Mobile counterion distribution

Effects Due to Polarization of Counterion Distribution.—We consider first spherical particles (of radius a) with a layer of counterions which are freely mobile on the surface, but which cannot escape into the solvent because of the strong attractive forces of the highly charged partide. Without external manipulations, a symmetrical distribution of counterions can be assumed. After application of an external field, a displacement of counterions will occur which leads to some asymmetry of the distribution. The final equilibrium is determined by the opposing effects of the field and the diffusion of counterions, which tends to restore a random distribution. It can be shown that the phenomenon may be quantitatively described by a frequency-dependent complex surface conductivity... 

In most cases an external electric field is applied across the material with the result that the mobile carrier distribution will experience drift in the field toward a new position. Even in the absence of an applied field, the nonuniform distribution of the mobile charge carriers created will lead to their relocation due to diffusion. Although the free carriers are generated where the optical intensity is high, their recombination with counterions (in the case of hole transport these are anions) may occur anywhere in the medium. This includes recombination where the intensity is low, resulting in the separation of the charge distributions. Subsequent optical excitation is unlikely in these darker regions. We know that the counterions exist in... 

The mobile charge distribution becomes displaced relative to the static counterion distribution. This leads to localized regions with a nonzero net charge density, whilst the material remains close to neutral as a whole. Gauss law of electrostatics... 

The translational mobility of an ion is different by one to two orders of magnitude between moving freely in a solution and diffusing with an entity of colloidal dimensions such as a micelle. This allows counterion self-diffusion coefficients to be used for characterization of counterion distribution, for example, in terms of a counterion association degree. 

In Fig. 6, the star size R and the excess concentration of counterions at the outer cell boundary, r = D, are presented as a function of the number of arms, p, for different values of a (shown by solid lines). Dotted lines in Fig. 6b, indicate the corresponding expectations for uniform distribution of the cell counterions. An increase in the number of arms in each star implies an increase in the number of charged monomers Q = paN, and in the corresponding number of mobile counterions in the cell. Figures 6 and 7 clearly demonstrate a transition from a barely charged to an osmotic star behavior upon the increase in p. At a relatively small number of arms, the star size and the concentration of counterions at the outer cell boundary grow as a function of p. The latter is approximately proportional to p and is close to the average counterion concentration in the cell. This proves that ions... 

A charged molecule or surface P attracts the mobile salt ions that have the opposite charge to P, called the counterions. P repels the mobile ions of the same sign, called the co-ions (see Figure 23.1). The counterions distribute around P and act as a sort of electrostatic shield, reducing the electrostatic potential that is felt by a particle more distant from P. The interface between P and the neighboring salt solution is called the electrical double layer, the first layer is the charge on P, and the second layer is the adjacent diffuse sea of excess counterions. 

As mentioned above, experimental protocols are challenging in order to directly probe isolated polyelectrolyte chains, such as their sizes, counterion distributions, and electric potential variations inside and outside the coils. These quantities are sometimes deduced from measurements of other quantities, such as the electrophoretic mobility. The interpretation of data in these indirect measurements also depends heavily on reliable theories. The theoretical... 

An analysis of the hydration structure of water molecules in the major and minor grooves in B-DNA has shown that there is a filament of water molecules connecting both the inter and the intra phosphate groups of the two strands of B-DNA. However, such a connectivity is absent in the case of Z-DNA confirming earlier MC simulation results. The probability density distributions of the counterions around DNA shows deep penetration of the counterions in Z-DNA compared to B-DNA. Further, these distributions suggest very limited mobility for the counterions and show well defined counter-ion pattern as originally suggested in the MC study. 

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. 

Later work (8,15) showed that the value of a increased with increasing electrolyte concentration and that it could be correlated with the electrophoretic mobility. Table IX shows that the electrophoretic mobility measured using the Micromeritics Mass Transport cell increased with increasing a as observed for IT, Na+, and Ba++ counterions. These results also show that the distribution of the counterions in the electric double layer is critically dependent upon the nature of the counterion, e.g.,... 

---