Interdisciplinary Applied Mathematics

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reasonable accuracy. Note that the strong electric field results in a much larger velocity than what is practically achievable in nanochannels. The external electric field strength used ranges from 0.38 V/nm to 0.55 V/nm. Table 12.2 summarizes the various simulations investigated in this section.


TABLE 12.2. Summary of the simulations performed.


Case ф


Channel


width


(nm)


( C/m2)


Ф Water molecules


ф Ions


Eext (V / nm)


Simulation


time


(ns)


1


3.49


+0.120


2246


32 (СГ)


-0.55


5.1


2


3.49


+0.320


2075


85 (СГ)


-0.55


2.5


3


3.49


-0.120


2246


32 (Na+)


+0.55


2.8


4


2.22


+0.120


1288


32 (СГ)


-0.46


6.3


5


0.95


+0.120


405


32 (СГ)


-0.55


9.4


6


10.00


+0.124


6606


32 (СГ)


-0.38


4.8

12.2 Ion Concentrations


Figure 12.3 (a) shows the concentration profile of Cl_ ions and water across the channel    for    case    1,    where the    channel width    is    3.49    nm and    the    wall


charge density is +0.120 C/m2. The ion distribution obtained from the Poisson-Boltzmann equation is also shown for comparison. To compute the ion distribution using the Poisson-Boltzmann equation, we have assumed that the position of the wall coincides with the position of the first peak of Cl_ ion concentration obtained from MD simulation. The MD simulation result deviates from the Poisson-Boltzmann equation prediction in several aspects:

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