Chemical Physics Letters 514 (2011) 134–140

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Chemical Physics Letters

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Enhanced nonlinearites of functionalized single wall carbon nanotubeswith diethynylsilane derivatives

Ana E. de A. Machado a, Hélio F. Dos Santos b, Wagner B. de Almeida a,⇑a Laboratório de Química Computacional e Modelagem Molecular (LQC-MM), Departamento de Química, ICEx, Universidade Federal de Minas Gerais (UFMG),Campus Universitário, Pampulha, Belo Horizonte, MG 31270-90, Brazilb Núcleo de Estudos em Química Computacional (NEQC), Departamento de Química, ICE, Universidade Federal de Juiz de Fora (UFJF), Campus Universitário Martelos,Juiz de Fora, MG 36036-330, Brazil

a r t i c l e i n f o a b s t r a c t

Article history:Received 30 July 2011In final form 18 August 2011Available online 23 August 2011

0009-2614/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.cplett.2011.08.044

⇑ Corresponding author. Fax: +55 31 3499 5700.E-mail address: wagner@netuno.qui.ufmg.br (W.B

B3LYP/6-31G(d) DFT calculations of static first hyperpolarizability (b) were performed for armchair (5,5)single wall carbon nanotube (CNT) functionalized with diethynylsilane (PDES) oligomers having electron-donor (D) or acceptor (A) groups attached to their ends. PDES oligomers were introduced longitudinallyand transversely to the CNT external surface. Remarkable b values were obtained for all substituted CNT(>2000 � 10�30 cm5 esu�1). Furthermore, all chemically modified CNT presented very large polarizabilityvalues and very small HOMO–LUMO energy gap, indicating their possible use as conducting materials.Our results demonstrated that CNT hybrid materials containing Si might be promising applied in opto-electronics and photonics.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Carbon nanotubes (CNTs) exhibit very interesting magnetic, elec-tronic and transport properties that are required for the manufac-ture of molecular devices [1–3]. Furthermore, these carbon-basedmaterials also exhibit unique mechanical and structural propertieshaving attracted the attention of multidisciplinary research groups.A survey of works have been reported in the literature showing var-ious applications as biosensors [4,5], photovoltaics devices [6], fieldeffect transistors [7,8], solar cells [9,10], encapsulating of differentmaterials [11,12], adsorbents of inorganic and organic compounds[13,14], catalysis [15], among others. The unique properties of thisclass of carbon-based material open a large perspective of applica-tions in different areas, in special in the nanotechnology and healthfields. Hence, CNTs have been investigating by experimental andtheoretical groups giving emphasis in structural and electronicmodifications resulting from the decoration of the CNT surface[16–18]. A better processing of the single wall carbon nanotube(SWCN) is found when the supramolecular complexes are formed,since they are insoluble in usual solvents. In addition, some practicalapplications of SWCN have been explored due to the cylindricalgeometry and their nanometric scale. Besides, some materials withhigh resistance are required for applications in nanoelectronics[19,20]. Thus, the composites of CNTs are prominent candidatesdue to the synergistic effect observed for the nonlinear optical and

ll rights reserved.

. de Almeida).

electric properties [19,20]. Therefore, these materials can be envi-sioned for the manufacture of nonlinear optics (NLO) devices.

CNTs having well-defined atomic structure, with high length todiameter ratio, associated with their chemical stability constitutea one-dimensional molecule [1–3]. Few experimental and theoreti-cal papers have been reported on SWCN derivatives with potentialapplications in the field of nonlinear optics [17,18,21–25]. Single-and multi-walled carbon nanotubes are characterized as a nonlinearmaterial having large second hyperpolarizability (c) [21–23,25].Theoretical studies using a point–dipole interaction model demon-strated that the nanotubes display large c values compared to thefullerene having the same number of carbon atoms [26]. Further-more, it was observed that the increasing of the diameter of arm-chair and zigzag CNT contributes for the enlargement of the valuesof this nonlinear coefficient. Early theoretical studies show anempirical exponential law of the static c for armchair and zig-zagnanotubes with topological dimensions [25]. De Dominicis et al.[23] performed experimental investigation of the second-harmonicgeneration (SHG) of SWCN films at nanosecond time scale, whichwas observed only in the nanotubes synthesized in laboratory incontrast with the commercially available, indicating a certain degreeof anisotropy of prepared samples. Previous experimental workdemonstrated the third-order nonlinearities of SWCN by the THGexperiment at the femtosecond time scale [21]. Furthermore, forchiral nanotubes it was observed that the quadratic susceptibilitybecame smaller as the nanotube diameter is increased, while thisnonlinear response is not observed for the armchair and zig-zagnanotubes [24].

A.E. de A. Machado et al. / Chemical Physics Letters 514 (2011) 134–140 135

Theoretical investigation has used the strategy of attachingsome substituted stilbenes with donor (D) or acceptor (A) groupson the external surface of the armchair (5,5) SWCN to increasethe first hyperpolarizability (b) via covalent bond [17]. The CNTshave a null value of b due to their highly symmetric structure.The b value for the chemically modified nanotube enhanced upto 70% relative to the free 4,40-substituted stilbene according withthe DFT calculations [17]. Moreover, it was observed that b valuesfor substituted derivatives are increased almost linearly with thestrength of the electron D or A groups as indicated by the Hammettparameter. In addition, SWCN nanotubes with Zn(II) porphyrin ad-sorbed showed nonlinear properties according with recent DFTstudies [18]. In Ref. [18] De Souza et al. claimed that the breakingof symmetry due to the interaction with Zn(II) porphyrin adsorbedon CNT is the major reason for the remarkable increase of the b va-lue for the hybrid nanocomposite.

Having in mind the promising extremely applications as for fab-rication of devices for use in nanotechnologies, molecular modelsof chemically modified SWCN were proposed in this work to obtainderivatives with enhanced values of the b hyperpolarizability.Materials with large values of this nonlinear coefficient are re-quired for applications as electro-optical modulation and all-opti-cal switching, among others [27]. For donor–acceptor alicyclicorganic molecules the magnitude of b is strongly correlated withthe molecular asymmetry, the donor–acceptor pair strength, thesize of conjugation between the D and A substituents as well astheir nature and the molecular conformation [27–31]. Further-more, the lowest energy electronic absorption (charge transfer pro-cess) contributes to enhance the first hyperpolarizability accordingto approaches based on the perturbation theory [27]. Also, thetransparency and stability are fundamental for nonlinear materialscandidates for use in opto-electronic and photonic [27]. When asubstitution is performed on the SWCN surface the result is a mod-ification of their optical and electrical properties, similar to thoseobserved when inclusion defects are verified [2,17,18,32,33].Therefore, in this work we made use of donor or acceptor substit-utents that would contribute to increase charge transfer betweenthe armchair CNT, which is a metallic nanotube, and the diethy-nylsilane (PDES) oligomers, and so, to the enhancement of the bmagnitude for this carbon-based material.

In the present Letter it was performed a molecular modeling ofthe CNT derivatives with enhanced nonlinear responses, using DFTcalculations with the B3LYP functional employing the 6-31G(d) ba-sis set. The goal of the present work was to assess the functional-ized SWCN with PDES decamers that are candidates’nanocomposites as second-order nonlinear materials of high per-formance. The introduction of Si atoms on nanotubes and fuller-enes structures has been investigated since it can be very usefulas a site to functionalization of these carbon-based materials aswell as to increase the material resistance [19,20,32,33]. Further-more, the Si atom incorporated into nonlinear materials is interest-ing due to applications in nanoelectronics. The literature reportsthat the covalent reaction of SWCN with polymers have been per-formed by experimental groups resulting in a marked increase ofthe solubility of the tubes in a range of solvents even at low degreeof functionalization [2,19,20]. Therefore, it can be expected that thederivatives investigated in the present work will display a betterprocessing facility in comparison with the nanotube itself, whichis useful for the manufacture of devices, as well as to open a novelchemistry branch for this important class of nonlinear materials.

2. Methodology

Quantum chemical methods have been considered as a useful ap-proach for the prediction of the hyperpolarizabilities of small and

large molecules, as well molecular clusters [17,18,27–31,34,35]. Inparticular, the DFT methods have been satisfactorily applied to largemolecules for which more rigorous methods such as Møller–Plessetperturbation theory (MP) and coupled cluster (CC), that estimate thefirst hyperpolarizability (b) magnitude with increased accuracy, areprohibitive [27,34,35]. Therefore, DFT methods are the best choice interms of accuracy and computational time. The choice of the basisset also plays a role in the quality of the results [27,34,35]. Accordingto the literature, calculations using a large basis set with polarizationand diffuse functions are required to reproduce the experimentalmagnitude of b [27,34,35]. Nonetheless, several systematic theoret-ical studies indicate that the inclusion of an augmented set does notpromote large differences in the b values for extended systems, withresults found in accordance with the experimental data even whenmedium-size basis sets are used [17,18,27,34,35]. Therefore, for verylarge molecules such those studied in the present work, the6-31G(d) basis set was selected for structural determination as wellas for the calculation of b values. It is opportune to mention that DFTcalculations of the static b were recently performed for PDES deca-mers substituted with electron donor and acceptor groups [36]. Veryenhanced b values were obtained for all di-substituted oligomerswhen compared to the oligomer missing the D–A pair using boththe pure and hybrid DFT methods. The results strongly suggestedthat di-substituted PDES decamers are potential building blocksfor molecular-based materials with second-order nonlinearresponses, what strongly motivated the present work on CNTcomposites.

Firstly a PDES decamer was linked on the external surface of thearmchair (5,5) CNT with 14 Å length and 6.8 Å diameter, both intransversal (Figure 1, structure Nano-Ia) and longitudinal (Figure2, structure Nano-Ib) orientations. Then, electron-donor and/oran acceptor groups were attached to its ends (structures Nano-IIa and Nano-IIIa, Figure 1 and structures Nano-IIb and Nano-IIIb,Figure 2). When donor–acceptor pair is present (Nano-IIa andNano-IIIa, Figure 1), two possibilities were explored to increasethe molecular asymmetry. In the first case, the linking is performednear to the donor group, whereas in the second one the CNT bond-ing is near to the electron-acceptor group. Therefore, the D–A oli-gomer is transversal to the tubular structure of the SWCN.Besides of accounting for the effect of the D–A pair, we also per-formed calculations on the structure where the D–A pair is missingin the oligomer structure (structures Nano-Ia and Nano-IIa).

The geometries of the CNT derivatives and non-substituted andsubstituted PDES decamers were fully optimized using DFT meth-od with the B3LYP hybrid functional [37,38] and the 6-31G(d)polarized basis set [39] (hereafter abbreviated as B3LYP/6-31G(d)). DFT calculations of first hyperpolarizability (b) and polar-izability (a) were performed with the same method used for geom-etry optimizations, namely B3LYP/6-31G(d). It must bear in mindthat all hybrid functional overestimates the first hyperpolarizabil-ity [34,40,41], with the sensitive of the method being dependent onthe magnitude of the property. For instance, for p-nitroaniline (p-NA) the B3LYP/6-31G(d) is only 24% higher than the experimentalvalue, however, for molecules with b > 500 � 10�30 cm5 esu�1 thedifference can be larger than 100% (unpublished results). The basisset also play a role as pointed out by Suponitsky et al. [34], whorecommend the 6-31+G(d) basis set for large molecules. For p-NA, commonly used as probe molecule, the B3LYP/6-31G(d) andB3LYP/6-311G(d) levels show essentially the same b value, equalto 11.5 � 10�30 cm5 esu�1 (unpublished data), which is around20% larger than the reference data. It is also opportune to makeclear that we are looking for trends over a series of analog mole-cules and not necessarily analyzing absolute values of electricalproperties, thus it is expected a smaller error on the relative values.The NLO properties were calculated using the coupled perturbedKohn–Shan (CPKS) approach. The CPKS method is based on the

Figure 1. B3LYP/6-31G(d) fully optimized structures for the Nano-Ia (a), IIa (b) and IIIa (c), nano-derivatives.

136 A.E. de A. Machado et al. / Chemical Physics Letters 514 (2011) 134–140

finite field (FF) method [42], where the tensor elements bijk (wherei, j and k are equal to x, y and z, respectively) are obtained by partialderivatives of the molecular energy perturbed by the externaltime-dependent electric field. From the tensor elements bijk, theCartesian components bx, by and bz can be calculated according toEq. (1) [43]:

bi ¼13

Xik

bikk þ bkik þ bkkið Þ 8 k ¼ x; y; z; i ¼ x; y; z ð1Þ

Thus, the total molecular first hyperpolarizability (bmol) is cal-culated according to Eq. (2):

bmol ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2

x þ b2y þ b2

z

qð2Þ

The GAUSSIAN quantum mechanical package [44] uses therelationship bij = bji and provides a tensor with 10 elements only.The averaged polarizability is evaluated according to Eq. (3) [43]:

aav ¼13

axx þ ayy þ azz� �

ð3Þ

All calculations were carried out using the GAUSSIAN-03/09program [44].

3. Results and discussions

The B3LYP/6-31G(d) fully optimized geometries for the modelsystems studied here are depicted in Figures 1 and 2 and the

Figure 2. B3LYP/6-31G(d) fully optimized structures for the Nano-Ib (a), IIb (b) and IIIb (c) nano-derivatives.

A.E. de A. Machado et al. / Chemical Physics Letters 514 (2011) 134–140 137

electrical properties for isolated nanotube and oligomers, and thenonocomposites, are given in Table 1. The CNT derivative withthe PDES decamer having the dicyanovinyl (A) and propyl (D)groups that is linked transversely to one nanotube, structure Na-no-IIa (Figure 1b), presents the largest value of bmol at the DFT le-vel, in spite of being smaller than the corresponding value for theisolated di-substituted oligomer (Oligom-IIa, Table 1). The vectorcomponent of b along the dipole moment direction (denominatedbvec [43]) is also quoted in the footnote of Table 1 for the nanocom-posite Nano-IIa and respective free oligomer, which is the quantitymeasured in the electric field-induced second-harmonic genera-tion (EFISH) experiment. The deviation between bvec and bmol canbe considered small, so the second-order response to the appliedfield will be sampled in EFISH measurements. Furthermore, verylarge values of bmol (>2000 � 10�30 cm5 esu�1) were also obtainedfor all CNT derivatives designed, with the values for structuresNano-IIb, -IIIa and -IIIb being slightly bigger than the respectivevalues for the corresponding free oligomers. Despite the error onthe methodology that overestimates the absolute b values, these

Table 1B3LYP/6-31G(d) calculated electric propertiesa for the nanocomposites Nano-Ia, Ib, IIa, IIb,Figures 1 and 2).

Nanocomposites

Nano-Ia Nano-Ib Na

eHLb/eV 0.78 0.77 0.5

l/Debye 10.07 13.17 5.7aav/10�25 cm3 5426 5994 659bmol/10�30 cm5 esu�1 1799 1820 21

Isolated Nanotube and Substituted Oligomers

Free Nanotube Oligom-I Oli

eHLb/eV 0.79 1.76 1.1

l/Debye 0.0 10.87 4.9aav/10�25 cm3 2189 3261 487bmol/10�30 cm5 esu�1 1.15 2553 33

Polarizability: (a) 1 a.u. = 1.48184709 � 10�25 cm3; first-hyperpolarizability (b): 1 a.u. =a Dipole moment: 1 a.u. (Bohr-electron) = 2.541765 Debye = 2.541765 � 10�18 esu-cmb eHL: energy gap (HOMO–LUMO difference). 1 a.u. = 27.2114 eV.c The bvec (the vector component of b along the dipole moment direction [43])�32669 � 10�30 cm5 esu�1 respectively.

are still quite large when compared to reference systems in the lit-erature. For instance, the bacteriorhodopsin (bR), one of the threephotosensitive system of nature, possesses very large molecularb, around 2100 � 10�30 cm5 esu�1 measured at 1064 nm using hy-per-Reyleigh scattering technique [45]. An analysis of Table 1 re-veals that the oligomer-CNT composites exhibit b values close tothe corresponding free oligomers and so, a composite with veryhigh value of b can be designed by choosing an adequate oligomerhaving very large value of b. In addition to, the CNT derivativesshow smaller values of the HOMO–LUMO energy gap in compari-son with the isolated substituted oligomers. These results indicatethe potential use of these derivatives as nanoelectronics devicesdue to the very small band gap. It is worth saying that calculatedB3LYP band gap is in good agreement with experimental measuresfor several classes of materials [46]. Moreover, recent theoreticalwork showed that the B3LYP/6-31G(d) method calculate the bandgap of metallic CNTs in excellent agreement with the experimentalvalues [47]. Furthermore, according to the simple approach of twoelectronic levels for molecules that display electron transfer, the b

IIIa and IIIb and the corresponding isolated nanotube and substituted oligomers (See

no-IIac Nano-IIb Nano-IIIa Nano-IIIb

9 0.77 0.78 0.774 27.62 33.71 10.327 6212 6499 6551

991 2390 7628 7509

gom-IIa Oligom-IIb Oligom-IIIa Oligom-IIIb

5 1.84 1.69 1.596 27.36 33.97 7.266 3544 4216 3812

170 2266 7592 7487

8.639418 � 10�33 cm5 esu�1..

values for Nano-IIa and respective free oligomer structure are �18118 and

138 A.E. de A. Machado et al. / Chemical Physics Letters 514 (2011) 134–140

values are directly related to the oscillator strength and inverselyto the energy gap [27]. Therefore, one direction to optimize theinvestigated systems is increasing the force of oscillator and so,the chromophores substituent selection is crucial to set up thephotophysic properties that will contribute for optimized nonlin-ear response.

The results reported in Table 1 indicate that the introduction ofthe donor–acceptor decamer transversely or longitudinally to thenanotube external surface is an efficient strategy to enhance thenonlinear response, even though the predicted b values can besmaller than the corresponding free polymer (see Table 1). More-over, the strength of the D–A pair, as well as the site selected forthe linking of the PDES decamer to the nanotube external surfaceis fundamental to enhance the value of the bmol as can be observedby comparing, for example, the results for the Nano-IIa and Nano-IIIa derivatives, which have quite different b magnitudes. TheNano-Ia nanocomposite, where the D/A pair is missing, havingthe oligomer introduced transversely to the nanotube surface,has bmol magnitude with similar magnitude to the correspondingNano-Ib species that has the oligomer linked longitudinally andalso misses the D or A groups. These results demonstrated the fun-damental role of the D/A pair to polarize the CNT in order to en-hance the nonlinear coefficients.

The Nano-IIa derivative with the oligomer having a dicyanovi-nyl-propyl acceptor–donor pair that is transversal to the nanotubeexternal surface has a b magnitude slightly lower than that pre-dicted for the free polymer (�34% lower). This might be due to

Scheme 1. The CNT-oligomer linking types for all hybrid compounds studied here. To m

the position of substitution, with the tube linked in the middle ofthe chain, decreasing the effective conjugation length comparedto the free polymer. For the structure Nano-IIIa, the value dropsto 7628 � 10�30 cm5 esu�1, which is due to the very short chain be-tween the push–pull moieties, namely the phenylamine and theCNT. Therefore, a very simple empirical structure–property rela-tionship might be proposed saying that the insertion of the tubeon a push–pull polymer decreases the non-linear response and,this effect is much more pronounced as the bond position ap-proaches to the electron-donor group, which is an evidence ofthe electron-withdrawing characteristic of the CNTs. The Nano-IIa derivative presents the highest value of b among the hybrid sys-tems investigated as well the smallest HOMO–LUMO energy gap.Therefore, the introduction of a PDES p-conjugated oligomer, hav-ing D/A groups, on the CNT surface promotes markedly increase onthe polarization of these systems. Thus, it can be concluded that acharge transfer process between the CNT and the PDES oligomersshould take place. Recent resonance Raman spectroscopic studiesdemonstrated that such process occurs between the CNTs andthe polyaniline p-conjugated polymer nanocomposites [19,20].

The linking of the oligomers in the structures Nano-Ia, Nano-IIa, Nano-IIIa derivatives, which is transversal to the nanotubeexternal surface, occurs through the Si atom (Scheme 1), whilewhen the oligomer is linked longitudinally it takes place througha carbon atom belonging to the oligomer ( Nano-Ib, Nano-IIb,Nano-IIIb) (Scheme 1). It can be said that there is a compromisebetween the polarization and electronic delocalization that is

ake easier the visualization the CNT was represented by a flat portion of its surface.

A.E. de A. Machado et al. / Chemical Physics Letters 514 (2011) 134–140 139

needed to achieve the enhancement of bmol for this nonlinearmaterial, as have been also observed for other classes of nonlinearmaterials [27,46]. The link of donor–acceptor pairs for differentclasses of compounds have been one efficient strategy for theincreasing of b magnitude as demonstrated experimentally andtheoretically by several research groups [27–31].

Some monosubstituted aniline oligomers with the dicyanovinylstrong acceptor show very high values of b according to AM1/TDHF(Austin Model 1 (AM1)/time-dependent Hartree–Fock approach(TDHF)) theoretical calculations [29]. The introduction of this elec-tron-acceptor group increases the polarization since aniline oligo-mers are electron-donor as observed experimentally [48]. Severalmolecules containing the dicyanovinyl group show large chargetransfer bands that contribute for the large nonlinearities observedin different compounds [49]. Moreover, multiple electron excita-tion channels as well as charge delocalization in CNTs can partici-pate in the mechanism of high-order harmonic generation. It mustbe emphasized that the introduction of different nonlinear chro-mophores (D and A groups) on carbon nanotubes should modifythe spectroscopic properties of the hybrid material, therefore themodel systems investigated can be utilized at selected wave-lengths for applications in different spectral ranges.

The ground state dipole moment values (see Table 1) of the D–Ananotube derivatives investigated as well as the ones having onlythe acceptor (or donor) group attached to the oligomer linked longi-tudinally or transversely to the CNT are comparable in magnitudewith the respective calculated value for the isolated substitutedoligomer. The non-substituted CNTs have a null dipole momentvalue. For the nanocomposites with large dipole moment a chargeseparation in the ground state should be observed. Therefore, thepresence of the oligomer in all designed derivatives contributes tothe enhancement of the dipole moment in comparison with thenon-substituted nanotube. Hence, it can be envisioned applicationsfor these nanocomposites via poling field.

For the linear polarizability an interesting behavior is observed.It can be seen that all derivatives showed increased values of aav ifcomparing with the non-substituted nanotube or to the isolatednon-substituted and di-substituted oligomers. In fact, the aav valuefor each nanocomposite structure is approximately the sum of theindividual values for the corresponding substituted oligomer andfree nanotube. In particular, the Nano-IIa exhibits the largestvalues of aav among all derivatives, which is the system with thepropyl-dicyanovinyl oligomer linked transversely to the nanotube.Therefore, the donor–acceptor pair polarizes the system moreefficiently than when only one acceptor or donor group is used.Also, the derivative Nano-IIIb with the mono-substituted oligomerlongitudinally linked to the external of nanotube surface, havingonly the phenylamine strong donor group attached to the oligomerend, and IIIa which is di-substituted and linked transversely to thenanotube, show a very large polarizability value, comparable to theNano-IIa structure.

4. Conclusions

In this work DFT calculations of static first hyperpolarizability forvarious oligomer-CNT composite structures with electron donor andacceptor substituent groups attached at the ends of the diethynylsi-lane (PDES) decamer using the B3LYP functional and 6-31G(d) basisset were carried out. The oligomer was introduced longitudinallyand transversely on the CNT external surface. The link of ap-conjugated polymer having very enhanced b values to carbonnanotubes results in potential nonlinear nanocomposites of sec-ond-order response. The largest value of the first hyperpolarizabilitycalculated at the B3LYP/6-31G(d) level for the transversely linkedoligomer-CNT structure Nano-IIa was 21991 � 10�30 cm5 esu�1,

undoubtedly a stimulating remarkable value of b. It was observedthat the effect of the interaction of the substituted oligomers withthe CNT depends strongly on the nature of the donor–acceptorgroups attached to the oligomer end and also on the spatial disposi-tion of the nanocomposite.

The b values of the nanocomposites do not differ substantiallyfrom the corresponding free oligomer respective values and so, oli-gomer-CNT composites exhibiting high values of first hyperpolar-izability can be designed by choosing adequately a oligomer withvery large value of b. It can also be seen that the free substitutedoligomers acquires substantial conduction capacity through theinteraction with the nanotube, with the energy gap found lowerthan 1 eV. Furthermore, the extraordinary properties of CNT asso-ciated to the PDES oligomers contribute to relevant properties ofthese hybrid materials. In special, it can be envisioned applicationsin the nonlinear field since the values obtained of the first hyper-polarizability are very large in comparison with other nonlinearmaterials. Further enhancement of the nonlinear coefficient canbe achieved by the introduction of stronger nonlinear chromoph-ores in the carbon nanotubes. Also, the number of moieties intro-duced can be augmented to increase yet more the asymmetry,and hence the magnitude of b. The present work demonstratedthat derivatives of carbon nanotubes are prominent candidates asnonlinear second-order materials, besides of the already wellknown property as the third-order material.

A very important result of this work is the remarkable trend inthe calculated B3LYP/6-31G(d) b values for the nanocomposites ascompared with the free oligomers. Our results strongly indicatesthat no matter the level of calculation employed for the evaluationof the first hyperpolarizability the b value for the oligomer-CNTcomposite structures tend to be comparable to the respective valuefor the free oligomer. If the level of theory and basis set are chan-ged the absolute value of b can be larger or smaller, but the effectwould be the same for composite and free oligomer structures.Therefore, it can be expected that the procedure of adding an oligo-mer to a CNT will certainly produce a composite material withnon-linear response similar to the free oligomer, what is a wel-come result.

Acknowledgments

We gratefully acknowledge the financial support of the Conse-lho Nacional de Desenvolvimento Científico e Tecnológico (MCT/CNPQ) and Fundação de Amparo à Ciência e Tecnologia do Estadode Minas Gerais (FAPEMIG) to our laboratories. A.E. De A. Machadothanks the FAPEMIG for a post-doctoral grant. This work is a col-laboration research project of members of the Rede Mineira deQuímica (RQ-MG) supported by FAPEMIG. We also thank Dr. DiegoPaschoal (UFJF) for helpful discussion on the revision of themanuscript.

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