Simulation and model details

The validity of MD simulation is impacted by the choice of system, interaction potential and algorithm implemented. We first discuss the choice of system. In this work we chose to simulate Nafion with an equivalent weight (EW) of 1144 g/mol, which is a practically reasonable EW. In order to have a direct comparison of the effect of side chain length, SSC PFSA polymer electrolyte was simulated with an EW of 978 g/mol. (Commonly used SSC iono-mer has an EW 800 g/mol). The repeat units of these PFSA membranes are shown in Fig. 3. These two materials have the same backbone separating side chains thus the only differentiating feature is side chain length. 

For most of the simulations performed, each polymer is modeled with three monomers, resulting in a total of 48 CFx (x = 2 or 3) groups along the backbone. The real structure of both the oh-gomers contains at least 90 monomer units. Our choice is motivated by the following considerations. The simulation time in an MD is limited to nanoseconds. Long polymer chains have a relaxation time that can be on the order of seconds. The choice the simulator must make is whether to simulate an artificially short 

In this first task, each excess proton is permanently attached to a hydronium ion. This assumption prohibits stractural diffusion of the proton. However, for the purposes of the first task, namely the generation of molecular-level stmcture of the hydrated membrane and its interfaces, this approximation is adequate. For the second task, namely the generation of transport properties, this limitation is removed. Although, the classical MD simulations in task I cannot quantitatively characterize the stmctural diffusion mechanism, from the analysis of the hydration structure of the hydronium ions in these simulations the characteristics of Zundel and Eigen ion (which are necessary for structural diffusion) can be studied. 

For simulations that included a carbon support, a graphite surface was modeled four atomic layers deep with rigidly held carbon atoms. LJ potentials were used to describe their interaction with other atoms in the system through the parameters Gc = 3.4 A and 8c/k = 28.0 K. For simulations that included a catalyst surface, [100] Pt was modeled six atomic layers deep and was also held rigid and used the parameters apt = 2.41 A and Spt/k = 2336.0 K. The positions of carbon and Pt were taken from the literature. The number of graphite and Pt atoms used at various water contents is listed in Table 1. 

Constant temperatnre is maintained by Nose-Hoover thermostat and the equations of motion were integrated using the two time scale r-RESPA with a large time step of 2 fs and a small time step of 0.2 fs. Equilibration using these initial configurations was then carried out for at least 2 ns before beginning any produc- 

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The procedures used for estimating the service life of solid rocket and gun propulsion systems include physical and chemical tests after storage at elevated temperatures under simulated field conditions, modeling and simulation of propellant strains and bond tine characteristics, measurements of stabilizer content, periodic surveillance tests of systems received after storage in the field, and extrapolation of the service life from the detailed data obtained (21—33). 

The integral equation method is free of the disadvantages of the continuum model and simulation techniques mentioned in the foregoing, and it gives a microscopic picture of the solvent effect within a reasonable computational time. Since details of the RISM-SCF/ MCSCF method are discussed in the following section we here briefly sketch the reference interaction site model (RISM) theory. 

The important issue of size effects was addressed by Karaborni and Siepmann [368]. They used the same chain model and other details employed in the Karaborni et al. simulations described earlier [362-365] and the 20-carbon chain. System sizes of 16, 64, and 256 molecules were employed with areas of 0.23, 0.25 and 0.27 nm molecule simulations with 64 molecules were also performed for areas ranging from 0.185 to 0.40 nm molecule . The temperature used was 275 K, as opposed to 300 K used in the previously discussed work by Karaborni et al. with the 20-carbon chain. At the smaller areas no significant system size dependence was found. However, the simulation at 0.27 nm molecule showed substantial differences between N = 64 and N = 256 in ordering and tilt angle. The 64-molecule system showed more order than the 256-molecule system and a slightly lower tilt angle. The pressure-area isotherm data for these simulations are not... 

The present book is devoted to both the experimentally tested micro reactors and micro reaction systems described in current scientific literature as well as the corresponding processes. It will become apparent that many micro reactors at first sight simply consist of a multitude of parallel channels. However, a closer look reveals that the details of fluid dynamics or heat and mass transfer often determine their performance. For this reason, besides the description of the equipment and processes referred to above, this book contains a separate chapter on modeling and simulation of transport phenomena in micro reactors. 

Beginning with values of ]r) and ]v) at time 0, one calculates the new positions and then the new velocities. This method is second-order in At, too. For additional details, see Allen, M. R, and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford (1989) Frenkel, D., and B. Smit, Understanding Molecular Simulation, Academic Press (2002) Haile, J. M., Molecular Dynamics Simulation, Wiley (1992) Leach, A. R., Molecular Modelling Principles and Applications, Prentice-Hall (2001) Schlick, T., Molecular Modeling and Simulations, Springer, New York (2002). 

Using these methods, the elementary reaction steps that define a fuel s overall combustion can be compiled, generating an overall combustion mechanism. Combustion simulation software, like CHEMKIN, takes as input a fuel s combustion mechanism and other system parameters, along with a reactor model, and simulates a complex combustion environment (Fig. 4). For instance, one of CHEMKIN s applications can simulate the behavior of a flame in a given fuel, providing a wealth of information about flame speed, key intermediates, and dominant reactions. Computational fluid dynamics can be combined with detailed chemical kinetic models to also be able to simulate turbulent flames and macroscopic combustion environments. 

In PNCs, the details of molecular structure and dynamics in the periphery of the nanoparticles (for example, within the lamellar gallery or at the interface) is quite difficult to establish by regular experimental techniques. The inability to monitor the thermodynamics and kinetics of the molecular interactions between the different constituents that determine the structural evolution and final morphology of the materials hinders progress in this field. This is probably the domain where there is an increasing need for computer modeling and simulations. 

This approach was successfully used in modeling the CVD of silicon nitride (Si3N4) films [18, 19, 22, 23]. Alternatively, molecular dynamics (MD) simulations can be used instead of or in combination with the MC approach to simulate kinetic steps of film evolution during the growth process (see, for example, a study of Zr02 deposition on the Si(100) surface [24]). Finally, the results of these simulations (overall reaction constants and film characteristics) can be used in the subsequent reactor modeling and the detailed calculations of film structure and properties, including defects and impurities. 

To demonstrate the potential of two-dimensional nonresonant Raman spectroscopy to elucidate microscopic details that are lost in the ensemble averaging inherent in one-dimensional spectroscopy, we will use the Brownian oscillator model and simulate the one- and two-dimensional responses. The Brownian oscillator model provides a qualitative description for vibrational modes coupled to a harmonic bath. With the oscillators ranging continuously from overdamped to underdamped, the model has the flexibility to describe both collective intermolecular motions and well-defined intramolecular vibrations (1). The response function of a single Brownian oscillator is given as,... 

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