Dispersion of Single-Walled Carbon Nanotubes with Oligo(p

Article pubs.acs.org/JPCC

Dispersion of Single-Walled Carbon Nanotubes with Oligo(p‑phenylene ethynylene)s: A DFT Study Suad Aljohani,† Ahmad I. Alrawashdeh,† Mohammad Zahidul H. Khan,† Yuming Zhao,‡ and Jolanta B. Lagowski*,† †

Department of Physics and Physical Oceanography and ‡Department of Chemistry, Memorial University of Newfoundland, St. John’s, NL Canada, A1B 3X7 S Supporting Information *

ABSTRACT: Pure carbon nanotubes (CNT) and CNT− polymer composites have many useful properties, ranging from electrical conductivity to superior mechanical strength. However, the full potential of using CNTs as reinforcements (in a polymer matrix, for example) has been severely limited because of complications associated with the dispersion of CNTs. CNTs tend to entangle with each other, forming materials with properties that fall short of expectations. One of the effective ways of dispersing CNTs is the use of short πconjugated oligomers like oligo(p-phenylene ethynylene)s (OPEs) as dispersants. In this study, we provide a comprehensive investigation of the interactions between single-walled CNTs (SWCNTs) and OPEs with two different end groups; aldehyde (ALD) and dithiafulvene (DTF). The hybrid B3LYP and the dispersion (D)- and/or the long-range (LR)corrected density functional theory (DFT) methods such as B97D, wB97XD, and CAM-B3LYP with the 6-31G(d) basis set are employed in obtaining electronic structure information (dipole moments and energy levels) for the gas-phase (single) oligomers and the (6,5) SWCNT and their combinations. In addition, the D- and/or LR-corrected DFT methods are used in determining binding energies and intermolecular distances for the OPE/SWCNT combinations. We focus on understanding the roles of oligomer’s end groups and side chains in the dispersion of SWCNTs. In agreement with the experimental observations, the electronic structure and the binding energy results show that OPE-DTF interacts more strongly with the SWCNT than OPEALD. This work also provides insight into why OPEs end-capped with DTFs are much more effective in the dispersion of CNTs than OPEs end-capped with ALDs. Furthermore, this computational analysis can be of use in choosing an appropriate D- and/or LR-corrected DFT method when studying properties of systems containing CNTs. θ (n,m). The indices (n,m) are positive integers, and the chiral vector and the chiral angle are defined as

1. INTRODUCTION Carbon nanotubes (CNTs) were first synthesized in 1991 by Iijima.1 Since then, CNTs and CNT-based materials have attracted immense research interest in the field of nanotechnology and nanomaterials because of their unusual structural and physical properties.2−8 These novel properties also allow a vast number of applications in organic solar cells,2 biosensors,3 conductive textiles,4 electronics,6 optics,7 medicinal science,8 and others. CNTs can be classified into two major groups, single-walled carbon nanotubes (SWCNTs)9 and multiwalled carbon nanotubes (MWCNTs),10 which are characterized by high aspect ratios with few or more nanometers in diameter. SWCNTs are very useful in the fundamental investigations of the structure/property relationships of CNTs since they do not include the interactions between concentric tubes as in MWCNTs, which tend to further complicate the study of their properties. The structures of SWCNTs can be described by their chiral indices (n,m), chiral vectors Ch, and chiral angles © XXXX American Chemical Society

C h = na1 + ma 2 = (n , m), ⎛ 3m ⎞ θ = arctan⎜ ⎟ ⎝ (2n + m) ⎠

0≤n≤m

(1)

(2)

where a1 and a2 are the unit vectors of the hexagonal lattice and θ is the angle between Ch and a1. According to the chiral indices or the chiral angles, there are three types of SWCNTs; zigzag with (m = 0 and θ = 0), armchair with (n = m and θ = 30°), and chiral with (n ≠ m ≠ 0 and 0 < θ < 30°).10−12 In this work, the chiral (6,5) SWCNT has been studied. Pristine SWCNTs have many drawbacks in terms of processing and device fabrication. In order to address some of these drawbacks, researchers have developed a number of Received: December 19, 2016 Revised: February 2, 2017 Published: February 3, 2017 A

DOI: 10.1021/acs.jpcc.6b12747 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

the transformation of ALD end-capped OPE 1 into DTF endcapped OPE 3 through an olefination reaction with 1,3dithiole-2-thione 2 in the presence of trimethyl phosphite. It was discovered that DTF end-capped OPEs can interact strongly with SWCNTs to form stable SWCNT/oligomer suspensions in organic solvents, whereas their OPE-ALD precursors completely lack the ability to disperse SWCNTs.27,28 Zhao et al. stated that “the performance of these relatively short DTF-functionalized oligomers in enhancing the binding strength toward SWNTs was remarkable, which in turn prompted us to conceive that polymer systems carrying DTF groups would serve as more effective SWNT dispersants”.28 Of interest to this work, OPEs belong to a class of fully conjugated molecules where the phenylene, alkynylene, and end-capping groups constitute a fully conjugated π-framework to allow extended π-electron delocalization. This particular type of molecules has recently attracted much attention due to the high electron conductivity of their (delocalized) backbones.30 The main motivation behind this work is to investigate the noncovalent interactions between SWCNTs with dithiafulvene (DTF) and aldehyde (ALD) end-capped OPEs (henceforth referred to as OPE-DTFs and OPE-ALDs, respectively). In particular, we aim to understand the contrasting outcomes between OPE-DTFs and OPE-ALDs in dispersing SWCNTs.27 Experimentally, Zhao et al. discovered that OPE-DTFs dispersed the (6,5) SWCNT most effectively among other SWCNT species in organic solvents. In this work, we employ the density functional theory (DFT) calculations to simulate various SWCNT/OPE interactions, where a segmental (6,5) SWCNT is built as the model for SWCNTs. For the OPE systems, a series of ALD and DTF end-capped OPEs is set up for the modeling studies. Herein, the numbering of the πframeworks is provided to facilitate later discussions on structural and geometric properties (see Figure 1). The absence and presence of long decyl (C10H21) groups in these model OPEs are intended to disclose the side-chain effects on the interactions of OPE with SWCNTs.

methods that improve the functionality of CNTs, which can be classified into two categories, covalent and noncovalent methods.13−16 The covalent functionalization involves the surface modification of carbon nanotubes that is associated with a change of the carbon atoms hybridization from sp2 to sp3. On the other hand, the noncovalent functionalization typically preserves the sp2 hybridization of the carbon atoms.13,16 CNTs are functionalized noncovalently by πconjugated aromatic compounds, surfactants, synthetic oligomers and polymers, peptides, and DNA molecules.13,17,18 Noncovalent functionalization presents a particularly useful approach because it not only provides a direct solution to the problems of insolubility and poor processability of pristine SWCNTs but also provides easy ways for sorting specific types of SWCNTs out of as-produced SWCNT mixtures.18 In addition to enhancing the material properties of CNTs, one of the aims of functionalization methods is to improve the dispersion of CNTs as they aggregate to form bundle-like structures19 in their as-produced state. These bundle-like aggregates affect adversely the material properties of CNTs. In general, the dispersion of CNTs is influenced by at least two competitive interactions; π-stacking and van der Waals interactions among nanotubes and the interactions between CNTs and dispersive medium.20 A number of different approaches is used for dispersing CNTs that can be broadly classified into mechanical (physical) methods and chemical methods.11,15,21−23 One of the basic mechanical dispersion methods is ultrasonication, which is often used in conjunction with chosen chemical dispersants to form stable suspensions by exfoliating CNT bundles.11,24,25 Dispersants bound with CNTs noncovalently do not alter the unique structure of the tubes; thus, they are considered to be more useful for dispersing CNTs in aqueous and organic solvents than covalently bonded dispersants.16 It has been shown that conjugated oligomers, with their conducting as well as other optoelectronic properties, can noncovalently interact with CNTs and act as effective CNT dispersants.26−29 Recently, Zhao and Mulla synthesized a series of oligo(p-phenylene ethynylene)s (OPEs) and oligo(phenylene vinylene)s (OPVs) by sequential cross-coupling reactions. The termini of these π-oligomers were end-capped with electron-withdrawing carboxaldehyde (ALD) and electron-donating dithiafulvenyl (DTF) groups, respectively, at different stages of synthesis.27 For example, Scheme 1 illustrates Scheme 1. Synthesis of OPE-DTF through Olefination of OPE-ALD

Figure 1. OPE-ALDs and OPE-DTFs investigated in this work.

2. COMPUTATIONAL DETAILS The Gaussian 0931 package is used to perform all the computations. For all of the calculations, the polarized splitvalence double-ζ 6-31G(d) basis set is employed with the following four DFT methods: the hybrid B3LYP,32,33 the longrange (LR)-corrected CAM-B3LYP,34 the dispersion (D)corrected B97D,35 and the LR- and D-corrected wB97XD36 functionals. The B97D and wB97XD functionals include semiempirical dispersion corrections, which are of great B


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where dtotal is the distance determined using the mean (approximately center of the mass) coordinates of the nanotube and the oligomer without the side chains (side chains are removed in all cases even when the combination in question includes side chains) and r is the radius of the nanotube (see Figure 2).

importance when acounting for noncovalent interactions (e.g., van der Waals forces) between oligomers and nanotubes. We use CAM-B3LYP, which is LR-corrected functional and has the hybrid qualities of B3LYP for comparison purposes. The geometries of all isolated oligomers and the (6,5) SWCNT are fully optimized using the four functionals. Using B97D, wB97XD, and CAM-B3LYP, with the help of the Gaussian keyword (opt = modredundant), we perform partial geometry optimizations on the oligomer-SWCNT combinations which involves freezing the (previously optimized) coordinates of the nanotube atoms while keeping the oligomer geometry parameters active during the optimizations. Visual Molecular Dynamics (VMD 1.9.1)37 is used to generate the initial geometry of the (6,5) SWCNT, and GaussView 5.0.838 is used to generate the initial geometries of oligomers and oligomer/ nanotube combinations and to determine bond lengths (R), bond angles (A), dihedral angles (Dh), and dipole moments (μ’s) of all molecular systems. All dipole moment directions are determined relative to the standard orientation coordinate system of molecular arrangements. The highest occupied and the lowest unoccupied molecular orbital (HOMO and LUMO) energies and their gaps, ΔϵH−L = ϵLUMO − ϵHOMO, are also obtained with the four functionals for all molecular systems studied. The results of the computations obtained using the four DFT functionals are analyzed, and their similarities and differences are discussed. In this work, we investigate the strength and quality of the intermolecular interactions between oligomers and SWCNT in a number of ways. For each combination, we consider the difference between the HOMO energy of the donor (oligomer) and LUMO energy of the acceptor (nanotube), i.e., ΔϵHA−LD = ϵLUMO(acceptor) − ϵHOMO(donor), since according to the perturbation molecular orbital theory (PMO),39 the smaller the difference, ΔϵHA−LD, the stronger the intermolecular interaction between oligomer and nanotube. Hence, the relative values of ΔϵHA−LD are indicative of the relative strength of the intermolecular interactions in the various oligomer/nanotube combinations. In addition, the effect of the dispersion on the dipole moments of the isolated oligomers is determined by comparing the respective magnitudes of the dipole moments of isolated oligomers (μtotal’s) to those of the oligomer/nanotube ′ ’s). That is, the differences between the combinations (μtotal total magnitudes of the dipole moments, Δμtotal = |μ⃗ total − μ⃗ ′total|, are calculated to assess the polarizability effect of the nanotube on the oligomers. Finally, the strength of the dispersive forces for each combinations is directly assessed by the computation of the binding energies, Eb, between the nanotube and each oligomer. Eb is computed using the equation E b = Etotal − (ESWCNT + Eoligomer)

Figure 2. Distance between the center of the (6,5) SWCNT and the center of OPE.

3. RESULTS AND DISCUSSION 3.1. Isolated OPEs and SWCNT. The representative optimized geometries of the ALD and DTF end-capped OPEs with and without side chains (OC10H21, SC10H21) as well as the SWCNT are shown in Figure 3. The chemical structures and the atom numbering (for backbones) of ALD and DTF end-capped OPEs are depicted in Figure 1. Full geometry optimizations of all oligomers considered are achieved with B3LYP, CAM-B3LYP, B97D, and wB97XD in linear-shaped molecular structures. In our analysis of single oligomers (see below), we consider the effects of the DFT method and the end group on their structural parameters (all lengths and angles, i.e., R, A, and Dh) and electronic properties (i.e., dipole moments, HOMO and LUMO eigenvalues, and energy gaps). Regarding the structural parameters, we focus only on the backbone (−C6H4CCC6H4CCC6H4−) of the oligomers in our discussion. The (6,5) chiral SWCNT consists of 364 carbon atoms and is terminated with 22 hydrogen atoms. All of the DFT methods (B3LYP, B97D, wB97XD, and CAM-B3LYP) give similar optimized structures of the SWCNT as shown in Figure 3. 3.1.1. Effect of the DFT Method. It is well-known that B3LYP gives geometrical parameter values of conjugated organic molecules in good agreement with experimental (Xray) data.41 Thus, we examine the effect of D- and/or LR-DFT methods on the OPE-ALD and OPE-DTF geometries (with and without side chains) by comparing them with the B3LYP results. Selected (along the backbone, see Figure 1) structural parameters of optimized geometries of the isolated OPEs are given in the Supporting Information (Tables S1−S4). The differences between the B3LYP geometrical parameters (all lengths and angles, i.e., R, A, and Dh) and the respective ones as obtained from the other three DFT methods are displayed in Figures S1−S4. Overall, a good agreement is found between the DFT methods for bond lengths (in most cases the differences are less than ∼0.01 Å) and bond angles (where most differences are less than ∼2°) in all OPEs. One trend that

(3)

where Etotal, ESWCNT, and Eoligomer are the total electronic energies of the SWCNT bound with the oligomer, the isolated SWCNT, and the isolated oligomer, respectively. Typically, for a stable compound Eb is less than zero; however, in this work for simplicity we will discuss the absolute values of Eb’s only (and hence drop the minus signs from now on). In each case, Wolfram Mathematica version 940 is used to obtain the mean intermolecular distance, Δd, between the given oligomer and the (6,5) SWCNT Δd = d total − r

(4) C


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Figure 3. Representative optimized structures of the isolated (gas phase) OPE-ALDs and OPE-DTFs with and without side chains and the (6,5) SWCNT obtained using B97D (similar results were obtained with B3LYP, wB97XD, and CAM-B3LYP) with the 6-31G(d) basis set.

Table 1. Dipole Moment Components (μx, μy, μz) and Total Magnitude (μ) (in Debye) and HOMO and LUMO Eigenvalues and Their Difference (ΔϵH−L = ϵLUMO − ϵHOMO) (in eV) for OPE-ALDs, OPE-DTFs (without and with Side Chains), and the (6,5) SWCNT Determined Using B97D, wB97XD, CAM-B3LYP, and B3LYP with the 6-31G(d) Basis Set method

(μx, μy, μz)

(1) OPE-ALD without SCs B97D (0.00, 0.00, 0.00) wB97XD (0.00, −0.00, 0.00) CAM-B3LYP (0.00, 0.00, 0.00) B3LYP (0.00, 0.00, 0.00) (2) OPE-ALD with SCs B97D (0.00, 0.00, 0.00) wB97XD (−0.00, −0.00, 0.00) CAM-B3LYP (0.00, 0.00, 0.00) B3LYP (0.00, 0.00, −0.00) (3) OPE-DTF without SCs B97D (−0.00, 0.00, 0.77) wB97XD (0.00, 0.00, 1.31) CAM-B3LYP (0.00, 0.00, 0.90) B3LYP (0.03, −0.01, 0.50) (4) OPE-DTF with SCs B97D (3.01, 1.10, 4.66) wB97XD (0.65, −1.40, 4.54) CAM-B3LYP (0.00, 0.00, 1.77) B3LYP (−1.80, −1.34, 3.09) (5) (6,5) SWCNT B97D (−0.00, 0.03, 0.14) wB97XD (0.00, 0.00, 0.09) CAM-B3LYP (0.00, 0.00, 0.11) B3LYP (0.00, 0.00, 0.13)

μ

ϵHOMO

ϵLUMO

ΔϵH−L

0.00 0.00 0.00 0.00

−5.26 −7.72 −7.15 −5.92

−3.15 −0.85 −1.36 −2.58

2.11 6.87 5.79 3.34

0.00 0.00 0.00 0.00

−4.72 −7.20 −6.63 −5.42

−2.96 −0.71 −1.23 −2.43

1.76 6.49 5.41 3.00

0.77 1.31 0.90 0.50

−4.10 −6.66 −6.06 −4.79

−2.29 −0.18 −0.69 −1.82

1.81 6.48 5.37 2.97

5.65 4.79 1.77 3.82

−3.89 −6.45 −5.88 −4.61

−2.15 −0.06 −0.58 −1.71

1.74 6.39 5.30 2.90

0.15 0.09 0.11 0.13

−4.25 −5.76 −5.26 −4.58

−3.18 −1.96 −2.26 −2.89

1.07 3.80 3.00 1.69

Figure 4. Top view of OPE-ALD and OPE-DTF (B97D method) displaying the twist in the backbone of OPE-DTF relative to the planar OPE-ALD structure.

has been observed is that B97D gives bond lengths that are typically longer than those of B3LYP, while wB97XD and CAM-B3LYP give bond lengths that are shorter than those of B3LYP. For dihedral angles, substantial differences are found in the central (between the phenylene rings) dihedral angles, i.e., {6−7−8−9}, {7−8−9−10}, {11−12−13−14}, {12−13−14− 15} in the OPE-ALD (with and without side chains) and {6− 7−8−9}, {7−8−9−10}, {8−9−10−11}, {12−13−14−15}, {13−14−15−16}, {14−15−16−17} in the OPE-DTF (with and without side chains). The largest differences in these dihedral angles are of the order of ∼20° in OPE-ALD without a side chain and of the order of ∼60° in OPE-ALD with side chains and OPE-DTF with and without side chains. These results indicate that CAM-B3LYP, B97D, and wB97XD tend to give somewhat distorted (nonplanar) OPE geometries relative to the ones produced by B3LYP. D


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Figure 5. Representative (partially) optimized structure of OPE-ALD without side chains interacting with the (6,5) SWCNT obtained using B97D with the 6-31G(d) basis set (similar results were obtained with wB97XD and CAMB3LYP): (a) side view, (b) front view, and (c) top view with the oligomer highlighted.

The dipole moment components (μx, μy, μz) and total magnitudes (μ) for OPE-ALD and OPE-DTF with and without side chains and for SWCNT for all DFT methods are given in Table 1. In the case of OPE-ALDs, both oligomers (with and without side chains) have vanishing dipole moments with all DFT methods. In contrast, for OPE-DTF without side chains DFT methods predict dipole of the order of 1 D, and for OPEDTF with side chains the dipole moments approximately range from 2 to 6 D. For OPE-DTF without side chains, the dipole moment points out of the oligomer’s backbone plane. When side chains are present, the direction of the dipole moment of OPE-DTF is more complicated since all three components of μ have non-negligible magnitudes (except for CAM-B3LYP where only μz is finite; i.e., in this case, the dipole points out of the plane similar to what is observed in the oligomer without side chains; see Table 1). All DFT methods give a negligible (close to 0.1 D) dipole moment for the SWCNT. The HOMO and LUMO eigenvalues (ϵHOMO, ϵLUMO) and the energy gaps (ΔH−L) for all DFT methods for all of the OPEs and SWCNT are also given in Table 1. B97D gives the lowest ΔH−L values for all OPEs that are smaller than those of B3LYP by approximately 1.2 eV. On the other hand, wB97XD and CAM-B3LYP give values that are larger than those of B3LYP by approximately 3.5 and 2.5 eV, respectively. A similar trend has been obtained for the SWCNT; B97D gives a value of 0.6 eV smaller than that of B3LYP (which is close to 1.7 eV), and both wB97XD and CAM-B3LYP give ΔH−L values (3.0 and 3.8 eV, respectively) that are larger than that of B3LYP.

3.1.2. Effect of the End Group on the Structure and Electronics of OPEs. In investigating the effect of the end groups (ALD and DTF) on the structure of OPE, we compare the backbone structure of OPE-ALD with OPE-DTF which starts with atom 2 and ends with atom 19 for OPE-ALD and starts with atom 3 and ends with atom 20 for OPE-DTF as depicted in Figure 1. The differences between the geometrical parameters of OPE-ALD and OPE-DTF obtained using different DFT methods are shown in Figures S5 and S6 for oligomers without and with side chains, respectively (note in these figures, for clarity only R, A, and Dh corresponding to the OPE-ALD are shown). For the oligomers without side chains, only the end bonds ((2−3) and (3−4) in OPE-ALD and (3−4) and (5−6) in OPE-DTF) have shown differences in their lengths, and these differences are on the order of 0.02 Å with all DFT methods. Similarly for bond angles, the largest differences are observed at the ends of the oligomer backbones which are in the range of 2°−5°. In contrast, significant differences in the dihedral angles are observed for the central angles (e.g., {5−6− 7−8}, {6−7−8−9}, {7−8−9−10}, {11−12−13−14}, {12− 13−14−15}, and {13−14−15−16} in OPE-ALD) located between the phenylene rings. The DTF end group gives rise to a somewhat twisted OPE-DTF structure in comparison to the planar OPE-ALD structure (see Figure 4). Similar trends have been found for bond length, bond angle, and dihedral angle differences (with somewhat larger magnitudes) between OPE-ALD and OPE-DTF with side chains as can be seen in Figure S6. In addition, as discussed above the DTF end-capped oligomers are more polarized (i.e., have larger dipole moments) E


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Figure 6. Representative (partially) optimized structure of OPE-DTF without side chains interacting with the (6,5) SWCNT obtained using B97D with 6-31G(d) basis set (similar results were obtained with wB97XD and CAMB3LYP): (a) side view, (b) front view, and (c) top view with the oligomer highlighted.

and have smaller HOMO−LUMO gaps than the ALD endcapped oligomers (see Table 1). 3.2. Interacting Systems: OPEs with SWCNT. The representative (partially) optimized geometries of the ALD and DTF end-capped OPEs without side chains in combination with SWCNT are shown in Figures 5 and 6, respectively. The (partially) optimized (top view) structures of SWCNT with OPEs with side chains for the three dispersion and/or longrange corrected DFT methods (B97D, wB97XD, and CAMB3LYP) are shown in Figure 7. Selected (along the backbone, see Figure 1) structural parameters of optimized geometries of the “interacting” OPEs are given in Tables S5−S8. As in the case of isolated molecules, first we consider the effect of the DFT method on the geometrical and electronic results. We also discuss the electronic structures (i.e., top energy levels) and binding energies of the oligomer/nanotube combinations. Finally we consider the effect of dispersion on the oligomers’ geometry and dipole moments. 3.2.1. Effect of DFT Method. In the case of OPE-ALD and OPE-DTF without side chains interacting with the (6,5) SWCNT, all three of the DFT methods give very similar results. As can be seen in Figures 5 and 6, the oligomers stretch along and slightly wrap around the nanotube. In contrast, the three DFT methods give different results for the SWCNT with OPE-ALD and OPE-DTF with side chains as displayed in Figure 7 (for more details, see Figures S7−S12). Qualitatively, it can be seen from Figure 7 that the main difference between the methods is that, in the cases of the B97D and wB97XD, the side chains of oligomers strongly wrap around the nanotube,

Figure 7. Optimized structures (front views) of OPE-ALD and OPEDTF molecules with side chains interacting with the (6,5) SWCNT obtained using B97D, wB97XD, and CAMB3LYP with 6-31G(d) basis set. F


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Figure 8. HOMO and LUMO energies of SWCNT, OPEs, and their combinations obtained using B3LYP with 6-31G(d) basis set. In the case of combinations, the optimized B97D structures are used in single-point B3LYP computations.

All energy levels are computed with DFT/B3LYP. In the case of the combinations, the optimized structures of B97D are used in single-point B3LYP calculations. This figure clearly illustrates that the striking feature of these combinations is that for the OPE-DTF with or without side chains the HOMO levels are very close to the HOMO level of the SWCNT. The respective differences are 0.03 and 0.21 eV which are much smaller than 0.84 and 1.34 eV for the OPE-ALD. The fact that the HOMO of the OPE-DTF and SWCNT are so close to each other is significant, since the difference between the HOMO energy of the donor (oligomer) and the LUMO energy of the acceptor (nanotube), i.e., ΔϵHA−LD = ϵLUMO(acceptor) − ϵHOMO(donor) determines the electron transport as well as the strength of the intermolecular interaction between two (noncovalently) bonded compounds. These respective differences are 2.53 and 3.04 eV for OPE-ALD with and without the side chains and 1.72 and 1.90 eV for OPE-DTF with and without side chains. That is, ΔϵHA−LD’s for OPE-DFTs are approximtely 1 eV smaller than those for OPE-ALDs. It is known that the smaller ΔϵHA−LD the larger the intermolecular interaction between the two systems (since the perturbation theory states that the size of the energy perturbation is inversely proportional to ΔϵHA−LD). These results indicate that OPE-DTF interacts more strongly with SWCNT than OPE-ALD and that the dominant factor in determining the strength of these interactions is the type of the oligomer end group. The presence of side chains reduces the value of ΔϵHA−LD by 0.2 eV (the effect of side chains will be discussed further below). For completeness, Figure 8 also displays top energy levels of the respective oligomer/nanotube combinations which are close to the energy levels of the nanotube since, in combinations, the nanotube levels dominate the frontier orbital energy levels. 3.2.3. Binding Energies and Intermolecular Distances. Table 3 shows the absolute values of the binding energies (Eb) and the intermolecular distances (Δd) between the SWCNT and OPEs calculated (see eqs 3 and 4, respectively) using the B97D, wB97XD, and CAM-B3LYP methods. For all the oligomers, with and without side chains, and all of the DFT methods used, the binding energies of the OPE-DTF/SWCNT are larger than those of the OPE-ALD/SWCNT combinations (see Figure 9). In order to assess the dependence of Eb on the length of oligomers, we also compute, in the case of B97D and wB97XD, the binding energies for oligomers (without side

while in the case of the CAM-B3LYP, the side chains stretch away from the nanotube. It should be noted that in the case of the wB97XD method the backbone of the oligomers is positioned at an angle relative to the nanotube instead of being parallel to it (see Figures S9 and S12). The previous discussion (see section 3.1.1) regarding the comparison of DFT methods was based on a direct comparison of the geometrical and electronic parameters as obtained with the D- and/or LR-corrected DFTs with the DFT/B3LYP results for the isolated systems. This type of comparison is not possible for the combinations. Instead, for each method, standard deviations of bond lengths, bond angles, and dihedral angles for the oligomers with and without side chains in the presence of SWCNT are computed (see Figure S13). Figure S13a shows the standard deviation of bond lengths for the OPE-ALD and OPE-DTF with and without side chains obtained using the B97D, CAM-B3LYP, and wB97XD methods. For all of the oligomers, the B97D method has the smallest spread in the bond length values (approximately 0.068 Å for OPE-ALDs and 0.065 Å for OPE-DFTs). The largest and comparable variations (of the order of 0.074 Å for OPE-ALDs and 0.070 Å for OPE-DTFs) in the bond lengths are obtained with the CAM-B3LYP and wB97XD methods for oligomers with and without side chains. Bond angle deviations are shown in Figure S13b. The largest bond angle standard deviation of approximately 26° is obtained with CAM-B3LYP method for all oligomers. The wB97XD method gives bond angle standard deviations on the order of 24°. B97D gives comparable results for bond angle spread (close to 26°) as those obtained with the CAM-B3LYP except for the OPE-DTF with side chains (which is close to 23.5°). Figure S13c shows that standard deviations of the dihedral angles for all the oligomers are very similar for all the DFT methods. In summary, the structural differences as observed along the oligomer backbones due to the use of different DFT methods are not large in comparison to clearly different behaviors when considering their intermolecular interactions with the SWCNT (see Figure 7). For completeness, the geometrical parameters for the “interacting” oligomers are given in Tables S5−S8 (see section 3.2.4 for more discussion). It can be noted that they are similar to those obtained for isolated oligomers (see section 3.1.1). 3.2.2. Electronic Structure of the OPE/SWCNT Combinations. Figure 8 shows the electronic structure (HOMO and LUMO eigenvalues) for the isolated oligomers and SWCNT (see Table 1) and their respective combinations (see Table 2). G


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The Journal of Physical Chemistry C Table 2. Dipole Moment Components (μx, μy, μz) and Total Magnitude (μ) (in Debye) and HOMO and LUMO Eigenvalues and Their Difference (ΔϵH−L = ϵLUMO−ϵHOMO) (in eV) for the Combinations of the (6,5) SWCNT with OPE-ALDs and OPE-DTFs (without and with Side Chains) Determined Using B97D, wB97XD, CAM-B3LYP, and B3LYP with the 6-31G(d) Basis Set (μx, μy, μz)

method (1) OPE-ALD B97D wB97XD CAMB3LYP B3LYP// B97Da B3LYP// wB97XDb (2) OPE-ALD B97D WB97XD CAMB3LYP B3LYP// B97Da B3LYP// wB97XDb (3) OPE-DTF B97D wB97XD CAMB3LYP B3LYP// B97Da B3LYP// wB97XDb (4) OPE-DTF B97D wB97XD CAMB3LYP B3LYP// B97Da B3LYP// wB97XDb

μ

without SCs and SWCNT (−0.02, 0.70, 0.15) 0.72 (0.02, 0.60, −0.08) 0.60 (−0.25, 0.90, −0.21) 0.96

ϵHOMO

ϵLUMO

ΔϵH−L

−4.23 −5.74 −5.25

−3.17 −1.95 −2.24

1.06 3.80 3.00

(0.01, 0.70, 0.14)

0.71

−4.58

−2.91

1.67

(0.02, 0.38, −0.08)

0.39

−4.55

−2.83

1.72

with SCs and SWCNT (−0.04, 1.29, 0.10) (−0.15, −1.44, 0.20) (−0.01, 1.76, 0.8)

1.29 1.46 1.98

−4.26 −5.78 −5.23

−3.21 −1.98 −2.23

1.05 3.80 3.00

(0.039, −1.40, 0.09)

1.41

−4.62

−2.96

1.66

0.85

−4.60

−2.88

1.72

without SCs and SWCNT (−0.01, 2.41, 0.07) 2.41 (0.71, 1.08, −0.29) 1.32 (0.04, 0.98, 0.14) 0.99

−4.11 −5.70 −5.21

−3.12 −1.90 −2.21

0.99 3.80 3.00

(−0.01, 1.98, −0.07)

1.98

−4.53

−2.86

1.67

(−0.80, 1.04, 0.28)

1.34

−4.51

−2.79

1.72

with SCs and SWCNT (1.22, −4.90, 2.07) (1.29, 3.72, 0.97) (0.10, 1.50, −0.33)

5.46 4.05 1.53

−3.93 −5.70 −5.21

−3.22 −1.89 −2.20

0.71 3.79 3.00

(1.20, −5.84, 2.15)

6.34

−4.58

−2.98

1.60

(1.23, 3.65, 0.86)

3.96

−4.54

−2.83

1.71

(−0.14, −0.83, 0.10)

chains) with four benzene rings (in addition to oligomers with three rings). It can be seen that when the length dependence is accounted for, once again the Eb per unit benzene ring is approximately 0.1−0.2 eV larger for OPE-DTF/SWCNT relative to OPE-ALD/SWCNT. The Eb’s (and the interactions) of the OPEs with the nanotube increase when side chains are present since they wrap around the nanotube (see Figure 7) and thus strengthen the binding forces between these molecular systems. The CAM-B3LYP method, in which the direct dispersion correction is absent, significantly underestimates the binding energies in all of the combinations (with and without side chains). As a consequence, its intermolecular distances are larger than those obtained using B97D and wB97XD. The B97D and wB97XD values, for both the binding energy and the intermolecular distance, are comparable to one another for a given compoud (see Figure 7 and Table 3). The one exception is the OPE-DTF/SWCNT system with side chains, which has the largest binding energy of 5.66 eV (B97D) and 4.71 eV (wB97XD). The reason for the nearly 1 eV difference between the two numbers can be seen in Figure 7, where for the OPE-DTF (B97D) all six side chains wrap themselves around the nanotube but only four side chains wrap around the nanotube in the case of OPE-DTF (wB97XD). In order to further evaluate the effect of side chains vs the end group effect, we determine a binding energy for OPEDTF/SWCNT with just two (central) side chains, similar to what is observed in OPE-ALD/SWCNT (see Table 3). It is clear from these results that the extra (four more) side chains in OPE-DFT enhance the Eb by approximately 2.5 eV relative to the combination with just two side chains. Hence, it can be said that end group effect is of the order of 0.6 eV for both B97D and wB97XD (i.e., it is equal to the difference between Eb’s of ALD and DTF combinations without side chains), while the side chain effect is of the order of 2 eV (B97D) and 1 eV (wB97XD) (i.e., it is equal to the difference between Eb’s of ALD and DTF combinations with side chains minus 0.6 eV). It follows that the magnitude of Eb, and hence the stability of the given combination, depends on the end group as well as the number of side chains present in the oligomer. Table 3 also shows that the binding energy is slightly inversely proportional to the intermolecular distance between the oligomer and the nanotube in all cases considered. In summary, we can see that the electronic structure and binding energy analysis clearly indicate that OPE-DTF is much more effective than OPE-ALD in binding to SWCNTs and hence in their dispersion. 3.2.4. Effect of Dispersion on the Stucture and Polarizability of OPEs. In this section, we comment on the effect of

a

Single-point calculations at B3LYP/6-31G(d) are performed on geometries optimized at B97D/6-31G(d). bSingle-point calculations at B3LYP/6-31G(d) are performed on geometries optimized at wB97XD/6−3 lG(d).

Table 3. Absolute Values of Binding Energies, Eb’s (in eV), and Intermolecular Distances, Δd’s (in Å), between the OPE Molecules (with and without Side Chains, SCs) and the SWCNT Obtained Using B97D, wB97XD, and CAM-B3LYP with the 631G(d) Basis Seta Δd

Eb oligomer OPE-ALD without SCs OPE-DTF without SCs OPE-ALD-4 without SCs OPE-DTF-4 without SCs OPE-ALD with 2SCs OPE-DTF with 6SCs OPE-DTF with 2SCs a

B97D 1.65 2.30 2.18 2.73 3.15 5.66 4.12

(0.55) (0.77) (0.55) (0.68)

wB97XD 1.68 2.27 2.11 2.73 3.13 4.71

(0.56) (0.76) (0.53) (0.68)

CAM-B3LYP

B97D

wB97XD

CAM-B3LYP

0.18 0.24 0.22 0.26 0.23 0.37

3.18 3.14 3.15 3.10 3.20 3.18 3.16

3.30 3.35 3.28 3.19 3.23 3.14

3.76 3.69 3.71 3.67 3.64 3.64

The numbers in parentheses indicate the Eb’s per benzene ring. H


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Figure 9. Binding energies, Eb (in eV), between the OPE molecules (with and without side chains) and the (6,5) SWCNT obtained using B97D, wB97XD, and CAM-B3LYP with the 6-31G(d) basis set.

Figure 10. Dipole moment differences, Δμtotal, between μtotal of the isolated OPEs and μtotal with and without side chains.

somewhat larger changes in dipole moments compared to the values of its isolated compound (one exception being B97D result for OPE-DTF). This difference in dipole moments is amplified further in OPE-ALD systems with side chains (see Figure 10). For the OPE-DTF without and with side chains (with one exception mentioned above), there are no significant changes in dipole moments between the isolated oligomers and the respective oligomer/nanotube combinations. This is because the dipole moment of DTF end-capped oligomers is already quite large, and it does not change significantly in the presence of the nanotube (see Tables 1 and 2). In contrast, the presence of the nanotube polarizes the OPE-ALDs a bit more; however, their dipole moments are still quite a bit smaller than those of OPE-DFT combinations. In addition, we also considered the effect of the side chains on the dipole moments of oligomers (see Figure S18). In both cases, for the gas-phase oligomers and for the “interacting” oligomers (i.e., oligomers in combinations), the presence of side chains increases the dipole moment of OPE-DTF more than that of OPE-ALD for B97D and wB97XD (CAM-B3LYP is an exception). Consistent with the previous discussions above (see sections 3.1.1 and 3.1.2), we also note that the presence of the DTF end group increases the dipole moment of the (isolated and “interacting”) oligomers relative to ALD end group as can be seen from Figure S19 for all DFT methods.

the intermolecular interactions between the SWCNT and OPEs on main geometrical parameters and dipole moments of the OPEs considered in this work relative to their corresponding gas phase properties. This comparison is carried out by looking at differences in R, A, Dh, and dipole moments between the isolated and the “interacting” OPEs (see Figures S14−S17). No significant differences are observed in bond lengths (

Dispersion of Single-Walled Carbon Nanotubes with Oligo(p

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