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MOLECULAR DYNAMICS MODELLING

MOLECULAR DYNAMICS MODELLING. What is Molecular Dynamics (MD). A computer simulation technique where the time evolution of a set of interacting atoms is followed by integrating their equations of motion.

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MOLECULAR DYNAMICS MODELLING

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  1. MOLECULAR DYNAMICS MODELLING

  2. What is Molecular Dynamics (MD) • A computer simulation technique where the time evolution of a set of interacting atoms is followed by integrating their equations of motion. • Laws of Classical Mechanics, notably Newton’s law are followed, to predict the position and momentum space trajectories of a system of classical particles. • The measurement of the physical quantity by simulation is obtained as an arithmetic average of the various instantaneous values assumed by that quantity during the MD run.

  3. Role of MD in Nanoscale heat transfer • Most powerful tool for investigation of microscopic heat transfer phenomenon, where the empirical macroscopic laws like Fourier Law, Stefan-Boltzmann law become practically invalid. • Can compute both kinetic and thermodynamic properties. . • Can be applied to all phases of gas, liquid and solid and to interfaces of these three phases.

  4. Limitations of MD • Use of Classical forces • Difficulty in selecting characteristic potential for the material under study. • Time and size limitations.

  5. Some common terminologies • Ensembles (NVE, NPT,NVT) • Periodic boundary conditions, Minimum image criterion • Integration Schemes • Gear predictor • Verlet • Leap Frog • Runge - kutta

  6. Reduced Units

  7. Procedural Steps in MD INITIALIZATION: Assigning initial positions and velocities to all particles in the system compatible with the structure that is simulated. • Lattice initialization • Assigning velocities EQUILIBRATION: Rescaling the velocities to get the desired instantaneous temperature. • Verlet Algorithm: Derived from the Taylor series expansion of position vector. -- Compute Accelerations -- Force Calculation • Temperature Calculation

  8. Initialization • Consider anFCC Lattice: (minimum energy configuration for a LJ system) • N = 4 * M 3 : M unit cells in each direction, with 4 particles in each. • Velocity : -- gasdev( ) * -- adjust CM velocity to zero (Total momentum is to be conserved) *from “Numerical Recipes in C” by William Vetterling

  9. Equilibration Verlet Algorithm Newton’s Equation of Motion (For an LJ system) Equipartition Formula

  10. Main Function Void main() { initpositions(); initvelocities(); for(i=0; i< tstep; i++) { velocityVerlet(dt); instantaneousTemperature(); if(i%200==0) rescaleVelocities(); } lj(); }

  11. Potential Functions • Lennard- Jones Potential • Effective Pair Potential* *from Ref No. 3, Shigeo Maruyama et al

  12. Variation of Lennard - Jones potential

  13. Green Kubo Model • An approach based in real space • Transport properties can be obtained from equilibrium systems. • Time correlation function expression for the thermal conductivity. • Fluctuation Dissipation Theorem.

  14. System evolution in time Variation of System Energies during the simulation, for T=320K, and Volume fraction of nanoparticles=0.06

  15. Thermal Conductivity Enhancement predictions MD predictions :Variation of thermal conductivity ratio with volume fraction at different temperatures

  16. Comparison with experimental works Comparison of MD results with the theoretical model and the experimental results for water-Cu nanofluid, by Xuan & Li.

  17. Publications from the work • C. B. Sobhan, N. Sankar, Nithin Mathew and Rahul Ratnapal, "Molecular Dynamics Modeling of Thermal Conductivity of Engineering Fluids and its Enhancement Using Nanoparticles,"  CANEUS 2006 Micro-Nano Technology for Aerospace Applications, Toulouse, France, 2006 • N. Sankar, Nithin Mathew, C. B. Sobhan “Molecular Dynamics Modeling of Thermal Conductivity Enhancement in Metal Nanoparticle Suspensions” AIAA Journal of Thermo physics and heat transfer (under review)

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