Interdisciplinary Applied Mathematics

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Figure 11.8 shows 20-A segments of the center of mass corrected water oxygen atom density profiles along the channel axis (z-direction) for atomic hydrophobic (A), LJ hydrophobic (B), and hydrophilic channels (C) with R = 2.6 A, 4.1 A, and 5.6 A. Note that for both hydrophobic channels, a transition occurs at R = 4.1 A, where the water becomes highly structured, and well-defined layers emerge. The similar results for the two hydrophobic channels suggest that an explicit treatment of the atomic structure of the channel does not have an appreciable effect on water structure. Hence, the atomic hydrophobic channels are well represented by a one-dimensional potential function. The LJ 5-3 function can be used to significantly reduce the simulation times, since this gives a good reproduction of structural properties of water. In the hydrophilic channels, the water structure exhibits a markedly different behavior, with only the narrow 2.6-A channel exhibiting some order along the channel axis.

Figure 11.9 shows the dipole orientation distribution for channels of effective radius 2.6 A (panel A), 4.1 A (panel B) and 5.6 A (panel C). The left panels    show the    average    projection    of    dipole    orientation    onto    the    z-

FIGURE 11.7. Water-oxygen atom radial density profiles: Density profiles for the atomic hydrophobic (solid curve), LJ hydrophobic (dotted curve), and hydrophilic (dashed curve) channels are compared for effective channel radii 2.1-5.6 A. All profiles are plotted against the distance from the effective wall, of the channel R-r. The left-hand vertical axis represents the effective wall, while the right-hand axis represents the channel axis г. Each graph is labeled with the effective channel radius R. (Courtesy of S.-H. Chung.)

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