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Thermal boundary conditions for molecular dynamics simulations

A pragmatic approach to. Thermal boundary conditions for molecular dynamics simulations. Simon P.A. Gill and Kenny Jolley Dept. of Engineering University of Leicester, UK. Overview. Imposing a steady state temperature gradient Remote boundary conditions by coarse-graining.

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Thermal boundary conditions for molecular dynamics simulations

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  1. A pragmatic approach to Thermal boundary conditions for molecular dynamics simulations Simon P.A. Gill and Kenny Jolley Dept. of Engineering University of Leicester, UK

  2. Overview • Imposing a steady state temperature gradient • Remote boundary conditions by coarse-graining

  3. Temperaturegradient Heat flux Thermalconductivity T1 temperature Classical model(Ficks law) TN position, x 1.0 Imposing a steady state temperature gradient • Consider a 1D LJ chain of 100 atoms subjected to a different temperature at each end

  4. T(x) T(x) ? T1 T1 T2 T2 x x 1.1 Thermostats • Nosé-Hoover • a global deterministic thermostat • enforces average temperature only • Langevin • a local stochastic thermostat • enforces temperature on each atom • no feedback from actual temperature

  5. 1.2 Results for 1D LJ chain

  6. 1.2 Results for 1D LJ chain • Kapitza effect – boundary conductivity different from bulk conductivity Langevin cannot control temperature in a 1D chain away from equilibrium

  7. Reduced k at boundary for NH k nearly zero at boundary for Langevin 1.3 Boundary effect • Steady state • constant heat flux at all points • Green-Kubo (assuming local equilibrium) Reduce boundary effect using Memory Kernels?

  8. NH : Unphysically large temp gradient maintained at boundary Cooling of 1000 atom LJ chain 1.4 Cooling of Ubiquitin (NAMD)

  9. 1.5 Thermostatting far from equilibrium • Concept – use feedback control loop to regulate temp in centre of chain by thermostating ends boundaryzone boundaryzone { TN T1 { Thermostat at T1c to maintain T1 Thermostat at TNc to maintain TN Controlled region

  10. 1.6 Feedback Control of 1D chain • Algorithm { Thermostat at T1c Adjust T1c to maintain T1 here

  11. in 1D in 2D in 3D. 1.7 Divergence of k • The thermal conductivity of a body with a momentum-conserving potential scales with the system size N as • 3D molecular chain exhibits convergent conductivity • Transverse and longitudinal waves in higher dimensions

  12. 1.8 Feedback control results • 3D rod (8x8x100) • Nosé-Hoover thermostat

  13. 1.9 Feedback control results • Langevin thermostat Langevin can control temperature in 3D but less effective than Nosé-Hoover

  14. 1.10 Feedback control results • Stadium damping thermostat

  15. 1.11 Feedback control results • Temperature distributions

  16. 2.0 Remote boundary conditions by coarse-graining • Some problems are not well represented by : • periodic boundary conditions, particularly where there are long range interactions, e.g. elastic fields in solids • standard ensembles, especially in cases where we are doing work on the system, e.g. NVE, NVT, NPT Work dissipated as heat. Only N is constant

  17. Punch Dynamic atomistic region DOF : positions of atoms, q momenta of atoms, p Elastostatic continuum region DOF : positions of nodes, q temperatures at nodes, T 2.2 Concurrent modelling approach • Do not model dynamics in continuum region

  18. Stadium damping 2.3 Stadium damping • Diffuse thermostatting interface • Proposed by B.L. Holian & R. Ravelo (1995) • Constant temperature simulation embedded in elastostatic FE (Qu, Shastry, Curtin, Miller 2005) • Shown to produce canonical ensemble • Simple solution to phonon reflection problem MD Damping zone

  19. 2.4 Steady State Concurrent model { { Thermostat at T1c to maintain Thermostat at TNc to maintain continuum FD region continuum FD region unthermostatted MD region

  20. 2.5 Steady state FD/MD simulation Nosé-Hoover Stadium damping Blue line is full FD solution Red line is FD at ends (1-20 and 101-120) and MD in middle Blue line is MD boundary zone Red line is FD/MD result

  21. Heat must be conserved on average 2.6 Transient Concurrent model { { Thermostat at T1c to maintain Thermostat at TNc to maintain continuum FD region continuum FD region unthermostatted MD region

  22. 2.6 Transient FD/MD simulation Blue line is full FD solution Red line is FD at ends (1-20 and 101-120) and MD in middle

  23. 3.0 Conclusions • Kapitza boundary effect • conductivity near an interface (real or artificial) is less than bulk value • can obtain desired temperature by feedback control of thermostatted boundary zone. • Thermostats for non-isothermal boundary conditions • deterministic NH thermostat minimizes Kapitza effect • although Langevin naturally thermostats each particle individually.. • ..global NH thermostat determines average temp but not distribution • responsiveness of global NH thermostat depends on no. of thermostatted atoms (important for transient b.c.s) • FD/MD coupling • Stadium damping effectively removes spurious phonon reflection from atomistic/coarse-grained interface • simple matching conditions ensure coupling between continuum and atomistic regions

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