The Molecular Dynamic Technique

In addition to the study of atomic motion during chemical reactions, the molecular dynamics technique has been widely used to study the classical statistical mechanics of well-defined systems. Within this application considerable progress has been made in introducing constraints into the equations of motion so that a variety of ensembles may be studied. For example, classical equations of motion generate constant energy trajectories. By adding additional terms to the forces which arise from properties of the system such as the pressure and temperature, other constants of motion have been introduced. 

Using a realistic model for PE, the molecular dynamics technique is used to simulate atomic motion in a crystal. The calculations reveal conformational disorder above a critical temperature. The customarily assumed RIS model is found to be a poor description of the crystal at elevated temperature. 

The molecular dynamic technique has been validated for water structures through comparison of calculated properties with experimental thermodynamic water data, such as the density maximum, the high heat capacity, and diffraction patterns (Stillinger and Rahman, 1974) as well as the hydrate infrared (vibrational) spectral data by Bertie and Jacobs (1977, 1982). With acceptable comparisons of many computed and experimental properties of water structures, there is little doubt that a substance similar to water has been simulated. 

The computer simulations employed the molecular dynamics technique, in which particles are moved deterministically by integrating their equations of motion. The system size was 864 Lennard-Jones atoms, of which one was the solute (see Table II for potential parameters). There were no solute-solute interactions. Periodic boundary conditions and the minimum image criterion were used (76). The cutoff radius for binary interactions was 3.5 G (see Table II). Potentials were truncated beyond the cutoff. 

We illustrate the molecular dynamics technique by application to the ion beam deposition technique. Molecular dynamics could be used to investigate the effect of deposition conditions on the microstructure of the growing film. The microstructural characteristics of interest include film roughness and porosity. 

The trend pointing to the future is the molecular dynamics technique, and treatments ofthis kind were discussed in Section 2.17. The leaders here are Heinzinger and Palinkas (in the 1990 s), and the major thing to note is that the technique provides needed information on the number of waters in the first shell. The MD method does this by calculating the distribution function (Section 2.17.2) and may also provide information on a second layer, lifetimes of the solvent molecules in the hydration sheath, and so on. 

An interesting application of the molecular dynamics technique on single chains is found in the work of Mattice et al. One paper by these authors is cited here because it is relevant to both RIS and DRIS studies and deals with the isomerization kinetics of alkane chains. The authors have computed the trajectories for linear polyethylene chains of sizes C,o to Cioo- The simulation was fully atomistic, with bond lengths, bond angles, and rotational states all being variable. Analysis of the results shows that for very short times, correlations between rotational isomeric transitions at bonds i and i 2 exist, which is something a Brownian dynamics simulation had shown earlier. 

Finally, diffusion of SFs in the globular [18] and cylindrical pore[19] models of the silica gel was studied by the molecular dynamics technique as a function of coverage. 

Dynamical properties of the commensurate and uniaxial incommensurate phases according to the model of Refs. 232, 340, and 342 could also be explored by the molecular dynamics technique used [203, 352]. It is found that in-plane and out-of-plane motions can be analyzed separately for ori-entationally ordered N2 on graphite [203]. The 40-ps simulations below the orientational ordering transition (see Ref. 342) show [203] that the amplitude of reorientation is small and the out-of-plane motion nearly harmonic in both phases, whereas the in-plane motion is more complex, because it is anhar-monic and collective. The out-of-plane motion in the disordered phases is still harmonic, but more strongly damped, and the in-plane dynamics cannot be analyzed any more in terms of a cumulant expansion. Thus, there is little qualitative difference between the reorientational motion observed in the commensurate and uniaxially compressed solids. Only the out-of-plane motion is slightly less damped in the uniaxial phase, and the fluctuations from the planar configuration are more pronounced. 

Molecular dynamics simulations have proven to be very useful in understanding I2 photodissociation and recombination in a variety of solvents. The work by many groups is a beautiful example of the productive interaction between analytic theory, simulation, and experiment. Although the more recent experiments on this system from Harris and co-workers,i i Hopkins and co-workers,and Zewail and co-workers i i raise a number of new and interesting questions, we have little doubt that the molecular dynamics techniques can be extended to help understand these new results as well. 

In the next section, the basic features of the structure of silicate glasses will be reviewed, followed by a description of the molecular dynamics technique. Then, its application to a number of systems will be discussed. The general theme will be how compositional changes alter the atomic structure, and how the changing structure controls an important transport property, the migration of alkali ions in the structure. 

LIMITS AND RESTRICTIONS OF THE MOLECULAR DYNAMICS TECHNIQUE FOR SURFACTANT SIMULATIONS... 

Limits and Restrictions of the Molecular Dynamics Technique for Surfactant... 

One of the most powerful theoretical tools for modeling carbohydrate solution systems on a microscopic scale and evaluating the degree of flexibility of these molecules is the molecular dynamics technique (MD) which has become popular over the last two decades. The first reported works of MD carbohydrate simulation appeared in 1986 and since then an in-... 

Although the molecular-dynamics techniques sketched above will continue to be useful in a wide variety of applications, they do have some important shortcomings. Reasonably converged results often require rather large trajectory samples (e.g.,... 

For many problems, however, it is more convenient to keep the temperature, pressure, or chemical potential constant, instead of the total energy, volume, and number of particles. Generalizations of the molecular dynamics technique to virtually any ensemble have been developed, and they will be discussed in the following chapters. Of course, constant temperature MD does not conserve the total system energy, allowing it to fluctuate as is required at constant temperature. Similarly, volume is allowed to fluctuate in constant pressure molecular dynamics. The trick is to make these quantities fluctuate in a manner consistent with the probability distribution of the desired ensemble. 

Vakhrushev A. V., Fedotov A. Yu., Vakhrushev A.A. Modeling of processes of composite nanoparticle formation by the molecular dynamics technique. Part 1. Structure of composite nanoparticles. Nanomechanics Science and Technology. An International Journal, DOI 10.1615/NanomechanicsSciTechnoUntJ.v2.il.20, vol. 2, issue 1, pp. 9-38,2011. 

Acknowledgments The results presented in this chapter were obtained during a 5 years collaboration with Dr. Christophe Krzeminski. I acknowledge Pr. Fabrizio Cleri for the numerous discussions on the molecular dynamics technique and on the physics of recrystallization. 

The dissipative particle dynamics (DPD) method is a recent variation of the molecular dynamics technique. Here, in addition to Newtonian forces between hard particles, soft forces between particles are also introduced. These pairwise damping and noise forces model slower molecular motions. The dissipative forces also reduce the drift in kinetic energy that occurs in molecular dynamics simulations. These two reasons mean that DPD can be used to model longer time-scale processes, such as hydrodynamic flows or phase separation processes. 

In the hybrid materials based on the SiC nanoparticles and host polymer matrixes, the origin of the EO behaviour is intimately connected to the hyperpolarizabilities intrinsically involved in the SiC and depends on the interactions at the host-guest interfaces. The intrinsic effect originates from the nanocrystallite bulk in agreement with the EO behavior of 3C-SiC thin films (Vonsovici et al. 2000). The effect of the surrounding polymer on the nanocrystal nonlinear optical behavior was evaluated by numerical methods. In this case the molecular dynamic technique was first used to build the relevant architectures, which combine SiC nanocrystals and the polymers. In a second step, the EO parameters were computed and exhaustive comparison with experimental results was achieved and underlines the strength of the developed theoretical and numerical approaches. 

Both equilibrium and nonequilibrium information can be obtained by the molecular dynamics technique. If the initial state of the system simulates a specific nonequilibrium state, the relaxation of the system toward equilibrium can be studied, giving information on transport properties. After a sufficient time, the molecules will settle into motions that simulate the motions of molecules in equilibrium liquids, and equilibrium properties can be calculated. 

Molecular dynamics simulation techniques maintain certain advantages over other simulation techniques. The primary advantage of the molecular dynamics techniques is that during a simulation the time evolution of a system follows a reversible trajectory through phase space. As a result, dynamic properties of the system can be determined directly. Expression of the potential energy of a system of molecules in terms of simple intramolecular and intermolecular potential functions allows for the calculation... 

The molecular dynamics technique is well suited for parallel computations, since the necessary computations are the same for all particles. We can use this natural parallelism if during the computation each processor calculates the trajectories of all particles that are assigned to this processor. An alternative would be not to distribute parts of the simulation box, but to assign particles to processors. However, this would imply communication between every pair of processors, in order to look for close atoms. This is known to perform poorly for large simulation systems and processor networks. 

These particular quantities were calculated for system of 108 particles using the Molecular Dynamics technique (Hentschke et al.), but Metropolis Monte Carlo could have used instead. 

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