This paper presents a study on structural and mechanical properties of a series of fluorinated armchair
single-walled carbon nanotubes (SWCNTs) by using density functional theory. At the PBE / SVP level, the
data obtained compare well with experimental and theoretical studies. The results show that fluorination,
in general, distort SWNCTs framework, but there exists the difference between ‘axial’ and ‘circumferential’
functionalization. It turns out that elastic properties diminish with increasing concentration of adsorbents,
however, the fluorinated SWCNTs remain strong enough to be suitable for reinforcement of composites

Petrushenko, I.K.

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 7 No 1, 01005(4pp) (2015) Том 7 № 1, 01005(4cc) (2015) 
 
 
2077-6772/2015/7(1)01005(4) 01005-1  2015 Sumy State University 
Structural and Mechanical Properties of Fluorinated SWCNTs: a DFT Study 
 
I.K. Petrushenko* 
 
Physical and Technical Institute, Irkutsk State Technical University, 83, Lermontov Str., 664074 Irkutsk, Russia 
 
(Received 11 November 2014; published online 25 March 2015) 
 
This paper presents a study on structural and mechanical properties of a series of fluorinated armchair 
single-walled carbon nanotubes (SWCNTs) by using density functional theory. At the PBE / SVP level, the 
data obtained compare well with experimental and theoretical studies. The results show that fluorination, 
in general, distort SWNCTs framework, but there exists the difference between ‘axial’ and ‘circumferential’ 
functionalization. It turns out that elastic properties diminish with increasing concentration of adsorbents, 
however, the fluorinated SWCNTs remain strong enough to be suitable for reinforcement of composites.  
 
Keywords: DFT, PBE, Single-walled carbon nanotubes, Fluorination, Young’s modulus. 
 
 PACS numbers: 31.15.E –, 61.48. – c, 
62.20.de,71.15.Mb,  
 
 
                                                 
* igor.petrushenko@istu.edu 
1. INTRODUCTION 
 
Single-walled carbon nanotubes (SWCNTs), hollow 
cylinders formed by rolled graphene sheets, are novel 
unique material with outstanding structural, mechanical, 
electrical, physical and chemical properties [1-6]. Since the 
first Iijima’s paper, SWCNTs attracted enormous atten-
tion of researchers worldwide [7]. There are two main 
fields of SWCNTs usage which of especial interest for sci-
entists. First, they have unique electronic properties de-
pendent from their structure. Semi-conducting or metallic 
SWCNTs can be used in the design of novel NEMS, as 
electron emitters and transparent electrodes [8-10]. Se-
cond, one may highlight sound mechanical properties of 
SWCNTs. It was established that their mean Young’s 
modulus is ca. 1 TPa [11]. However, there exists difference 
of experimentally obtained Young’s modulus values and 
theoretical predictions. It is caused by many reasons, such 
as various computational techniques used, different ap-
proaches of determination of nanotubes walls thickness 
and so on. Summarized data on SWCNTs strength can be 
found, for example, in [12]. 
Unfortunately, the usage of pristine SWCNTs does 
not always improve the mechanical properties of com-
posites under development [13]. Pristine SWCNTs have 
substantial disadvantages, namely they tend to self-
assemble into tangled bunches in which a lot of nano-
tubes are interlaced together by van der Waals forces 
[14]. Such a bunch can not be effectively embedded in 
composite matrix. Thus, for nanocomposite designers, it 
is crucial to separate bunches into individual tubes. To 
diminish SWCNTs aggregation properties non-covalent 
and covalent functionalization techniques are common-
ly used. Fluorination is a simple and effective way to 
improve SWCNTs assembling properties [14, 15]. It is 
fluorinated nanotubes (F-SWCNTs) which are often 
being used in the production of nanocomposites [5, 14, 
15]. On the other hand, fluorination significantly dis-
torts the framework of SWCNTs [16]. Imperfect 
SWNTs addition may even reduce the strength of nano-
composites. Hence, it is important to select the degree 
of functionalization of SWNTs carefully. Novel tech-
niques can change it gradually and tubes with given 
fluorine to carbon ratio can be created [14].  
In this work, we report density functional theory 
(DFT) study on the structure and Young’s modulus of 
fluorinated armchair SWCNTs series in comparison 
with pristine SWCNTs. To the best of our knowledge, 
there are a few papers deal with theoretical investiga-
tions of Young’s modulus of functionalized nanotubes 
[4, 5, 11, 17], and only two articles focus on the deter-
mination of elastic properties of fluorinated SWCNTs 
[5, 17]. However, in the work of Kudin et al. the 3-21G 
basis set is implemented. It is probably insufficient to 
describe accurately the structure and elastic properties 
of such models of SWCNTs, therefore more reliable 
results are needed to clarify the geometry and elasticity 
of fluorinated SWCNTs. In the Petrushenko’s et al. 
work only one degree of fluorination was studied. 
Thus, motivated by the above considerations, in this 
paper, we study the structural and elastic properties of 
armchair SWCNTs by techniques based on the DFT, 
which has been successfully applied to predict many 
SWCNT properties with high reliability and less compu-
tational efforts than the majority of the traditional ab 
initio methods. The emphasis of this work is on struc-
tures and Young’s moduli of finite-length fluorinated 
SWCNTs with various degrees of functionalization. 
 
2. COMPUTATIONAL METHODS 
 
For all simulations, finite armchair (5,5) SWCNTs 
(C60H20) containing 2, 4, 6, 8, 10 fluorine atoms at-
tached to the ‘axial’ or ‘circumferential’ positions were 
used as the fluorinated SWCNTs (F-SWCNT) models. 
The detailed description of these cases will be given 
below. Here, the term ‘degree of functionalization’ de-
notes the F/C ratio. Therefore, we study F-SWCNTs 
with the following degrees of functionalization: 3.3 %, 
6.7 %, 10 %, 13.3 %, and 16.7 %. The dangling bonds at 
the edges of all studied tubes were saturated by the 
hydrogen atoms. The fluorine atom links exclusively on 
the tube outer wall. The places of its addition are the 
‘axial’ and the ‘circumferential’ one (Fig. 1).  
 I.K. PETRUSHENKO J. NANO- ELECTRON. PHYS. 7, 01005 (2015) 
 
 
01005-2 
  
 
Fig. 1 – Side view of a fragment of F-SWCNTs. The balls are 
fluorine atoms: 1,2-fluorination (‘axial’) (a), 1,4-fluorination 
(‘circumferential’) (b) 
 
The analysis of the two isomers with various sites of 
fluorine addition was performed owing to the uncer-
tainty of an energetically favored type of F-SWCNT. 
Semi-empirical and DFT calculations in works of Kelly 
et al. [18] and Kudin et al. [19] gave opposite results 
about equilibrium structure of F-SWCNT, but calculat-
ed total energies of the two species were quite the same 
in both papers. It gave us the firm belief that the both 
structures exist. 
For all calculations, we used Orca 2.9.1 program 
package [20] employing the DFT method with the PBE 
functional [21, 22]. To calculate equilibrium geometries 
of the studied structures, we used SVP (split valence 
polarization) basis set, which is equivalent to the com-
monly used 6-31G* basis set [23]. In SVP the inner 
shell atomic orbitals are described by a single basis 
function, and two basis functions are provided for each 
valence shell atomic orbital, augmented by a set of po-
larization functions. In order to calculate Young’s mod-
ulus of every model we used the following formula: 
 
 Y   / ε  2(∆E / S)(L / (∆L)2), (1) 
 
where  is the stress, ε is the strain, E is the increment 
of the total energy, S is the area upon which stretching 
force acts, L is the length of a tube and ∆L is the elon-
gation (1 %) upon stretching. The S area can be calcu-
lated by the formula: S  2ar, where r is the radius of 
the NT, a  3.4 Å, which is equal to the graphite inter-
layer distance. The stability of the functionalized 
SWCNTs can be assessed by considering the binding 
energy Eb defined as: 
 
 Eb  1 / N(ESWCNT + fluorine – ESWCNT – NEfluorine), (2) 
 
where ESWCNT + fluorine, ESWCNT, and Efluorine are the total 
energies оf the functionalized SWCNTs, pristine 
SWCNTs, and fluorine, respectively; N denotes number 
of attached molecules. 
 
3. RESULTS AND DISCUSSIONS 
 
3.1 Pristine SWCNTs 
 
Before we turn to the elastic moduli of the  
F-SWCNTs, we would like to present our results for 
pristine neutral (5,5) armchair SWCNTs. This allows 
one to compare the results of this paper with previous 
works and to assess the reliability of obtained data. 
Young’s moduli for pristine SWCNTs are summarized 
in Table 1. 
The calculated Young’s modulus of the pristine 
SWCNT (1.05 TPa) compare well to experimental find-
ings (0.32-1.80 TPa) and previous theoretical works 
(0.8-5.5 TPa). Based on the present observations our 
choice of models seem to be justified. 
Table 1 – Summarized Young’s modulus values of SWCNTs 
 
 This paper Literature data 
Y, TPa 1.05 0.32-1.80 [1,12]  
0.8-5.5 [1, 4, 5] 
1.02 [11]  
 
3.2 Fluorinated SWCNTs 
 
Previous papers were shown that there are two in-
dependent bond lengths in SWCNTs: axial and circum-
ferential [4-6]. We studied the both isomers and used 
the following notation: 1a, 2a, 3a, 4a, and 5a for the  
2F-SWCNT, 4F-SWCNT, 6F-SWCNT, 8F-SWCNT and 
10F-SWCNT functionalized at the ‘axial’ positions; 1c, 
2c, 3c, 4c, and 5c for the 2F-SWCNT, 4F-SWCNT,  
6F-SWCNT, 8F-SWCNT and 10F-SWCNT functional-
ized at the ‘circumferential positions, respectively. The 
1a, c and 2a, c model are shown in Fig. 2 as an example. 
The addition of fluorine atoms to the pristine 
SWCNTs leads to both b1 and b2 lengths changes. 
Thus, the optimized b1 and b2 lengths in pristine nano-
tubes (1.44 and 1.43 Å) are much shorter than those in 
F-doped nanotubes. Functionalization elongates them 
from 1.44 to 1.56 Å (b1), and from 1.43 to 1.65 Å (b2). 
We can see that in the former case we observe elonga-
tion, and one can say that the fluorination ‘opens’ the 
bond. In the latter case we can make the assumption 
that the bond brake occurs. Thus, the framework of  
F-doped SWCNTs rearranged and perfect tubular form 
of a pristine SWCNT became deformated. Calculated 
Young’s moduli for studies F-doped SWCNTs are tabu-
lated in Table 2. 
Table 2 shows that the fluorination generally leads 
to the decrease in Young’s modulus. One can highlight 
the comparatively high value for the 1c model. It is not 
strange as such a functionalization leaves the perfect 
framework of the SWCNT practically undisturbed 
(Fig. 2). In turn, the 1a counterpart loses the perfect 
shape upon functionalization (Fig. 2). This leads to the 
smaller Young’ modulus in comparison with 1c. The 
further fluorination leads to the moderate decrease in 
Young’s modulus for all studied models. It should be 
noted, however, that the decrease is not very high, and 
the F-SWCNTs remain elastic enough. Although ‘axial-
ly’ and ‘circumferentially’ doped F-SWCNTs show the 
same trend in Young’s modulus diminishing, their elas-
tic moduli are not equal. Young’s moduli of 1a, 2a, 3a, 
4a, and 5a are equal to 0.96 (9.5 % drop in comparison 
with the pristine SWCNT), 0.95 (10.0 %), 0.93 (12.1 %), 
0.88 (15.9 %), and 0.86 (18.3 %) TPa, respectively. The 
F-SWCNTs models 1c, 2c, 3c, 4c, and 5c have the fol-
lowing Young’s modulus values: 1.01 (4.0 %), 0.93 
(11.7 %), 0.90 (14.5 %), 0.87 (17.8 %), and 0.85 (19.8 %) 
TPa, respectively. It is very likely that in all cases sp2 
hybridization of pristine SWCNT being changed to sp3 
one in the neighborhood of the fluorine attachment. 
The framework of F-SWCNTs rearranged and perfect 
tubular form of a pristine SWCNT became strongly 
deformated. The effect is more pronounced for the larg-
er number of attached fluorine atoms. However, even in 
the case of the highest degree of functionalization, the 
Young’s modulus drop is only 18.3 % (5a) and 19.8 % 
(5c). In order to identify the fluorination effect in detail,  
а b 
 STRUCTURAL AND MECHANICAL PROPERTIES… J. NANO- ELECTRON. PHYS. 7, 01005 (2015) 
 
 
01005-3 
 
  
1a 1c 
  
2a 2c 
 
Fig. 2 – Cross-sections of 1a, c and 2a, c models. White balls denote carbon, grey balls – fluorine. Hydrogen atoms omitted for 
clarity 
 
Table 2 – Young’s moduli of the F-doped (5,5) SWCNT. The studied degrees of functionalization: 1a, c – 3.3 %, 2a, c – 6.7 %,  
3a, c – 10 %, 4a, c – 13.3 %, 5a, c – 16.7 %. 
 
Type of F-doped 
SWCNT 
Young’s modulus, 
TPa 
Young’s modulus 
drop, % 
Type of F-doped 
SWCNT 
Young’s 
modulus, TPa  
Young’s modulus 
drop, % 
1a 0.96 9.5 1c 1.01 4.0 
2a 0.95 10.0 2c 0.93 11.7 
3a 0.93 12.1 3c 0.90 14.5 
4a 0.88 15.9 4c 0.87 17.8 
5a 0.86 18.3 5c 0.85 19.8 
 
we examine SWCNT functionalization by a series of flu-
orine atoms. The computed binding energies are shown 
in Fig. 3. To eliminate mutual interaction between fluo-
rine molecules they being step-by-step linked as far as 
possible around the circumference of the tube. It can be 
seen that the molecules bind to the surface of the (5,5) 
nanotube (i.e. the adsorption energy is negative). How-
ever, the strength of the bonding differs depending on 
the site of addition. For ‘circumferential’ functionaliza-
tion, the adsorption energies decrease with increasing 
number of attached molecules (Fig. 3). In terms of the 
thermal stability, the more negative values demonstrate 
the ease of functionalization with fluorine. 
It is natural that the fluorine attack of the sidewall 
of the SWCNT is accompanied by the distortion of the 
ideal SWCNT framework. Such a deformation is fol-
lowed by the easier adsorption of other fluorine mole-
cules. The opposite is in the case of ‘axial’ functionali-
zation. One can see the clear minimum when two mole-
cules attached that reflects the strong binding. Further, 
the adsorption energy per molecule gets less negative 
(indicating that the bonding weakens) with increasing 
number of attached molecules. In this case, the reaction 
energies differ little, except the minimum value. The 
difference between ‘axial’ and ‘circumferential’ values 
-3
-2,95
-2,9
-2,85
-2,8
-2,75
-2,7
-2,65
-2,6
-2,55
-2,5
0 1 2 3 4 5 6
Degree of functionalization
E
b
, 
e
V
 
 
Fig. 3 – Binding energies (Eb) of the (5,5) SWCNT functional-
ized with fluorine as a function of the number of adsorbed 
molecules. The studied degrees of functionalization: 1 – 3.3 %, 
2 – 6.7 %, 3 – 10 %, 4 – 13.3 %, 5 – 16.7 %; ■ – ‘axial’ function-
alization, ♦ – ‘circumferential’ functionalization 
 
confirms the difference between induced changes in 
geometry and elastic moduli of SWCNTs. 
We can set the connection between Young’s modu-
lus and binding energies in studied tubes. As it has 
been shown above, in general, ‘circumferentially’ func-
tionalized SWCNTs exhibit lower Young’s modulus 
than their counterparts. Their binding energies get 
more negative on going from low to high degree of func-
tionalization. It confirms the tendency that the mole-
 I.K. PETRUSHENKO J. NANO- ELECTRON. PHYS. 7, 01005 (2015) 
 
 
01005-4 
cules with stronger binding to the SWCNTs surface 
modify the properties in a stronger manner. 
To sum up, fluorination of SWCNTs is exothermic. 
All studied reactions are spontaneous, although the 
binding energies on ‘circumferential’ and ‘axial’ func-
tionalization are different. Young’s modulus gradually 
diminishes when the number of adsorbed species in-
creases. Our future works will review various types of 
nanotubes functionalized with a wide range of attached 
molecules.  
 
4. CONCLUSION 
 
We have presented the DFT study of the structural 
and mechanical properties of fluorinated SWCNTs. 
When functionalized, the SWCNT model acquires a 
distorted structure. Any fluorine reaction on SWCNTs 
is exothermic. At low concentrations of attached fluo-
rine, the structural properties of nanotubes are moder-
ately modified. We observe, however, that these proper-
ties are dependent on the site of fluorine addition. The 
larger degree of fluorination leads to the significant 
structural changes. The local deformations include re-
hybridization of the C-C bonds that leads to the dimin-
ishing of strength of studied systems. 
 For ‘axially’ modified SWCNTs, Young’s modulus 
decreases from 0.96 (the degree of functionalization is 
3.3 %,) to 0.86 (16.7 %) TPa. For ‘circumferentially’ 
modified SWCNTs, Young’s modulus decreases from 
1.01 (3.3 %) to 0.85 (16.7 %) TPa. Despite the fact, that 
the fluorination leads to the gradual drop of the elastic 
moduli of SWCNTs and this effect cannot be generally 
neglected, the Young’s moduli remain high enough to 
guarantee successful involvement of fluorinated 
SWCNTs in reinforcement of composite materials. 
 
ACKNOWLEDGEMENTS 
 
This work was supported by RFBR, research project 
No. 14-03-31231 мол_а. IKP thanks Dr. V. Malkin for 
his continued support and encouragement. IKP thanks 
SAIA for its support. 
 
 
REFERENCES 
 
1. М.М.J. Treacy, T.W. Ebbesen, J.M. Gibson, Nature 381, 678 
(1996). 
2. E.W. Wong, P.E. Sheehan, C.M. Lieber, Science 277, 1971 
(1997). 
3. V.N. Popov, Mater. Sci. Eng. R 43, 61 (2004).  
4. I.K. Petrushenko, N.A.  Ivanov, Fullerenes Nanotubes Car-
bon Nanostruct. 22, 405 (2014). 
5. I.K. Petrushenko, N.A. Ivanov, Fullerenes Nanotubes Carbon 
Nanostruct. 22, 781 (2014). 
6. I.K. Petrushenko, N.A. Ivanov, Phys. E 54, 262 (2013). 
7. S. Iijima, Nature 354, 568 (1991). 
8. J. Zhao, J. Han, J.P. Lu, Phys. Rev. B 65, 193401 (2002). 
9. J.O. Island, V. Tayari, A.C. McRae, A.R. Champagne, Nano 
Lett. 12, 4564 (2012). 
10. T.M. Barnes, J. van de Lagemaat, D. Levi, G. Rumbles, 
T.J. Coutts, C.L. Weeks, D.A. Britz, I. Levitsky, J. Peltola, 
P. Glatkowski, Phys. Rev. B 75, 235410 (2007). 
11. K.Z. Milowska, J.A. Majewski, Phys. Chem. Chem. Phys. 15, 
14303 (2013). 
12. M.M. Shokrieh, R. Rafiee, Mech. Compos. Mater. 46 No 2, 
155 (2010). 
13. J.-P. Salvetat, A. Rubio, Carbon 40, 1729 (2002). 
14. V.N. Khabashesku, Russ. Chem. Rev. 80 No 8, 705 (2011). 
15. V.V. Ivanovskaya, A.L. Ivanovskii, Russ. Chem. Rev. 80 
No 8, 761 (2011). 
16. V.N. Khabashesku, W.E. Billups, J.L. Margrave, Acc. Chem. 
Res. 35, 1087 (2002). 
17. K.N. Kudin, G.E. Scuseria, B.I. Yakobson Phys. Rev. B 64, 
235406 (2001). 
18. K.F. Kelly, I.W. Chiang, E.T. Mickelson, et al., Chem. Phys. 
Lett. 313, 445 (1999). 
19. K.N. Kudin, H.F. Bettinger, G.E. Scuseria, Phys. Rev. B 63, 
045413 (2001). 
20. F. Neese, Wires Comput. Mol. Sci. 2, 73 (2012). 
21. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 
3865 (1996). 
22. J.P. Perdew, K. Burke, M. Ernzerhof, Phys Rev Lett 78, 1396 
(1997). 
23. A. Schafer, R. Ahlrichs, J. Chem. Phys. 97, 2571 (1992). 
 


English

Structural and Mechanical Properties of Fluorinated SWCNTs: a DFT Study

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 7 No 1, 01005(4pp) (2015) Том 7 № 1, 01005(4cc) (2015)   2077-6772/2015/7(1)01005(4) 01005-1  2015 Sumy State University Structural and Mechanical Properties of Fluorinated SWCNTs: a DFT Study  I.K. Petrushenko*  Physical and Technical Institute, Irkutsk State Technical University, 83, Lermontov Str., 664074 Irkutsk, Russia  (Received 11 November 2014; published online 25 March 2015)  This paper presents a study on structural and mechanical properties of a series of fluorinated armchair single-walled carbon nanotubes (SWCNTs) by using density functional theory. At the PBE / SVP level, the data obtained compare well with experimental and theoretical studies. The results show that fluorination, in general, distort SWNCTs framework, but there exists the difference between ‘axial’ and ‘circumferential’ functionalization. It turns out that elastic properties diminish with increasing concentration of adsorbents, however, the fluorinated SWCNTs remain strong enough to be suitable for reinforcement of composites.   Keywords: DFT, PBE, Single-walled carbon nanotubes, Fluorination, Young’s modulus.   PACS numbers: 31.15.E –, 61.48. – c, 62.20.de,71.15.Mb,                                                     * igor.petrushenko@istu.edu 1. INTRODUCTION  Single-walled carbon nanotubes (SWCNTs), hollow cylinders formed by rolled graphene sheets, are novel unique material with outstanding structural, mechanical, electrical, physical and chemical properties [1-6]. Since the first Iijima’s paper, SWCNTs attracted enormous atten-tion of researchers worldwide [7]. There are two main fields of SWCNTs usage which of especial interest for sci-entists. First, they have unique electronic properties de-pendent from their structure. Semi-conducting or metallic SWCNTs can be used in the design of novel NEMS, as electron emitters and transparent electrodes [8-10]. Se-cond, one may highlight sound mechanical properties of SWCNTs. It was established that their mean Young’s modulus is ca. 1 TPa [11]. However, there exists difference of experimentally obtained Young’s modulus values and theoretical predictions. It is caused by many reasons, such as various computational techniques used, different ap-proaches of determination of nanotubes walls thickness and so on. Summarized data on SWCNTs strength can be found, for example, in [12]. Unfortunately, the usage of pristine SWCNTs does not always improve the mechanical properties of com-posites under development [13]. Pristine SWCNTs have substantial disadvantages, namely they tend to self-assemble into tangled bunches in which a lot of nano-tubes are interlaced together by van der Waals forces [14]. Such a bunch can not be effectively embedded in composite matrix. Thus, for nanocomposite designers, it is crucial to separate bunches into individual tubes. To diminish SWCNTs aggregation properties non-covalent and covalent functionalization techniques are common-ly used. Fluorination is a simple and effective way to improve SWCNTs assembling properties [14, 15]. It is fluorinated nanotubes (F-SWCNTs) which are often being used in the production of nanocomposites [5, 14, 15]. On the other hand, fluorination significantly dis-torts the framework of SWCNTs [16]. Imperfect SWNTs addition may even reduce the strength of nano-composites. Hence, it is important to select the degree of functionalization of SWNTs carefully. Novel tech-niques can change it gradually and tubes with given fluorine to carbon ratio can be created [14].  In this work, we report density functional theory (DFT) study on the structure and Young’s modulus of fluorinated armchair SWCNTs series in comparison with pristine SWCNTs. To the best of our knowledge, there are a few papers deal with theoretical investiga-tions of Young’s modulus of functionalized nanotubes [4, 5, 11, 17], and only two articles focus on the deter-mination of elastic properties of fluorinated SWCNTs [5, 17]. However, in the work of Kudin et al. the 3-21G basis set is implemented. It is probably insufficient to describe accurately the structure and elastic properties of such models of SWCNTs, therefore more reliable results are needed to clarify the geometry and elasticity of fluorinated SWCNTs. In the Petrushenko’s et al. work only one degree of fluorination was studied. Thus, motivated by the above considerations, in this paper, we study the structural and elastic properties of armchair SWCNTs by techniques based on the DFT, which has been successfully applied to predict many SWCNT properties with high reliability and less compu-tational efforts than the majority of the traditional ab initio methods. The emphasis of this work is on struc-tures and Young’s moduli of finite-length fluorinated SWCNTs with various degrees of functionalization.  2. COMPUTATIONAL METHODS  For all simulations, finite armchair (5,5) SWCNTs (C60H20) containing 2, 4, 6, 8, 10 fluorine atoms at-tached to the ‘axial’ or ‘circumferential’ positions were used as the fluorinated SWCNTs (F-SWCNT) models. The detailed description of these cases will be given below. Here, the term ‘degree of functionalization’ de-notes the F/C ratio. Therefore, we study F-SWCNTs with the following degrees of functionalization: 3.3 %, 6.7 %, 10 %, 13.3 %, and 16.7 %. The dangling bonds at the edges of all studied tubes were saturated by the hydrogen atoms. The fluorine atom links exclusively on the tube outer wall. The places of its addition are the ‘axial’ and the ‘circumferential’ one (Fig. 1).   I.K. PETRUSHENKO J. NANO- ELECTRON. PHYS. 7, 01005 (2015)   01005-2    Fig. 1 – Side view of a fragment of F-SWCNTs. The balls are fluorine atoms: 1,2-fluorination (‘axial’) (a), 1,4-fluorination (‘circumferential’) (b)  The analysis of the two isomers with various sites of fluorine addition was performed owing to the uncer-tainty of an energetically favored type of F-SWCNT. Semi-empirical and DFT calculations in works of Kelly et al. [18] and Kudin et al. [19] gave opposite results about equilibrium structure of F-SWCNT, but calculat-ed total energies of the two species were quite the same in both papers. It gave us the firm belief that the both structures exist. For all calculations, we used Orca 2.9.1 program package [20] employing the DFT method with the PBE functional [21, 22]. To calculate equilibrium geometries of the studied structures, we used SVP (split valence polarization) basis set, which is equivalent to the com-monly used 6-31G* basis set [23]. In SVP the inner shell atomic orbitals are described by a single basis function, and two basis functions are provided for each valence shell atomic orbital, augmented by a set of po-larization functions. In order to calculate Young’s mod-ulus of every model we used the following formula:   Y   / ε  2(∆E / S)(L / (∆L)2), (1)  where  is the stress, ε is the strain, E is the increment of the total energy, S is the area upon which stretching force acts, L is the length of a tube and ∆L is the elon-gation (1 %) upon stretching. The S area can be calcu-lated by the formula: S  2ar, where r is the radius of the NT, a  3.4 Å, which is equal to the graphite inter-layer distance. The stability of the functionalized SWCNTs can be assessed by considering the binding energy Eb defined as:   Eb  1 / N(ESWCNT + fluorine – ESWCNT – NEfluorine), (2)  where ESWCNT + fluorine, ESWCNT, and Efluorine are the total energies оf the functionalized SWCNTs, pristine SWCNTs, and fluorine, respectively; N denotes number of attached molecules.  3. RESULTS AND DISCUSSIONS  3.1 Pristine SWCNTs  Before we turn to the elastic moduli of the  F-SWCNTs, we would like to present our results for pristine neutral (5,5) armchair SWCNTs. This allows one to compare the results of this paper with previous works and to assess the reliability of obtained data. Young’s moduli for pristine SWCNTs are summarized in Table 1. The calculated Young’s modulus of the pristine SWCNT (1.05 TPa) compare well to experimental find-ings (0.32-1.80 TPa) and previous theoretical works (0.8-5.5 TPa). Based on the present observations our choice of models seem to be justified. Table 1 – Summarized Young’s modulus values of SWCNTs   This paper Literature data Y, TPa 1.05 0.32-1.80 [1,12]  0.8-5.5 [1, 4, 5] 1.02 [11]   3.2 Fluorinated SWCNTs  Previous papers were shown that there are two in-dependent bond lengths in SWCNTs: axial and circum-ferential [4-6]. We studied the both isomers and used the following notation: 1a, 2a, 3a, 4a, and 5a for the  2F-SWCNT, 4F-SWCNT, 6F-SWCNT, 8F-SWCNT and 10F-SWCNT functionalized at the ‘axial’ positions; 1c, 2c, 3c, 4c, and 5c for the 2F-SWCNT, 4F-SWCNT,  6F-SWCNT, 8F-SWCNT and 10F-SWCNT functional-ized at the ‘circumferential positions, respectively. The 1a, c and 2a, c model are shown in Fig. 2 as an example. The addition of fluorine atoms to the pristine SWCNTs leads to both b1 and b2 lengths changes. Thus, the optimized b1 and b2 lengths in pristine nano-tubes (1.44 and 1.43 Å) are much shorter than those in F-doped nanotubes. Functionalization elongates them from 1.44 to 1.56 Å (b1), and from 1.43 to 1.65 Å (b2). We can see that in the former case we observe elonga-tion, and one can say that the fluorination ‘opens’ the bond. In the latter case we can make the assumption that the bond brake occurs. Thus, the framework of  F-doped SWCNTs rearranged and perfect tubular form of a pristine SWCNT became deformated. Calculated Young’s moduli for studies F-doped SWCNTs are tabu-lated in Table 2. Table 2 shows that the fluorination generally leads to the decrease in Young’s modulus. One can highlight the comparatively high value for the 1c model. It is not strange as such a functionalization leaves the perfect framework of the SWCNT practically undisturbed (Fig. 2). In turn, the 1a counterpart loses the perfect shape upon functionalization (Fig. 2). This leads to the smaller Young’ modulus in comparison with 1c. The further fluorination leads to the moderate decrease in Young’s modulus for all studied models. It should be noted, however, that the decrease is not very high, and the F-SWCNTs remain elastic enough. Although ‘axial-ly’ and ‘circumferentially’ doped F-SWCNTs show the same trend in Young’s modulus diminishing, their elas-tic moduli are not equal. Young’s moduli of 1a, 2a, 3a, 4a, and 5a are equal to 0.96 (9.5 % drop in comparison with the pristine SWCNT), 0.95 (10.0 %), 0.93 (12.1 %), 0.88 (15.9 %), and 0.86 (18.3 %) TPa, respectively. The F-SWCNTs models 1c, 2c, 3c, 4c, and 5c have the fol-lowing Young’s modulus values: 1.01 (4.0 %), 0.93 (11.7 %), 0.90 (14.5 %), 0.87 (17.8 %), and 0.85 (19.8 %) TPa, respectively. It is very likely that in all cases sp2 hybridization of pristine SWCNT being changed to sp3 one in the neighborhood of the fluorine attachment. The framework of F-SWCNTs rearranged and perfect tubular form of a pristine SWCNT became strongly deformated. The effect is more pronounced for the larg-er number of attached fluorine atoms. However, even in the case of the highest degree of functionalization, the Young’s modulus drop is only 18.3 % (5a) and 19.8 % (5c). In order to identify the fluorination effect in detail,  а b  STRUCTURAL AND MECHANICAL PROPERTIES… J. NANO- ELECTRON. PHYS. 7, 01005 (2015)   01005-3    1a 1c   2a 2c  Fig. 2 – Cross-sections of 1a, c and 2a, c models. White balls denote carbon, grey balls – fluorine. Hydrogen atoms omitted for clarity  Table 2 – Young’s moduli of the F-doped (5,5) SWCNT. The studied degrees of functionalization: 1a, c – 3.3 %, 2a, c – 6.7 %,  3a, c – 10 %, 4a, c – 13.3 %, 5a, c – 16.7 %.  Type of F-doped SWCNT Young’s modulus, TPa Young’s modulus drop, % Type of F-doped SWCNT Young’s modulus, TPa  Young’s modulus drop, % 1a 0.96 9.5 1c 1.01 4.0 2a 0.95 10.0 2c 0.93 11.7 3a 0.93 12.1 3c 0.90 14.5 4a 0.88 15.9 4c 0.87 17.8 5a 0.86 18.3 5c 0.85 19.8  we examine SWCNT functionalization by a series of flu-orine atoms. The computed binding energies are shown in Fig. 3. To eliminate mutual interaction between fluo-rine molecules they being step-by-step linked as far as possible around the circumference of the tube. It can be seen that the molecules bind to the surface of the (5,5) nanotube (i.e. the adsorption energy is negative). How-ever, the strength of the bonding differs depending on the site of addition. For ‘circumferential’ functionaliza-tion, the adsorption energies decrease with increasing number of attached molecules (Fig. 3). In terms of the thermal stability, the more negative values demonstrate the ease of functionalization with fluorine. It is natural that the fluorine attack of the sidewall of the SWCNT is accompanied by the distortion of the ideal SWCNT framework. Such a deformation is fol-lowed by the easier adsorption of other fluorine mole-cules. The opposite is in the case of ‘axial’ functionali-zation. One can see the clear minimum when two mole-cules attached that reflects the strong binding. Further, the adsorption energy per molecule gets less negative (indicating that the bonding weakens) with increasing number of attached molecules. In this case, the reaction energies differ little, except the minimum value. The difference between ‘axial’ and ‘circumferential’ values -3-2,95-2,9-2,85-2,8-2,75-2,7-2,65-2,6-2,55-2,50 1 2 3 4 5 6Degree of functionalizationEb, eV  Fig. 3 – Binding energies (Eb) of the (5,5) SWCNT functional-ized with fluorine as a function of the number of adsorbed molecules. The studied degrees of functionalization: 1 – 3.3 %, 2 – 6.7 %, 3 – 10 %, 4 – 13.3 %, 5 – 16.7 %; ■ – ‘axial’ function-alization, ♦ – ‘circumferential’ functionalization  confirms the difference between induced changes in geometry and elastic moduli of SWCNTs. We can set the connection between Young’s modu-lus and binding energies in studied tubes. As it has been shown above, in general, ‘circumferentially’ func-tionalized SWCNTs exhibit lower Young’s modulus than their counterparts. Their binding energies get more negative on going from low to high degree of func-tionalization. It confirms the tendency that the mole- I.K. PETRUSHENKO J. NANO- ELECTRON. PHYS. 7, 01005 (2015)   01005-4 cules with stronger binding to the SWCNTs surface modify the properties in a stronger manner. To sum up, fluorination of SWCNTs is exothermic. All studied reactions are spontaneous, although the binding energies on ‘circumferential’ and ‘axial’ func-tionalization are different. Young’s modulus gradually diminishes when the number of adsorbed species in-creases. Our future works will review various types of nanotubes functionalized with a wide range of attached molecules.   4. CONCLUSION  We have presented the DFT study of the structural and mechanical properties of fluorinated SWCNTs. When functionalized, the SWCNT model acquires a distorted structure. Any fluorine reaction on SWCNTs is exothermic. At low concentrations of attached fluo-rine, the structural properties of nanotubes are moder-ately modified. We observe, however, that these proper-ties are dependent on the site of fluorine addition. The larger degree of fluorination leads to the significant structural changes. The local deformations include re-hybridization of the C-C bonds that leads to the dimin-ishing of strength of studied systems.  For ‘axially’ modified SWCNTs, Young’s modulus decreases from 0.96 (the degree of functionalization is 3.3 %,) to 0.86 (16.7 %) TPa. For ‘circumferentially’ modified SWCNTs, Young’s modulus decreases from 1.01 (3.3 %) to 0.85 (16.7 %) TPa. Despite the fact, that the fluorination leads to the gradual drop of the elastic moduli of SWCNTs and this effect cannot be generally neglected, the Young’s moduli remain high enough to guarantee successful involvement of fluorinated SWCNTs in reinforcement of composite materials.  ACKNOWLEDGEMENTS  This work was supported by RFBR, research project No. 14-03-31231 мол_а. IKP thanks Dr. V. Malkin for his continued support and encouragement. IKP thanks SAIA for its support.   REFERENCES  1. М.М.J. Treacy, T.W. Ebbesen, J.M. Gibson, Nature 381, 678 (1996). 2. E.W. Wong, P.E. Sheehan, C.M. Lieber, Science 277, 1971 (1997). 3. V.N. Popov, Mater. Sci. Eng. R 43, 61 (2004).  4. I.K. Petrushenko, N.A.  Ivanov, Fullerenes Nanotubes Car-bon Nanostruct. 22, 405 (2014). 5. I.K. Petrushenko, N.A. Ivanov, Fullerenes Nanotubes Carbon Nanostruct. 22, 781 (2014). 6. I.K. Petrushenko, N.A. Ivanov, Phys. E 54, 262 (2013). 7. S. Iijima, Nature 354, 568 (1991). 8. J. Zhao, J. Han, J.P. Lu, Phys. Rev. B 65, 193401 (2002). 9. J.O. Island, V. Tayari, A.C. McRae, A.R. Champagne, Nano Lett. 12, 4564 (2012). 10. T.M. Barnes, J. van de Lagemaat, D. Levi, G. Rumbles, T.J. Coutts, C.L. Weeks, D.A. Britz, I. Levitsky, J. Peltola, P. Glatkowski, Phys. Rev. B 75, 235410 (2007). 11. K.Z. Milowska, J.A. Majewski, Phys. Chem. Chem. Phys. 15, 14303 (2013). 12. M.M. Shokrieh, R. Rafiee, Mech. Compos. Mater. 46 No 2, 155 (2010). 13. J.-P. Salvetat, A. Rubio, Carbon 40, 1729 (2002). 14. V.N. Khabashesku, Russ. Chem. Rev. 80 No 8, 705 (2011). 15. V.V. Ivanovskaya, A.L. Ivanovskii, Russ. Chem. Rev. 80 No 8, 761 (2011). 16. V.N. Khabashesku, W.E. Billups, J.L. Margrave, Acc. Chem. Res. 35, 1087 (2002). 17. K.N. Kudin, G.E. Scuseria, B.I. Yakobson Phys. Rev. B 64, 235406 (2001). 18. K.F. Kelly, I.W. Chiang, E.T. Mickelson, et al., Chem. Phys. Lett. 313, 445 (1999). 19. K.N. Kudin, H.F. Bettinger, G.E. Scuseria, Phys. Rev. B 63, 045413 (2001). 20. F. Neese, Wires Comput. Mol. Sci. 2, 73 (2012). 21. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 22. J.P. Perdew, K. Burke, M. Ernzerhof, Phys Rev Lett 78, 1396 (1997). 23. A. Schafer, R. Ahlrichs, J. Chem. Phys. 97, 2571 (1992).  

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Structural and Mechanical Properties of Fluorinated SWCNTs: a DFT Study

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