Interdisciplinary Applied Mathematics

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FIGURE 16.1. MD simulation of hydrophobic hydration of two (16, 0) carbon nanotubes of 5 nm diameter. The white color represents hydrogen, the dark oxygen, and the grey shows molecules of the single-wall carbon nanotubes. (Courtesy of P. Koumoutsakos.)

16.1 Molecular Dynamics (MD) Method

The molecular dynamics (MD) method is suitable for simulating very small volumes of    liquid flow,    with    linear dimensions    on    the    order    of    100 nm    or

less and    for    time    intervals    of    several    tens    of    nanoseconds.    It can deal    ef

fectively with nanodomains and is perhaps the only accurate approach in simulating flows involving very high shear where the continuum or the Newtonian hypothesis may not be valid. For dimensions less than approximately ten molecules, the continuum hypothesis breaks down even for liquids (see Chapters 10 and 12), and MD should be employed to simulate the atomistic behavior of such a system. MD is, however, inefficient for simulating gas microflows due to the large intermolecular distances that require relatively large domains. Gas microflows are simulated more efficiently using the DSMC method that we describe in Section 15.1.

Another emerging application of MD simulation is investigation of the fluid-thermal behavior of carbon nanotubes, such as the one shown in Figure    1.23,    from    first    principles.    Carbon    nanotubes    have    very    interest

ing hydrophobic and hydrophilic behavior, as discussed in Section 13.2.1.

In Figure 16.1 we show the results of a constant-temperature (300 K) MD simulation of hydrophobic hydration around two carbon nanotubes of 5 nm diameter (Walther et al., 2001b). The objective is to quantify the behavior of water in the presence of single-wall carbon nanotubes and obtain the wetting angles for different systems.

Molecular dynamics (MD) computes the trajectories of particles that model the atoms of the system, since they result from relatively simplified interaction force fields. The MD simulations generate a sequence of points in phase space as a function of time; these points belong to the same ensemble, and they correspond to the different conformations of the system and their respective momenta. An ensemble is a collection of points in phase space satisfying the conditions of a particular thermodynamic state. Several ensembles, with different constraints on the thermodynamic state of the system, are commonly used in MD. For example:

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