Charged cylindrical pores

One attraction of MD simulation is the possibility of computer animation. The mobility of ions inside a charged cylindrical pore can be visualized. Some movie clips of EMD and NEMD are downloadable at http //chem.hku.hk/ kyc/movies/. mpg. Some features that escape statistical averages can be learned in watching the animation. While the coions are present mainly in the center of the pore, occasional collisions with the wall do occur, as observed in the movie. The time scale of a coion staying near the wall is of the order of 1 ps, compared to 10 ps for the counterion. While the averaged equilibrium distributions indicate an infinitesimal concentration of coion at the wall, reaction of coion with the wall can occur within a time scale of 1 ps. From the video, it can also be observed that the radial mobility of the counterion is more significant compared to the coion s and compared to the axial mobility. It is consistent with the statistical results. 

W.R. Bowen and A.O. Sharif, The hydrodynamic and electrostatic interactions on the approach and entry of a charged spherical particle to a charged cylindrical pore in a charged planar surface—with implications for membrane separation processes, Proc. R. Soc. Lond. A 452 (1996) 2121-2140. 

The negative sign in Equation 8.90 gives the correct direction of the flow. For positively charged cylindrical pore > 0), the flow is in the opposite direction... 

We have seen in Section 8.8 that the EOF velocity generated by electric fields on the counterions adsorbed on immobile charged interfaces can be very significant. In this section, we address the effect of the EOF on the capture rate of the polymer chains in the steady state. As a specific example, consider a positively charged cylindrical pore (Figure 9.6a) with a surface electric potential... 

Fig. 4. Diagram of the two-step process to manufacture nucleation track membranes, (a) Polycarbonate film is exposed to charged particles in a nuclear reactor, (b) Tracks left by particles are preferentially etched into uniform cylindrical pores (8).

FIG. 8 Salt exclusion as a function of surface charge in a cylindrical pore in equilibrium with a 0.1 molar electrolyte. The open circles are GCMC results for 1 1 RPM electrolyte in a pore ofR = 5d The circles with a centered cross are results for a 2 1 electrolyte in a pore of = 5d. The up-trian-gles are results for a 2 1 electrolyte in a pore ofR = lOd. The solid circles are results for a 1 1 SPM model with 0.3 solvent packing fraction in a pore of = 5d. The solid squares are the same results for a pore of R = Id. 

FIG. 10 Nomalized unbalanced surface charge in a cylindrical pore with R = 5din the presence of an external potential The results, from left to right, are for original surface charge densities of —0.001, —0.005, —0.01, —0.02, —0.04, —0.05, —0.07123 C/m respectively. The x-intercepts are values of the corresponding equilibrium Donnan potentials. 

In order to see how the electrode thickness might be optimized in order to provide the lowest electrode resistivity, we have developed a theoretical model to describe the charge/discharge processes in porous carbon electrodes. As a first approximation, let us consider an electrode having two sets of cylindrical pores, namely, nanopores (NP) of less than 3 nm in diameter and transport channels (TC) of more than 20 nm in diameter, with each nanopore having an exit to only one TC. ... 

In the case of the current distribution, for the charge transfer and ohmic limitations within a wetted cylindrical pore, the complex expression in (16.76) can be reduced in the case of small activation overpotentials (or large values of electrolyte conductivity within the pores at large r2 — rx differences). 

The above model qualitatively illustrates one of the reasons for an increase in resistance, namely, that pores reduce the volume in which the current can flow. Quantitatively, however, the situation is more complex, because the pores will attain a charge in order to direct the current flow around them. The charge distribution will, in general, depend upon a pore s shape and whether or not it is isolated from other pores (i.e. has neutral material in between). Juretschke et al. [6] have shown that, for cylindrical pores that are parallel to the magnetic field (h direction) and... 

For completeness, we also consider cylindrical pores, which are appropriate for defects such as threading dislocations or nanopipes. Here the charge-conservation condition is n(w2 - rp2)LNp = 2jTrpLNss, where L is the pore length. By solving Poisson s equation in the cylindrical coordinate system [let r2 r, in Equation (9.5)], we get, again for rp [Pg.239]

FIG. 4 Radial distribution of potential inside cylindrical pores with charge-regulated walls. The charge-regulation model used in the calculation was based on the reaction set... 

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