Rapid thermal equilibration in coarse-grained molecular dynamics

Coarse-grained representations of matter are required for the investigation of material phenomena that occur simultaneously at different length and time scales. Multiple scales cause problems at finite temperature, where phonon reflection at interfaces separating different scales causes unphysical local heating in the region of the smallest (atomic) scale. A physical model is proposed, which effectively controls the temperature in coarse-grained regions while preserving correct dynamics in the atomistic region. This is achieved using a multiscale dynamic-stochastic heat bath. The validity of the model is demonstrated within the context of a coarse-grained one-dimensional Lennard-Jones chain.

Figure 1

Coarse-grained geometry of a 1D chain with ten representative atoms (●) and eight slave atoms (엯).

Figure 2

Average thermal expansion force in a fully atomistic chain with predictions from the coarse-grained potential (5).

Figure 3

(Color online) Redistribution of thermal energy between the atomistic region (AR), initially at $600\mathrm{K}$, and the coarse-grained region (CG), initially at $300\mathrm{K}$. The fully atomistic simulation (CG1) rapidly reaches an equilibrium temperature of $348\mathrm{K}$. Any coarse graining drastically reduces the rate of convergence to the equilibrium. Increasing the level of coarse graining in the CG region from $n_i=3$ (CG3) up to $n_i=9$ (CG9) exacerbates the effect. Note that this is not a model of heat conduction. Thermal equilibrium is achieved when each degree of freedom (DOF) has the same average kinetic energy. Coarse graining reduces the DOF so the average kinetic energy (and equilibrium temperature) is higher. The time scales have been adjusted so that the results are directly comparable for the reduced temperature gradients.

Figure 4

(Color online) Comparison of different thermostatting techniques to the {CG9,IF,AR,IF,CG9} chain. The AR is initially at $600\mathrm{K}$ and the rest at $300\mathrm{K}$. Results are for (a) NP to the whole chain, (b) NP to IF only, and (c) RMT to IF only, where the latter two are achieved using PTMD.

Figure 5

(Color online) Running average of temperature in the AR for no thermostatting (CGMD), thermostatting with NP applied to IF and CG9, and thermostatting with RMT applied to IF and CG9. Only RMT absorbs the high-frequency phonons at the IF, and hence correctly regulates the temperature in the AR.

Figure 6

(Color online) Velocity autocorrelation functions (in terms of momenta) of 20 atoms at the center of the AR for fully NP, PTMD with RMT, and atomistic models: applying strong thermostatting to IF and CG9 regions has not distorted the velocity autocorrelation functions inside the AR.

Figure 7

(Color online) Instantaneous temperature fluctuation of 20 atoms at the center of the AR, for fully (NP) and partially (PTMD) thermostatted simulations, compared with a fully atomistic model.