Coions

Referring to Section XI-6B, the effect of the exclusion of coions (ions of like charge to that of the interface) results in an increase in solution concentration from rq to Rq. Since the solution must remain electrically neutral, this means that the counterions (ions of charge opposite to that of the interface) must also increase in concentration from Ro to Rq. Yet Fig. V-1 shows the counterions to be positively adsorbed. Should not their concentration therefore decrease on adding the adsorbent to the solution Explain. 

When this equation is applied to a system composed of a macromolecule immersed in an aqueous medium containing a dissolved electrolyte, the fixed partial charges of each atom of the macromolecule result in a charge density described by p, and the mobile charges of the dissolved electrolyte are described by /O , which i derived from a Boltzmann distribution of the ions and coions. 

Membrane Efficiency The permselectivity of an ion-exchange membrane is the ratio of the transport of electric charge through the membrane by specific ions to the total transport of electrons. Membranes are not strictly semipermeable, for coions are not completely excluded, particularly at higher feed concentrations. For example, the Donnan eqmlibrium for a univalent salt in dilute solution is ... 

The transport number is a measure of the permselec tivity of a membrane. If, for example, a membrane is devoid of coions, then all current through the membrane is carried by the counterion, and the transport number = 1. The transport numbers for the membrane and the solution are different in practical ED applications. 

One of the most rational means for displacing a broad zone is electrolyte desorption under the conditions of decreasing degree of ionization, i.e., when counterions are converted into dipolar ions, uncharged molecules and coions. This conversion corresponds to a sharp decrease in distribution coefficients of the desorbed substance. Hence, the displacement of equilibrium parame ters at a high rate of mass-exchange is one of the methods of selective stepwise chromatography. 

In the theoretical approaches of Poisson-Boltzmann, modified Gouy-Chapman (MGC), and integral equation theories such as HNC/MSA, concentration or density profiles of counterions and coions are calculated with consideration of the ion-waU and ion-ion in-... 

FIG. 5 Normalized concentration distribution in the pore of Figure 4 but charged with —0.05 C/m. The symbols are the same as in Figure 4, with the cations being the counterions. The anions (coions) of the RPM and SPM model are not distinguishable on the present scale. The dotted line is the prediction of the modified Gouy-Chapman theory and approximates the simulation results of the RPM. 

RPM model, but theories for the SPM model electrolyte inside a nanopore have not been reported. It is noticed that everywhere in the pore, the concentration of counterion is higher than the bulk concentration, also predicted by the PB solution. However, neutrality is assumed in the PB solution but is violated in the single-ion GCMC simulation, since the simulation result of the counterion in the RPM model is everywhere below the PB result. There is exclusion of coion, for its concentration is below the bulk value throughout the pore. Only the solvent profile in the SPM model has the bulk value in the center of the pore. 

Since there is normally adsorption of counterion, the exclusion of electrolytes has been conventionally defined based on the exclusion of the coion. The exclusion coefficient is de-fmed as... 

FIG. 17 Diffusion coefficients of the counterions and coions of a 1 1 RPM model electrolyte in a cylindrical nanopore of i = lOd. The circles and triangles represent the results of coions and counterions, respectively. 

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. 

Hole Correction of the Debye-Huckel Coion Density Profile The DHH Theory... 

So far in our revision of the Debye-Hiickel theory we have focused our attention on the truncation of Coulomb integrals due to hard sphere holes formed around the ions. The corresponding corrections have redefined the inverse Debye length k but not altered the exponential form of the charge density. Now we shall take note of the fact that the exponential form of the charge density cannot be maintained at high /c-values, since this would imply a negative coion density for small separations. Recall that in the linear theory for symmetrical primitive electrolyte models we have... 

Now we see that if k is large enough and a small enough then i(r) will become negative for small r before the truncation arises at r = cr. This is, of course, impossible and we must either abandon the use of the linearized DH (Debye-Hiickel) approach altogether or eliminate the negative portion of the coion density profile. 

An ion-exchange membrane consists of an ionomer, which contains fixed ions that are covalently bound to the polymer backbone. It is electrically neutral because of included counterions . If water-or probably another sufficiently polar solvent - is absorbed and if the fixed and counterions can be separately solvated to an adequate degree, the counterions become mobile and the ion-exchange membrane can work as an ion conductor. Owing to the electric field of the fixed ions coions with the same charge as the fixed ions are rejected and are typically absent inside the membrane. Thus the membrane is selective for the transfer of counterions ( permselectivity = permeation selectivity, e.g. [70]). 

OH r H CO2H HO H Marine fungi -Exserohilum rostratum Rostratin A - disuifide containing diketopiperazine with cytotoxicity against human coion carcinoma 232... 

TrCP F-Box protein substrate-recognizing part of SCF iigase Breast cancer, coion cancer, pancreatic cancer, prostrate cancer 379-382... 

CMC will change if the additive has an effect on the monomer-micelle equilibrium, and also if the additive changes detergent solubility. The CMC of all ionic surfactants will decrease if coions are added. However, nonionic surfactants show very little change in CMC on the addition of salts, which is to be expected from theoretical considerations. The change of CMC with NaCl for SDS is as follows (Figure 3.10) ... 

The positive-positive particles will show repulsion. On the other hand, the positive-negative particles will attract each other. The ion distribution will also depend on the concentration of any counterions or coions in the solution. Even glass, when dipped in water, exchanges ions with its surroundings. Such phenomena can be easily investigated by measuring the change in the conductivity of the water. 

To illustrate the principles, we simplify the ensuing discussion by considering an electrolyte consisting of two ions only, where is the counterion to the fixed charges and the coion. Keeping in mind that Equation 15.46 is of more general validity than the G-C model, it is now written... 

In Equation 15.47, the contact layer is positioned at the surface, i.e., x=0, i.e., c,(0)=c,. We now make the following assumptions first, the electrostatic repulsion is so strong that the coion concentration in the contact layer is zero, i.e., Ca=0, second, the accumulation of counterion is so high that Cbi is much higher than and Equation 15.47 is approximated to... 

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