MD simulation, atomistic

In structure matching methods, potentials between the CG sites are determined by fitting structural properties, typically radial distribution functions (RDF), obtained from MD employing the CG potential (CG-MD), to those of the original atomistic system. This is often achieved by either of two closely related methods, Inverse Monte Carlo [12-15] and Boltzmann Inversion [5, 16-22], Both of these methods refine the CG potentials iteratively such that the RDF obtained from the CG-MD approaches the corresponding RDF from an atomistic MD simulation. 

Site-site W-W radial distribution function obtained from CGMD simulation and compared with that of the atomistic MD simulation using the force-matching procedure. 

These two facts motivated a critical check of the validity of Eq. 4.11 in a wide Q-range [9,105,154,155]. For this purpose the information obtainable from fully atomistic MD simulations was essential. The advantage of MD simulations is that, once they are validated by comparison with results on the real system, magnitudes that cannot be accessed by experiments can be calculated, as for example the time dependence of the non-Gaussian parameter. The first system chosen for this goal was the archetypal polymer PL The analysis of the MD simulations results [105] on the self-motion of the main chain hydrogens was performed in a similar way to that followed with experimental data. This led to a confirmation of Eq. 4.11 beyond the uncertainties for Q<1.3 A (see Fig. 4.15). However, clear deviations from the Q-dependence of the Gaussian behaviour... 

The method aims to pass the distribution of structural parameters from the atomistic structure to the coarse-grained. The procedure involves performing an atomistic MD simulation and calculating the... 

FIGURE 2.14 Two cracked tips (under stress) are pushed onto each other in an atomistic MD simulation. Only the microstructure of dislocations (comprised by a tiny percentage of the atoms) is displayed in green all other atoms are hidden from view. 

In (98) it was mentioned that a straightforward atomistic MD simulation of a semicrystalline material is not yet achievable, since crystallite dimensions may range from several 10 nm to several microns and crystallites often aggregate to form larger domains of macroscopic dimensions (35,36). In contrast, typical MD simulations use, for completely amorphous structures, cells with a length of a few nm. Therefore to simulate a semicrystalline cell several orders of magnitude larger seems to be completely out of question for nowadays computers. The possibility to adopt a less atomistic viewpoint and use a Monte-Carlo 2-phase simulation technique for semicrystalline polymers was analysed in (98). 

Several attempts have been made to simulate transport in realistic fully atomistic MD simulations of water/Nafion mixtures. Vishnyakov and Neimark [72-74] investigated alkali transport in aqueous and methanolic solution (and in mixed solvents) in the presence of Nafion. They found indications for the existence of the fluctuative bridging mechanism. The group by Kokhlov and Khalatur has also performed extensive yet unpublished studies of simple ion transport in Nafion. Goddard and coworkers [75] compared structural and dynamical properties of two different copolymerisation patterns, in order to estimate the effect of statistical vs. regular copolymerisation of TFE with the sulfonated vinyl ether. 

Figure 15.10. Snapshots from full atomistic MD simulations showing microphase-separated structure of hydrated Nafion, at hydration levels of (a) /i = 4 and (b) h = 20. Spherical domains were cut out from the cubic MD simulation box. For visual clarity, three-dimensional Connolly surfaces were generated for the subsystem of hydrophobic atoms. The equilibrium Nafion structure consists of water-filled pores (diameter 40 A) that are connected by channels having diameter of order 10 A. This pore-channel nanostructure provides energetically favorable pathways through the nonpolar fluorocarbon matrix of the membrane for water and other mobile species.

Several other attempts have been made to model the humidified Nation nano-phase-separated structure and the temperature dependence of proton transport by atomistic MD simulations [53,59-64], It was observed that more filamentous aqueous regions at low humidity change into clusters of more micellar shape at intermediate water content, which connect into channels at high water content [60]. Other studies noted a certain effect of sidechain arrangement (statistical vs. blocks) on the size of the phase-separated regions [59]. These calculations frequently suffer from an ergodicity problem due to the different characteristic time scales of water and polymer. 

For the most part, the timescales for the aforementioned kinetic processes are well beyond the accessible timescale for fuUy atomistic MD simulations. Local dynamics such as rotation of a methyl group or a polymer side chain can certainly be explored. For example, in a polymer melt at a temperature of lOOK above the T, the timescale for methyl-group rotations is about Ips and approximately 1-lOns for segmental a-relaxation in a polymer [4b]. Diffusion for even a small molecule such as water in... 

Atomistic MD simulation/Coarse-grained MD simulation Continuum elastic modeling... 

Zuniga et al. performed fully atomistic MD simulations of isolated polyethylene chains in a vacuum [42]. Chains of 50 and 100 carbon atoms were investigated. The results of their study were in qualitative agreement with Helfand s BD simulations of polyethylene. While cooperative transition irs most often involved second-neighbors, overall most of the transitions were isolated. 

Atomistic MD simulations use the laws of classical physics and therefore can only approximate full quantum-mechanical reality. The most straightforward type of MD simulation tracks the motion of a fixed number N of atoms, constrained to move inside a fixed volume V. Because any today computer can operate only with a drastically smaller number of particles than in a real maaoscopic system, where N is 10, for emulating a large sample of matter, all the particles are placed in a box - a basic cell - which usually is a cube with a specified edge L To eliminate the influence of surface effects, one can use periodic boundary conditions in which the basic cell is surrounded by identical translated images. Any particle is free to ctoss the box boundary, and when this happens, an identical particle enters the box from the opposite side, with the same velocity vector. One can picture a periodic system either as extending infinitely far in all directions, or as a finite system in which opposite sides are artificially coupled together (see Box 5). 

In modem atomistic MD simulations the required computing power is typically proportional to N x logiV or, with well-parallelized algorithms and good spherical cutoff techniques, to N/P, where P is the number of processors. However, even one level less refined than QM, the classical MD or atomistic level, requires input of intra- and intermolecular interaction potentials. 

---