Interdisciplinary Applied Mathematics

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Time Lag (ps)

FIGURE 11.22. Water dipole correlation function inside nanotubes at 300 K.

Dipole Correlation

The reorientability of the water molecules can also be characterized by an autocorrelation function (ACF) of the water dipoles. The ACF is defined


c(t) = <M0) • »(t)>/<v2>,

where ц is the water dipole and the angle bracket denotes average over time and molecules. The reorientability of the water molecules plays an important role in determining the dynamic properties of water (e.g., viscosity, diffusivity).

(Mashl et al., 2003) studied the reorientability of the water molecules inside carbon    nanotubes;    Figure    11.22    shows    the    ACF    obtained    for    wa

ter inside carbon nanotubes of various diameters. It was observed that for water in wide nanotubes, the ACFs generally take a bulk-like character. However, for smaller nanotubes, the appearance of a plateau suggests that the hydrogen bonds tend to form very rapidly and can be maintained for a much longer time compared to those in the bulk. An interesting observation is that the water molecules in the 8.6-A nanotube show the largest degree of rotational immobilization, while the ACF of water molecules inside nanotubes that are slightly narrower or wider shows almost bulk-like behavior.

FIGURE 11.23. The distribution of the x- (circles), y- (triangles) and г-components (rhombi) of the translational velocities of water molecules at steady state. The solid line corresponds to the Boltzmann-Maxwell distribution. (Courtesy of J. Fischer.)

Velocity Distribution Function

The velocity distribution of water at a given temperature is a fundamental property, and in bulk it follows the Boltzmann-Maxwell distribution. However, whether water confined in a nanochannel would still obey the same velocity distribution is not that obvious. (Lishchuk and Fischer, 2001) studied the velocity distribution function of water confined in a 2.06 nm wide slit pore under an external microwave electric field. Figure 11.23 shows the distribution of the x-, y- and z-components of the velocity of water inside a 2.06 nm slit pore. It is observed that the velocity distribution obtained from the simulation agrees very well with the classical Boltzmann-Maxwell distribution.

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