of the process can be found in [35]).

According to existing concepts [34, 36, 47], such kind of functionalization can enhance uptake of Cr(VI) compounds by the materials due to the following factors: (a) chemical reactions of Cr(VI) compounds with OSG can change the valence state of chromium ions Cr(VI) → Cr(ІІI), whereas trivalent chromium ions are by several orders less toxic than hexavalent ones; (b) compounds of Cr(VI) can be chemically bound directly to atoms of OSG, that is, the groups can create additional adsorption cites for chromium compounds if compared with nonfunctionalized CNT surface; and (c) positively charged OSG+ can be the centers of Coulomb attraction for negatively charged chromate anions like CrO4 2− that enhances adsorption capability of functionalized CNT material (this concept is analyzed in [36]).

However, there were several experimental indications that Coulomb attraction to positively charged groups is a less important factor for enhancement of Cr(VI) uptake by the OSG-functionalized CNTs, and this enhancement occurs mainly due to creation of additional OSG-related adsorption sites [34]. In this subsection, we examine computationally, could the OSGs form such sites.

Particular objects of the calculations and motivation for their choice are the following. As it was shown in [35], the FTIR spectra of OSG functionalized CNT materials reveal spectral peaks corresponding to several oxygen-containing groups, in particular –OH (hydroxyl group), –COOH (carboxyl group), and –COO− (deprotonated carboxyl group). So, in our calculations we consider such groups and some of their combinations.

Here, we consider only one type of carbon nanotube, namely, CNT(5,5), since the main focus of the study is bonding of the anions to the OSGs, and the curvature of carbon surface is obviously expected to have a low importance.

The following functional groups are considered (see also Fig. 21.11):

  1. 1.

    CNT(5,5)-COOH. A neutral carboxyl group –COOH has one unpaired electron, whereas neutral cluster of CNT(5,5) has even number of electrons. An even number of electrons is a necessary condition for stability of the chemical bonds; so to model functionalization of the CNT by –COOH group, we assigned the +1e charge to CNT(5,5)-COOH adsorbent (accordingly, the −1e charge was assigned to CNT(5,5)-COOH-СrO4 2− complex). So in fact we model a removal of an extra electron from the region of adsorption (from the OSG). Physically, this electron can be localized on some other defect in the CNT which is left beyond the study.

  2. 2.

    CNT(5,5)-B-COOH. Creation of BC requires an extra electron, so it compensates the COOH group providing chemical stability for the complex. In this case, the adsorbent was taken electrostatically neutral, and correspondingly −2e charge was assigned to CNT(5,5)-B-COOH-СrO4 2− system.

  3. 3.

    CNT(5,5)-COOH-OH. Carboxyl and hydroxyl groups are bound to two nearest C atoms of the nanotube. Unpaired electrons of both groups are mutually compensated, and such complex is considered as one of the most probable kings of coexistence of -COOH and -OH groups on the CNT surface (see [35] and references therein).

    As it was found experimentally [35, 36], adsorption capability of OSG-functionalized CNT materials with respect to Cr(VI) compounds in water solution substantially depends on the pH level. It is well-known that at high pH levels, OSG can be deprotonated (this process can be schematically denoted as –COOH → COO− + H+ or –OH → –O− + H+). To study the influence of deprotonation on adsorption of CrO4 2−, we consider the following two complexes with deprotonated carboxyl groups:

  4. 4.

    CNT(5,5)-COO−-OH. Analogous to case (3) but with carboxyl group missing H+ proton. The negative charge of carboxyl group is modeled by adding one extra electron, that is, assigning −1e charge to the system.

  5. 5.

    CNT(5,5)-N-COO−. The negative charge of carboxyl group is supplied by aliovalent impurity N C.

    Functionalization of the CNTs by ammonia is a commonly applied method of influence on the adsorption properties of the CNT-based materials [76]. To study adsorption of СrO4 2− on ammonia-functionalized CNTs, we consider the following cases:

  6. 6.

    CNT(5,5)-OH-NH3+. The ammonia –NH3 + and hydroxyl –OH groups are bound to the neighboring C atoms of the nanotube providing even number of electrons.

  7. 7.

    CNT(5,5)-1-NH3 + (1 = C8H16O2N = -C2H4-N-CH2-CH2-O-CH2-CH2-O-CH2-CH2-). Such kind of functionalization with ammonia can substantially enhance hydrophilicity of the CNT-based materials [100], even when functionalization procedures are rather complex [76, 101].

  8. 8.

    CNT(5,5)-2-NH3+ (2 = C4H8N = -C2H4-N-CH2-CH2-). Another group with NH3 + at the end, however, with different (approximately, a half-shorter) atomic chain between ammonia and the nanotube. Such shorter chain represents an intermediate case of distance between the NH3 + and the CNT surface if compared with corresponding distances in groups (6) and (7).

Fig. 21.11
figure 11

Geometry-optimized structures of OSG-functionalized CNT(5,5) with (columns 2 and 4) and without (columns 1 and 3) adsorbed CrO4 2− anions

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Calculation results on adsorption of CrO4 2− anions on functionalized CNTs both in vacuo and in aqua are given in Table 21.6. As the calculations show, adsorbents (4), (5), and (6) are not stable in vacuo without CrO4 2− anions (geometry optimizations unconverged), so the corresponding binding energies cannot be calculated.

As Table 21.6 shows for adsorbents (1)–(5), in all these cases, the R min distances are typical for the covalent bonding between two oxygen atoms, that is, the anions are bound to the OSG by O-O covalent bonds both in vacuo and in aqua. At that, the R min distances for in-vacuum and in-water adsorption on adsorbents (1)–(5) are very close (they differ by only few thousandths of Å); however, the binding energies E b are significantly different. For vacuum, the E b energies are negative, whereas for water they are positive, indicating that adsorption on adsorbents (1)–(5) in vacuo is energetically unfavorable.

Table 21.6 Binding energies E b (eV), charge differences Δq (e) of CrO4 2− anions adsorbed on functionalized CNT(5,5), and the shortest internuclear distances R min between the anion and adsorbents (Å) calculated in vacuo
Full size table

Adsorption configurations of CrO4 2− on adsorbents (7) and (8) in vacuo are characterized by the binding energies (near −10 eV) which are substantially higher than E b values of other adsorption configurations on functionalized CNTs found in vacuo (cases (1)–(3); see Table 21.6).

A distinctive feature of these configurations is that two O-H bonds between the anion and NH3 + group are created. One of them has R min distance (0.985 Å) typical to covalent O–H bonding. However, the H atom of this bond lies closer to the anion than to the N atom of NH3 + group (corresponding H-N distance is 2.004 Å, whereas other H-N distances in the group are in the range 1.2–1.3 Å). So, attached to CNT surface OSGs of (1), (2), and (3) types as well as ammonia-containing groups (7) and (8) can be the centers of efficient adsorption of CrO4 2− anions in vacuo.

The negative E b values (about −1 eV) are also obtained for in aqua adsorption of CrO4 2− on ammonia-functionalized CNTs (cases (6)–(8)). In each of these three cases, two O-H bonds between the oxygen atoms of the anion and the hydrogen atoms of NH3 + groups are created (correspondingly, two values are given in the R min column of Table 21.7 for cases (6)–(8)). Such R min values are typical for the hydrogen-type bonds [94].

Table 21.7 Binding energies E b (eV), charge differences Δq (e) of CrO4 2− anions adsorbed on functionalized CNT(5,5), and the shortest internuclear distances R min between the anion and adsorbents (Å) calculated in aqua
Full size table

So, taking into account generally weak adsorption of CrO4 2− on undoped and B(N)-doped carbon nanostructures, it can be concluded that functionalization by ammonia-containing functional groups can enhance the adsorption capability of the CNT-based materials with respect to CrO4 2− anions in water surrounding.

5.3 Adsorption of HCrO4 − and Cr2O7 2− Anions on Pristine, B(N)-Doped, and Functionalized Carbon Nanostructures

Results obtained in Sect. 5.1 definitely indicate that almost all adsorption cases of M(VI)O4 2− anions on MWCNT reveal E b, Δq, and R C–O min values which are intermediate between CNT(5,5) and graphene cases, both in vacuo and in aqua. This result implies that considering only two absorbents representing the “edge” cases of the nanotube surface curvature [CNT(5,5) and graphene] may provide quite sufficient information about adsorption properties with respect to oxoanions of hexavalent chromium. For this reason, we limit our studies of HCrO4 − and Cr2O7 2− adsorption on undoped and B(N)-doped carbon nanostructures to only two types of adsorbents, namely, CNT(5,5) and graphene sheets.

As it follows from calculations (see Tables 21.8 and 21.9), adsorption of Cr2O7 2− and HCrO4 − anions on undoped and B(N)-doped carbon nanostructures in aqua is characterized by either positive or nominally negative but very low in absolute values binding energies (not greater than |0.13| eV). Such E b values, together with relatively long R min (in 3.2–4 Å range; see Table 21.8), unambiguously reveal the absence of chemical bonding between the adsorbents and the anions. At that, the cases with negative E b values presented in Table 21.9 can be regarded as physisorption. Such results, together with results for adsorption of CrO4 2− anion (see above) can lead to a conclusion that neither undoped nor B(N)-doped CNTs cannot by efficient adsorbents of the considered anions of hexavalent chromium in water surrounding.

Table 21.8 Binding energies E b (eV), charge differences Δq (e) of HCrO4 − and Cr2O7 2− anions adsorbed on undoped and B(N)-doped carbon nanostructures, and the shortest internuclear distances R min between the anions and adsorbents (Å) calculated in vacuo
Full size table
Table 21.9 Binding energies E b (eV), charge differences Δq (e) of HCrO4 − and Cr2O7 2− anions adsorbed on undoped and B(N)-doped carbon nanostructures, and the shortest internuclear distances R min between the anions and adsorbents (Å) calculated in aqua
Full size table

However, adsorption configurations with chemical bonds and substantially negative binding energies exist in vacuo (see Table 21.8). As the table shows, the aliovalent doping of adsorbents in the case of HCrO4 − and Cr2O7 2− adsorption has in general the same effect on the E b values as it was in CrO4 2− case (see above). Doping with N substantially lowers the E b values (by ∼2 and ∼4 eV for HСrO4 − and Cr2O7 2− adsorption, respectively) relatively to corresponding adsorption cases on undoped adsorbents. Doping with B, in contrast, leads to positive binding energies (in Cr2O7 2− case) or to the absence of adsorbed configurations (HСrO4 − case).

Rather long R min (near 3 eV; see Table 21.8) are obtained for all adsorption configurations of HСrO4 − in vacuo. At that, simultaneously, two [CNT(5,5)-N-HСrO4 − case] or even three (all other converged cases) oxygen atoms of HСrO4 − anion are located at approximately equal distance from the adsorbent.

Long R min together with substantially negative E b values are obtained in vacuo also for Cr2O7 2− adsorption on CNT(5,5) and GR-N adsorbents. So, taking into account these results (and also results for CrO4 2− presented above), we can conclude that carbon nanostructures will be efficient materials for removal of all three considered anions of Cr(VI) in gaseous state, whereby doping with N will enhance the adsorption capability of the materials.

Results for adsorption of Cr2O7 2− and HCrO4 − anions on functionalized CNT(5,5) in aqua are presented in Table 21.10 (the adsorbents have the same notation as in Sect. 5.3) As Table 21.10 shows for both anions, all adsorbents reveal adsorbed configurations with negative binding energies (in −0.1 to −0.6 eV range) excluding adsorbent (5), for which the energy is positive. For both anions on adsorbent (5), the R min distances (Table 21.10) show O-O chemical bonding between oxygen atoms of the anions and functional group –COO−.

Table 21.10 Binding energies E b (eV), charge differences Δq (e) of HCrO4 − and Cr2O7 2− anions adsorbed on functionalized CNT(5,5), and the shortest internuclear distances R min between the anion and adsorbents (Å) calculated in aqua
Full size table

However, significantly positive E b values (above 2.5 eV) clearly indicate that adsorption on this adsorbent is energetically unfavorable. Adsorption of HCrO4 − on adsorbent (3) and adsorption of Cr2O7 2− on adsorbent (4) do not lead to creation of chemical bonds between the anions and functional groups, whereas the absolute values of binding energies in these two cases are low (fall between −0.1 and −0.2 eV). So evidently, the physisorption mechanism is realized in both cases.

For the rest of configurations presented in Table 21.10, the O-H bonds between the anions and functional groups are created (even two O-H bonds are observed for ammonia-containing adsorbent (6)). Such results indicate that chemisorption mechanism is realized in all these cases.

So, our calculations show that Cr2O7 2− and HCrO4 − anions can be efficiently adsorbed by the OSG and ammonia-functionalized carbon nanostructures in water.

Our results can explain the experimentally observed dependencies of Cr(VI) uptake by the OSG-functionalized CNT-based materials on pH level of water solution, which were presented in, for example [35]. The Cr(VI) uptake reaches the highest values when pH < 2, it decreases when 2 < pH < 6, and the Cr(VI) compounds are practically not adsorbed when pH > 6 [36]. It is known that at pH < 6 compounds of Cr(VI) exist predominantly as Cr2O7 2− and HCrO4 −, whereas at pH > 6 they exist as СrO4 2− [35, 36]. Our results show that OSG-functionalized carbon nanostructures are good adsorbents of Cr2O7 2− and HCrO4 − in water, while they poorly adsorb СrO4 2−. So, the observed dependence of Cr(VI) uptake on pH level can be explained by this particular selectivity of the adsorbents with respect to the anions.

The above presented computational results and their analysis allow formulation of recommendations for functionalization of the CNT-based materials to enhance their adsorption capability with respect to Cr(VI) compounds in water. Functionalization of the materials both with OSG and ammonia-containing groups is feasible at low pH levels, whereas at high pH (>6), only functionalization by ammonia-containing groups will make sense. Undoped carbon nanostructures are poor adsorbents of Cr(VI) compounds in water, and aliovalent doping with B or N atoms does not improve the situation.

6 Conclusions

The results of the study of the system “HX molecule (X = F, Cl, Br), adsorbed on the surface of undoped, B-, and N-doped CNT(3,3), CNT(5,5) and graphene” clusters allow the following conclusions. The calculated binding energies and charges on adsorbates reveal the mechanism of physisorption of HX molecules on undoped graphene and undoped CNTs and on N-doped materials. Therefore, undoped, B-, and N-doped carbon nanotubes are less attractive to elaboration of sensors of hydrogen halide gases. Materials based on the B-doped CNTs are perspective for sensing of HCl and HBr hydrogen halides as the molecules are chemisorbed on the nanotube surfaces.

The DFT-based electronic structure calculations predict that the CNT-based materials can efficiently adsorb MVIO4 2− (MVI = Cr, Mo, W), Сr2O7 2−, and HСrO4 − anions in gaseous surrounding. Doping of carbon nanostructures with nitrogen provides additional adsorption sites for the anions, so such kind of doping can enhance adsorption capability of the materials with respect to MVIO4 2−, Сr2O7 2−, and HСrO4 − anions.

Calculations predict that neither pristine nor B- or N-doped CNTs can be efficient adsorbents of MVIO4 2− (MVI = Cr, Mo, W), Сr2O7 2−, and HСrO4 − anions in water. Functionalization of CNTs by the ammonia-containing functional groups enhances their adsorption capability with respect to CrO4 2−, Сr2O7 2−, and HСrO4 − anions in water, so such functionalization can enhance removal of Cr(VI) compounds from wastewaters by CNT-based materials. Functionalization of CNTs by the oxygen-containing functional groups does not enhance their adsorption capability in water with respect to CrO4 2−; however it enhances adsorption of Сr2O7 2− and HСrO4 − anions.