Interdisciplinary Applied Mathematics

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FIGURE 11.30. Trajectories of individual water molecules in a nanopore in a silicon dioxide membrane 8 A in diameter and 6 nm long.


is empty.


Sensitivity to Nanotube Radius and Partial Charges on the Wall


(Allen et al., 2003) studied the filling and emptying in an artificial ion channel with varying diameter and different permittivities of the membrane surrounding the channel. They found that the permeation of a pore of fixed    length    is    very sensitive    to the    pore    radius.    For very    narrow    pores


(R < 0.55 nm in their simulations), water molecules are excluded from the pore. As the pore radius increases to a threshold value (R = 0.60 nm when the permittivities of the membrane is 1.0), intermittent permeation occurs, and the pore fluctuates between the “filled” and “empty” states stochastically. Further increase of the pore radius (e.g., R > 0.65 nm) then leads to    the    complete    filling    of    the    pore.    The    threshold    radius    is sensi


tive to the permittivity of the channel membrane, and using a polarizable membrane results in a decreased threshold radius for the intermittent permeation. In contrast to what was reported for a small carbon nanotube, where the water filled in the nanotube forms a one-dimensional chain, the authors    found    that the    filled    channel    contains a    much    larger    number    of


water molecules, and these water molecules exhibit a bulk-like behavior. Such a difference is mainly caused by the different properties of the pore surface. The simulations also reveal that the filling process is preceded by formation of a percolating chain of water molecules through the nanopore (see Figure 11.32), and the channel filling seems to “nucleate” around a percolating cluster. The proposed filling mechanism can be understood by

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