Atomistic system

Molecular dynamics simulations ([McCammon and Harvey 1987]) propagate an atomistic system by iteratively solving Newton s equation of motion for each atomic particle. Due to computational constraints, simulations can only be extended to a typical time scale of 1 ns currently, and conformational transitions such as protein domains movements are unlikely to be observed. 

Fig. 4.1. Schematic representation of three numbered steps in a MC simulation on a high coordination lattice (solid arrows) that replace a simulation of the fully atomistic system in continuous space (single dashed line)...

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. 

Figure 8-1. Coarse-graining procedure, (a) A snapshot of an atomistic system, (b) Groups of atoms of the atomistic system are combined into CG sites in order to reduce the number of degrees of freedom, (c) The atomistic system of (a) as represented by CG sites...

Model systems can be, on the one hand, subjected to a static structure optimization. There, the fact is considered that the potential energy of a relaxed atomistic system (cf. Equation 1.1) should show a minimum value. Static optimization then means that by suited numeric procedures the geometry of the simulated system is changed as long as the potential energy reaches the next minimum value [16]. In the context of amorphous packing models, the main application for this kind of procedure is the reduction of unrealistic local tensions in a model as a prerequisite for later molecular dynamic (MD) simulations. 

ReaxFF describes the total energy of an atomistic system with three main terms i) covalent (bonds, angles, torsions, etc.), ii) electrostatics with environment-dependent charges, and iii) van der Waals interactions. Covalent interactions are based on the concept of partial bond orders that are calculated solely from atomic positions (no pre-determined connectivities). Once the bond order between every pair of atoms is known, bond energies, angles, and torsions are determined. The second key concept in reactive force fields (also used in the... 

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). 

All optimizations were performed with the open-source MS IBI Python package we developed [33], which calls HOOMD-Blue [34-36] to run the CG simulations and uses MDTraj [37, 38] for RDF calculations and file-handling. CG simulations were run at the same states as the atomistic systems. Initial CG configurations were generated from the CG-mapped atomistic trajectories at each state. As a result of the 4 1 mapping, CG water simulations contained 1,458 water beads. All CG simulations were run with a 10 fs timestep. The derived CG potential was set to 0 beyond the cutoff of 12 A. 

The basic concept to connect both scales of simulation is illustrated in Fig, 7, The model system is a periodic box described by a continuum, tessellated to obtain finite elements, and containing an atomistic inclusion, Any overall strain of the atomistic box is accompanied by an identical strain at the boundary of the inclusion. In this way, the atomistic box does not need to be inserted in the continuum, or in any way connected (e,g, with the nodal points describing the mesh at the boundary of the inclusion). This coupling via the strain is the sole mechanism to transmit tension between the continuum and the atomistic system. The shape of the periodic cells is described by a triplet of continuation (column) vectors for each phase (see also [21]), A, B, and C for the continuous body, with associated scaling matrix H = [ABC], and analogously a, b, and c for the atomistic inclusion, with the scaling matrix h = [abc] (see Fig, 8),... 

The material morphology is specified by a set of nodal points in the continuum description. The inclusion boundary is defined by a mesh of vertices xf b for boundary). The exterior of the inclusion contains the vertices xt (c for continuum). Inside the atomistic system, the (affine) transformations obtained by altering the scaling matrix from ho to h can be expressed by the overall displacement gradient tensor matrix M(h) = hho, The Lagrange strain tensor [40] of the atomistic system is then... 

The MC and MD simulation approaches have become viable only after the introduction of fast computers. Starting from the pioneering works of Metropolis etal. [101] and Alder and Wainwright [102], the basic algorithms on which computer simulations are based were developed in the ensuing 20-30 years. They are now well established and described in standard textbooks [95,96], and able to provide a useful link between experiment and theory. Nowadays MC simulations are typically used for lattice and simple off-lattice models, while MD models are largely employed for atomistic systems (which are tricky to sample with MC) but also for coarse-grained models. 

In the following, a recipe is provided of typical CGMD simulations of the PEM microstructure. In the first step, the atomistic system must be mapped onto a coarsegrained model, in which spherical beads with predefined, subnanoscopic length scale replace groups of atoms. The CGMD model uses polar, nonpolar, and charged beads to represent water, polymer backbones, anionic sidechains, and hydronium ions in a hydrated ionomer system (Marrink et al., 2007). 

The first calculation on atomistic systems of chain molecules near solid surfaces was performed in Ref. 21 modeling the surfaces as two impenetrable walls placed at a distance much greater than the molecular dimensions. The overall chain density of the model has been chosen such that the local density far from the walls was equal to that of the bulk liquid at 300 K. Since all the properties of molecules far from the walls were found to match those of unperturbed chains, as described by the rotational isomeric state (RIS) model at this temperature, the chains in contact with the impenetrable walls can be considered to be in equilibrium with the unperturbed bulk liquid. 

As discussed in Section 8.2, the atomistic systems have been limited to rather low molecular weight hydrocarbon systems. In attempting to gain general understanding for high molecular weight polymer systems, one popular... 

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