of carbon nanostructures Olga E. Glukhova, DSc, Professor Saratov - - PowerPoint PPT Presentation

The theoretical study

• f carbon nanostructures

Olga E. Glukhova, DSc, Professor Saratov State University Physics Department, Institute of nanostructures and biosystems 410012, Russia, Saratov, Astrakhanskaja, 83 E-mail: glukhovaoe@info.sgu.ru

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COMPUTATIONAL METHODS: QUANTUM MECHANIC, MOLECULAR DYNAMICS

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Tight-binding method

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The phenomenon energy

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The TB parameters for carbon nanoclusters

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The Hamiltonian

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The interaction of P-orbitals

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The rehybridization

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The electron spectra

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To describe the intermolecular interaction the van der Waals potential was added in to the system energy (1). The van der Waals potential is given as the Lennard-Jones potential

   



     

            

, 6 12 6 6 vdW

r 1 r 1 y 2 1 A E , (12) where 42 . 1   is a length of the C-C bond, 7 . 2 y0  and

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m J 10 3 . 24 A   



are empirically chosen parameters (Qian D., Liu W. K., and Ruoff R. S. (2003) C. R. Physique 4: 993-100). However, the Lennard-Jones potential is incorporated only if the phenomenon intermolecular energy becomes zero (at distance about 0.25 nm for the carbon-carbon interaction). The motions of the atoms are determined by the classical MD method where Newton’s equations of motion are integrated with a third-order Nordsieck predictor corrector. Time steps of 0.15–0.25 fs were used in the simulations. The forces on the atoms were calculated using TB method.

To research the nanoribbons using tight-binding potential our own program was used. Our own program provides the calculation of the total energy of nanostructures, which consist of 500-5000 atoms. We have adapted our TB method to be able to run the algorithm on a parallel computing machine (computer cluster). During consideration of the algorithm we can note two points: solution of eigenvalues problem and, possibly, eigenvectors problem for the M*NxM*N matrix - one-electron Hamiltonian (N is the number of atoms, M is maximum number of valence electrons);

• solution
• f
• ptimization

problem – the total system energy minimization. It's necessary to consider the available computing power. We have a number of dual-processor servers which are the distributed SMP-system. MPI (stands for Message Passing Interface) was chosen as mechanism for implementing parallelism.

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NANODEVICES: MATHEMATICAL MODELS

Nanoreactor (nanoautoclave) Dimerization of miniature C20 and C28 fullerenes in nanoautoclave

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In our nanoautoclave model a closed single-wall carbon nanotube (10,10)

740

C

is represented as a capsule that is closed from both ends with

240

C fullerene caps. The pressure is controlled by a shuttle-molecule encapsulated into a nanotube that may move inside the tube. In the present case a shuttle-molecule is the C60 fullerene. The shuttle must have some electric charge for its movement to be controlled by an external electric field. The positively charged endohedral complex K+@C60 (the ion of potassium inside the fullerene C60) is a shuttle-molecule in the present model of the

• nanoautoclave. So, the hybrid compound

740 60

tubeC @ C @ K is a nanoautoclave model. The

740 60

tubeC @ C @ K nanoparticle is located between two electrodes connected with a power

• source. Changing the potentials at the electrodes, we control the movement of the

60

C @ K fullerene.

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At the start moment, the mutual positions of all nanoautoclave components correspond to the ground state

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When the pressure created in the tube provides both the overlap of -electrons of the

n

C fullerenes (that corresponds to the interatomic distance of about 1.9 Å) and the covalent bonds formation, the intermediate phase of the  2

n

C

dimer is synthesized: 

  

5 5 C

2 20

 (at 20 n  ) or

   

6 6 C

2 28

 (at 28 n  ). Here a number of fullerene atoms participating in the intermolecular bonds formation is shown in square brackets. Figure shows a stable dimer of the

20

C (

28

C ) fullerene and the

60

C molecule that suffered a certain deformation.

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The structure of stable dimers with the horizontal symmetry plane, symmetry axes, and the plot of electron states density are shown in Figure.

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Characteristics of stable fullerenes dimers Dimer Symmetry group of the dimer

max min r

r

, Å

D , Å

b

E , eV H  ,

atom mol kcal 

g

E , eV

HOMO, eV

   

2 2 C

2 20



D2h 1.43/1.62 1.65 6.44

• 5.01

0.66 7.00

   

1 1 C

2 28



C2h 1.41/1.56 1.56 6.57

• 2.07

0.14 7.16

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At the moment of the covalent bonds formation, the pressure is calculated according to the energy

rep vdW er

E E E  

int

. The potential difference at the electrodes

  that provides

the pressure necessary for the dimerization is calculated according to the relationship

     e E

er int

, where

er

Eint 

is a potential barrier overcome by the

60

C

fullerene when it goes from the well (the area of the tube end) to the position providing the dimer

• formation. The strength is calculated as

L  

, where a distance L is taken to be equal to the capsule length added to value of 3.4 Å (closing the capsule to electrodes by a less distance may cause sticking due to Van-der-Waalse interaction). The energy of the

60

C fullerene and parameters of the outer field necessary for the  2

n

C

dimer synthesis

 2

n

C

 

1 Einter

, eV

nter i

E 

, eV

  , V F, V/m

   

2 2 C

2 20



• 3.574

5.42 8.90 0.18

8

10 

   

1 1 C

2 28



• 3.574

6.50 10.16 2

8

10 

Graphene: electron properties

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With increasing of the number of atoms the nanoribbon becomes stable (finite size effect)

Density of Mulliken charge

• f carbon atoms
• f nanoribbon

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Scroll of nanoribbon (finite size effect)

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The dependency of IP on the nanoribbon length (finite size effect)

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IP of nanoribbons

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Energy gap of nanoribbons

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Defected nanoribbons

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GRAPHENE: MECHANICAL PROPERTIES

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Multicsale modeling to investigate the mechanical properties

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Study of deformations and elastic properties of nanoparticles and nanoribbons was implemented

• n the following algorithm

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Young’s pseudo-modulus (Y2D) of

• nanoribbons. Y3D =Y2D *0.34 nm

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Two- dimensional Young’s modulus

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Strain energy of nanoribbons undergoing axial tension

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Nanoribbon undergoing axial compression

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Dependence of strain energy on the relative compression nanoribbons

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The curve of the strain energy collapse occurs at the axial compression 0.03- 0.04. Plane atomic network undergoing axial compression becomes wave-like.

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Dependency of the strain energy on the relative compression nanoparticles

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THE INFLUENCE OF A CURVATURE ON THE PROPERTIES OF NANORIBBONS

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Research of the local stress field of the atomic grid of graphene nanoribbons and prediction of the appearance of defects in compression process

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The compression of defected nanoribbons

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The distribution of the local stress in atomic network

(the compression 20 %)

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The absorption of H-atom

• n the atomic network

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The total energy of the structure depends on the distance between the hydrogen atom and the carbon atom.

(The dashed line is the interaction of the hydrogen atom with planer graphene nanoribbon; the solid line is the interaction of the hydrogen atom from wave-like graphene nanoribbon )

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THE ELECTRON AND MECHANICAL PROPERTIES OF THE MODIFIED GRAPHENE NANORIBBONS

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Graphane

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The electron properties

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Parameters of elasticity

• f graphane-nanostructures

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