Molecular Dynamics Simulations Of Carbon Dioxide Molecules Confined In Single-walled Carbon Nanotubes

1

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 CO 2 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 CO 2 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].

3 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: C h = naˆ1 + maˆ 2

(2.1)

4 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

5 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;

a1 =

3a a 3 x+ y 2 2

a2 =

3a a 3 x− y 2 2

(2.2) (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;  3 2 2  dt =  π ac −c m + nm + n  

(

)

1/ 2

(2.4)

6 where ac-c is the distance between neighboring carbon atoms in the flat sheet. In turn, the chiral angle is given by; θ = tan

−1

 3n     2m + n   

A SWNT is considered metallic if the value

(2.5)

n − m 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

7 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]

Material

Young'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, highstrength 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.

9 Table 2.2. Physical Properties of SWNT [21]

Equilibrium Structure Average Diameter of SWNT's

Optical Properties

1.2-1.4 nm

Distance from opposite Carbon Atoms (Line 1)

Fundamental Gap

2.83 Å

Analogous Carbon Atom Separation (Line 2) Parallel Carbon Bond Separation (Line 3) Carbon Bond Length (Line 4)

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

2.46 Å 2.45 Å

Electrical Transport Conductance Quantization

n x (12.9 k)-1

Resistivity

4-Oct-cm

Maximum Current Density

1013 A/m2

Thermal Conductivity

~ 2000 W/m/K

Phonon Mean Free Path

~ 100 nm

Relaxation Time

~ 10-11 s

1.42 Å

C - C Tight Bonding ~ 2.5 eV Overlap Energy Group Symmetry C5V (10, 10) Lattice: Bundles of Triangular Lattice (2D) Ropes of Nanotubes Lattice Constant 17 Å Lattice Parameter (10, 10) Armchair 16.78 Å (17, 0) Zigzag 16.52 Å (12, 6) Chiral 16.52 Å Density (10, 10) Armchair 1.33 g/cm3 (17, 0) Zigzag 1.34 g/cm3 (12, 6) Chiral 1.40 g/cm3 Interlayer Spacing (n, n) Armchair

3.38 Å

(n, 0) Zigzag

3.41 Å

(2n, n) Chiral

3.39 Å

Elastic Behavior Young's Modulus (SWNT)

~ 1 TPa

Young's Modulus (MWNT)

1.28 TPa

Maximum Tensile Strength

~30 GPa

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 C h . CNTs are conductive if the integers are:

n = m (armchair) and

n − m = 3i (where i is an integer). In all other cases,

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

10

Eg =

2γ o a c −c d

(2.6)

where, γ 0 = 2.45 eV is the nearest-neighbour overlap integral [14], a c −c 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]:  e2 G = Go M =  2  h

 M 

(2.7)

where, Go = ( 2e2 h ) = (12 .9 kΩ) is the quantum unit of conductance. M is the apparent −1

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 selfassemble 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].

12 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, C 2, 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

13 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 C 2-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 singlelayer 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].

14 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.

15

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)

Who

Ebbesen and Ajayan, NEC, Japan 1992 [30]

Endo, Shinshu University, Nagano, Japan [31]

Smalley, Rice, 1995 [32]

How

Connect two graphite Place substrate in oven, heat to rods to a power supply, 600 oC, and slowly add a place them a few carbon-bearing gas such as millimetres apart, and methane. As gas decomposes it throw the switch. At 100 frees up carbon atoms, which amps, carbon vaporises recombine in the form of NTs and forms a hot plasma.

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

SWNT

Short tubes with diameters of 0.6-1.4 nm

Long tubes with diameters ranging from 0.6-4 nm

Long bundles of tubes (5-20 microns), with individual diameter from 1-2 nm.

Short tubes with inner diameter of 1-3 nm and Long tubes with diameter MWNT outer diameter of ranging from 10-240 nm approximately 10 nm SWNTs have few structural defects; Easiest to scale up to industrial MWNTs without production; long length, simple Pro catalyst, not too process, SWNT diameter expensive, open air controllable, quite pure synthesis possible Tubes tend to be short with random sizes and NTs are usually MWNTs and Con directions; often needs a often riddled with defects lot of purification

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

Primarily SWNTs, with good diameter control and few defects. The reaction product is quite pure. Costly technique, because it requires expensive lasers and high power requirement, but is improving

16 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)

17 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:

mi ri = f i = −

∂ U ∂ri

(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

18 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

19

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). E = E kin

+ E pot

(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:

pk

∂H ∂p k

= kT

(2.10)

For N atoms, each with three degrees of freedom, the following relation can be obtained. T =

2 E kin 3 Nk

(2.11)

Alternatively, it can be considered that T to be the average of instantaneous temperature contributions (t) [37].

t=

2 E kin 3 Nk

(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].

20

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:

ν =

νc N23

(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, N ( N −1) / 2 calculations are required for each configuration.

21

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: U non −bonded (r N ) = ∑u ( ri ) + ∑∑ν (ri , r j ) + ... i

i

j >i

(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:  σ  σ  ν LJ ( r ) = 4ε   −   r  r  12

6

  

(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:

ν Coulomb ( r ) =

Q1Q2 4π εo r

(2.16)

where Q1 and Q2 are the charges and ε0 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) 1 r ∑ ki j( ri j − re q) 2 2bo n d s 1 2 + ∑ k iθ j k(θ i j k− θ e q) 2b e n d

U i n t r a mu ol al =re c

(2.17b)

a ng les

+

1 ∑ ∑ kiφj,mk l(1 + c o( ms φ i j k −l γ m ) 2t o r s io n a ng les

(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.

V

(r

N

1 (r )= k ∑ 2 r ij

b o n d s

i j

− req

)

2

θ− θ)

1 + ∑ k iθ ( j k 2 b e n d

2

ij k

e q

a n g l e s

1 ,m ( + ∑ k ijφ 1+ c o s ∑ k l 2 to r s io n a n g l e s

 ε σ 

  N N  ij    + 4 ∑ ∑   rij   i= 1 j= i+ 1   

1 2



(mφ i jk l

γ ))

(2.18)

− m

 σ Q Q  +  4π εr 

 ij  −  rij 

6

i

j

o

i j

    

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 10 ×10 ×10 cube. Nearly half the atoms are on the outer faces, and these will have a large

24 effect on the measured properties. Even for 10 6 = 100 3 atoms, the surface atoms amount to 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:

25 • A list of atom types. • 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

26 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 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 nonscale 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 1×10 4 - 2 ×10 4 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 8 ×10 6 to 25 ×10 6 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 N CO 2 , 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

N CO 2

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 CO 2, (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 CO2CO2 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, CO 2 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

35 third simulation a ring shape structure of CO 2 molecules inside nanotube was observed as 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 CO 2 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

38 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 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

39 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 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

40 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.

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

42 difference here is the bulk density is 5.9 nm-3 and in the nanotube, this density rises to 10 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 CO 2 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

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

44 supercritical CO2 molecules reached the steady-state value faster than the CO2 molecules. 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 CO 2 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 CO 2 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, CO 2 forms a hallow cylinder inside the nanotube, MWNTs should be studied for more effective CO2 removal.

47

REFERENCES 1.

Carbon Nanotubes & Buckyballs, University of Wisconsin, Madison, Materials Research Science and Engineering Center, 2008. http://mrsec.wisc.edu/Edetc/nanoquest/carbon/index.html

2.

Endo, M., Mecanisme de Croissance en Phase Vapeurde Fibres de Carbone (The Growth Mechanism of Vapor-Grown Carbon Fibers), PhD Thesis, Nagayo University, Japan, 1978.

3.

Iijima, S., Helical Microtubules of Graphitic Carbon, Nature, Vol. 354, pp. 56-58, 1991.

4.

Firkowska, I., and P. Zdroj, “Carbon Nanotube Substrates for Tissue Engineering Applications, Analysis of Surface Nanotopography, Cellular Adhesion, and Elasticity”, Mathematisch-Naturwissenschaftlichen Fakultät and Rheinischen Friedrich-Wilhelms-Universität Bonn, 2008. http://hss.ulb.uni-bonn.de/diss_online/math_nat_fak/2009/firkowska_izabela/1652.pdf

5.

Dresselhaus, M., G. Dresselhaus., and P. Eklund, “Carbon Nanotubes”, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, US, 1998 http://physicsworld.com/cws/article/print/1761

6.

Lu, D., “Empirical Nanotube Model for Biological Applications”, Theoretical and Computational Biophysics Groups, NIH Resource for Macromolecular Modeling and Bioinformatics, University of Illinois, Urbana Champaign, 2006. http://www.ks.uiuc.edu/Research/nanotube/

7.

Foldvari, M., “Single-walled CNT and Multi-walled CNT”, Pharmaceutical Sciences School of Pharmacy, Canada, 2009. http://www.pharmacy.uwaterloo.ca/research/foldvari/about/index.html John, D. L., “Simulation Studies of Carbon Nanotube Field-Effect Transistors”, PhD Thesis, The University of British Columbia, 2006.

8. 9.

“What is a Carbon Nanotube?”, Department of Materials Science and Engineering, Philadelphia, 2009. http://www.seas.upenn.edu/mse/research/nanotubes.html

10.

Spires, T., and M. R. Brown, “High Resolution TEM Observations of Single-Walled Carbon Nanotubes”, Department of Botany, The University of Texas at Austin, Austin, Tx., 78713, 1996. http://www.botany.utexas.edu/facstaff/facpages/mbrown/ongres/tspires/nano.htm

11.

Avouris, P., Lecture given at Michigan State University, IBM labs, 2000.

12.

Wilder, W. G., L. C. Venema, A. G. Rinzler, R. E. Smalley, and C. Dekker, “Types of SWNTs and Detailed Structure” Nature, Vol. 391, pp. 59-62, 1998.

48 13.

Odom, T. W., J. L. Huang, P. Kim, and C. M. Lieber, “Atomic Structure and Electrical Properties of Single-Walled Carbon Nanotubes”, Nature, Vol. 391, pp. 6264, 1998.

14.

Pan, Z. W., S. S. Xie, B. H. Chang, C. Y. Wang, L. Lu, W. Liu, W. Y. Zhou, W. Z. Li, and L. X. Qian, Very Long Carbon Nanotubes, Nature, Vol. 394, pp. 631 – 632, 1998.

15.

Nanopedia, The Web Course of Nanotechnology, “The Strength of Nanotubes”, 2009 http://nanopedia.case.edu/NWPage.php?page=nanotube.strength

16.

Overney, G., W. Zhong, and D. Tomanek, “Structural Rigidity and Low Frequency Vibrational Modes of Long Carbon Nanotubes”, Journal for Physics, Vol. 27, pp. 93- 96, 1993.

17.

Yu, M. F., B. S. Files, S. Arepalli, and R. S. Ruoff, “Tensile Loading of Ropes of Single Wall Carbon Nanotubes and Their Mechanical Properties”. Physical Review Letters, Vol. 84, pp. 5552-5555, 2000.

18.

Pan, Z. W., S. S. Xie, L. Lu, B. H. Change, L. F. Sun, W. Y. Zhou, G. Wang, and D. L. Zhang, “Tensile Test Ropes of Very Long Aligned Multiwall Carbon Nanotubes”. Applied Physics Letter, Vol. 74, pp. 31-35, 1999.

19.

Ren, Z. F., Z. P. Huang, J. W. Xu, J. H. Wang., P. Bush, M. P. Siegel, and P. N. Provencio, “Synthesis of Large Arrays of Well-Aligned Carbon Nanotubes on Glass”, Science, Vol. 282, pp. 1105-1107, 1998.

20.

Iijima S., C. Brabec, A. Maiti, and J. Bernholc, “Structural Flexibility of Carbon Nanotubes”, Journal of Chemistry and Physics, Vol. 104, pp. 2089-2092, 1996.

21.

Adams, T. A., “Physical Properties of Carbon Nanotubes”, Michigan State University, 2000. http://www.pa.msu.edu/cmp/csc/ntproperties/

22.

Meyyappan, M., Carbon Nanotubes Science and Application, CRS Press: Boca Raton, Florida, 2005.

23.

Prakash, R., R. Superfine, S. Washbum, and M. R. Falvo, “Functionalization of Carbon Nanotubes with Proteins and Quantum Dots in Aqueous Buffer Solution”. Applied Physics Letter, Vol. 8, pp. 63-68, 2006.

24.

Singh, K. V., R. R. Pandey, X. Wang, R. Lake, C. S. Ozkan, K. Wang, and M. Ozkan, “Covalent Functionalization of Single Walled Carbon Nanotubes with Peptide Nucleic Acid: Nanocomponents for Molecular Level Electronics”, Carbon, Vol. 44, pp. 1730-1739, 2006.

25.

Daenen, M. J. M., R. Fouw, B. Hamers, P. G. A. Janssen, K. Schouteden, and M. A. J. Veld, Wondrous World of Carbon Nanotubes, a Review on Current Carbon Nanotube Technologies, 2003. http://students.chem.tue.nl/ifp03/

49 26.

Yasuda, A., N. Kawase, and W. Mizutani, “Carbon-Nanotube Formation Mechanism Based on in Situ TEM Observations”, Journal of Physical Chemistry B, Vol. 106, pp. 13294–13298, 2002.

27.

Sinnot, S. B., R. Andrews, D. Qian, A. M. Rao, Z. Mao, E. C. Dickey, and F. Derbyshire, “Model of Carbon Nanotube Growth Through Chemical Vapor Deposition”, Chemical Physics Letters, Vol. 315, pp. 25-30, 1999.

28.

Thess A., R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y. H. Lee, S. G. Kim, A. G. Rinzler, D. T. Colbert, G. Scuseria, D. Tománek, J. E. Fischer, and R. E. Smalley, “Crystalline Ropes of Metallic Carbon Nanotubes”, Science, Vol. 273, pp. 483-487, 1996.

29.

Maser W. K., E. Munoz, A. M. Benito, M. T. Martinez, G. F. de la Fuente, Y. Maniette, E. Anglaret, and J. L. Sauvajol, “Production of High-Density SingleWalled Nanotube Material by a Simple Laser-Ablation Method”, Chemical Physics Letters, Vol. 292, pp. 587-593, 1998.

30.

Yudasaka M., R. Yamada, N. Sensui, T. Wilkins, T. Ichihashi, and S. Iijima, “Mechanism of the Effect of NiCo, Ni and Co Catalysts on the Yield of Single-Wall Carbon Nanotubes Formed by Pulsed Nd:YAG Laser Ablation”, Journal of Physical Chemistry B, Vol. 103, pp. 6224-6229, 1999.

31.

Ebbesen, T. W., and P. M. Ajayan, “Carbon Nanotubes: From Macromolecules to Nanotechnology”, Nature, Vol. 358, pp. 220-222, 1992.

32.

Endo M., K. Takeuchi, S. Igarashi, K. Kobori, M. Shiraishi, and H. W. Kroto, “The Production and Structure of Pyrolytic Carbon Nanotubes (PCNTs)”, Journal of Physics and Chemistry of Solids, Vol. 54, pp.1841-1848, 1993.

33.

Guo, T., P. Nikolaev, A. Thess, D. T. Colbert, and R. E. Smalley, “Catalytic Growth of Single-Walled Nanotubes by Laser Vaporization” Chemical Physics Letters, Vol. 243, pp. 49-54, 1995. Poliakoff, S., An Introduction to Supercritical Fluids, University of Nottingham, 2001. http://www.nottingham.ac.uk/supercritical/scintro.html

34. 35.

McHugh, M. A., and V. J. Krukonis, Supercritical Fluid Extraction: Principles & Practice; Butterworth-Heinemann, Boston, 1994.

36.

Allen, M. P., “Introduction to Molecular Dynamics Simulation”, John von Neumann Institute for Computing, NIC Series, Vol. 23, pp. 1-28, 2004.

37.

Sadus, R. J., Molecular Simulation of Fluids; Theory, Algorithms and Object Orientation, Elsiver, Netherlands, 2002.

38.

Insight II, Molecular Simulations, “Force Field Based Simulations”, 2000. http://www.scripps.edu/rc/softwaredocs/msi/insight2K/ffbs/1_Intro.html#738996

39.

Accelrys, “Cerius2”, 2009, http://accelrys.com/products/cerius2/

50

40.

Andersen, H. C., “Molecular Dynamics at Constant Pressure and/or Temperature”, Journal of Chemical Physics, Vol. 72, pp. 2384-2393, 1980.

41.

Nosé, S., “A Unified Formulation of the Constant Temperature Molecular Dynamics Methods”, Journal of Chemical Physics, Vol. 81, pp. 511-519, 1984.

42.

Hoover, W. G., “Canonical Dynamics: Equilibrium Phase-Space Distributions”, Physical Review A, Vol. 31, pp. 1695-1697, 1985.

43.

Maitland, G. C., M. Rigby, E. B. Smith, and W. A. Wakeham, Intermolecular forces: Their Origin and Determination, Clarendon Press, Oxford, 1981.

44.

Gray, C. G., and K. E. Gubbins, Theory of Molecular Fluids: Fundamentals, Clarendon Press, Oxford, 1984.

45.

Sprik, M., “Effective Pair Potentials and Beyond”, Computer Simulation in Chemical Physics, Vol. 397 of NATO ASI Series C, pp. 211-259, 1993.

46.

Stone, A. J., The Theory of Intermolecular Forces, Clarendon Press, Oxford, 1996.

47.

Rahman, A., “Correlations in the Motion of Atoms in Liquid Argon”, Physics Review A, Vol. 136, pp. 405-411, 1964.

48.

Verlet, L., “Computer Experiments on Classical Fluids in Thermodynamical Properties of Lennard-Jones Molecules”, Physics Review, Vol. 159, pp. 98-103, 1967.

49.

Weeks, J., D. Chandler, and H. C. Andersen, “Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids”, Journal of Chemical Physics, Vol. 54, pp. 5237-5247, 1971.

50.

Price, S. L., “Toward More Accurate Model Intermolecular Potentials for Organic Molecules”, Reviews in Computational Chemistry, Vol. 14, pp. 225-289, 2000.

51.

Huang, L., “Molecular Simulation of Confined Fluids in Carbon Nanotubes”, Department of Computer & Information Science, University of Pennsylvania, 2007. http://gubbins.ncsu.edu/Seminar_Abstracts_Bios/Liangliang_Huang_Seminar_Octob er_5_2007.pdf

52.

Ye, Y., C. C. Ahn, C. Witham, B. Fultz, J. Liu, A. G. Rinzler, D. Colbert, K. A. Smith, and R. E. Smalley, “Hydrogen Adsorption and Cohesive Energy of SingleWalled Carbon Nanotubes”, 1999, Applied Physics Letters, Vol. 74-16, pp. 23072309, 1999.

53.

Alexiadis, A., and S. Kassinos, “Influence of Water Model and Nanotube Rigidity on the Density of Water in Carbon Nanotubes”, Chemical Engineering Science, Vol. 63, pp. 2793-2797, 2008.

51 54.

Allada, R. K., S. Arepalli, C. Huffman, H. Fireman, P. Moloney, P. Nikolaev, E. Sosa, M. Waid, and L. Yowell, “Carbon Nanotubes for Human Spaceflight Applications”, NASA- Johnson Space Center Report, 2009. http://research.jsc.nasa.gov/PDF/Eng-9.pdf

55.

Alexiadis, A., and S. Kassinos, ”Molecular Dynamic Simulations of Carbon Nanotubes in CO2 Atmosphere”, Chemical Physics Letters, Vol. 460, pp. 512-516, 2008.

56.

Shenogin, S. and R. Ozisik, XenoView: Visualization for atomistic simulations, 2007 http://www.rpi.edu/~shenos3/xenoview.html