Theoretical Investigation on the Solubilization inWater of Functionalized Single-Wall Carbon Nanotubes

An important technique to increase the solubility and reactivity of carbon nanotube is through functionalization. In this study, the effects of functionalization of some single-walled carbon nanotubes (SWCNTs) were investigated with the aid of density functional theory. The SWCNT model used in the study consists of a finite, (5, 0) zigzag nanotube segment containing 60 C atoms with hydrogen atoms added to the dangling bonds of the perimeter carbons. There are three water-dispersible SWCNTs used in this study that were functionalized with (a) formic acid, as a model of carboxylic acid, (b) isophthalic acid, as a model aromatic dicarboxylic acid, and (c) benzenesulfonic acid, as a model aromatic sulfonic acid. Binding energies of the organic radicals to the nanotubes are calculated, as well as the HOMO-LUMO gaps and dipole moments of both nanotubes and functionalized nanotubes. Binding was found out to be thermodynamically favorable. The functionalization increases the electrical dipole moments and results in an enhancement in the solubility of the nanotubes in water manifested through favorable changes in the free energies of solvation. This should lower the toxicity of nanotubes and improve their biocompatibility.


Introduction
Single-walled carbon nanotubes (SWCNTs) are allotropes of carbon and possess various novel properties that make them useful in the field of nanotechnology and pharmaceuticals.SWCNTs are tubular in shape, made of graphite, nanometers in diameter, and several millimeters in length and have a very broad range of electronic, thermal, and structural properties.These properties vary with the kind of nanotubes defined by its diameter, length, chirality or twist, and wall nature.Their unique surface area, stiffness, strength, and resilience have led to much excitement in the field of pharmacy.Nanostructured materials hold promise for a wide range of technological applications and are increasingly studied, not only for their possible applications in electronics, optics and mechanical materials, but also specifically having enormous potential in nanomedicine [1][2][3][4][5][6][7][8][9][10][11].Because of this, it is imperative to examine the toxicity of these carbon-based nanostructures.Previous toxicological evaluations of single-walled carbon nanotubes have been conducted, both in cell culture and in vivo.One example, using an SWCNT surfactant stabilized system where the Fe content was significantly high, reported an elevated cytotoxic response [12].Warheit et al. [13] observed an increase in inflammatory response in the lung cavities of rats.While these studies report potential negative implications of SWCNT, they did not use a SWCNT sample easily dispersed in water via covalently bound functional groups.
Carbon nanotubes (CNTs) are insoluble in water.For successful biomedical applications of nanotubes the solubility problem may be overcome in part by chemical functionalization of the CNT surface, resulting in an increased compatibility of the functionalized CNT with water [1].Functionalization has led to improved compatibility with a variety of biological components.Functionalization has been obtained both through non-covalent-binding schemes [10] or covalent binding at the CNT surface [7][8][9].
Studies done previously, evaluated the differential cytotoxicity of water-suspendable fullerenes on human dermal fibroblasts (HDFs) in culture [14].It was concluded that as the degree of functionalization on the surface of the fullerene cage increases, the cytotoxicity of the fullerene decreases significantly.The simple act of functionalizing the fullerene with either carboxyl or hydroxyl groups decreased the cytotoxic response over seven orders of magnitudes for HDF, human liver carcinoma cells, and neuronal human astrocyte cell lines.Different molecules have been employed to functionalize CNT into customized species that may simultaneously carry several nanostructures (multifunctionalization) to detect, allow imaging; and deliver therapeutical loads [15].
Essentially, the need to improve biodistribution, pharmacokinetics, and solubility, as well as the need to diminish the toxicity of the CNT [1] are fundamental problems addressed through computational simulation and modeling.The aim of this research is to perform density functional theory (DFT) calculations [16] to investigate how the nanotube properties change due to covalent functionalization of certain organic groups to side walls and tips of the nanotubes, improving its solubility in water.Functionalization enhances the biocompatibility, potentially diminishing toxicity and therefore paves the way to rational modifications and/or design of new nanostructured species for efficient targeting and drug delivery.

Methodology
To investigate the effects of functionalization of SWCNT in increasing their solubility we build a finite model (5, 0) zigzag nanotube segment containing 60 C atoms with hydrogen atoms added to the dangling bonds of the perimeter carbons and the resulting formula is C 60 H 20 , see Figure 1.This nanotube model system is similar to Jaffe's model [17].The nanotubes are covalently functionalized with the following organic molecules: (a) formic acid, CO 2 H 2 , as a model of carboxylic acid, Figure 2 shows the functionalization at the sidewall and Figure 3 shows the functionalization at the tip of the SWCNT which is a typical product of the oxidation of carbon nanotubes [9,10], (b) isophthalic acid, C 6 H 4 (CO 2 H) 2 , as a model aromatic dicarboxylic acid, see Figure 4, [18], and (c) benzenesulfonic acid, C 6 H 5 SO 3 H, as a model aromatic sulfonic acid, see Figure 5 [18].These molecules have been investigated for their capability of drug delivery and diagnostic applications.
All calculations were performed using DFT with a hybrid functional B3LYP [19][20][21][22] and a 3-21 G basis set [23].Charge densities were analyzed by the Mulliken method [24].For open-shell molecular radicals, the unrestricted  formalism was used.The present level of calculation, DFT (UB3LYP)/3-21 G, is known to produce reasonable results [25] for bond lengths, bond angles, and bond energies for a wide range of molecules.The computations were carried out on a computer using the ab initio quantum chemistry package, Gaussian 09 (G09) [26], with the default convergence thresholds for DFT optimization calculations.
Electronic structure descriptors have been computed to analyze the geometrical and electronic changes that may lead to a better solubility of the functionalized nanotubes.Among them are the electronic HOMO-LUMO gap (H-L gap), the dipole moment (µ dip ), and the Gibbs free energy of solvation (ΔG solv ).The HOMO-LUMO gap, in the case of open electronic shell systems, is computed between the highest of the HOMOs and the lowest of the LUMOs, regardless of the spin type.For all systems with a doublet multiplicity (one unpaired electron), this always resulted in the HOMO (alpha)-LUMO (beta) gap.
The solubility of a given molecule in a solvent can be assessed by measuring its Gibbs free energy of solvation.A number of quantum mechanical continuum solvation models were developed for this purpose [27,28].We have chosen the polarizable continuum model (PCM) as implemented in G09.This originated from the Onsager continuum model [28] and was formulated by Tomasi et al. [27,[29][30][31], which takes into account the solute interactions with the solvent, modeled as a continuum dielectric medium in which a cavity is built to accommodate the solute molecule.

Structural Parameters.
We have used the G09 code to optimize the geometries for the finite SWCNT.The resulting  optimized structures are shown in Figure 1.The finite (5, 0) nanotube C 60 H 20 has an optimized length of 11.32 Å and a diameter of 3.90 Å. Computed length agrees with a value of 11.36 Å obtained by Jaffe's model [17] and computed SWCNT diameter also compares well with the value 3.92 Å in their paper.
Presented in Figures 2 and 3 are the optimized structures for two possible ways of functionalizing the finite SWCNT with formic acid.Figure 2 the functionalization at the sidewall of the nanotube wherein we take the organic molecule already in its radical form, .CO 2 H, attached by its C atom to the nanotube sidewall.In Figure 3 the functionalization at the tip of the SWCNT was carried out as another possibility because it is known that closed nanotube tips react with strong oxidizing agents, opening the tip and filling the dangling bonds with carboxylic acid molecules.The optimized structure for the functionalization of the SWCNT sidewall with the isophthalic acid radical .C 6 H 3 (CO 2 H) 2 .is given in Figure 4. We have also studied the functionalization of the SWCNT sidewall with the benzenesulfonic acid, .C 6 H 4 SO 3 H; the optimized structure is shown in Figure 5.These molecules have been used in studies of covalent functionalization of SWCNT capability for drug delivery [15,18].

Binding Energies.
Binding energies of the radicals to the nanotube, E b , are defined for the reaction where ORG is any of the studied organic radicals and ORG-SWCNT is the corresponding functionalized nanotube.Therefore The binding energy is negative if functionalization is thermodynamically favorable.To avoid considering the artificial rupture of C-H bonds involving functionalization at the tip, one H atom was previously removed and the nanotube structure was reoptimized before functionalization with the formic acid radical.The studied reactions are: Since the energies of the organic radicals are required in (2), their structures were also optimized.The functionalization reactions (3) to ( 6) are thermodynamically favorable, as can be seen in Table 1, and the resulting binding energies are between −2 eV to -4 eV.

Electronic Properties.
Electronic properties computed for the functionalized SWCNT is displayed in Table 1 for the C 60 H 20 nanotube and the functionalized SWCNT.These include the HOMO-LUMO gaps (H-L gap), the dipole moments (µ dip ); and the Gibbs free energy of solvation (ΔG solv ).The HOMO-LUMO gap of the infinite (5, 0) SWCNT is zero, because that nanotube is metallic.A negligible HOMO-LUMO gap develops in the finite nanotube model (0.05 eV), in agreement.The spatial distributions of the HOMO orbitals of the SWCNT and the tube with H atom missing from the tip, SWCNT radical, are shown in Figure 6.These orbitals display a similar delocalization over the whole tube, but the main difference is that the HOMO of the SWCNT radical has a noticeable lobe at the defect, suggesting a dangling bond at this site.Spatial distributions of the LUMO orbitals for the same nanotubes are given in Figure 7.A prominent accumulation of the orbital distribution appears at the vacancy position of the missing H atom in the SWCNT radical.The localized lobes are responsible for the reactivity of the nanotube.
In Table 1 we can observe an important increase of the magnitude of the dipole moments of the functionalized nanotubes compared to the nanotube that is not functionalized.The C 60 H 20 has a small dipole moment of 0.34 debye and the values of the dipole moments of the functionalized SWCNT are much larger.The substantial increase in the dipole moment is expected to modify the interaction of the functionalized nanotubes with a polar solvent such as water, potentially increasing their solubilities in the physiological medium.
3.4.Solubilization.Solubility can be assessed by measuring its Gibbs free energy of solvation.The Gibbs free energy of solvation, ΔG solv , is computed as the difference between the optimized energies of the species in the solvent (PCM) and vacuum (gas phase), The PCM; as implemented in G09 which takes into account the solvent interactions with the solute within a cavity in a continuum dielectric medium approximation for the solvent; was used to calculate the optimized energies of the species in the solvent such as water.Solubility of a given molecule in water requires a negative value of ΔG solv .All the calculated ΔG solv of the functionalized nanotubes, given in Table 1, are negative.If we compare with the ΔG solv obtained for the unfunctionalized nanotube, we see that solubility in water is larger for the functionalized nanotubes.This is in agreement with the experiment performed in vitro cytotoxicity screens on HDF by Sayes et al. [18] wherein the sidewall functionalized SWCNT with phenyl-SO 3 H and phenyl-(COOH) 2 samples are found out to be substantially less cytotoxic than unfunctionalized SWCNT in water.On the other hand, the solvation Gibbs free energy for the SWCNT is -0.73 eV, which is predicted to be slightly soluble.
It is a little surprising for the tube, but this is an artifact of the finite model with artificial C-H bonds at the tips.These slightly polarizable bonds induce an artificial minor solubility in the model SWCNT.However, in all cases, the solubility increases dramatically and substantially by using the technique of functionalization with the said organic radicals.

Conclusions
Density functional theory using mainly the G09 code was used to investigate the functionalization of SWCNT with open ends capped with H atoms with three different kinds of acids that help to improve their solubility in water and could make nanotubes more biocompatible.The nanotube has been functionalized with formic acid, isophthalic acid; and benzenesulfonic acid.Electronic exchange and correlation effects have been treated with the gradient-corrected B3LYP functional.
The functionalization with these organic molecules, either on the nanotube sidewall or tip sites where a hydrogen atom has been removed, is thermodynamically favorable.The enhanced dipole moment of the nanotubes due to functionalization is manifested in the improvement of their solubility in water as assessed by a calculation of the solvation free energies of the functionalized nanotubes employing the PCM polarizable continuum model.Functionalization enhances nanotubes biocompatibility, thus reducing the toxicity and the chance of tissue accumulation, for their future use in drug delivery.

Figure 2 :
Figure 2: Optimized geometry of the finite (5, 0) zigzag SWCNT (C 60 H 20 ) with the formic acid radical at the tube sidewall.Gray color depicts carbon atoms; light gray is hydrogen and red is oxygen.

Figure 3 :
Figure 3: Optimized geometry of the finite (5, 0) zigzag SWCNT (C 60 H 19 ) with the formic acid radical at the tube tip.Gray color depicts carbon atoms; light gray is hydrogen and red is oxygen.

Figure 4 :
Figure 4: Optimized geometry of the finite (5, 0) zigzag SWCNT (C 60 H 20 ) with the isophthalic acid radical at the tube sidewall.Gray color depicts carbon atoms; light gray is hydrogen and red is oxygen.

Figure 5 :
Figure5: Optimized geometry of the finite (5, 0) zigzag SWCNT (C 60 H 20 ) with the benzenesulfonic acid radical at the tube sidewall.Gray color depicts carbon atoms; light gray is hydrogen, yellow is sulfur and red is oxygen.

Figure 6 :Figure 7 :
Figure 6: Spatial distribution of the HOMO orbitals for (a) the C 60 H 20 nanotube and (b) the nanotube radical with a missing H atom from the tip C 60 H 19 .The wave function isosurfaces of values +0.01 and −0.01 (e/ Å3 ) 1/2 are shown in red and green, respectively.

Table 1 :
Electronic properties for the C 60 H 20 nanotube and the functionalized SWCNT formed in the reactions (3)-(6).The properties are HOMO-LUMO gap (H-L gap), magnitude of the dipole moment (µ dip ), and the Gibbs free energy of solvation (ΔG solv ).