Crystallization time scales, simulations

Experimentally, tire hard-sphere phase transition was observed using non-aqueous polymer lattices [79, 80]. Samples are prepared, brought into the fluid state by tumbling and tlien left to stand. Depending on particle size and concentration, colloidal crystals tlien fonn on a time scale from minutes to days. Experimentally, tliere is always some uncertainty in the actual volume fraction. Often tire concentrations are tlierefore rescaled so freezing occurs at ( )p = 0.49. The widtli of tire coexistence region agrees well witli simulations [Jd, 80]. 

In the world of molecular simulation, it would be more conventional to consider that the present model is a coarse grained model of real polymers, where the real time-scale is much longer than that of the present MD simulation time-scale. However, we did not intend to make a coarse grained model. The crystallization of polymers was shown to be rather universal. Various kinds of polymers, either fast crystallizing or slow crystallizing, were known to follow the same scheme with respect to the molecular mechanism of crystallization. So we studied this simple model expecting that the present model would also follow the same crystallization scheme and show the general molecular mechanisms of polymer crystallization. 

S Atomistic simulation assisted synthesis and investigations The classical atomistic simulation techniques based on the pair potentials are suitable for the simulations of ceria nanoparticles even with a real sized model. Molecular d)mamics studies with several thousands of ions and up to hundreds of nanoseconds in a time scale have been carried out to interpret the diffusion, and crystal growth behaviors for pure and doped-ceria nanoparticles. Traditionally, the technique has been used to explore the oxygen ionic conductivity in ionic conductors such as ceria and zirconia (Maicaneanu et al., 2001 Sayle et al., 2006). 

Crystallization usually involves very long time scales (at least when compared to time scales of routine calculations) and complicated potential energy landscapes. Computer simulations of this process are, therefore, considered to be difficult in general. In a series of papers, Haymet and coworkers investigated the structure and dynamics of the ice/water interface. In their approach, the pre-built patches of water and ice were put together to create the interface. The necessity to simulate the highly improbable creation of the crystallization nucleus was thus avoided. Similar setup was used by other groups to assess various properties of the ice/water interface. ... 

All of the simulation approaches, other than harmonic dynamics, include the basic elements that we have outlined. They differ in the equations of motion that are solved (Newton s equations, Langevin equations, etc.), the specific treatment of the solvent, and/or the procedures used to take account of the time scale associated with a particular process of interest (molecular dynamics, activated dynamics, etc.). For example, the first application of molecular dynamics to proteins considered the molecule in vacuum.15 These calculations, while ignoring solvent effects, provided key insights into the important role of flexibility in biological function. Many of the results described in Chapts. VI-VIII were obtained from such vacuum simulations. Because of the importance of the solvent to the structure and other properties of biomolecules, much effort is now concentrated on systems in which the macromolecule is surrounded by solvent or other many-body environments, such as a crystal. 

The initial state of the simulations consisted of RDX perfect crystals using simulation cells containing 8 molecules (one unit cell, 168 atoms) and 3D periodic conditions. After relaxing the atomic positions at each density with low temperature MD, we studied the time evolution of the system at the desired temperature with isothermal isochoric (NVT ensemble) MD simulations (using a Berendsen thermostat the relaxation time-scale associated with the coupling between the thermostat and the atomistic system was 200 femtoseconds). 

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