Abstract
Elastic and engineering properties of nanoparticle enhanced composites and their constituents (matrix, reinforcement and interface) are calculated. The nanocomposites considered in this study consist of a single-wall carbon nanotube (SWCNT) embedded in polyethylene matrix. Molecular dynamics simulations are used to estimate the elastic properties of SWCNT, interfacial bonding, polyethylene matrix and composites with aligned and randomly distributed SWCNTs. The elastic properties of bundles with 7, 9, and 19 SWCNTs are also compared using a similar approach. In all simulations, the average density of SWCNT–polymer nanocomposite was maintained in the vicinity of CNTs, to match the experimentally observed density of a similar nanocomposite. Results are found to be in good agreement with experimentally obtained values by other researchers. The interface is an important constituent of CNT–polymer composites, which has been modeled in the present research with reasonable success.
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Abbreviations
- H :
-
Hamiltonian of the system
- Ψ:
-
Wave function
- R :
-
Position vector of atomic nucleus
- r i :
-
Position vector of an electron in the atom (or any particle in general)
- Θ:
-
Force field
- m :
-
Mass of the particle
- t :
-
Time
- E total, U :
-
Total potential energy of the system
- K 2, K 3, K 4 :
-
Force constants associated with bond length change
- b :
-
Changed bond length
- b o :
-
Equilibrium bond length
- K 2θ , K 3θ , K 4θ :
-
Force constants associated with bond angle change
- θ :
-
Changed angle between two bonds
- θ o :
-
Equilibrium angle between two bonds
- \( K_{{1\phi }} ,K_{{2\phi }} ,K_{{3\phi }} \) :
-
Force constants associated with bond torsion
- \( \phi \) :
-
Torsion angle
- K2χ :
-
Force constants associated with out of plane angle change
- χ :
-
Out of plane angle
- χ 0 :
-
Equilibrium out-of-plane angle
- Kbθ :
-
Force constants associated with bond length change and bond angle change coupling
- K 1b, K 2b, K 3b :
-
Force constants associated with bond length change and bond torsion coupling
- \( K_{{1\theta \phi }} ,K_{{2\theta \phi }} ,K_{{3\theta \phi }} \) :
-
Force constants associated with bond angle change and bond torsion coupling
- \( K_{{\theta \phi }} \) :
-
Force constants associated with second order bond angle change and bond torsion coupling
- e :
-
Charge of an electron
- C ijkl :
-
Stiffness matrix
- σ ij :
-
Stress component
- ε kl :
-
Strain component
- A :
-
Helmholtz free energy
- V :
-
Volume of the simulation cell
- V o :
-
Undeformed volume of the simulation cell
- v :
-
Velocity of the particle
- f i :
-
Force acting on the particle i
- p i :
-
Momentum of the atom (particle) in original system
- \( \ifmmode\expandafter\bar\else\expandafter\=\fi{F},\ifmmode\expandafter\bar\else\expandafter\=\fi{G} \) :
-
Trajectory average of any thermodynamic property
- N :
-
Total number of atoms in the system
- ρ i :
-
Position vector in the scaled coordinate system
- Q :
-
Same as volume, V
- η, M :
-
Constants
- π i :
-
Momentum conjugate to ρ i
- Π:
-
Momentum conjugate to Q
- S:
-
Stochastic collision term for atoms
- γ:
-
Mean rate of stochastic collision
- C ij :
-
Material stiffness matrix
- E ij , υ ij , μ ij , K ij :
-
Engineering constants (Youngs modulus, Poisson’s ratio, shear modulus and bulk modulus)
- E pull-out :
-
Pull-out energy
- τ i :
-
Interfacial shear stress
- a :
-
Radius of the nanotube
- L :
-
Length of the nanotube
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Acknowledgement
Authors wish to acknowledge partial support for this research by ONR Grant#N00014-06-1-0577, Office of Naval Research, Solid Mechanics Program (Dr. Yapa D.S. Rajapakse, Program Manager); and by the NASA EPSCoR Research Infrastructure Grant.
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Al-Ostaz, A., Pal, G., Mantena, P.R. et al. Molecular dynamics simulation of SWCNT–polymer nanocomposite and its constituents. J Mater Sci 43, 164–173 (2008). https://doi.org/10.1007/s10853-007-2132-6
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DOI: https://doi.org/10.1007/s10853-007-2132-6