Nose-Hoover Barostat

Similar to the Nosd-Hoover thermostat, the extended system method has been applied to create a barostat (Hoover 1986) that is coupled with a Nose-Hoover thermostat. In this case, the extra 

In addition to the variables that are a part of the equations of motion, there is a variable Q that represents the mass of the piston. This is analogous to the mass variable in the Nos -Hoover thermostat. In practice, the required input for the Nos6-Hoover barostat will include  

Like in the case of the Nos6-Hoover thermostat, care must be taken when selecting the value of the variable Q. A small value of Q is representative of a piston with small mass, and thus will have rapid oscillations of the box size and pressure, whereas a large value of Q will have the opposite effect. The infinite limit of Q results in normal molecular dynamics behavior. 

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Here the constant k is the compressibility of the system. Such barostat methods are again widely used, both in MC and MD simulations, but do not produce strictly correct ensembles. Alternatively, the pressure may be maintained by a Nose-Hoover approach in order to produce a correct ensemble. 

Nose-Hoover thermostat [40] and Shinoda barostat [41] are applied at MD runs. As a fluid medium is simulated, the external pressure is established by changing only the size of the simulation box to fit the pressure tensor component to the target value. The sizes Lx and Ly remain the same during the simulation, and the isotropic stress tensor is maintained hydrostatically by the fluid phases. The simulations are carried out for 1.5 million timesteps, or 6 ns, and component densities are then averaged over the last 500,000 timesteps in 100 bins along the z-axis to obtain the profiles. 

The simulations are performed with the Nose-Hoover thermostat and Shinoda barostat. The MSDs are calculated by both time averaging along the individual MD trajectories and ensemble averaging over several trajectories. 

The MD simulations can be perfomed in maity different ensembles, such as grand canonical (pVT), microcanonical (NVE), canonical (NVT) and isothermal-isobaric (NPT). The constant temperature and pressure can be controlled by adding an appropriate thermostat (e g., Berendsen, Nose, Nose-Hoover, and Nose-Poincare) and barostat (e.g., Andersen, Hoover, and Berendsen), respectively. Applying MD into polymer composites allows us to investigate into the effects of fillers on polymer stracture and dynamics in the vicinity of polymer-filler interfaee and also to probe the effects of polymer-filler interactions on the materials properties. 

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