Interaction of Surfactants Containing a Sulfuric Group with a (5,5

Sep 22, 2010 - Priyanka Pandey , Smita Mohanty , Sanjay K. Nayak. Journal of Materials Engineering and Performance 2014 23, 4385-4393 ...
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J. Phys. Chem. C 2010, 114, 17249–17256

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Interaction of Surfactants Containing a Sulfuric Group with a (5,5) Carbon Nanotube Nicolas A. Cordero*,†,‡ and Julio A. Alonso¶,§ Departamento de Fı´sica, UniVersidad de Burgos, C/ Villadiego s/n, E-09001 Burgos, Spain, Department of Materials Science and Engineering, UniVersity of PennsylVania, 3231 Walnut Street, ´ ptica, UniVersidad de Philadelphia, PennsylVania 19104, Departamento de Fı´sica Teo´rica, Ato´mica y O Valladolid, Prado de la Magdalena, E-47011 Valladolid, Spain, and Departamento de Fı´sica de Materiales, UniVersidad del Paı´s Vasco, and Donostia International Physics Center (DIPC), Paseo Manuel de Lardiza´bal 4, E-20018 San Sebastia´n, Spain ReceiVed: March 10, 2010; ReVised Manuscript ReceiVed: August 4, 2010

Sulfuric acid is a good nanotube disperser but surfactants containing a sulfuric head group with a Na atom are better for dispersing carbon nanotubes. Nevertheless, there is no explanation for the importance of the sodium atom in the head group. We have studied the interaction of sulfuric acid, sodium bisulfate and sodium butyl sulfate molecules with a (5,5) single-walled carbon nanotube using density functional theory (DFT), calculating equilibrium configurations, binding energies, charge transfers, and densities of states. In all cases there is charge transfer from the tube to the molecules when these are adsorbed, as has been previously found for sulfuric acid adsorbed on graphene. The presence of these molecules with their hydrogen atoms pointing to the tube does not affect the density of states of the tube close to the Fermi energy, but the presence of sodium bisulfate or sodium butyl sulfate with the Na atom close to the tube enhances the density of states in the region below and near the Fermi energy. This difference could play a role in the superior surfactant properties of molecules with a Na atom in the head group. 1. Introduction

2. Computational Details

The extraordinary mechanical, electronic, and transport properties1 of single-walled carbon nanotubes (SWCNTs) have led to an enormous interest in them from both fundamental and technological points of view. SWCNTs are produced in bundles2,3 held together by van der Waals forces4,5 and have to be disentangled in order to separate them by length and chirality. The problem is their insolubility in either water or organic solvents. Both mechanical and chemical methods can be used to disperse SWCNTs in a liquid environment.6 These can be grouped in three categories:7 sonication, chemical functionalization, and dispersion with surfactants. Sonication can break the nanotubes,8 while functionalization can modify the surface of the tubes and affect its electrical, mechanical, and optical properties.9,10 The use of surfactants appears then as the most appealing alternative. Among the best surfactant molecules for dispersing SWCNTs are sodium dodecyl sulfate (SDS),11,12 sodium dodecylbenzene sulfonate (NaDDBS),13,14 and sodium polystyrene sulfonate (NaPSS).15 All of them have in common a sulfonate head group with a Na atom. Sulfuric acid itself is a good nanotube disperser, the proposed reason being the protonation of SWCNTs by this acid.16,17 There are experimental results on the interaction of sulfuric acid and nanotubes18-22 but, to the best of our knowledge, no theoretical study of this interaction exists. We have thus studied the interaction between sulfuric acid (H2SO4), sodium bisulfate (NaHSO4), and sodium butyl sulfate (NaSO4-C4H9 or NaBS) molecules with a (5,5) SWCNT.

We have used the Density Functional Theory (DFT)23 within the Local Density Approximation (LDA)24 for exchange and correlation employing the Vosko Wilk Nusair (VWN) correlation functional.25 The calculations have been performed with DACAPO,26 a code that uses supercells and a plane wave basis set for the valence electronic states, while the electron-ion interactions are described with Vanderbilt ultrasoft pseudopotentials.27 In the case of sodium and sulfur the pseudopotentials used contain nonlinear core-valence interaction corrections. A plane wave cutoff of 350 eV and a density cutoff of 500 eV were taken. Total energies were converged to 10-5 eV and all atomic positions were relaxed until the Cartesian forces on each atom were below 0.05 eV/Å. We have previously studied the interaction of sulfuric acid with graphene,28 of Li atoms with graphene,29 and of Li atoms with a (5,5) SWCNT30 using similar techniques. To avoid tube-tube interactions we have used an orthorhombic unit cell with dimensions 20 Å × 20 Å (30 Å × 30 Å in the case of NaBS) in the directions perpendicular to the tube axis. To minimize molecule-molecule interactions the cell was chosen containing 80 carbon atoms (120 for NaBS), which corresponds to eight (12 for NaBS) carbon rings along the axis of the tube (see Figure 3 and Figure 10). The length of the cell along this axis was optimized, obtaining a value of 9.85 Å (14.77 Å for NaBS) and a tube radius of 3.4 Å in very good agreement with previous calculations performed with a different code.30 The integrations over the Brillouin zone were done with use of the Monkhorst-Pack scheme.31 The number of k points was 1 × 1 × 2 (1 × 1 × 1 for NaBS) for geometry optimizations as well as for energy and charge transfer calculations. It was increased to 1 × 1 × 16 (1 × 1 × 12 for NaBS) for the determination of the density of states (DOS).

* To whom correspondence should be addressed. E-mail: [email protected]. † Universidad de Burgos. ‡ University of Pennsylvania. ¶ Universidad de Valladolid. § Universidad del Paı´s Vasco and DIPC.

10.1021/jp102187j  2010 American Chemical Society Published on Web 09/22/2010

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Cordero and Alonso TABLE 1: LDA Structural Parameters for the Equilibrium Configuration of the Trans Isomer of a Sodium Bisulfate Molecule Calculated with DACAPO and GAUSSIAN03a LDA LDA MP2 (DACAPO) (GAUSSIAN03) (GAUSSIAN03) d(Na-O1) d(S-O1) d(S-O2) d(S-O3) d(O2-H) ∠(O1-Na-O1) ∠(O1-S-O1) ∠(O1-S-O2) ∠(O2-S-O3) ∠(S-O2-H) τ(S-O1-Na-O1) τ(O3-S-O2-H) τ(Na-S-O2-H)

2.134 1.495 1.629 1.458 0.991 69.0 108.0 116.4 105.6 104.9 0.4 0.0 180.0

2.168 1.500 1.636 1.461 0.980 68.1 108.1 116.5 105.6 104.2 0.6 0.0 180.0

2.239 1.498 1.644 1.460 0.969 65.8 108.5 116.4 105.6 105.1 0.4 0.0 180.0

Figure 1. Equilibrium geometries for the cis and trans conformers of a sodium bisulfate molecule.

Distances d are given in angstroms, and planar ∠ and dihedral τ angles in deg. MP2 results calculated with GAUSSIAN03 are given for comparison. See Figure 1 for atom labels.

Binding energies were calculated as the difference between the energy of the adsorbed configuration and the sum of the energies corresponding to the isolated molecule and the isolated tube calculated with the same cell. Charge transfers were determined by a Mulliken population analysis.32 This analysis does not give reliable absolute values for the charge transfer but it is suitable for comparison of relative values. We have rounded these charges to 0.01 e in the tables, but all the operations involving them have been done with greater accuracy to avoid truncation errors. As in our previous work,28 we have used the convention of assigning a negative value to e throughout the paper, which simplifies expressions for charge transfers.

TABLE 2: LDA Structural Parameters for the Equilibrium Configuration of the Cis Isomer of a Sodium Bisulfate Molecule Calculated with DACAPO and GAUSSIAN03a

3. Results and Discussion 3.1. Sulfuric Acid, Sodium Bisulfate, and Sodium Butyl Sulfate Molecules. The ability of the pseudopotentials used for describing S, O, and H atoms to calculate the properties of sulfuric acid molecules already has been established.28 We have shown that our model properly describes both cis- and transH2SO4. We have calculated the equilibrium energies of the cis and trans isomers of the sulfuric acid molecules in the orthorhombic cell used in this work and obtained a difference of 0.068 eV favoring the trans isomer as the ground state, in good agreement with the result previously obtained in a hexagonal cell (0.070 eV).28 To test the validity of the Na pseudopotential to study our system of interest, we have calculated the equilibrium geometry of an isolated sodium bisulfate molecule using the same orthorhombic cell. As in the case of sulfuric acid, we have found both cis and trans conformers for this molecule and the cis conformer is more stable than the trans conformer (energy difference 0.103 eV). The two highly symmetrical configurations obtained are depicted in Figure 1. The first column in Table 1 (respectively Table 2) gives the corresponding structural parameters. As can be seen from the figure and the data in Tables 1 and 2, the atoms lie in two perpendicular planes, one containing Na, S, O2, O3, and H atoms and the other containing S and both O1 atoms. In the trans conformer the Na atom is very close to the latter plane while in the cis conformer the distance is bigger due to the Na-H repulsion that is also responsible for the cis conformer being less stable than the trans conformer. The same geometries were obtained by using spinpolarized LDA (LSDA). To determine the accuracy of these

a

LDA LDA MP2 (DACAPO) (GAUSSIAN03) (GAUSSIAN03) d(Na-O1) d(S-O1) d(S-O2) d(S-O3) d(O2-H) ∠(O1-Na-O1) ∠(O1-S-O1) ∠(O1-S-O2) ∠(O2-S-O3) ∠(S-O2-H) τ(S-O1-Na-O1) τ(O3-S-O2-H) τ(Na-S-O2-H)

2.140 1.502 1.623 1.448 0.990 68.8 107.3 106.0 103.4 107.5 8.5 180.0 0.0

2.175 1.507 1.629 1.451 0.979 67.7 107.0 105.7 103.9 107.1 8.6 180.0 0.0

2.246 1.505 1.637 1.451 0.968 65.4 107.5 105.6 103.8 107.4 9.0 180.0 0.0

a Distances d are given in angstroms, and planar ∠ and dihedral τ angles in deg. MP2 results calculated with GAUSSIAN03 are given for comparison. See Figure 1 for atom labels.

results we have done LDA calculations using GAUSSIAN0333 with a 6-31G** basis set. This code performs all-electron calculations and does not use periodic boundary conditions. The results obtained appear in the second column of Tables 1 and 2. The energy difference between the cis and trans conformers is 0.125 eV. Direct comparison of the first columns in the two tables shows that pseudopotential results are very close to allelectron values. The structures of two sodium bisulfate crystals are known34-36 but to the best of our knowledge there are no experimental data for the equilibrium geometry of this molecule in the gaseous phase, so we have also performed second-order Møller-Plesset (MP2)37 calculations using GAUSSIAN03 with 6-31G** and 6-311G** basis sets. The results obtained with the 6-31G** basis are presented in the third column of Tables 1 and 2. Those obtained with the 6-311G** basis set both with and without spin polarization were very similar. The energy difference between the cis and trans conformers is 0.119 eV. These results show that the highly symmetrical configurations obtained are not an artifact of LDA, periodic boundary conditions, or the lack of spin polarization and that the sodium atom is in fact bonded to two oxygen atoms. Summarizing, LDA is capable

Interaction of Surfactants with a (5,5) Carbon Nanotube

J. Phys. Chem. C, Vol. 114, No. 41, 2010 17251 TABLE 4: LDA Structural Parameters for the Equilibrium Configuration of the Nonsymmetric Isomer of a Sodium Butyl Sulfate Molecule Calculated with DACAPO and GAUSSIAN03a

Figure 2. Equilibrium geometries for the two isomers of a sodium butyl sulfate molecule.

TABLE 3: LDA Structural Parameters for the Equilibrium Configuration of the Symmetric Isomer of a Sodium Butyl Sulfate Molecule Calculated with DACAPO and GAUSSIAN03a d(Na-O1) d(S-O1) d(S-O2) d(S-O3) d(O3-C1) ∠(O1-Na-O1) ∠(O1-S-O1) ∠(O1-S-O2) ∠(O2-S-O3) ∠(S-O3-C1) τ(S-O1-Na-O1) τ(O2-S-O3-C1) τ(Na-S-O3-C1)

LDA (DACAPO)

LDA (GAUSSIAN03)

2.136 1.503 1.449 1.620 1.434 69.0 107.3 116.0 104.1 114.5 9.2 0.5 0.5

2.167 1.507 1.451 1.631 1.419 68.2 107.4 116.7 103.7 114.6 4.7 0.0 0.0

d(Na-O1) d(Na-O2) d(S-O1) d(S-O2) d(S-O3) d(S-O4) d(O4-C1) ∠(O1-Na-O2) ∠(O1-S-O2) ∠(O2-S-O3) ∠(O3-S-O4) ∠ (S-O4-C1) τ(S-O1-Na-O2) τ(O3-S-O4-C1) τ(Na-S-O4-C1)

LDA (DACAPO)

LDA (GAUSSIAN03)

2.175 2.185 1.500 1.489 1.464 1.613 1.442 67.7 108.7 115.2 107.8 112.8 21.8 50.1 131.9

2.172 2.175 1.507 1.496 1.459 1.635 1.426 68.4 108.7 117.2 107.8 112.9 0.4 52.5 128.1

Distances d are given in angstroms, and planar ∠ and dihedral τ angles in deg. See Figure 2 for atom labels. a

a Distances d are given in angstroms, and planar ∠ and dihedral τ angles in deg. See Figure 2 for atom labels.

of describing the structure of a sodium bisulfate molecule and the pseudopotentials adequately reproduce all-electron results. The term sodium dodecyl sulfate (or sodium lauril sulfate) is loosely used for describing a group of molecules with a sulfonic head containing a sodium atom attached to an alkyl tail with an average length of 12 carbon atoms. We have chosen sodium butyl sulfate as a representative of this family because it is the smallest molecule in this group with the tail bigger than the head. This fact allowed us to work with a supercell containing a tractable number of atoms. We have found the two isomers depicted in Figure 2. In the symmetric isomer the carbon backbone of the tail is contained in the symmetry plane of the head (see the value of τ(O2-S-O3-C1) in Table 3). The nonsymmetric molecule is the result of rotating the head around the bond linking the sulfur atom to the oxygen atom connected to the tail. Tables 3 and 4 show the comparison between the geometries obtained with pseudopotentials (DACAPO) and all the electrons (GAUSSIAN03 with a 6-31G** basis set). The nonsymmetric isomer is slightly more stable than the symmetric molecule and we have used it in all the calculations of the interaction with the tube. 3.2. The Interaction of Sulfuric Acid with the Tube. We have calculated the equilibrium geometries for both a cis- and a trans-H2SO4 molecule on a (5,5) SWCNT. In both cases the change in the geometry of the tube is negligible. This is similar to what happens to graphene when this acid is adsorbed.28 The

Figure 3. Equilibrium geometry for a cis-H2SO4 molecule adsorbed on a (5,5) carbon nanotube.

equilibrium configuration for the cis conformer is shown in Figure 3. It corresponds to its two hydrogen atoms pointing to the tube. The line passing through these two atoms is not parallel to the tube axis. The reason is that the O-H bonds tend to point to carbon atoms in the tube and the C atoms closer to the molecule form a zigzag line. The first line in Table 5 presents the binding energy and the charge transfer from the tube to the acid molecule. These results are slightly bigger than those obtained for the adsorption of low-concentration cis-H2SO4 on graphene (Eb ) 0.36 eV, ∆Q ) 0.41 e)28 due to the curvature of the tube that enhances charge transfer to the H atoms. A

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TABLE 5: Calculated Binding Energies Eb and Charge Transfers from the Tube to Different Molecules ∆Q molecule

configuration

Eb (eV)

∆Q (e)

cis-H2SO4 trans-H2SO4 cis-NaHSO4 trans-NaHSO4

both H atoms pointing to the tube one H atom pointing to the tube Na and H atoms pointing to the tube a: Na atom pointing to the tube b: H atom pointing to the tube a: parallel to the tube b: Na atom pointing to the tube c: H atom pointing to the tube

0.41 0.31 0.60 0.39 0.23 0.59 0.44 0.12

0.50 0.40 0.45 0.38 0.37 0.31 0.25 0.18

NaSO4-C4H9

TABLE 6: Distances d from the Atoms in the Two Isomers of a H2SO4 Molecule Adsorbed on a (5,5) SWCNT to the Wall of the Tube, and Charge Differences ∆Q between the Adsorbed and Isolated Molecules Calculated by Using Mulliken Population Analysis cis

trans

atom

d (Å)

∆Q (e)

d (Å)

∆Q (e)

H H S O O O O total

2.1 2.2 3.6 3.0 3.1 3.2 5.0

0.19 0.20 -0.18 0.03 0.02 0.11 0.14 0.50

2.1 4.8 3.7 2.9 3.1 3.9 5.0

0.21 0.05 -0.18 0.14 0.02 0.06 0.11 0.40

more detailed analysis of the charge transfer is given in Table 6. The second column in this table presents the differences between the Mulliken charges of the atoms in the adsorbed and in the isolated molecule. The two hydrogens gain 0.39 e and the four oxygens gain 0.29 e while the S atom loses 0.18 e. The minimum energy configuration for a trans-H2SO4 molecule on the tube is shown in Figure 4. In this case only one hydrogen points toward a carbon atom in the tube wall. The corresponding binding energy and charge transfer are reported in the second line of Table 5. Once again, the values are larger than those for the adsorption of trans-H2SO4 on graphene (Eb ) 0.29 eV, ∆Q ) 0.30 e)28 due to the curvature of the tube. As can be seen from the table both binding energy and charge transfer are bigger for the cis isomer that for the trans isomer. This follows the trend for the adsorption of the acid on graphene for low coverage.28 The distances of the atoms in the trans molecule to the tube wall are given in the third column of Table 6 and its Mulliken charge differences between the adsorbed and the isolated molecule in the fourth column. The O atoms gain 0.31 e and the S atom loses 0.18 e. These values are very similar to those for the cis conformer, but the hydrogen atoms (mainly the one pointing to the tube) gain only 0.26 e. This is about 68% of the value for the cis isomer. The reason is that one of the H atoms is far from the tube. The difference between the adsorption energies of both isomers (0.10 eV) is larger than the difference between the energies of the cis and trans isolated molecules (see subsection 3.1) and the cis isomer adsorbed on the tube is then the true minimum energy configuration. When the H2SO4 concentration increases the trans isomer is expected to be more tightly bound than the cis isomer (as in the graphene case28) and the tube could template the growth of a sulfuric acid crystal.20,21 The charges indicate protonation of the tube by the acid as has been previously suggested.16,17 To see if the charge transfer from the tube to the sulfuric acid molecules affects the electronic properties of the tube we have plotted in Figure 5 the DOS for the tube with and without H2SO4 molecules. The acid molecules introduce new states in

Figure 4. Equilibrium geometry for a trans-H2SO4 molecule adsorbed on a (5,5) carbon nanotube.

Figure 5. Density of states for the cis (red) and trans (green) conformers of a sulfuric acid molecule adsorbed on a (5,5) carbon nanotube. The DOS of the bare tube is given in black as a reference. The Fermi energy is taken as energy origin.

the low energy region but the van Hove singularities38 between -18 and -15 eV are preserved and the DOS remains unchanged close to the Fermi energy. This means that the conducting properties of the tube are not altered by the adsorption of the acid molecules. This is similar to what happens for H2SO4 adsorbed on graphene. In that case the graphene sheet remains a zero-gap semiconductor28 while in this one the (5,5) SWCNT remains a conductor. To sum up, the interaction of sulfuric acid molecules with a (5,5) SWCNT is similar to that of this acid with graphene. The curvature of the graphene sheet does not seem to play a crucial role in this interaction.

Interaction of Surfactants with a (5,5) Carbon Nanotube

J. Phys. Chem. C, Vol. 114, No. 41, 2010 17253 TABLE 7: Distances d from the Atoms in the Two Isomers of a NaHSO4 Molecule Adsorbed on a (5,5) SWCNT to the Wall of the Tube, and Charge Differences ∆Q between the Adsorbed and Isolated Molecules Calculated with Mulliken Population Analysis cis

Figure 6. Equilibrium geometry for a cis-NaHSO4 molecule adsorbed on a (5,5) carbon nanotube.

3.3. The Interaction of Sodium Bisulfate with the Tube. We have performed an analysis for the adsorption of a sodium bisulfate molecule on a (5,5) SWCNT similar to that presented in the previous subsection for sulfuric acid. In this case we have found three equilibrium configurations for the adsorbed molecule. As for H2SO4 adsorption, the change in the geometry of the tube is negligible. The first equilibrium geometry corresponds to cis-NaHSO4 with both Na and H atoms pointing to the tube and is shown in Figure 6. The line passing through these two atoms is not parallel to the tube axis for the same reason given in subsection 3.2 and because the sodium atom is bigger than the hydrogen atom. The binding energy and the charge transfer for this configuration are given in the third line of Table 5. If we compare them to those for the cis-H2SO4 molecule, we see that the binding energy is bigger in this case in spite of the charge transfer being slightly smaller. The distances of the atoms in the molecule to the tube wall and the differences in the Mulliken charges for each atom between the adsorbed and isolated molecules are given in Table 7. The charge gained by the Na and H atoms is 0.36 e while the S atom loses 0.15 e. These values are similar to those for the cis sulfuric acid adsorbed on the tube. The oxygens gain 0.24 e, 82% of the value for cis-H2SO4. We present in Figure 7 the equilibrium geometry for a trans sodium bisulfate molecule adsorbed on the tube with the Na atom pointing to a C atom (configuration a). The values for the binding energy and the charge transfer appear in the fourth line of Table 5. Both values are smaller than those for the cis configuration and, while the charge transfer is similar to that for the trans-H2SO4 molecule, the binding energy is nevertheless bigger. In this case, as can be seen in the fourth column in Table 7, the Na and H atoms (mainly the Na atom, because the hydrogen is far from the tube) gain 0.29 e, 77% of the value for the cis configuration. The oxygens gain 0.21 e and the sulfur

trans a

trans b

atom

d (Å)

∆Q (e)

d (Å)

∆Q (e)

d (Å)

∆Q (e)

Na H S O O O O total

2.5 2.2 3.8 3.1 3.2 3.6 5.2

0.18 0.18 -0.15 0.05 0.04 0.03 0.12 0.45

2.4 6.7 4.9 4.0 4.2 5.7 5.9

0.23 0.06 -0.12 0.03 0.03 0.06 0.10 0.38

6.1 1.9 4.0 2.7 3.4 4.8 4.8

0.06 0.14 -0.17 0.08 0.11 0.07 0.06 0.37

loses 0.12 e. These two values are similar to those for the cis configuration. The third equilibrium configuration corresponds to a transNaHSO4 molecule with its H atom pointing to a C atom in the tube (configuration b). It is shown in Figure 8 and the values for its binding energy and charge transfer are given in the fifth line of Table 5. Both of them are smaller than those for configuration a and for trans-H2SO4. The last column in Table 7 shows that the sulfur atom loses 0.17 e (similar to the cis configuration), the four oxygens gain 0.34 e (161% of the value for the cis configuration), while the Na and H atoms (mainly the latter because the sodium is far from the tube) gain 0.19 e (51% of the value for the cis configuration). The difference between the adsorption energies of cisNaHSO4 and trans-NaHSO4 is larger than the difference between the energies of the cis and trans isolated molecules (given in

Figure 7. Equilibrium geometry for a trans-NaHSO4 molecule adsorbed on a (5,5) carbon nanotube with the Na atom pointing to the tube (configuration a).

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Figure 9. Density of states for a sodium bisulfate molecule adsorbed on a (5,5) carbon nanotube with different orientations: H atom pointing to the tube (blue), Na atom pointing to the tube (green), and both H and Na atoms pointing to the tube (red). The DOS of the bare tube is given in black as a reference. The Fermi energy is taken as energy origin.

Figure 8. Equilibrium geometry for a trans-NaHSO4 molecule adsorbed on a (5,5) carbon nanotube with the H atom pointing to the tube (configuration b).

subsection 3.1). The cis isomer adsorbed on the tube is then the minimum energy configuration, as in the case of sulfuric acid. There are two trends for both sulfuric acid and sodium bisulfate adsorbed on the tube: (1) the lowest energy configurations correspond to cis isomers with two atoms pointing to the tube instead of one, and (2) when there are only H atoms pointing to the tube, the larger the charge transfer the bigger the binding energy. It is easy to understand these two features. In the first case, having two atoms pointing to the surface of the tube maximizes the charge transfer to the molecule and with it the binding energy. The gain in binding energy with respect to trans conformers is bigger than the energy difference between the two isolated isomers and this leads to the cis conformers being the preferred adsorbed configuration. With respect to the second feature, the monotonous increase in the binding energy as the charge transfer grows is due to the electrostatic attraction between the tube and the negatively charged molecules. Nevertheless, there is an interesting point. If we compare cisNaHSO4 to cis-H2SO4 or configuration a of trans-NaHSO4 to trans-H2SO4, whenever there are Na atoms pointing to the tube the binding energy is bigger than when there are only H atoms pointing to it, in spite of the charge transfer being smaller. This breaks the general rule of a one-to-one correspondence between charge transfer and binding energy for sulfuric acid on graphene and for sulfuric acid and sodium bisulfate on the tube. To understand this point it is necessary to take into account that the charge transfer from the tube to the molecule is not equally distributed among the different atoms in the adsorbed molecules. The charge of the S atom is nearly the same in the five adsorbed configurations studied and is screened by the surrounding atoms. Therefore it is possible to consider the interaction between the tube and the sulfur atom constant in a first approximation. The interaction is then mainly affected by Na, H, and O atoms. The greater the number of Na and/or H atoms pointing to the

tube, the greater the charge transfer to these atoms that form bonds with carbon atoms in the tube similar to hydrogen bridge bonds. The electrostatic attraction between the negatively charged O atoms and the positively charged tube depends on the distance. By looking at Tables 6 and 7 we can divide the five configurations into two groups. The first one corresponds to the lowest energy configurations (cis-H2SO4 and cisNaHSO4). In these configurations there are three O atoms close to the tube. The second group includes the three metastable configurations. In these, there are only two oxygens close to the tube. It is the interplay between the number of atoms pointing to the tube and the number of oxygens close to it that explains the trend in the adsorption energies. We present in Figure 9 the densities of states for the three equilibrium configurations of a sodium bisulfate molecule adsorbed on the tube. As in the case of sulfuric acid, the presence of the molecule introduces new low energy levels and the van Hove singularities between -18 and -15 eV are preserved. There is nonetheless a difference. When there is only the H atom pointing to the tube, the region close to the Fermi energy remains unperturbed with respect to that of the bare tube, but when a Na is pointing to the tube, there is an increase in the DOS in that zone. This increase means that at a nonzero temperature the conductance of the tube could slightly increase when NaHSO4 molecules with Na atoms pointing to it are adsorbed. 3.4. The Interaction of Sodium Butyl Sulfate with the Tube. We have found three equilibrium configurations for the NaBS molecule adsorbed on the tube. In all cases the deformation of the tube is negligible. The first equilibrium configuration corresponds to the molecule lying nearly parallel to the tube (configuration a shown in Figure 10). In the other two geometries the molecule is perpendicular to the tube. In configuration b (Figure 11) the head is pointing to the tube while in configuration c (Figure 12) the tail faces the tube. The corresponding binding energies and charge transfers appear in the bottom lines of Table 5. The higher the charge transfer the bigger the binding energy. A more detailed analysis is presented in Table 8. The distance from the Na atom to the tube and the charge transfer to the head of the molecules are the same in configurations a and b. The absolute minimum corresponds to the parallel configuration because there is charge transfer not

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Figure 10. Equilibrium geometry for a NaSO4-C4H9 molecule adsorbed on a (5,5) carbon nanotube with the molecule aligned with the tube (configuration a).

Figure 12. Equilibrium geometry for a NaSO4-C4H9 molecule adsorbed on a (5,5) carbon nanotube with the tail H atom pointing to the tube (configuration c).

TABLE 8: Distances d from the Atoms in the Head of a NaSO4-C4H9 Molecule Adsorbed on a (5,5) SWCNT to the Wall of the Tube, and Charge Differences ∆Q between the Adsorbed and Isolated Molecules Calculated with Mulliken Population Analysis configuration a

configuration b

configuration c

atom

d (Å)

∆Q (e)

d (Å)

∆Q (e)

d (Å)

∆Q (e)

Na S O O O O total

2.5 4.3 4.2 5.6 3.9 3.2

0.20 -0.07 -0.04 0.05 0.08 -0.02 0.19

2.5 4.6 3.6 5.0 5.9 4.3

0.21 -0.06 -0.01 0.07 0.02 -0.05 0.19

11.5 9.8 10.7 9.8 8.3 10.1

0.02 -0.04 0.02 0.03 0.02 0.01 0.06

by the molecules, the only significant change is that the DOS increases near the Fermi energy whenever there is a Na atom close to the tube. Figure 11. Equilibrium geometry for a NaSO4-C4H9 molecule adsorbed on a (5,5) carbon nanotube with the Na atom pointing to the tube (configuration b).

only to the sulfuric head but also to the alkyl tail. Charge transfer is very small in configuration c when the head is far from the tube. When comparing the two perpendicular orientations, the one with the head close to the tube is preferred over that with the tail pointing to the tube. This behavior is the opposite to that expected when there are many water molecules present. In that case, the hydrophobic tail tends to point to the tube while the hydrophilic head faces the water molecules. The effect of the absorption of NaBS on the electronic structure of the tube can be seen in Figure 13. It is similar to that of NaHSO4. Apart from the low energy levels introduced

4. Conclusions We have studied the interaction of sulfuric acid, sodium bisulfate, and sodium butyl sulfate molecules with a (5,5) SWCNT. The interaction does not affect the geometrical structure of the nanotube. The binding energies are large enough for the adsorbed molecules to act as surfactants. But these energies are at the same time small enough for the nanotube to be easily cleaned afterward. There is electronic charge transfer from the nanotube to the adsorbed molecule, but the interaction cannot be completely understood only in terms of the global charge transfer. It is necessary to consider the charge transfer to the atoms close to the tube and the number of oxygen atoms not far from it. When these molecules are adsorbed on the tube there is protonation of the latter. In spite of the curvature, the

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Figure 13. Density of states for a sodium butyl sulfate molecule adsorbed on a (5,5) carbon nanotube with different orientations: tail H atom pointing to the tube (red), Na atom pointing to the tube (green), and aligned with the tube (blue). The DOS of the bare tube is given in black as a reference. The Fermi energy is taken as energy origin.

results for sulfuric acid are similar to those previously obtained for its interaction with graphene. Binding energy and charge transfer are bigger for the cis conformer than for the trans conformer. Besides, the DOS of the tube close to the Fermi energy is not affected by the presence of the acid. In the case of sodium bisulfate three equilibrium configurations have been studied. Once again, there is protonation of the tube and the cis isomer is more tightly bound than the trans isomer, but a new feature appears: The presence of a sodium atom pointing to the tube increases the DOS in the region close to the Fermi energy. This feature also appears in the case of sodium butyl sulfate. When the alkyl tail is pointed to the tube there is no change in the DOS near the Fermi energy but when the molecule head is close to the tube (independently of the molecule orientation) this DOS enhancement is observed. This fact could play a role in molecules with a sodium atom in a sulfonate head being better nanotube surfactants than those with a hydrogen atom in its place. To check if this is so, it will be necessary to include solvent (i.e., water) molecules in the calculations. Acknowledgment. We gratefully acknowledge financial support from the Spanish MICINN and the European Regional Development Fund (grant MAT2008-06483-C03) as well as from Junta de Castilla y Leo´n (grants GR23, VA017A08 and BU023A08). J.A.A. acknowledges an Ikerbasque fellowship from the Basque Foundation for Science. References and Notes (1) Charlier, J.-C.; Blase, X.; Roche, S. ReV. Mod. Phys. 2007, 79, 677–732. (2) Thess, A.; Lee, R.; Nikolaev, P.; Dai, H.; Petit, P.; Robert, J.; Xu, C.; Lee, Y. H.; Kim, S. G.; et al. A. G. R. Science 1996, 273, 483–487.

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