Interdisciplinary Applied Mathematics

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(Note that p,dip, e, Dseif, Econflg, and Tmax denote the dipole moment, dielectric constant, self diffusion coefficient, average configurational energy, and maximum    density    temperature.    All    the    data    are    at    25° and 1    atm,

except * at 20°.

density distribution and dipole orientation of the water molecules near a surface is crucial for understanding the electrochemical reaction at a surface (Henderson et al., 2001). In recent years, experimental techniques have improved dramatically, and it is now possible to probe the structure of a liquid at atomistic detail (Toney et al., 1994; Cheng et al., 2001). For example, based on x-ray scattering measurements, (Toney et al., 1994) have proposed that water is ordered in layers extended to about three molecular diameters from an electrode surface and that water density near a charged electrode is very high. Though these experiments can provide good insight into water density distribution and dipole orientation, they cannot provide detailed and direct information of these functions; rather, they provide information about the integrals involving these functions. In addition, these experiments can probe only relatively simple geometry and cannot be used easily to study how the various parameters (e.g., surface characteristics) influence the static behavior of water in confined states. To this end, atomistic simulations have been more sucessfully used, and we will review some of the interesting results here.

11.2.1 Density Distribution and Dipole Orientation

There is an extensive literature on the density distribution and dipole orientation of water near a one-dimensional surface (Henderson et al., 2001; Yeh and Berkowitz, 2000; Spohr et al., 1998; Galle and Vortler, 1999; Gordillo and Marti, 2003; Puibasset and Pellenq, 2003; Muller and Bubbins, 1998) (1-D confinement), inside a cylindrical pore (Henderson et al., 2001; Allen et al., 1999; Rovere and Gallo, 2003; Walther et al., 2001a; Allen et al., 2002;

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