Chapter 4
Small Molecules [CO 2, H 2O, CH 4, NH4 and H 2]
Interactions with Carbon Nanostructures
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
CHAPTER 4: SMALL MOLECULES [CO 2 , H 2 O, CH 4 , NH 3 AND
H 2 ] INTERACTIONS WITH CARBON NANOSTRUCTURES
4.1 Abstract
Carbonaceous materials are promising class of materials for potential application as
chemical and bio-molecule sensors. In this chapter we have done first principles
calculations to study the interaction of various small molecules, such as CO 2 , H 2 O,
NH 3 , CH 4 and H 2 , on the surface of CNTs and graphene in order to study their
feasibility as gas sensors (Scheme 4.1). Model systems for armchair and zigzag CNTs
of different diameter have been considered to study the effect of chirality and
curvature of the carbon nanomaterials on binding with these small molecules. Our
results reveal that these gas molecules have been weakly physisorbed on the surface
and act as charge donors to the carbon nanomaterials. Charge transfer between the gas
molecules and the carbon materials impacts the physical properties of the carbon
materials which may be traced to their sensitivity. As the gas molecule physisorb on
the carbon materials they may be suitable for repetitive sensor operation.
Scheme 4.1: A schematic representation of the interaction gas molecules with CNSs.
75
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
4.2 Introduction
The topical carbon allotropes graphene and CNTs have gained significant research
interest due to their unique properties and potential applications. The exceptional
electronic, thermal, optical, mechanical, and transport properties of these carbon
materials make them promising candidates for various potential applications.150 It has
been observed from several experimental and theoretical studies that the transport and
electronic properties are extremely sensitive to changes in the local chemical
environment.183-185 This inference paved the way for the progress of carbon
nanomaterials based gas sensors. Development of chemical and biological sensors
based on carbon nanomaterials is an area of recent interest.186-187 Gas sensing
materials have gained considerable research interest due to their widespread
applications in various sectors such as energy and environment, homeland security
and as chemical warfare agents.188-189 Recent experimental studies show that reduced
graphene oxide exhibits superior gas sensing properties.190-191 There is immense
demand for high sensitive gas sensors to detect explosive and poisonous gas leakages
in various chemical and pharmaceutical industries. The advancement in the carbon
based nanotechnology has enhanced the possibility of low cost and high sensitive
sensors for various applications.192
The structure and physical properties of carbon nanostructures (CNSs) make them
promising candidates as sensors to detect different gases. Dai and co-workers were
the first to report the gas sensors based on CNTs to detect gases such as NO 2 and
NH 3 .193 A recent experimental study stated that graphene based sensors possess very
high sensitivity such that the adsorption of individual gas molecules could be
detected.114 In general, the principle of gas sensing involves adsorption and desorption
of gas molecules on the sensing materials. The extremely high surface to-volume ratio
76
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
and hollow structure of nanomaterials is ideal for gas molecules adsorption. The
adsorption of various substrates such as metal ions, gas molecules, drug molecules,
organic molecules, and bio-molecules such as proteins and nucleic acids on the
surface of the carbon materials has gained significant interest because of their
fundamental importance and potential industrial applications.136,
159, 194-196
If the
substrates thus adsorbed be capable of modifying the electronic and magnetic
properties of the carbon materials then by monitoring such specific changes, the
presence of different species can be detected. Selective detection of gas molecules
based on the change in the dielectric constant of the CNTs has been studied.197
Meyyappan and co-workers developed a CNT sensor platform for gas and organic
vapour detection at room temperature and explained the molecular sensing in terms of
charge transfer mechanism.198 Mirica et al. developed a solvent-free approach for
fabricating carbon nanotube gas sensors on the surface of cellulosic chapter by
mechanical abrasion.199 Besides, hybrid carbon nanomaterials have also been found to
show promising gas sensing abilities.200-201
The adsorption/desorption mechanism will be more effective if the substrate
molecules are weakly bound on the surface of the carbon nanostructures. Hence a
noncovalent type of interaction is preferred rather than a covalent binding where there
is a bond formation and bond breaking. Understanding the noncovalent interactions
on the surfaces of carbon materials is very important to get fundamental and
molecular level understanding about the various applications of these carbonaceous
materials.202-206 Factors influencing the noncovalent interactions such as size and
curvature of the π system have been studied extensively.18, 49, 51, 207 Graphene is a two
dimensional sheet of sp2 carbon atoms and CNTs are the wrapped up graphene sheets
77
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
in one dimension.113, 160, 208 It is interesting to compare and contrast the reactivity of
these two allotropes which vary in their curvature towards various species.160, 165, 208210
Besides, the CNTs can be classified into different types such as armchair, zigzag
and chiral nanotubes based on the orientation of the tube axis with respect to the
hexagonal lattice.7 It has been shown in the literature that functionalization of the
carbon nanomaterials would enhance the adsorption of various species.33, 166, 211 The
covalent and noncovalent functionalization of graphene has been systematically
investigated in a recent study.211 Apart from the traditional CNTs, the inorganic
nanotubes have also been shown to have promising potential for sensor
applications.212-213
The current study aims to provide a comprehensive and comparative analysis of the
noncovalent interaction of various gas molecules such as CO 2 , H 2 O, CH 4 , NH 3 and
H 2 with CNTs of varying diameter and chirality and graphene nano ribbons (GNRs).
The orientation of these gas molecules on the surface of the CNSs and their binding
strength have been quantum chemically estimated. The effect of curvature and
chirality of the carbon materials on the binding strength has been investigated. The
charge transfer occurred during the complex formation has also been explored. The
change in the polarizability of the CNSs upon the binding of these gas molecules has
been systematically estimated.
4.3 Computational methods and model systems
The geometry of all the structures considered were optimized using two layer
ONIOM calculations at (M06–2X/6–31G*: AM1) level of theory, in which a seven
ring fragment resembling coronene is considered as high layer and the rest of the
system is considered as low layer as shown in the Figure 4.1. The geometries were
optimized using berny optimization and the convergence criteria. Though many
78
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
popular functionals fail to describe the noncovalent interactions the de novo
parameterized M06-2X functionals developed by Zhao and Truhlar77 has been shown
to give a good performance for the noncovalent interactions. All stationary points
were characterized as minima after verifying the presence of all real frequencies.
To test the reliability of our ONIOM approach for accurate description for
geometric parameters, we have also done full optimization at M06-2X/6-31G* level
for the CNT (4,4) complexes. The binding energy and the geometric parameters of the
full systems have been compared with the ONIOM results in the Table 4.1. A quick
look at the Table 4.1 shows that the results obtained in the ONIOM approach are in
good agreement with the full system optimization.
Figure 4.1: The atoms shown by ball and bond model were considered for high layer
and the rest of the atoms shown by tube model were considered for low layer in the
ONIOM calculation. (a) armchair CNT, (b) zigzag CNT, (c) chiral CNT, and (d)
graphene.
79
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
Table 4.1: BE (kcal/mol) and distance (Å) of the gas molecules with CNT (4,4)
obtained using ONIOM approach and full optimization
Molecules
M06-2X/6-31G*
M06-2X/6-31G*
// ONIOM (M06-2X/6-31G* : AM1)
CO 2
H2O
CH 4
NH 3
H2
BE
d
BE
d
4.07
4.35
2.26
3.63
1.13
2.987
2.522
2.892
2.733
2.677
4.07
4.33
2.27
3.61
1.13
2.956
2.501
2.856
2.748
2.683
Subsequently we calculated the single point calculation using M06-2X/6-311G**
level of theory for the complete system of the optimized structures. The binding
energy (BE) was calculated by the supermolecule approach using eq. 1 as the
difference between sum of the total energies of the parent CNSs (E CNSs ) and the gas
molecules (E X ) (where X=CO 2 , H 2 O, NH 3 , CH 4 and H 2 ) and the total energy of the
complex (E CNSs_ X ).
𝐵𝐵𝐵𝐵 = (𝐸𝐸𝐶𝐶𝐶𝐶𝐶𝐶 + 𝐸𝐸𝑋𝑋 ) − 𝐸𝐸𝐶𝐶𝐶𝐶𝐶𝐶_𝑋𝑋
4.1
Polarizability is considered to be a measure of the potential of a molecule to respond
to an external electric field. When a molecule is subjected to an external electric field,
some of its electrons obtain adequate energy to move along the direction of the
electric field. The average molecular polarizability (ά) was calculated as the average
of the diagonal components of the polarizability tensor as given in eq. 2.2.
All the calculations were done in Gaussian 09 suite of program.182 We have
considered a wide range of model systems to represent the CNTs and graphene as
80
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
shown in the Scheme 4.2. A set of armchair CNTs such as CNT (4,4), CNT (5,5),
CNT (6,6), CNT (7,7) and a set of zigzag CNTs such as CNT (8,0), CNT (10,0),
CNT (12,0), CNT (14,0) have been modeled. In addition to that we have generated
models for chiral CNTs such as CNT (4,2), CNT (6,3), CNT (8,4) and CNT (10,5).
The eclectic model systems considered will help to determine the effect of chirality of
the CNTs on binding with the gas molecules. Further, in order to study the effect of
curvature on the binding energy, we have considered graphene nanoribbons GNR1,
GNR2, GNR3 and GNR4 which were the opened flat models of the nanotubes CNT
(4,4), CNT (5,5), CNT (6,6) and CNT (7,7) respectively. The binding of various gas
molecules such as CO 2 , H 2 O, CH 4 , NH 3 and H 2 on these CNSs have been studied.
4.4 Results and discussion
In this section, at the outset we discuss the orientation of the gas molecules on the
CNSs surface in the optimized structure as well as the change in their geometric
parameters upon complex formation. Subsequently we look at the binding energy of
the carbon nanostructures with various gas molecules and correlated them with the
trend observed in the charge transfer during the complex formation. The change in the
characteristic vibration frequency of these gas molecules on binding with the CNSs
has been analyzed. This is followed by a discussion on the change in the properties of
the CNSs such as polarizability and HOMO-LUMO energy gap on binding with the
gas molecules.
4.4.1 Structure and geometry
We have considered various possible orientations of these gas molecules on the
surface of the CNSs and reported only the minimum energy orientations. The nearest
distance (d) between the surface of the CNSs and the gas molecules has been
measured and given in Table 4.2 for all the complexes considered. The‘d’ values
81
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
given in the Table 4.2 represents the distance from the surface of the CNSs to the
nearest H atom in the gas molecules except in the case of CO2 where the ‘d’ value
represents the distance between the surface of the CNSs and the C atom of the CO2
molecule.
Scheme 4.2: Model systems considered for CNSs.
82
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
CO 2
H2O
CH 4
NH 3
H2
Armchair
CNT (4,4)
CNT (5,5)
CNT (6,6)
CNT (7,7)
# of atoms
88
110
132
154
2.987
2.995
3.030
3.018
2.522
2.584
2.578
2.607
2.892
2.753
2.783
2.738
2.733
2.772
2.797
2.825
2.677
2.666
2.668
2.686
Zigzag
CNT (8,0)
CNT (10,0)
CNT (12,0)
CNT (14,0)
80
100
120
140
2.966
2.961
2.981
2.966
2.732
2.731
2.706
2.704
2.149
2.803
2.425
2.495
2.901
2.878
2.811
2.867
2.825
2.777
2.756
2.754
Chiral
CNT (4,2)
CNT (6,3)
CNT (8,4)
CNT (10,5)
96
118
140
162
2.994
2.985
3.002
3.013
2.461
2.510
2.556
2.615
2.515
2.646
2.684
2.721
2.741
2.765
2.796
2.808
2.693
2.663
2.674
2.663
Graphene
Table 4.2: Distance (Å) between the gas molecules and the carbon nanostructures in
the optimized geometry at ONIOM (M06-2X/6-31G* : AM1) level of theory
CNSs
GNR1
GNR2
GNR3
GNR4
96
118
140
162
3.028
3.029
3.030
2.995
2.650
2.649
2.658
2.663
2.790
2.791
2.787
2.807
2.861
2.787
2.868
2.819
2.693
2.688
2.698
2.679
CO 2 molecule has been observed to have a parallel mode of orientation above the
surface of CNSs in the optimized structures. The C atom of the CO 2 molecule is just
above the C-C double bond at a distance of around 2.961 to 3.030 Å as shown in the
Figure 4.2. H 2 O molecule is oriented above the CNSs surface such that the two OH
groups are pointing towards the surface. The distance between the H atom and the
surface of the CNSs has been found to be in the range of 2.461 to 2.732 Å. In the
minimum energy orientation of the NH 3 complexes, all the three N-H group are
pointing towards the surface of the carbon nanostructures, where as in the case of
CH 4 , three C-H bonds are oriented towards the CNSs surface and the fourth C-H
83
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
bond is away from that as shown in the Figure 4.2. From the surface of the CNSs, the
nearest distance between the NH 3 molecule ranges between 2.733 to 2.901 Å, while
the distance of the CH 4 molecule ranges between 2.149 to 2.892 Å. The H 2 molecule
oriented itself perpendicular to the surface of the CNSs at distances around 2.666 to
2.825 Å.
Figure 4.2: A representative case to show the mode of interaction and the distance
(Å) of (a,a’) CO 2 , (b,b’) H 2 O, (c,c’) NH 3 , (d,d’) CH 4 and (e,e’) H 2 with CNT
(6,6).The side and front views are given in the first and second rows, respectively. All
other carbon materials follow the same mode of interaction with the gas molecules.
The geometric parameters of the gas molecules before and after complex formation
have been given in Table 4.3. In the case of CO 2 , the C-O bond length in its free state
is 1.163 Å on both sides. A cursory look at the Table 4.3 reveals that in the CNSsCO 2 complexes there is a slight increase in the bond length of one of the C-O bonds.
For H 2 O, the O-H distance in the molecule is 0.965Å, whereas in the complexed state,
the O-H bond length increases up to 0.967 Å. The C-H bond length in the CH 4
molecule is 1.092 Å when it is in the unbound state. While three of the C-H bond
lengths remain the same on binding with the CNSs, the fourth C-H bond pointing
towards the CNSs in the optimized geometry shows a slight increase in the bond
length. In the unbound state the N-H bond length in NH 3 is 1.017 Å, however all the
84
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
three N-H bond lengths became 1.018 Å on binding with the CNSs. For H 2 molecule,
the H-H bond distance is 0.736 Å in the unbound state and it has been increased up to
0.739 Å while binding with CNSs.
Table 4.3: Geometric parameters of the gas molecules before and after complexation
with the CNSs at ONIOM(M06-2X/6-31G* : AM1) level of theory
Parent
CO 2
C-O
(1)
1.163
C-O
(2)
1.163
H2O
O-H
(1)
0.965
O-H
(2)
0.965
CH 4
C-H
(1)
1.092
C-H
(2)
1.092
C-H
(3)
1.092
C-H
(4)
1.092
NH 3
N-H
(1)
1.017
N-H
(2)
1.017
N-H
(3)
1.017
H2
H-H
CNT (4,4)
CNT (5,5)
CNT (6,6)
CNT (7,7)
1.163
1.163
1.163
1.163
1.164
1.164
1.164
1.164
0.967
0.966
0.966
0.966
0.967
0.966
0.966
0.966
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.093
1.093
1.093
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
0.739
0.739
0.739
0.738
CNT (8,0)
CNT
(10,0)
CNT
(12,0)
CNT
(14,0)
1.163
1.162
1.164
1.165
0.967
0.967
0.967
0.967
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.093
1.017
1.018
1.018
1.018
1.018
1.018
0.738
0.739
1.163
1.163
0.967
0.967
1.092
1.092
1.092
1.093
1.018
1.018
1.018
0.738
1.163
1.164
0.967
0.967
1.092
1.092
1.092
1.093
1.018
1.018
1.018
0.738
CNT (4,2)
CNT (6,3)
CNT (8,4)
CNT
(10,5)
1.163
1.163
1.163
1.163
1.163
1.164
1.164
1.164
0.967
0.966
0.966
0.966
0.967
0.967
0.966
0.966
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.093
1.093
1.093
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
0.738
0.739
0.738
0.738
GNR1
GNR2
GNR3
GNR4
1.163
1.163
1.163
1.163
1.164
1.164
1.164
1.164
0.967
0.967
0.967
0.967
0.967
0.967
0.967
0.967
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.092
1.093
1.093
1.093
1.093
1.093
1.093
1.093
1.093
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
1.018
0.739
0.739
0.739
0.738
0.736
4.4.2 Binding energy and charge transfer
We further calculated the binding energy of the all the molecules considered with
CNSs at M06-2X/6-311G** level. Table 4.4 shows the binding energy of the gas
molecules with armchair CNTs, zigzag CNTs, chiral CNTs and graphene
nanoribbons. It can be surmised from the table that these molecules have been weakly
adsorbed on the surface of the carbon materials with very less binding energy of about
~5 kcal/mol. In general, the order of magnitude of binding energy for the
85
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
physisorption process is considered to be lesser than 5 kcal/mol and the aforesaid
energy for the chemisorption is usually higher than 15 kcal/mol. Our numerical study
connotes that these gas molecules interacts with the CNTs and graphene by
physisorption and so the desorption phenomena will be easier. Such an
adsorption/desorption mechanism is the important prerequisite for various sensor
materials for repeatable sensor operation. A closer glance at the binding energy of the
gas molecules with different CNTs (armchair, zigzag and chiral) indicates that there is
no substantial effect of chirality on the binding energy in contrast to our earlier
observations on cation−π and π−π interactions with the carbon nanostructures. This
can be attributed owing to the very weak interactions between these gas molecules
and the CNTs. However, graphene shows marginally higher binding energy than the
corresponding CNTs in most of the cases.
CNSs
# of atoms
CO 2
H2O
CH 4
NH 3
H2
Armchair
CNT (4,4)
CNT (5,5)
CNT (6,6)
CNT (7,7)
88
110
132
154
4.26
4.72
3.84
4.51
5.09
4.78
5.11
4.63
2.51
2.75
1.83
2.97
3.79
3.75
3.77
3.70
1.14
1.20
1.36
1.36
Zigzag
CNT (8,0)
CNT (10,0)
CNT (12,0)
CNT (14,0)
80
100
120
140
4.04
3.77
3.99
4.41
5.09
4.94
4.86
4.85
2.36
2.94
2.53
2.74
3.80
3.76
3.75
3.73
1.26
1.33
1.17
1.23
Chiral
CNT (4,2)
CNT (6,3)
CNT (8,4)
CNT (10,5)
96
118
140
162
4.27
4.56
4.44
4.63
5.08
4.96
4.47
4.68
2.46
2.85
3.20
2.94
3.78
3.83
3.69
3.67
1.07
1.31
1.36
1.37
Graphene
Table 4.4: BE (kcal/mol) of CNSs with gas molecules at M06-2X/6-311G**//
ONIOM(M06-2X/6-31G* : AM1) level of theory
GNR1
GNR2
GNR3
GNR4
96
118
140
162
4.54
4.59
4.53
4.57
4.73
4.82
4.61
4.84
3.47
3.47
3.46
3.48
3.99
4.07
3.89
4.06
1.55
1.50
1.55
1.48
86
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
Figure 4.3: Binding energy (kcal/mol) of the gas molecules with (a) armchair CNTs (b)
zigzag CNTs (c) Chiral CNTs and (d) graphene nano ribbons (GNR) at M06-2X/6311G**//ONIOM (M06-2X/6-31G* : AM1) level of theory.
Figure 4.4: Mulliken charge (au) on the gas molecules in their complex form with (a)
armchair CNTs (b) zigzag CNTs (c) Chiral CNTs and (d) graphene nano ribbons (GNR) at
M06-2X/6-311G**//ONIOM (M06-2X/6-31G* : AM1) level of theory.
87
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
The order of binding energy of these gas molecules on the surface of the CNSs is
portrayed as H 2 O > CO 2 > NH 3 > CH 4 > H 2 as illustrated in the Figure 4.3. In order
to gauge the mechanism of these foregoing binding interactions, we have done the
Mulliken charge analysis at M06-2X/6-311G** level and given in the Figure 4.4.
Charge transfer is a phenomenon in which a large fraction of an electronic charge is
transferred from one molecular entity (charge donor) to another molecular entity
(charge acceptor). As a result of charge transfer electronic structure of the sensor
materials will be affected and thus leads to changes in their electronic properties. The
positive charge values on the gas molecules in the optimized complexes clearly point
out that these gas molecules act as charge donors to the carbon nanostructures. The
highest charge transfer has occurred in the case of H 2 O molecule. The neutral H 2 O
molecules obtained a partial positive charge of about 0.28 au on binding with different
CNSs. The amount of charge transfer occurred in the case of CO 2 and NH 3 have been
found to be very close in magnitude. H 2 molecule exhibits the slightest charge
transfer in most of the cases except in a few cases where CH 4 molecule shows the
least charge transfer as shown in the Figure 4.4. In line with the observation in the
case of binding energy, the extent of charge transfer from the gas molecule to the
CNTs is independent of the type and chirality of the CNTs, where as the charge
transfer is more in the case of flat graphene when compared to the curved CNTs.
4.4.3 Vibrational analysis
Spectroscopic signatures will be of immense importance in experimentally validating
the computational predictions. The shifts in the characteristic vibration frequencies of
the gas molecules upon complex formation with various carbon nanostructures have
been computed at ONIOM (M06-2X/6-31G*:AM1) level. The frequencies reported in
the Table 4.5 have not been scaled by any factor. For an isolated CO 2 molecule, there
88
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
exist three characteristic vibrations namely ν 1 = 668cm-1, ν 2 = 1421cm-1, and ν 3 =
2499cm-1 which correspond to the bending, symmetric and asymmetric stretching
modes of C-O bond respectively. A brief glance at the table shows that all the three
CO 2 characteristic vibrations decrease upon binding with the carbon materials which
indicates a red shift.
Table 4.5: Characteristic stretching and bending frequencies (cm-1) of the gas
molecules before and after complex formation with the CNSs
CO 2
δ C-O
CO 2
υ C-O
CO 2
υ C-O
668
1421
2499
4,4
5,5
6,6
7,7
647
647
648
651
1416
1417
1417
1417
8,0
10,0
12,0
14,0
644
645
646
646
4,2
6,3
8,4
10,5
G1
G2
G3
G4
H2O
δ O-
H2O
υ O-H
H2O
υ O-H
CH 4
δ C-H
CH 4
δ C-H
CH 4
υ C-H
CH 4
υ C-H
NH 3
δ N-H
NH 3
δ N-H
NH 3
υ N-H
NH 3
υ N-H
H2
υ H-H
1706
3814
3934
1381
1603
3087
3210
1138
1726
3485
3620
4523
2479
2480
2477
2478
1706
1702
1702
1703
3803
3800
3802
3801
3916
3915
3917
3916
1363
1370
1366
1382
1596
1598
1595
1597
3073
3078
3080
3072
3200
3203
3203
3193
1159
1150
1153
1157
1724
1721
1722
1725
3473
3478.
3474
3480
3606
3610
3606
3610
4550
4555
4555
4532
1418
1416
1418
1415
2481
2476
2472
2471
1705
1706
1702
1704
3808
3802
3809
380
3920
3915
3922
3921
1374
1371
1371
1370
1594
1594
1598
1598
3079
3077
3078
3078
3200
3202
3205
3205
1155
1153
1161
1157
1723
1721
1720
1724
3476
3476
3477
3480
3611
3606
3608
3612
4531
4554
4565
4541
643
645
649
647
1416
1416
1416
1419
2477
2477
2477
2483
1705
1702
1703
1705
3806
3808
3802
3811
3916
3921
3916
3923
1375
1375
1372
1378
1596
1598
1592
1592
3077
3081
3071
3073
3199
3203
3192
3193
1160
1153
1153
1171
1720
1725
1720
1720
3477
3478
3477
3482
3608
3609
3610
3614
4563
4545
4534
4528
654
651
654
651
1417
1417
1417
1417
2479
2478
2479
2479
1705
1709
1705
1708
3797
3805
3798
3804
3911
3920
3913
3918
1377
1376
1368
1368
1593
1593
1593
1593
3069
3068
3069
3068
3193
3192
3194
3192
1165
1170
1166
1163
1720
1723
1721
1723
3476
3474
3477
3469
3606
3605
3606
3609
4552
4553
4554
4527
H
Next, we look at the case of H 2 O molecule, there are three characteristic vibrational
modes ν1 = 1706cm-1, ν2 = 3814cm-1, and ν3 = 3934cm-1 which corresponds to O-H
bending and stretching. Our results indicate that the CNSs-H 2 O complexes, though
there is no significant change in the O-H bending frequency, O-H stretching
frequencies depict a red shift. For CH 4 molecule there are two C-H stretching and two
bending modes observed for the free molecule. It is clear from the Table 4.5 that these
frequencies show a red shift on binding with the carbon materials. In the case of NH 3
molecule, while the N-H bending frequency show a blue shift, the rest of the
89
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
vibrational modes show a red shift upon binding with the CNSs as given in the Table
4.5. The characteristic vibration mode of the H 2 molecule which arises due to the H-H
stretching at 4523 cm-1 in the free molecule exhibits a blue shift on binding with the
carbon materials.
4.4.4 Polarizability and frontier orbital energy
The primary requisite for a material to perform as a sensor is to undergo a change in
their physical property on interacting with the analyte. Such changes can be
monitored and recorded to determine the presence of the analyte.
CO 2
H2O
CH 4
NH 3
H2
Armchair
CNT (4,4)
CNT (5,5)
CNT (6,6)
CNT (7,7)
727.82
970.65
1196.33
1466.85
739.28
982.50
1208.28
1478.87
733.98
976.87
1202.84
1473.49
740.87
984.32
1210.20
1480.85
736.70
979.64
1205.26
1475.91
732.60
975.87
1201.45
1471.50
Zigzag
CNT (8,0)
CNT (10,0)
CNT (12,0)
CNT (14,0)
942.10
1235.52
1490.15
1779.35
952.62
1247.42
1501.59
1796.31
949.64
1242.83
1501.63
1797.54
954.66
1249.32
1503.82
1793.23
951.32
1244.54
1499.13
1788.39
948.27
1241.02
1495.45
1782.33
CNT (4,2)
CNT (6,3)
CNT (8,4)
CNT (10,5)
569.29
841.53
1307.38
1826.61
578.91
853.37
1319.70
1838.38
574.68
847.93
1314.16
1833.05
582.05
855.53
1322.09
1840.60
577.56
850.64
1316.19
1835.41
573.69
846.61
1312.25
1831.18
GNR1
GNR2
1862.88
2870.89
1869.68
2877.31
1865.38
2873.78
1870.42
2875.63
1866.36
2874.89
1865.75
2873.73
GNR3
GNR4
4071.56
5538.41
4077.99
5544.43
4074.54
5527.26
4078.55
5543.98
4075.42
5542.21
4072.62
5541.22
Graphene
Parent
Chiral
Table 4.6: Polarizability (au) of the CNSs and the CNSs-gas molecule complexes at
M06-2X/6-31G* level
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Small Molecules Interactions with Carbon Nanostructures
Chapter 4
In order to notice such depiction in the case of carbon materials, we have calculated
the polarizability and frontier orbital energy of the carbon materials both in the free
state and also in the complexed state. Polarizability is considered to be the ability of a
molecule to respond to an external electric field. The molecular polarizability of all
the systems considered have been computed and given in the Table 4.6.
Parent
CO 2
H2O
CH 4
NH 3
H2
Armchair
CNT (4,4)
CNT (5,5)
CNT (6,6)
CNT (7,7)
3.10
2.34
2.39
2.46
3.10
2.33
2.39
2.46
3.11
2.27
2.38
2.46
3.10
2.33
2.39
2.46
3.10
2.33
2.39
2.46
3.10
2.33
2.39
2.46
Zigzag
CNT (8,0)
CNT (10,0)
CNT (12,0)
CNT (14,0)
1.03
1.00
0.99
0.99
1.03
1.00
0.99
0.99
1.04
1.01
1.00
0.99
1.03
1.00
0.99
0.99
1.03
1.00
0.99
0.99
1.03
1.00
0.99
0.99
Chiral
CNT (4,2)
CNT (6,3)
CNT (8,4)
CNT (10,5)
2.36
3.16
1.92
2.57
2.37
3.16
1.92
2.57
2.37
3.16
1.92
2.56
2.37
3.15
1.92
2.57
2.36
3.15
1.92
2.57
2.36
3.16
1.92
2.57
Graphene
Table 4.7: HOMO-LUMO energy gap (eV) of CNSs before and after complex
formation with the gas molecules M06-2X/6-311G** level
GNR1
GNR2
GNR3
GNR4
0.72
0.48
0.36
0.30
0.72
0.48
0.36
0.30
0.72
0.48
0.37
0.30
0.72
0.47
0.37
0.30
0.72
0.48
0.36
0.30
0.72
0.48
0.36
0.30
A cursory look at the values reveals that, the flat graphene has higher polarizability
than the curved CNTs. This observed trend explains the higher binding affinity of
graphene compared to the CNTs. Among the CNTs, zigzag CNTs possess the highest
polarizability than the armchair and the chiral counterparts. Our results indicate that
the polarizability of the carbon materials increases on binding with the gas molecules.
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Small Molecules Interactions with Carbon Nanostructures
Chapter 4
Because polarizability has an effect on the electronic response of the system, change
in polarizability may be used to monitor the presence of gas molecules. We have also
calculated the HOMO-LUMO energy gap of the carbon materials and their complexes
as shown in the Table 4.7. It has been shown from our computations that the energy
gap for graphene is lower than it for the CNTs. Zigzag CNTs possess the lowest
energy gap among the CNTs considered. Notably, there is no significant change in the
HOMO-LUMO energy gap of the carbon materials upon binding with the gas
molecules.
4.5 Conclusions
In this chapter, to investigate the feasibility of carbon materials as gas sensors, we
have studied the interaction of various gas molecules such as CO 2 , H 2 O, CH 4 , NH 3
and H 2 with CNTs and graphene using DFT. It has been shown from our results that
the order of binding of these gas molecules is H 2 O > CO 2 > NH 3 > CH 4 > H 2 . These
molecules are very weakly physisorbed on the surface of these CNSs and the binding
energy is independent of the type of the carbon materials. The weak adsorption of the
gas molecules facilitates the adsorption/desorption mechanism which is a primary
requirement for sensor process. The Mulliken charge analysis reveal that these gas
molecules act as charge donors to the carbon nanostructures and influence the
physical properties of the carbon materials which leads to the sensitivity. The shifts in
the vibrational frequencies of the gas molecules upon complex formation with various
CNSs have also been computed. Significant changes in the polarizability value have
been observed for the carbon materials on binding with the gas molecules which can
be further monitored to detect the presence of the analyte for sensor applications. It
has also been found that the HOMO-LUMO energy gap of the CNSs remain
92
Small Molecules Interactions with Carbon Nanostructures
Chapter 4
unaffected by the binding of these gas molecules. We hope that our results would be
helpful to develop novel carbon material based sensors.
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Small Molecules Interactions with Carbon Nanostructures
94
Chapter 4