Molecular simulation, relative performances

Finally, we were led to the last stage of research where we treated the crystallization from the melt in multiple chain systems [22-24]. In most cases, we considered relatively short chains made of 100 beads they were designed to be mobile and slightly stiff to accelerate crystallization. We could then observe the steady-state growth of chain-folded lamellae, and we discussed the growth rate vs. crystallization temperature. We also examined the molecular trajectories at the growth front. In addition, we also studied the spontaneous formation of fiber structures from an oriented amorphous state [25]. In this chapter of the book, we review our researches, which have been performed over the last seven years. We want to emphasize the potential power of the molecular simulation in the studies of polymer crystallization. 

The difference in the preferred binding mode observed for the Pd- and Ni-based catalysts can be the crucial factor determining activity/inactivity of these two systems in polar copolymerization. However, the question arises about the stability of the alternative binding modes at finite temperature. If the minima were separated by relatively low barriers and fast interconversion between the two isomer complexes could occur, then this difference would be of minor importance. In order to check the stability of the two modes and get the insight into the mechanism of possible interconversions, a series of molecular dynamics simulations was performed. 

In most cases we apply now the method—coined by Coutinho and Canuto [81,82] as sequential MC (SMC) or sequential MD (SMD)—in which an all-classical simulation is performed from which, after equilibration, a relative small number of snapshots of uncorrelated solute-solvent configurations are collected. In Ref. [81] these authors show that a relatively small number of configurations—small with respect to the total number generated in the simulation—contains all statistically relevant information. Then from QM or QM/MM calculations on the snapshots the (electronic) molecular properties in solution are obtained by averaging, or otherwise collected. In the original paper the saved solute-solvent configurations were subjected to an all-QM calculation. We apply this technique generally with only the solute as QM part for reasons already mentioned above. 

The Relative Performances of Several Scientific Computers for a Liquid Molecular Dynamics Simulation... 

The extended simple point charge (SPC/E) model [59] is used. This model is known to give reasonably accurate values of static dielectric permittivity of liquid water at ambient conditions [60]. The MD simulations were performed for both H2O and D2O with the system size of 1024 particles at 220 K, 240 K, 267 K, 273 K, 300 K, and 355 K. The parallel molecular dynamics code for arbitrary molecular mixtures (DynaMix) is implemented by Lyubartsev and Laaksonen [61]. The simulations have been carried out on a Linux cluster built on the Tyan/Opteron 64 platform, which enables calculations of relatively long trajectories for a system of 1024 water molecules. The simulation run lengths depend on temperature and are in the range between 1 ns and 4 ns for the warmest and coldest simulation, respectively. As the initial condition was a cubic lattice, the equilibration time was chosen to be temperature dependent in the range from 200 ps at 355 Ktol ns at 200K. 

All of our atomistic simulations were performed using standard Grand Canonical Monte Carlo (GCMC) and Equilibrium Molecular Dynamics (EMD) simulation methods. The RASPA [15] code was employed. Electrostatic energies were calculated using Ewald summation [16, 17] with a relative error of 10 . A 12 A van der Waals cutoff was used for the short-range interactions. Periodic boundary conditions were employed. 

Two sets of methods for computer simulations of molecular fluids have been developed Monte Carlo (MC) and Molecular Dynamics (MD). In both cases the simulations are performed on a relatively small number of particles (atoms, ions, and/or molecules) of the order of 100simulation supercell. The interparticle interactions are represented by pair potentials, and it is generally assumed that the total potential energy of the system can be described as a sum of these pair interactions. Very large numbers of particle configurations are generated on a computer in both methods, and, with the help of statistical mechanics, many useful thermodynamic and structural properties of the fluid (pressure, temperature, internal energy, heat capacity, radial distribution functions, etc.) can then be directly calculated from this microscopic information about instantaneous atomic positions and velocities. 

The most striking news that one learns when studying vapor-liquid phenomena is that not only does the vapor need to nucleate a liquid droplet to condense, but that also the liquid needs to nucleate a gas bubble to evaporate [24]. On the theoretical side, the simulation is made easier because the vapor is relatively simple to handle, on the experimental side, vapor pressure measurements in vapor-liquid equilibrium are fairly easy to perform. The Gibbs ensemble Monte Carlo method (Section 9.8) can be applied to the vapor-liquid equilibrium with considerable success vapor pressure curves, second virial coefficients, and other equilibrium properties can be calculated by molecular simulation, and, remarkably, good results can apparently be obtained by highly accurate ab initio quantum mechanical potentials [25a] or by simple empirical potentials [25b]. 

Figure 2 A simulation of the autocorrelation function, AC(x), of the donor fluorescence calculated for different diffusion coefficients of one molecular end relative to the other end. The calculations were performed for a model oligopeptide whose end-to-end distance distribution function is given in Fig. 5, Ref. 15 (curve 8). R was assumed to be 25A. The time scale is given in units of 10 sec and each curve is marked by the value assumed for the intramolecular diffusion coefficients in units of 10 1( cm /sec. AC() is given in arbitrary units. (Reprinted with permission from Ref. 17).

In order to obtain information on the poly(PDBF) molecular structure, molecular dynamics (MD) simulations were performed for a PDBF 20-mer model created on the basis of the DBF oligomer conformation in crystal (see X-ray Crystal Analyses section) under a constant NVT condition with COMPASS force field at 300 K for 8.6 ns. The simulation afforded the structure shown in Fig. 40 in which the neighboring fluorene moieties stack on top of each other in a chiral, slightly twisted arrangement. The entire chain formed a relatively long-pitched helical structure in the simulation. Hence, the local twist and the helix may contribute to the CD spectra. 

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