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Abstract- Functionalized carbon nanotubes (CNTs) are being widely used in various applications related to the field of biomedical sciences. These modified nanotubes are generally functionalized extensively with specific biomolecules to increase biocompatibility. This process helps in decreasing the toxicity of nanotubes. In our study, we have investigated into the efficiency of CNTs when complexed with a) a DNA molecule and b) a biopolymer. Carbon nanotubes functionalized with DNA are being used for various applications like drug delivery, gene repair, biosensors etc. Study of interaction between CNT and DNA has been carried out by generating a single stranded DNA molecule and 134 single walled carbon nanotube structures. Molecular dynamic simulation of the DNA, CNTs and the DNA-CNT complexes has been performed and their properties have been studied and compared. It has been observed that 47 out of the 135 complexes are thermodynamically stable and can be used for various applications. Similarly, the interaction of Carbon Nano Tubes with cellulose has been studied by means of computational modeling and simulation. CNT when complexed with cellulose has proved to increase the stability of cellulose, giving rise to a wide range of applications. 134 CNT-cellulose complexes have been taken for the analysis. The thermodynamic and mechanical properties of these complexes have been computed to find whether the strength of biopolymer is increased by the combination. Bulk modulus of the CNT cellulose complexes has been computed to analyze the mechanical stability. Based on our computational analysis, seventy two structures have been found to be stable.
Keywords-carbon nanotubes; computational modeling and simulation; DNA-CNT complex; cellulose-CNT complex
Carbon nanotubes (CNTs) are allotropes of carbon with a cylindrical nanostructure . They have been extensively studied due to their unique mechanical and electronic properties which are closely related to their diameter and chirality. A CNT can be thought of as a graphene sheet rolled up along one of the graphene lattice vectors, indexed by an integer pair (n, m) called chiral vector. A chiral vector is defined to locate the position of all the atoms within a two-dimensional graphene sheet in the coordinates of m and n, where m and n are integers of the vector equation Ch = na1 + ma2 and a1 and a2 are unit vectors.
Carbon nanotubes are toxic in nature . To make nanotubes more easily dispersible in liquids and to remove the toxicity, functionalization is carried out. This is made possible by physically or chemically attaching certain molecules (lipids, proteins, biotins) or functional groups to their sidewalls without significantly changing their properties. DNA molecules are generally used in functionalizing CNTs by covalent or non-covalent interaction. This would enable medially and commercially significant applications such as gene therapy and drug delivery.
The reason why DNA wrap methods are so promising for CNT production and development is that, in contrast to most other methods of purification and separation, they do not destroy the initially produced structure of the tube walls. The aqueous solubility and cationic surface character of f-CNTs make them potentially novel delivery vehicles.
By using molecular dynamics simulations it has been shown that, in an aqueous environment, the ssDNA molecule could be inserted spontaneously into the CNTs and the ssDNA interacts strongly with SWNT to form a stable ssDNA-SWNT hybrid that effectively disperses SWNT in aqueous solution. Both, the Van Der Waals and hydrophobic forces have been found to be important for this interaction [3-6].
The biodegradable polymers and their degradation products must be environmentally compatible causing no deleterious effects to the environment and when disposed in biologically active environments they must be completely converted to biological products . They degrade by the enzymatic action of microorganisms such as bacteria, fungi, and algae. Their polymer chains may also be broken down by non enzymatic processes such as chemical hydrolysis. Starch, cellulose, proteins and peptides, DNA and RNA are examples of biopolymers and cellulose is the bio polymer that has been used for this analysis. It is an organic compound with the formula (C6H10O5)n, a polysaccharide consisting of a linear chain of several hundred to over ten thousand β (1→4) linked D-glucose units. There are intrachain and interchain hydrogen bonds, as well as Van Der Waals interactions, that cause cellulose chains to be straight and rigid. The cellulose chain has polar -OH groups. These groups form many hydrogen bonds with OH groups on adjacent chains, bundling the chains together but they are not stable enough to with stand harsh conditions. Strength of cellulose if increased by combining with CNT while retaining its biocompatibility will be useful.
The molecular dynamics simulation method is based on Newton's second law or the equation of motion, F=ma, where F is the force exerted on the particle, m is its mass and a is its acceleration. Knowing the force on each atom, it is possible to determine the acceleration of each atom in the system. Integration of the equations of motion then yields a trajectory that describes the positions, velocities and accelerations of the particles as they vary with time. From this trajectory, the average values of properties can be determined. The method is deterministic; once the positions and velocities of each atom are known, the state of the system can be predicted at any time in the future or the past.
Newton's equation of motion is given by
Where Fi is the force exerted on particle i, mi is the mass of particle i and ai is the acceleration of particle i.
The force can also be expressed as the gradient of the potential energy
Combining these two equations yields
Where V is the potential energy of the system.
The simplest choice of V is to write it as a sum of pair wise interactions:
The clause j>i, in the second summation has the purpose of considering each pair wise interaction only once.
Newton's equation of motion can then relate the derivative of the potential energy to the changes in position as a function of time.
Taking the simple case where the acceleration is constant
Expression obtained for the velocity after integration
we can once again integrate to obtain
Combining this equation with the expression for the velocity, the following relation is obtained which gives the value of x at time t as a function of the acceleration, a, the initial position, x0, and the initial velocity, v0.
The acceleration is given as the derivative of the potential energy with respect to the position, r,
Therefore, to calculate a trajectory, one only needs the initial positions of the atoms, an initial distribution of velocities and the acceleration, which is determined by the gradient of the potential energy function. The equations of motion are deterministic, e.g. the positions and the velocities at time zero determine the positions and velocities at all other times t. The initial positions can be obtained from experimental structures, such as the x-ray crystal structure of the molecule.
The sum-over-states macroscopic pressure of the system (P) and the instantaneous volume of the system are used to find the Bulk modulus which is obtained using the equation
MATERIALS AND METHODS
The carbon nanotubes have been generated using MSL nanomaterials Simulator of nanoHUB  which is used to design and analyze electronic properties of nano materials. Nanotubes (SWCNT) are generated by changing the integer pair (n, m) of the chiral vector. Here we have taken values of n from 9-18 and m values from 0-(n-1) and 134 CNT structures have been generated.
Several properties of CNT molecule generated includes torsion angle, number of atoms, Tube diameter, Chiral angle, Conduction band minimum, Valence band maximum, Band gap, Energy-minima and Energy maxima. Thermodynamic stability of a molecule is the key factor in deciding the feasibility of functionalization.
MD simulations provide detailed information on the fluctuations and conformational changes of molecules. These methods have been used to investigate the structure, dynamics and thermodynamics of DNA/cellulose, CNT and their complexes.
MD simulation has been done using the Forcite tool of Materials studio . This has been carried out at molecular mechanics level of computation with universal force field. Optimization of the geometry is done before the molecule is subjected to dynamics. Geometry Optimization is done in order to refine the geometry of a structure until it attains stability or the total energy of the structure is minimized. This is an iterative process, in which the atomic coordinates and the cell parameters are adjusted until the total energy of the structure is minimized. The optimized structure corresponds to a minimum in the potential energy surface. The forces on an atom are calculated from the potential energy expression and will, therefore, depend on the force field that is selected. Smart algorithm has been used for the geometric optimization.
Molecular dynamic simulation is done under the following conditions. In Canonical ensemble (NVT), dynamics are modified to allow the system to exchange heat with the environment at a controlled temperature and the thermostat used is Nose. Nose dynamics is a method for performing constant-temperature dynamics that produces true canonical ensembles in both coordinate space and momentum space. Simulation temperature has to be fixed at 310 K, the normal body temperature. Time steps option denotes the steps used to numerically integrate the equations of motion.
The time step selected for this application is 1.0. Total simulation time has been taken as 10 ps, which specifies the total time of dynamics simulation, which also determines the number of steps. The number of steps has been fixed as 10000 in all simulations. The output is framed for every 100 steps.
RESULTS AND DISCUSSION
The total energy (sum of kinetic energy and potential energy) of the complexes was found to be less than that of the individual components (DNA/cellulose). Thus the complexes have been proved to be more thermodynamically stable. In the case of DNA-CNT complexes, 47 out of 134 structures have been found to be stable. In the case of cellulose-CNT complexes, 72 out of 134 structures have been found to be stable. MOE  has been used to find out pressure and volume .The P and V values have been used to find the bulk modulus and the highest value of bulk modulus has been observed for the cellulose complex with CNT having (11,2) as n, m values. The graphs for bulk modulus of 3 stable structures of CNT cellulose complexes have been plotted.
From Molecular Dynamic Simulation of DNA-CNT interactions, it has been observed that out of 135 complexes, only 47 are thermodynamically stable. So, only these 47 interactions are thermodynamically feasible and used for various applications. Also 72 out of the 134 cellulose-CNT complexes are stable of which the (11, 2) complex has the highest strength.