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1. INTRODUCTION

Carbon nanotubes attracted a great interest due to their unique mechanical, electrical

and chemical properties since their discovery. They are shown as one of the most

promising material for applications in materials science and medicinal chemistry. Carbon

nanotubes are arrangements of carbon hexagons that are formed into tiny tubes having

diameter range from a few angstroms to tens of nanometers and can have lengths of up to

several centimeters. As developing the nanotechnology, carbon nanotubes are one of the

most famous materials used as prototype of confinement system to investigate by means of

molecular dynamics simulation methods the adsorption properties of H2, H2O and CO2.

CO2 is known as the most important fluid in biological, geological and chemical systems

after water. Because it has an important role in cellular respiration, it is utilized by plants

during photosynthesis, it can be produced by lots of human activities and it is one of the

most important green house gases. Therefore, molecular simulations of confined CO2 in

carbon nanotubes are necessary to improve the solutions for these problems.

In this study, the aim was to analyze the behavior of CO2 molecules confined in

single walled carbon nanotubes (SWNTs). To be able to accomplish this purpose, three

different simulations groups were prepared. In the first group four periodic computational

boxes were filled with CO2 and four SWNTs in different sizes were placed in those boxes

separately. In the second group, effect of SWNT amount on CO2 behavior was observed by

running simulations with two and four SWNTs in same size. Finally, as a third group,

behavior of supercritical CO2 was examined with one SWNT inside the box.

This report contains theory, molecular dynamics simulations, results and discussion

parts. In theory, structures, properties production techniques, of carbon nanotubes and

molecular dynamics approach was explained in detail. Molecular dynamics simulation

methods and parameters used and reasons were described in the molecular dynamics

simulations part. Corresponding results, relevant figures, comparisons and related

comments among the simulation groups were represented in the results and discussion part.

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2. THEORY

2.1. CARBON NANOTUBES

Carbon can form diamond which is known as one of the hardest materials and it can

also form one of the softest materials, graphite. In graphite, the carbon atoms are only

bonded in two dimensions. The carbon atoms form layered sheets of hexagons and those

layers may slip off one another easily because there are no bonds between the layers [1].

Figure 2.1. Representation of layered graphite sheets [1]

The properties of each material change according to arrangement of atoms. The

carbon atoms which form tiny tubes called as carbon nanotubes, and they are twice as

strong as steel but weigh six times less [1]. The first carbon fibers in nanodimensions were

discovered in 1976 by Endo [2] who synthesized carbon filaments of 7 nm in diameter

using a vapor-growth technique. But those filaments were not defined as carbon nanotubes

(CNTs) until Sumio Iijima’s report in 1991 [3] which brought CNTs to the attention of the

scientific community [4]. At the same time, researchers at the Institute of Chemical

Physics in Moscow also independently discovered carbon nanotubes and nanotube bundles

having a much smaller length-to-diameter ratio. The shape of these nanotubes led the

Russian researchers to call them ‘barrelenes’ [5].

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A single-walled carbon nanotube can be visualized as a seamless cylinder formed by

a hexagonal graphite layer (see Figure 2.2.). A SWNT may grow as long as several

microns in length but also, only a few nm in diameter ranging from 0.4 to 3 nm making it a

perfect one-dimensional material [6]. The structure of a carbon nanotube is like a sheet of

graphite rolled up into a tube. Depending on the direction of chirality vector, nanotubes can

be classified as either zigzag, armchair or chiral. Different types of nanotubes have

different properties [1].

A nanotube can also contain multiple cylinders of different diameters nested inside

one another depending on the synthesis procedure. This type is called a multi-wall

nanotube (MWNT) and also known as ‘Russian dolls’. (MWNTs), as shown in Figure 2.2.,

are composed of a concentric arrangement of numerous SWNTs, often capped at their ends

by one half of a fullerene-like molecule. The distance between two layers in MWNTs is

0.34 nm. Multiwalled nanotubes can reach diameters of up to 200 nm. Other varieties of

nanotubes include ropes, bundles and arrays. [6]

Figure 2.2. Schematic representation of SWNT and MWNT [7]

2.2. THE STRUCTURE OF CARBON NANOTUBES

A carbon nanotube is based on a two-dimensional graphene sheet. The chiral vector

is defined on the hexagonal lattice as:

(2.1)

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where â1 and â2 are unit vectors, and n and m are integers. The chiral angle, θ, is measured

relative to the direction defined by â1. This diagram has been constructed for (n, m) = (4,

2), and the unit cell of this nanotube is bounded by OAB'B. To form the nanotube, it can be

imagined that this cell is rolled up so that O meets A and B meets B', and the two ends are

capped with half of a fullerene molecule. Different types of carbon nanotubes have

different values of n and m [5].

Figure 2.3. a) Schematic of 2-D graphene sheet illustrating lattice vectors a1 and a2.

b) Possible vectors specified by the pairs of integers (n,m) for carbon nanotubes including

zigzag, armchair and chiral tubules [5]

Zigzag nanotubes correspond to (n, 0) or (0, m) and have a chiral angle of 0°,

armchair nanotubes have (n, n) and a chiral angle of 30°, while chiral nanotubes have

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general (n, m) values and a chiral angle of between 0° and 30°. According the theory,

nanotubes can either be metallic (green circles) or semiconducting (blue circles) [5]. In

Cartesian coordinates;

x y(2.2)

x y (2.3)

Where a is the nearest-neighbour carbon-carbon spacing of about 1.4Å, and x and y

are unit vectors in the x- and y-directions respectively [8].

Figure 2.4. Structure of armchair, zigzag and chiral carbon nanotubes [9]

The properties of nanotubes are determined by their diameter and chiral angle, both

of which depend on n and m. The diameter, dt, is simply the length of the chiral vector

divided by 0.25, and it was found that;

(2.4)

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where ac-c is the distance between neighboring carbon atoms in the flat sheet. In turn, the

chiral angle is given by;

(2.5)

A SWNT is considered metallic if the value is divisible by three. Otherwise,

the nanotube is semiconducting. Consequently, when tubes are formed with random values

of n and m, it would be expected that two-thirds of nanotubes would be semi-conducting,

while the other third would be metallic, which happens to be the case [10].

The average diameter of a SWNT is 1.2 nm. However, nanotubes can vary in size,

and they aren't always perfectly cylindrical. The larger nanotubes, such as a (20, 20) tube,

tend to bend under their own weight. The carbon bond length was first determined to be

1.42 Å [11] and later confirmed in 1998 [12]. The C-C tight bonding overlap energy is in

the order of 2.5 eV [12, 13].

2.3. PROPERTIES OF CARBON NANOTUBES

After the discovery of carbon nanotubes (CNTs) in 1991 [3], the world envisioned a

rapid growth of nanotube research. Both theoretical and experimental investigations

revealed that the unique structure of nanotubes provide remarkable mechanical, electronic,

and optical properties [6].

Nanotubes have been known to be up to one hundred times as strong as steel and

almost two millimeters long [14] having a hemispherical "cap" at each end of the cylinder.

They are light, flexible, thermally stabile, and are chemically inert and have the ability to

be either metallic or semi-conducting depending on the "twist" of the tube [5].

2.3.1. The Strength of Nanotubes

The carbon nanotube is the strongest and stiffest material known. Theoretically,

nanotubes have a tensile strength of 130-150 GPa. In the lab, individual tubes have been

produced with a tensile strength of up to 63 GPa stronger than diamond, Kevlar, or spider's

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silk with a Young's Modulus of over 1000 GPa, these tubes don't bend under the pressure

either [15].

The strength of the nanotube compared to other forms of carbon lies in its chemical

bonds. Nanotubes are composed of sp2 carbon bonds, forming a hexagonal lattice. These

are stronger than the sp3 bonds which form the cubic structure of diamond [15].

It is unknown whether macro scale nanomaterials can be made with the strength of

individual tubes. When nanotubes are combined with polymers they form super-strong

composites making projects like the space elevator closer to reality. However, these

materials still can't match the strength of the individual nanotube [15].

Table 2.1. Comparison of CNT strength: carbon nanotube-enhanced composite formed by

embedding carbon nanotubes in a polymer matrix [15]

MaterialYoung's Modulus

(GPa)Tensile Strength

(Gpa)Density (g/cm3)

SWNT 1054 150 1.4

MWNT 1200 150 2.6

Diamond 600 130 3.5

Kevlar 186 3.6 7.8

Steel 208 1.0 7.8

Wood 16 0.008 0.6

The extraordinary mechanical properties of carbon nanotubes arise from σ bonds

between the carbon atoms. Experimental measurements together with theoretical

calculations show that nanotubes exhibit the highest Young’s modulus (elastic modulus E)

and tensile strength among known materials. The elastic modulus of single walled CNTs

was reported to be can be up to 1.5 TPa [16]. The ultimate strength of CNTs, ranging from

13 to 150 GPa, surpasses that of materials well-known for their high tensile strength, such

as steel and synthetic fibers [17, 18]. Unlike electrical properties, Young’s modulus of

CNTs is independent of tube chirality, although it depends on tube diameter [19].

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Figure 2.5. Illustration of the elastic modulus and strength of carbon nanotubes [6] and

common tissue engineering materials: PGA, PLLA, bone, titanium, steel [4]

The elastic response of a nanotube to deformation is also outstanding. Both,

theoretical and experimental studies revealed that CNTs can sustain up to 15 per cent of

tensile strain before fracture. CNTs are shown to be very flexible with a reversible bending

up to angles of 110o and 120o for MWNTs and SWNTs, respectively [20].

The extraordinary mechanical properties of CNTs have met great interest in the

application of nanotubes in tissue engineering. Properties like the high tensile strength and

excellent flexibility give them superiority over popular materials used (PGA, PLLA,

titanium, steel) and make them ideal candidates for the production of lightweight, high-

strength bone materials. For comparison, Figure 2.5., shows the elastic modulus and

strength of CNTs, bone, and several other common materials used in one-tissue

engineering.

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Table 2.2. Physical Properties of SWNT [21]

Equilibrium Structure Optical Properties

Average Diameter of SWNT's

1.2-1.4 nm Fundamental Gap

Distance from opposite Carbon Atoms (Line 1)

2.83 Å

For (n, m); n-m is divisible by 3 [Metallic]

0 eV

For (n, m); n-m is not divisible by 3 [Semi-Conducting]

~ 0.5 eV

Analogous Carbon Atom Separation

(Line 2)2.46 Å Electrical Transport

Parallel Carbon Bond Separation

(Line 3)2.45 Å Conductance Quantization n x (12.9 k)-1

Carbon Bond Length (Line 4)

1.42 ÅResistivity 4-Oct-cm

C - C Tight Bonding Overlap Energy

~ 2.5 eV

Group Symmetry (10, 10)

C5V

Maximum Current Density 1013 A/m2

Lattice: Bundles of Ropes of Nanotubes

Triangular Lattice (2D)

Lattice Constant 17 ÅThermal Conductivity ~ 2000 W/m/K

Lattice Parameter(10, 10) Armchair 16.78 Å

Phonon Mean Free Path ~ 100 nm(17, 0) Zigzag 16.52 Å(12, 6) Chiral 16.52 Å

Relaxation Time ~ 10-11 sDensity

(10, 10) Armchair 1.33 g/cm3 Elastic Behavior(17, 0) Zigzag 1.34 g/cm3

Young's Modulus (SWNT) ~ 1 TPa(12, 6) Chiral 1.40 g/cm3

Interlayer SpacingYoung's Modulus (MWNT) 1.28 TPa

(n, n) Armchair 3.38 Å

(n, 0) Zigzag 3.41 ÅMaximum Tensile Strength ~30 GPa

(2n, n) Chiral 3.39 Å

2.3.2. Electrical Properties of Carbon Nanotubes

The electronic structure of carbon nanotubes is determined by their chirality and

diameter, or, in other words, by their chiral vector . CNTs are conductive if the integers

are: (armchair) and (where i is an integer). In all other cases, they are

semiconducting. The energy band gap Eg for semiconducting nanotubes is given by [22]:

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(2.6)

where, eV is the nearest-neighbour overlap integral [14], the nearest

neighbor C-C distance (~ 1.42 Å), and d is the diameter of the nanotube. Thus, the Eg of a

1 nm wide semiconducting tube is roughly 0.7 eV to 0.9 eV [22]. It has been

experimentally verified that SWNTs and MWNTs behave like quantum wires because of

the confinement effect on the tube circumference [4]. The conductance for a carbon

nanotube is given by [2]:

(2.7)

where, is the quantum unit of conductance. M is the apparent

number of conducting channels including electron-electron coupling and intertube

coupling effects in addition to intrinsic channels (M equals 2 for perfect SWNTs), e is the

electron charge, and h is Planck’s constant.

2.3.3. Chemical Properties of Carbon Nanotubes

Small radius, large specific surfaces, and σ - π rehybridization make carbon

nanotubes very attractive for chemical and biological applications because of their strong

sensitivity to chemical or environmental interactions [22]. The chemical functionalization

of carbon nanotubes is a very promising target since it can improve solubility,

processibility, and moreover allows the exceptional properties of carbon nanotubes to be

combined with those of other types of materials. Up to now, several methods for the

functionalization of CNTs have been developed. These methods include covalent

functionalization of sidewalls, noncovalent exohedral functionalization (for example with

surfactants and polymers), endohedral fictionalization, and defect functionalization as

shown in Figure 2.6. Chemical groups on CNTs can serve as anchor groups for further

fictionalization, e.g. with biological and bio-active species such as proteins or nucleic acids

[23, 24]. This bioconjugation is especially attractive for biomedical applications of carbon

nanotubes.

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Figure 2.6. Various functionalizations of carbon nanotubes: (A) covalentsidewall

functionalization, (B) defect-group functionalization, (C) noncovalent exohedral

functionalization with polymers, (D) endohedral functionalization with, for example, C60,

(E) noncovalent exohedral functionalization with surfactants [4]

2.4. PRODUCTION OF CARBON NANOTUBES

Carbon nanotubes are generally produced by three main techniques, arc discharge,

laser ablation and chemical vapour deposition. In arc discharge, a vapour is created by an

arc discharge between two carbon electrodes with or without catalyst. Nanotubes self-

assemble from the resulting carbon vapour. In the laser ablation technique, a high-power

laser beam impinges on a volume of carbon - containing feedstock gas (methane or carbon

monoxide). At the moment, laser ablation produces a small amount of clean nanotubes,

whereas arc discharge methods generally produce large quantities of impure material. In

general, chemical vapour deposition (CVD) results in MWNTs or poor quality SWNTs.

The SWNTs produced with CVD have a large diameter range, which can be poorly

controlled. But on the other hand, this method is very easy to scale up, what favors

commercial production [25].

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2.4.1. Growth Mechanism

The way in which nanotubes are formed is not exactly known. The growth

mechanism is still a subject of controversy, and more than one mechanism might be

operative during the formation of CNTs. One of the mechanisms consists out of three

steps. First a precursor to the formation of nanotubes and fullerenes, C2, is formed on the

surface of the metal catalyst particle. From this metastable carbide particle, a rodlike

carbon is formed rapidly. Secondly there is a slow graphitisation of its wall. This

mechanism is based on in-situ TEM observations [26].

The exact atmospheric conditions depend on the technique used, later on; these will

be explained for each technique as they are specific for a technique. The actual growth of

the nanotube seems to be the same for all techniques mentioned.

Figure 2.7. Visualization of a possible carbon nanotube growth mechanism. [25]

There are several theories on the exact growth mechanism for nanotubes. One theory

[27] postulates that metal catalyst particles are floating or are supported on graphite or

another substrate. It presumes that the catalyst particles are spherical or pear-shaped, in

which case the deposition will take place on only one half of the surface (this is the lower

curvature side for the pear shaped particles). The carbon diffuses along the concentration

gradient and precipitates on the opposite half, around and below the bisecting diameter.

However, it does not precipitate from the apex of the hemisphere, which accounts for the

hollow core that is characteristic of these filaments. For supported metals, filaments can

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form either by "extrusion (also known as base growth)" in which the nanotube grows

upwards from the metal particles that remain attached to the substrate, or the particles

detach and move at the head of the growing nanotube, labeled "tip-growth". Depending on

the size of the catalyst particles, SWNT or MWNT are grown. In arc discharge, if no

catalyst is present in the graphite, MWNT will be grown on the C2-particles that are formed

in the plasma. [25]

2.4.2. Arc Discharge Method

The carbon arc discharge method, initially used for producing C60 fullerenes, is the

most common and perhaps easiest way to produce carbon nanotubes as it is rather simple

to undertake. However, it is a technique that produces a mixture of components and

requires separating nanotubes from the soot and the catalytic metals present in the crude

product.

This method creates nanotubes through arc-vaporization of two carbon rods placed

end to end, separated by approximately 1mm, in an enclosure that is usually filled with

inert gas (helium, argon) at low pressure (between 50 and 700 mbar). Recent investigations

have shown that it is also possible to create nanotubes with the arc method in liquid

nitrogen [28]. A direct current of 50 to 100 Å driven by approximately 20 V creates a high

temperature discharge between the two electrodes. The discharge vaporizes one of the

carbon rods and forms a small rod shaped deposit on the other rod. Producing nanotubes in

high yield depends on the uniformity of the plasma arc and the temperature of the deposit

form on the carbon electrode [25].

Insight in the growth mechanism is increasing and measurements have shown that

different diameter distributions have been found depending on the mixture of helium and

argon. These mixtures have different diffusions coefficients and thermal conductivities.

These properties affect the speed with which the carbon and catalyst molecules diffuse and

cool, which in turn influence nanotube diameter in the arc process. This implies that single-

layer tubules nucleate and grow on metal particles in different sizes depending on the

quenching rate in the plasma and it suggests that temperature and carbon and metal catalyst

densities affect the diameter distribution of nanotubes [25].

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Depending on the exact technique, it is possible to selectively grow SWNTs or

MWNTs, which is shown in Figure 2.8. Two distinct methods of synthesis can be

performed with the arc discharge apparatus.

Figure 2.8. Experimental setup of an arc discharge apparatus

2.4.3. SWNT versus MWNT

The condensates obtained by laser ablation are contaminated with carbon nanotubes

and carbon nanoparticles. In the case of pure graphite electrodes, MWNTs would be

synthesized, but uniform SWNTs could be synthesized if a mixture of graphite with Co,

Ni, Fe or Y was used instead of pure graphite. SWNTs synthesized this way exist as

'ropes', see Figure 2.9. Laser vaporization results in a higher yield for SWNT synthesis and

the nanotubes have better properties and a narrower size distribution than SWNTs

produced by arc-discharge. Nanotubes produced by laser ablation are purer (up to about 90

per cent purity) than those produced in the arc discharge process. The Ni/Y mixture

catalyst (Ni/Y is 4.2/1) gave the best yield [25].

The size of the SWNTs ranges from 1-2 nm, for example the Ni/Co catalyst with a

pulsed laser at 1470 °C gives SWNTs with a diameter of 1.3-1.4 nm [30]. In case of a

continuous laser at 1200 °C and Ni/Y catalyst (Ni/Y is 2:0.5 at. per cent), SWNTs with an

average diameter of 1.4 nm were formed with 20-30 per cent yield, as shown Figure 2.9.

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Figure 2.9. TEM images of a bundle of SWNTs catalyzed by Ni/Y (2:0.5 at. per cent)

mixture, produced with a continuous laser [29]

Table 2.3. A summary of the major production methods and their efficiency [24]

Method Arc discharge method Chemical vapor deposition Laser ablation (vaporization)

WhoEbbesen and Ajayan, NEC, Japan 1992 [30]

Endo, Shinshu University, Nagano, Japan [31]

Smalley, Rice, 1995 [32]

How

Connect two graphite rods to a power supply,

place them a few millimetres apart, and

throw the switch. At 100 amps, carbon vaporises and forms a hot plasma.

Place substrate in oven, heat to 600 oC, and slowly add a

carbon-bearing gas such as methane. As gas decomposes it frees up carbon atoms, which recombine in the form of NTs

Blast graphite with intense laser pulses; use the laser pulses rather than electricity to generate carbon gas from which the NTs form; try various conditions until hit on one that produces prodigious amounts

of SWNTs

Typical yield (%)

30 to 90 20 to 100 Up to 70

SWNTShort tubes with

diameters of 0.6-1.4 nmLong tubes with diameters

ranging from 0.6-4 nm

Long bundles of tubes (5-20 microns), with individual diameter

from 1-2 nm.

MWNT

Short tubes with inner diameter of 1-3 nm and

outer diameter of approximately 10 nm

Long tubes with diameter ranging from 10-240 nm

Not very much interest in this technique, as it is too expensive, but MWNT synthesis is possible.

Pro

SWNTs have few structural defects; MWNTs without catalyst, not too

expensive, open air synthesis possible

Easiest to scale up to industrial production; long length, simple

process, SWNT diameter controllable, quite pure

Primarily SWNTs, with good diameter control and few defects. The reaction product is quite pure.

Con

Tubes tend to be short with random sizes and

directions; often needs a lot of purification

NTs are usually MWNTs and often riddled with defects

Costly technique, because it requires expensive lasers and high

power requirement, but is improving

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2.5. SUPERCRITICAL FLUIDS

Supercritical fluids are highly compressed gases which combine properties of gases

and liquids in an intriguing manner. Fluids such as supercritical xenon, ethane and carbon

dioxide offer a range of unusual chemical possibilities in both synthetic and analytical

chemistry. The use of supercritical CO2 (scCO2) is explored as an environmentally

acceptable alternative to conventional solvents for reaction chemistry, so called "Clean

Technology". In addition, supercritical fluids can lead to reactions which are difficult or

even impossible to achieve in conventional solvents [34].

The definition of a supercritical fluid usually begins with a phase diagram, which

defines the critical temperature and pressure of a substance. (CO2 ; Tc = 31.1 °C, Pc = 73.8

bar) [35].

2.6. MOLECULAR DYNAMICS

Understanding the properties of assemblies of molecules in terms of their structure

and the microscopic interactions between them serves as a complement to conventional

experiments, enabling us to learn something new, something that cannot be found out in

other ways. The two main families of simulation technique are molecular dynamics (MD)

and Monte Carlo (MC); additionally, there is a whole range of hybrid techniques which

combine features from both. The obvious advantage of MD over MC is that it gives a route

to dynamical properties of the system: transport coefficients, time-dependent responses to

perturbations, rheological properties and spectra [36].

Computer simulations act as a bridge (see Figure 2.10.) between microscopic length

and time scales and the macroscopic world of the laboratory. It can be provided a guess at

the interactions between molecules, and obtain exact predictions of bulk properties. At the

same time, the hidden detail behind bulk measurements can be revealed. Simulations act as

a bridge in another sense, between theory and experiment. It may be tested a theory by

conducting a simulation using the same model and the model may be tested by comparing

with experimental results. Also, simulations on the computer that are difficult or

impossible in the laboratory (for example, working at extremes of temperature or pressure)

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may be carried out. Aim of so-called ab initio molecular dynamics is to reduce the amount

of fitting and guesswork in this process to a minimum. When it comes to aims of this kind,

it is not necessary to have a perfectly realistic molecular model; one that contains the

essential physics may be quite suitable [36].

Figure 2.10. Simulations as a bridge between (a) microscopic and macroscopic. (b) Theory

and experiment [36]

Molecular dynamics simulation consists of the numerical, step-by-step, solution of

the classical equations of motion, which for a simple atomic system may be written:

(2.8)

For this purpose it is need to be able to calculate the forces fi acting on the atoms, and

these are usually derived from a potential energy U(rN), where rN = (r1, r2,…,rN) represents

the complete set of 3N atomic coordinates [36].

Molecular simulations are almost invariably conducted in the context of an

ensemble. An ensemble can be regarded as an imaginary collection of a very large number

of systems in different quantum states with common microscopic attributes. For instance,

each system of the ensemble must have the same temperature, pressure and number of

molecules as the real system it represents. The choice of ensemble determines which

thermodynamic properties can be evaluated and it also governs the overall simulation

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algorithms. MC and MD algorithms for a specified ensemble are very different, reflecting

fundamental differences in the two simulation methods [37].

Typical uses of molecular dynamics include searching the conformational space of

alternative amino acid side chains in specific mutation studies, identifying likely

conformational states for highly flexible polymers or for flexible regions of

macromolecules such as protein loops, calculating free energies binding including

solvation and entropy effects, probing the locations, conformations and motions of

molecules on catalyst surfaces and running diffusion calculations [37].

2.6.1. Energy Minimization

A general minimization process contains two steps as energy evaluation and

conformation adjustment. Minimization of a model is also done in two steps. First, the

energy expression (an equation describing the energy of the system as a function of its

coordinates) must be defined and evaluated for a given conformation. Energy expressions

may be defined that include external restraining terms to tend the minimization, in addition

to the energy terms. Next, the conformation is adjusted to lower the value of the energy

expression. A minimum may be found after one adjustment or may require many

thousands of iterations, depending on the nature of the algorithm, the form of the energy

expression, and the size of the model. The efficiency of the minimization is therefore

judged by both the time needed to evaluate the energy expression and the number of

structural adjustments (iterations) needed to converge to the minimum [38].

Energy minimization is used for optimizing initial geometries of models constructed

in a molecular modeling program such as Cerius2 [39] or Insight®. It repairs poor

geometries occurring at splice points during homology building of protein structures and

maps the energy barriers for geometric distortions and conformational transitions using

torsion forcing to obtain Ramachandran type contour plots for protein or RIS statistical

weights for polymers. It also evaluates whether a molecule can adopt a template

conformation consistent with a pharmacophoric or catalytic site model which is known as

template forcing [38].

2.6.2. Simple Thermodynamic Averages

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Energy: The total energy (E) or Hamiltonian (H) of the ensemble can be obtained

from the ensemble averages of kinetic (Ekin) and potential energies (Epot).

(2.9)

The kinetic energy can be evaluated from the individual momenta of the particles and

the potential energy is the sum of the interparticle interactions which are usually calculated

by assuming a particular intermolecular function.

Temperature: The temperature can be obtained from the virial theorem. In terms of

generalized momenta (pk), the theorem can be expressed as:

(2.10)

For N atoms, each with three degrees of freedom, the following relation can be

obtained.

(2.11)

Alternatively, it can be considered that T to be the average of instantaneous

temperature contributions (t) [37].

(2.12)

2.6.3. Canonical (NVT) Ensemble

For generating a canonical ensemble, the number of particles, volume and

temperature should be constant and there are not so much different options for that. The

simplest method to make temperature constant includes velocity scaling or heat-bath

coupling. Alternatively, thermostats of Andersen [40], Nosé [41], Hoover [42] or a general

constraint approach can be used. These latter alternatives involve modifying the equation

of motion [37].

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Andersen [40] proposed an alternative to velocity scaling which combines molecular

dynamics with stochastic processes and guarantees a canonical distribution. At constant

temperature, the energy of a system of N particles must fluctuate. This fluctuation can be

introduced by changing the kinetic energy via periodic stochastic collisions. At the outset

of the simulation, the temperature (T) and the frequency (ν) of stochastic collisions are

specified. At any time interval (Δt), the probability that a particular particle is involved in a

stochastic collisions is νΔt [37]. A suitable value of ν is:

(2.13)

where νc is the collision frequency.

During the simulation, random numbers can be used to determine which particles

undergo stochastic collision at any small time interval. The simulation proceeds as follows.

Initial values of positions and momenta are chosen and the equations of motion are

integrated in the normal way until the time is reached for the first stochastic collision. The

momentum of the particle chosen for the stochastic collision is chosen randomly from a

Boltzmann distribution at temperature T. The collision does not affect any of the other

particles and the Hamiltonian equations for the entire particles are integrated until the next

stochastic collision occurs. The process is then repeated. [37]

2.7. MOLECULAR INTERACTIONS

A molecular dynamics simulation determines the individual forces experienced by

each molecule. This force is used to determine new molecular coordinates in accordance

with the equations of motion and evaluating the effect of molecular interaction is the most

computational time consuming step and as such, it governs the order of the overall

algorithms.

In principle, for a system of N molecules, the order of the algorithm scales as Nm

where m is the number of interactions that are included. If only the distinguishable

interactions are considered, calculations are required for each configuration.

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Molecular forces can be characterized as either short-range or long-range and

different techniques are required to simulate both types of properties. A long-range force is

defined as one which falls off no faster than r-d where d is the dimensionality of the system.

Typically, ion-ion and dipole-dipole potentials are proportional to r-1 and r-3, respectively.

Dispersion and repulsion are examples of short-range forces.

Many computation-saving devices can be employed to calculate short-range

interactions such as periodic boundary conditions and neighboring lists but, calculating

long-range interaction requires special methods such as Ewald sum, reaction field, and

particle-mesh methods, because the effect of long range interaction extends well past half

the length of the simulation box [37].

2.7.1. Non-bonded Interactions

The part of the potential energy Unon-bonded representing non-bonded interactions

between atoms is traditionally split into 1-body, 2-body, 3-body . . . terms:

(2.14)

The u(r) term represents an externally applied potential field or the effects of the

container walls; it is usually dropped for fully periodic simulations of bulk systems. Also,

it is usual to concentrate on the pair potential v (ri; rj) = v (rij) and neglect three-body (and

higher order) interactions. There is an extensive literature on the way these potentials are

determined experimentally, or modeled theoretically [43-46].

Differentiable pair-potentials (although discontinuous potentials such as hard spheres

and spheroids have also played a role). The Lennard-Jones potential is the most commonly

used form:

(2.15)

22

With two parameters: σ, the diameter, and ε, the well depth. This potential was used,

for instance, in the earliest studies of the properties of liquid argon [47-48]. For

applications in which attractive interactions are of less concern than the excluded volume

effects which dictate molecular packing, the potential may be truncated at the position of

its minimum, and shifted upwards to give what is usually termed the WCA model [49]. If

electrostatic charges are present, we added the appropriate Coulomb potentials:

(2.16)

where Q1 and Q2 are the charges and is the permittivity of free space.

2.7.2. Bonded interactions

For molecular systems, it is simply built the molecules out of site-site potentials of

the form of Equation 2.15 or similar. Typically, a single-molecule quantum-chemical

calculation may be used to estimate the electron density throughout the molecule, which

may then be modeled by a distribution of partial charges via Equation 2.16, or more

accurately by a distribution of electrostatic multipoles [46, 50]. For molecules it should

also be considered the intramolecular bonding interactions. The simplest molecular model

includes terms of the following kind:

(2.17a)

(2.17b)

(2.17c)

23

Figure 2.11. Geometry of a simple chain molecule, illustrating the definition of interatomic

distance r23, bend angle θ234, and torsion angle ϕ1234 [36]

Equation 2.17a shows the interaction between pairs of bonded atoms which can be

defined as bond stretching. Equation 2.17b is for angle bending which is deviation of

angles from the reference angle θ0 and it is calculated by the total value of angle between

three atoms 2-3-4 which illustrated in Figure 2.11. Another force that should be taken

account as bonding interactions is torsion terms which define the energy change due to

bond rotations. Equation 2.17c shows the calculation method of torsion angles and ω is the

torsion angle, Vn is the barrier height, γ is phase factor and n is the number of minimum

points in the function as the bond is rotated through 360o [36]. Sum of both intermolecular

and intramolecular interactions gives the total potential energy with respect to position.

(2.18)

2.8. PERIODIC BOUNDARY CONDITIONS

Small sample size means that, unless surface effects are of particular interest,

periodic boundary conditions need to be used. Consider 1,000 atoms arranged in a

cube. Nearly half the atoms are on the outer faces, and these will have a large

effect on the measured properties. Even for atoms, the surface atoms amount to

24

6 per cent of the total, which is still nontrivial. Surrounding the cube with replicas of itself

takes care of this problem. Provided the potential range is not too long, it can be adopted

the minimum image convention that each atom interacts with the nearest atom or image in

the periodic array. In the course of the simulation, if an atom leaves the basic simulation

box, attention can be switched to the incoming image. As a particle moves out of the

simulation box, an image particle moves in to replace it. In calculating particle interactions

within the cutoff range, both real and image neighbors are included. This is shown in

Figure 2.12. It is important to bear in mind the imposed artificial periodicity when

considering properties which are influenced by long-range correlations. Special attention

must be paid to the case where the potential range is not short: for example for charged and

dipolar systems [36].

Figure 2.12. Representation of periodic boundary conditions [36]

2.9. FORCE FIELDS

The force field contains the necessary building blocks for the calculations of energy

and force:

A list of atom types.

25

A list of atomic charges (if not included in the atom-type information).

Atom-typing rules.

Functional forms for the components of the energy expression.

Parameters for the function terms.

For some force fields, rules for generating parameters that have not been explicitly

defined.

For some force fields, a defined way of assigning functional forms and parameters.

This total package for the empirical fit to the potential energy surface is the force

field [32]. All the CFF force fields (CFF91, CFF, PCFF, COMPASS) have the same

functional form, differing mainly in the range of functional groups to which they were

parameterized (and therefore, having slightly different parameter values). These

differences can be examined by using the force field editing capabilities of Cerius2 [39] and

Insight® [38] or in the force field files. Atom equivalences for assignment of parameters to

atom types may also differ; as may some combination rules for non bond terms. Both

anharmonic diagonal terms and many cross terms are necessary for a good fit to a variety

of structures and relative energies, as well as to vibrational frequencies [38].

PCFF was developed based on CFF91 and is intended for application to polymers

and organic materials. It is useful for polycarbonates, melamine resins, polysaccharides,

other polymers, organic and inorganic materials, about 20 inorganic metals, as well as for

carbohydrates, lipids, and nucleic acids and also cohesive energies, mechanical properties,

compressibilities, heat capacities, elastic constants. It handles electron delocalization in

aromatic rings by means of a charge library rather than bond increments [38].

2.10. BEHAVIOR OF FLUIDS CONFINED IN CARBON NANOTUBES

With the development of high technology and modern research methods, chemical

engineering is intercrossing and co-developing with chemistry, physics, material science

and bi molecular technology and the new technologies in chemical industry include such

complex materials as polymer and electrolyte, such complex conditions as critical and

26

supercritical, and such complex phenomenon as interface, membrane solution. To achieve

the vision of completely automated product and process design in chemical industry, the

properties of the materials, the proper theoretical models and the mechanism of the

phenomena should be accurately obtained. The structural and dynamic properties of non-

scale confined fluids are one of the current research focuses, because they are closely

related with ion channels in life science, membrane separation in new style chemical

process and mesoporous catalyst synthesis in high-qualified materials manufacture [51].

As developing the nanotechnology, carbon nanotubes are usually being used as

prototype of confinement system to investigate with molecular simulation methods the

adsorption properties of H2, H2O and CO2. By experiments using relatively high purity

SWNTs, hydrogen storage capacity of about 8 per cent at 80 K and 120 atm was reported

[52]. Alexiadis and Kassinos [53] reported that one of the most striking consequences of

water confinement in CNTs is the complete change of certain of its properties. Because of

the importance of water in biology and medicine, a large number of articles have been

written about the interaction between H2O and CNT under different conditions. After

water, carbon dioxide is probably the most important fluid in biological, geological and

chemical systems. CO2, which is one of the green house gases, is released by human

activity due to fossil fuels usage. Vast majority of the studies is focused on diminishing the

CO2 release by absorbing it on a suitable material. Because of CO2 absorption ability on

CNTs [54], CNTs are very useful especially where CO2 emission level is high.

Due to importance of water and CO2 in each part of life some researches are

performed to compare their behavior by means of interaction with CNTs. Alexiadis and

Kassinos [55] reported that carbon dioxide molecules behave the opposite of water. CNTs

are, in fact, hydrophobic and the density of H2O molecules inside the nanotube is lower

than bulk. By increasing the diameter, however, the density rises and it reaches

asymptotically the value of bulk water. Carbon dioxide, on the other hand, accumulates

spontaneously in the nanotube and at 300 K and 10 bar the concentration can be more than

100 times higher inside than outside the CNT.

27

3. SIMULATION METHOD

As mentioned in theory part, the CO2 storage ability of CNTs is very important issue

especially in terms of global warming. Since industry is developing almost in each country,

CO2 release increases as well. Therefore some effective solutions are supposed to be

discovered to decrease the effect of CO2 emission. One of the ways proposed is the CO2

confinement in carbon nanotubes, but due to their nanoscale size and packed form, SWNTs

can not be seen alone, making it difficult and expensive to work with in laboratory

conditions. Molecular dynamics simulations were shown to be an alternative option.

In this project the behavior of CO2 confined in SWNTs and influence of size and

amount of single walled carbon nanotubes (SWNTs) on CO2 storage by means of

molecular dynamics was investigated. All molecular dynamics simulations were performed

by XenoView which was developed by Shenogin and Ozisik [57]. This program also

allows visualizing the atomistic simulations at different conditions and by using different

force fields.

Before getting started with the molecular dynamics part, all the systems were energy

minimized after all the molecules were packed into the simulation boxes. During the

preparation of SWNTs around - iterations of energy minimization were

performed. However, 100-200 iterations with 0 kcal/mol tolerance were sufficient enough

to minimize the energy for SWNT systems with CO2. After the completion of energy

minimization, molecular dynamics parameters were selected. For all the simulations, NVT

ensemble (constant volume and temperature) with Andersen thermostat were used to keep

the temperature of the system constant during the simulation and also periodic boundary

conditions were applied to all simulations. Time step (Δt) was set to 1 fs because above 1

fs, simulations were not stable enough. It was observed with a simulation which time step

was chosen as 2 fs and when the trajectory file was being visualized, system was not

running accurately, bonds lengths between two atoms were increasing and no observation

can be performed for this kind of a simulation. In addition, the reason not to chose time

step below 1 fs, for example 0.5 fs, is to save time. Because, as time step gets smaller, the

duration of simulation increases. Therefore, 1 fs was chosen as time step, instead of 2 fs

28

and 0.5 fs, to have most accurate results while saving time. Number of steps for simulation

was set from to which makes the total simulation time from 8 ns to 25 ns.

That total duration was decided by considering the time required for the simulation to

reach steady. PCFF was chosen as most appropriate force field for our systems and it was

used also to compare the results with previous SWNT/CO2 studies [49] which were

performed with AMBER and CHARMM.

In this work, (6,6), (8,8), (10,10), (16,16) armchair SWNTs were used to investigate

the influence of SWNT size on behavior of CO2 molecules at 300 K. When preparing the

simulations with CO2, in order to prevent the effect of pressure acting on molecules, the

bulk density (ρo) of CO2 molecules was kept constant around 0.04 nm-3. Bulk density is

measured in number of molecules per nm-3. Nanotube diameter d, length L, box size (H x H

x Z), number of CO2 molecules , and ratio between nanotube and box volume Vb/VCNT

are reported in Table 6.1.

Table 6.1 Parameters of first system (CNTs in different sizes)

(n,m) (6,6) (8,8) (10,10) (16,16)

d (Å) 8.0 10.7 13.6 21.4

L (Å) 30.2 39.9 48.4 76.3

NCNT 1 1 1 1

Z (Å) 200 260 300 400

H (Å) 150 160 180 300

189 288 408 1678

Vb/VCNT 2961 1857 1383 1319

ρo (nm-3) 0.042 0.043 0.042 0.046

Also, to figure out the effect of SWNT amount on behavior of CO2, (10,10) SWNT

simulations were repeated at 300 K with 2 and 4 SWNTs in the box as keeping the number

29

of CO2 molecules the same. In addition to CO2 and SWNT simulations, the behavior of

super critical CO2 confined in SWNT has also tried to investigate in 2 different box sizes at

400 K while keeping other parameters the same.

30

4. RESULTS AND DISCUSSION

This study focuses on the fluid behaviors confined in SWNT. CO2 was chosen as

fluid because of the health and environmental impact of CO2 especially as a one of the

most important green house gases, lots of studies are dedicated to improve the decrease

CO2 emission to the atmosphere. The ability of CO2 storage of carbon nanotubes makes

them one of the most promising materials. This study performed to find and optimum

configuration for CO2 storage in SWNT and to observe the behavior of CO2 in the

nanotubes.

Since the experimental studies in this area are very difficult to handle and also very

expensive, molecular dynamics (MD) approach was used in this research. For simulating

our systems, XenoView MD program was used with NVT ensemble (constant volume and

temperature) while using the Andersen thermostat to keep temperature the constant during

the simulation. Periodic boundary conditions were applied to all the simulations as well as

energy minimization. In addition, for all the simulations PCFF was chosen as force field

because its suitability for polymers and carbon related structures.

In this research, there were three main study groups. First simulation group was

prepared to observe the behavior of CO2 molecules when they are confined in nanotubes

which are different in diameter. These simulations were performed with (6,6), (8,8),

(10,10) and (16,16) armchair SWNTs to see the effect of SWNT size to CO2 behavior. The

parameters for this group are shown in Table 6.1. Second simulation group was prepared to

figure out the influence of the number of nanotube to the CO2 behavior. For this purpose,

two additional systems were prepared containing two and four (10,10) SWNTs to compare

with the simulation with single (10,10) nanotube which was performed in the first group.

Parameters for this group was the same with the first single (10,10) nanotube simulation to

make a reliable comparison. In addition to CO2 behavior, super critical CO2 behavior was

also in consideration. Therefore, a third simulation group was prepared including two

boxes in different dimensions and filled with super critical CO2 while putting the same

(10,10) nanotube used in previous simulation groups. The nanotube having same size was

used to be able to make comparison between systems with CO2 and supercritical CO2.

31

However in this case temperature of the system was chosen as 400 K due to properties of

super critical CO2. For all the simulations 1fs time step and 9Å cut-off radius was chosen

as MD parameters.

4.1 EFFECT OF SWNT SIZE ON CO2 BEHAVIOR

In order to observe the effect of SWNT size to CO2 behavior, 4 different simulations

were run with same bulk density but with different carbon nanotube sizes. As a first

simulation, (6,6) armchair SWNT was put in a simulation box whose dimensions are

shown in Table 6.1. with 189 CO2 molecules. This simulation was run about 15 ns and

after system reached the steady-state, then it was stopped. To investigate the behavior of

CO2 in the system, CO2 density inside carbon nanotube was plotted as a function of time.

Figure 4.1. Change in carbon dioxide density inside a (6,6) SWNT w.r.t. time

As it can be seen from Figure 4.1., at steady state, CO2 density inside SWNT is about

4.5 nm-3. At first sight, four horizontal lines attract the attention in some time intervals

because the density function behavior usually is expected as oscillations. In this case,

however, since nanotube size is very small, CO2 density inside nanotube remains constant

for a little bit long time and this makes those horizontal lines in the graph.

32

As shown in Figure 4.2, CO2 molecules inside (6,6) SWNT reside as a line, because

of intermolecular forces and some other CO2 molecules surround the external wall of

nanotube because of attractive forces between SWNT and CO2. In other words, (6,6)

nanotube has a diameter of approximately the same size of the C and O atoms. This

circumstance compels the CO2 molecules to align their O-C-O axis parallel to the nanotube

axis. The entrance in the nanotube is thus limited by geometrical consideration. Also, it

shows the carbon atoms tend to remain at the center and the O atoms near the walls. In

general both atoms show a strong interaction with the nanotube and carbon dioxide tends

to lie along the walls forming CO2 tubular layer all around the internal side. It can also be

observed that, cylinder shape of SWNT wasn’t damaged through the simulation because,

this nanotube is not a large one and it does not tend to bend as larger ones like (20,20)

mentioned in Section 2.2.

Figure 4.2 Finalized (6,6) SWNT simulation with CO2

As a second simulation, (8,8) SWNT was put in a simulation box which has

predefined size in Table 6.1. with 288 CO2 molecules. This simulation was run about 12 ns

and after system reached the steady-state, it was stopped. To be able to figure out the

behavior of CO2 in the system, change in CO2 density inside carbon nanotube was shown

with respect to time. In Figure 4.3, it is obvious that, density of CO2 molecules inside (8,8)

CNT increases slowly rather than (6,6) and it takes longer to reach the steady-state.

Because in the (6,6) simulation, there were less atoms than (8,8) and despite all the MD

parameters are the same for both simulation, it is easier and shorter to calculate all forces

between atoms and displacements of molecules.

33

Figure 4.3. Change in carbon dioxide density inside a (8,8) SWNT w.r.t. time

In the finalized snapshot of (8,8) simulation, it can be observed that intermolecular

forces between CNT and CO2 molecules increases. In this case CO2 molecules inside

nanotube do not appear as a line however, they appear as a ring shape. The reason for this

ring shape structure is, more CO2 molecules are entering into the carbon nanotube rather

than (6,6) and they can not be stay as one line because they have more space so, they

disperse through the nanotube according to inter and intramolecular forces. However, the

main reason for that ring shape structure is CNT-CO2 attraction is stronger than the CO2-

CO2 attraction. Therefore, all these reasons, forces, larger area and attractions etc. make a

ring shape CO2 structure in the nanotube.

In the (8,8) simulation, the CO2 molecules start to surround the external wall of

carbon nanotube more because of increase in intermolecular forces between nanotube and

fluid. And above that accumulation on the external wall of CNT, CO2 molecules are

observed as moving through an orbit around CNT and the reason for that kind of moving is

long range forces between CO2 and CNT which is smaller than CO2 molecules at the

external wall. The reason for CO2 molecules are not staying perpendicular to the nanotube

is the order parameters.

34

Figure 4.4. Finalized (8,8) SWNT simulation with CO2

As a third simulation (10,10) SWNT was put in a simulation box whose dimensions

are shown in Table 6.1. with 408 CO2 molecules in it. This simulation was run for 25 ns

and its density profile through the simulation is the following:

Figure 4.5. Change in carbon dioxide density inside a (10,10) SWNT w.r.t. time

The same comparison between (6,6) and (8,8) nanotube can being continued by

adding (10,10). It is so obvious that, the time that last for the (10,10) system to reach the

steady state in terms of CO2 density inside nanotube is longer than the first two simulations

as expected. This is again due to increase in the number of molecules in the system. In the

third simulation a ring shape structure of CO2 molecules inside nanotube was observed as

35

well. This time, however, the diameter of the ring shaped structure is larger than the

structure occurred in second simulation which performed with (8,8) SWNT. The reason is

again the CNT-CO2 attraction is stronger than the CO2-CO2 attraction so, CO2 molecules

have tendency to cover the internal walls of nanotube and empty the central part of the

CNT. Because of the diameter of (10,10) nanotube is larger than (8,8), the diameter of ring

shape structure is larger in (10,10) nanotube as well.

Figure 4.6. Finalized (10,10) SWNT simulation with CO2

As a fourth and last simulation to see the influence of SWNT size on CO 2 behavior,

(16,16) SWNT simulation was performed with 1678 CO2 molecules in the simulation box.

This simulation was run for about 10 ns. In the density profile (Figure 4.7.) the actual

steady state time is not clear but it is obvious that system is very close to steady state

because increase in density is very slow rather than the beginning of the simulation. This

system didn’t reach the steady state in terms of density inside (16,16) SWNT because lack

of time. However, still some important discussions can be performed on this simulation.

36

Figure 4.7. Change in carbon dioxide density inside a (16,16) SWNT w.r.t. time

First of all, the most obvious thing about this simulation which can be seen in Figure

4.8. that it has much more CO2 molecules in it rather than the previous smaller nanotubes

as expected. Since the diameter of this nanotube is larger than others, it has the ability to

store more CO2. Secondly, as mentioned in theory in Section 2.2, this nanotube has bended

under its own weight as expected. At the beginning of the simulation, it has a well cylinder

shape but as simulation runs, it started to bend. The third discussion about this simulation

is the structure of CO2 atoms in the nanotube and also around the external wall of it. It is so

interesting that at the beginning of the simulation, till about 3ns, the CO2 molecules inside

the nanotube are covering the internal wall of the nanotube and creating a ring shape

structure as the previous simulations. After 3-4 ns, however, as the density of CO2

molecules increases in the nanotube and they start to get together and form separate and

ordered lines in it. Also the CO2 molecules around the external wall of the nanotube they

have the same behavior as the ones inside of it. At the beginning of the simulation till 3-4

ns, they surround the nanotube and after that time, more CO2 molecules accumulate around

nanotube and they have ordered line shape. Both CO2 lines inside and outside of nanotube

were aligned as planes and those planes are located on the same axis.

37

Figure 4.8. Finalized (16,16) SWNT simulation with CO2

After making individual comparison between the simulations which contains same

bulk density but CNTs in different sizes, a comprehensive discussion can be made between

them.

Figure 4.9. Change in carbon dioxide density inside (6,6), (8,8), (10,10) and (16,16)

SWNT w.r.t. time

Since the aim of this section is to focus on the effect on SWNT size on CO2 behavior,

the density profile of all simulations were plotted in the same graph in Figure 4.9, and it

38

shows that density of CO2 in (8,8) nanotube is the highest one and in (16,16) nanotube is

the lowest one. This result shows us that for higher density inside CNT, we do not need

very large nanotubes but at the same time it should not be very small. Increase in density

continues till one point in terms of nanotube size, after that point it starts to decrease.

Figure 4.10. Relative carbon dioxide density (density in the nanotube/bulk density) versus

diameter at 5 atm and 300 K

This relation can be seen more clearly in the Figure 4.10. which was plotted by

dividing the density in nanotubes at steady state to their initial value (ρ/ρo). As nanotube

size increases the relative carbon dioxide density (density in the nanotube/ bulk density)

increases as well linearly and after reaching its maximum value it starts to decrease linearly

again but in slower fashion.

4.2 EFFECT OF SWNT AMOUNT ON CO2 BEHAVIOR

After nanotubes size, amount of nanotube is also can be considered as a factor that

affecting the CO2 behavior. For observing this relation, the same initial parameters with

(10,10) nanotube system was used but in this case 2 (10,10) SWNTs were places into the

simulation box just one nanotube instead. Bulk density was kept the same because the

nanotube volumes are very small compared to box volume and this change does not affect

39

the bulk density a lot. This simulation was run for about 10 ns and their density profiles in

the nanotubes are shown in the Figure 4.11.

Figure 4.11. Change in carbon dioxide density inside two (10,10) SWNT w.r.t. time

In this simulation, it is obvious that none of the carbon nanotubes obstruct the CO 2

catching ability of other. It can be just said that, density increment of first nanotube is

faster than the second one but, at some point very close to 10 ns, they have almost the same

density inside. When compared the first simulation which performed with a single

nanotube in the box with the same dimensions, the steady-state time is almost the same for

both simulations which means making the nanotube number twice in the simulation does

not affect the time that system needs to reach the steady-state. Also, this change doesn’t

affect the steady state density inside nanotubes.

As a third simulation, four (10,10) SWNT was placed into the simulation box again

which having the same parameters with the first two simulations and it was run for about

12 ns. In this simulation there were more atoms than other two so, even if the system could

not reach the steady state, it is obvious that the steady state time for this system will be

longer than the previous simulations. There is no specific increase or decrease in density

for the system having four nanotubes. Density values are not the same for the all nanotubes

in the system but, they are close to each other and towards the end of the simulation they

meet up on almost the same value.

40

Figure 4.12. Change in carbon dioxide density inside four (10,10) SWNT w.r.t. time

Figure 4.13 Change in density in (10,10) SWNTs for systems having one, two and four

nanotube

4.3. BEHAVIOR OF SUPERCRITICAL CO2 CONFINED IN SWNT

41

Beside the interaction between CO2 and SWNT, the interaction between supercritical

CO2 and SWNT also attracts a great interest. To observe this interplay, a simulation was

prepared with 531 CO2 molecules which makes the density of CO2 same as the super

critical CO2 (0.469 g/cm3). As the box size (30x30x100) Å is used and (10,10) SWNT was

used as nanotube also temperature is set to 400K as a difference from the previous

simulations because of the properties of supercritical CO2. The box size is not the same

with initial (10,10) nanotube simulations since, filling system with supercritical CO2

molecules means putting much more CO2 molecules than the other simulations which

performed with CO2 and it is a hard process because this procedure requires a very

powerful computer with a lot of time for creating system as well as requiring lots of time

for running the simulation. This simulation was run for approximately 6 ns and the steady

state was observed. The density profile of super critical CO2 molecules in the nanotube is

shown on the Figure 4.14.

Figure 4.14. Change in supercritical carbon dioxide density inside (10,10) SWNT w.r.t.

time with 30x30x100 box size

This system can be compared with the system which was run with 408 CO 2

molecules in a bigger box. While the density inside nanotube is about 10 nm -3 in this

simulation, in the other simulation with just CO2 molecules density is 5.5 nm-3. The

difference here is the bulk density is 5.9 nm-3 and in the nanotube, this density rises to 10

42

nm -3 which means it was twice. However, in the first simulation with CO2, the bulk density

was 0.042 nm-3 and in the nanotube the density of CO2 molecules was 5.5 nm-3 which

means the density inside nanotube is almost 100 times higher than bulk density.

As similar with the (16,16) nanotube system, at steady state the super critical CO2

molecules aligned in the box just behind the nanotube. This alignment is so clear in the

Figure 4.15. In this case (10,10) nanotube showed a bending behavior more than (16,16)

and the super critical CO2 molecules inside nanotube did not create a well shaped ring

structure and they didn’t have any aligned position as the molecules outside of the

nanotube as observed in previous (8,8) and (10,10) nanotube simulations.

Figure 4.15. Finalized (10,10) SWNT simulation with supercritical CO2 with 30x30x100

box size

Because of the periodic boundary conditions, when MD has started, as nanotube

moves in the box and since the dimensions of the box is not bigger than nanotube size,

some part of nanotube exiting the box and at the same time it enters to the box from the

other side and this makes the system to be seen as if there are two different nanotubes in

the box. Their interaction can easily be seen in the Figure 4.16. They cause to bend each

43

other and limiting their movements. Again, due to the periodic boundary conditions, even

if we put one nanotube to the system, in reality the system behaves as if there are other

boxes surrounding our main box and those imaginary boxes also contains nanotubes.

While the MD calculations are being made, surrounding nanotubes are also included; the

nanotube inside the box is obstructed in terms of free movement. Therefore, the same

simulation was repeated in a bigger box to decrease that obstruct effect.

The second simulation with super critical CO2 was prepared in a (60x60x100) Å box

putting 2260 CO2 molecules to make the system filled with super critical CO2. Putting

2260 CO2 molecules to this system makes the bulk density 6.3 nm-3 which is close to the

bulk density of the system with smaller box. This simulation was run for 3 ns and Figure

4.16. shows its density profile with respect to time.

Figure 4. 16. Change in supercritical carbon dioxide density inside (10,10) SWNT w.r.t.

time with 60x60x100 box size

Even if we increased the box size to decrease the interaction between nanotubes due

to periodic boundary conditions, the same response has occurred. In this case nanotubes

(separated forms) are not in succession and they do not cause each other to bend. However,

the rest of the things are the same in terms of structure except steady state time. Density of

supercritical CO2 molecules reached the steady-state value faster than the CO2 molecules.

44

In this simulation, perfect alignment among CO2 molecules is not seen yet since the system

didn’t run enough as the system with smaller box. But, anyway the tendency of CO2

molecules to align is observed in the Figure 4.17.

Figure 4.17. Finalized (10,10) SWNT simulation with supercritical CO2 with 60x60x100

box size

45

5. CONCLUSION AND RECOMMENDATIONS

5.1. CONCLUSION

In this project it was aimed to figure out the relation between CO 2 and SWNTs and

the behavior of CO2 molecules confined in SWNTs. To be able to investigate this

association, MD approach was used instead of experimental methods to avoid the

difficulties of handling SWNTs in laboratory conditions and also huge costs which should

be paid for these processes. This study contains three parts: effect of SWNT size to CO2

behavior, effect of number of SWNTs on CO2 behavior and the behavior of super critical

carbon dioxide confined in SWNT.

As a first group, four simulations filled with CO2 containing SWNTs in different

sizes were prepared while keeping the bulk density around 0.04 nm-3 and parameters of

these systems are shown in Table 6.1. By increasing the diameter, however, CO2 density

inside nanotubes decreases as shown in Figure 4.10. The density profile was not monotonic

at current conditions but it gave a maximum value for the (8,8) nanotube. Beside the

density inside nanotubes, the structure of CO2 molecules inside nanotube was an

interesting point. While CO2 molecules inside (6,6) nanotube residing on an axis as a line,

for (8,8) and (10,10) nanotubes this structure turned in to a ring structure. The reason is the

diameter of (6,6) nanotube is very close to the size of C and O atoms. Therefore CO 2

molecules aligned their O-C-O axis parallel to the nanotube axis. Since the carbon atoms

tend to remain at the center and the O atoms near the walls, in (8,8) and (10,10) nanotubes

CO2 molecules created a hallow cylinder. In (16,16) nanotube simulation, even if the CO2

molecules created a ring structure at the beginning, towards the end of the simulation they

aligned and made several lines both inside and outside of nanotube which are also parallel

to each other.

As a second group, two and four (10,10) SWNTs were placed separately in a

simulation box which has the same initial parameters with the single (10,10) nanotube

simulation which was performed in the first group. As a result of these simulations, no

effect of carbon nanotube number to the density in the nanotubes was observed.

46

As a third group, (10,10) SWNT was used to observe the behavior of supercritical

CO2. Two simulations were performed in different box sizes while adding enough CO2

molecules to make the density of the system around 0.469 g/cm3 which is the critical

density of CO2. In the first simulation since box size was small compared the length of

nanotube, after a point, nanotube inside the box was appeared as if there were two

nanotubes and they caused each other to bend. The density inside nanotube was not 100

times higher than the bulk density as in the first group. In this case it was just twice. As a

second simulation, to decrease the effect of box size and tube length ratio, box size was

increased from 30x30x100 to 60x60x100 while keeping the density of the system as

critical density of CO2. However, the result did not change too much. Nanotube turned in

the box and separated into two parts due to the periodic boundary conditions again. And

the density inside nanotube was not different than the first simulation performed with

smaller box. However, the time required to reach the steady state is much smaller for

(10,10) SWNT system in supercritical CO2 environment rather than CO2.

5.2. RECOMMENDATIONS

Since the prepared simulations contain a lot of molecules, they needed lots of time to

reach the steady-state. To decrease the time effect, more powerful computers should be

used. Also, creating and running supercritical CO2 systems were impossible in big boxes

used in first group. Because it requires adding a lot of molecules compared to CO2 systems

and this limited us make a real comparison between CO2 confined in (10,10) SWNT with

supercritical CO2 confined in (10,10). Therefore box size was decreased and undesired

nanotube behavior was observed.

To be able to observe the effect of nanotube amount on fluid behavior, smaller

simulation box should be used or, nanotubes should be placed into the box as nanoropes.

As a future work, due to importance of water in each part of life, SWNT simulations

should be performed with water and also with other important fluids. Since, CO2 forms a

hallow cylinder inside the nanotube, MWNTs should be studied for more effective CO2

removal.

47

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