Macroion-counterion interaction

The parameter n reflects the measure of deviation of the system from the behavior of the monomeric acid where n = 1, i.e., it characterizes the degree of interaction between the neighboring functional groups of the macroion. The value of n depends on the structure of the polyelectrolyte and the nature of the counterion pK = pK0 — log (1 — a)/a is the negative decadic logarithm of the effective dissociation constant of the carboxylic CP depending on a. 

The preceding analysis shows that there is a distinct lower bound for the size of the simulation cell. Below this bound, finite size artifacts heavily bias the thermodynamics and kinetics of ion accumulation. Therefore, it seems unadvisable to design simulations using neutralizing counterions alone, especially if the objective is to understand ion-mediated conformational transitions or to understand how ions interact with a macroion. The minimal number of excess ions needed to simulate 800 mm excess monovalent salt was nearly identical 800 pairs) for all of the systems studied (32 nt A-RNA, B-DNA, and the Tar—Tar RNA kissing-loop complex), indicating a simple dependence on net macroion charge. For other macromolecular solutes or other concentrations of excess salt, a box-size... 

As already indicated in Sect. 2, the osmotic coefficient 0 provides a sensitive test for the various models describing the electrostatic interaction of the counterions with the rod-like macroion. It is therefore interesting to first compare the PB theory to simulations of the RPM cell model [26, 29] in order to gain a qualitative understanding of the possible failures of the PB theory. In a second step we compare the first experimental values 0 obtained on polyelectrolyte PPP-1 [58] quantitatively to PB theory and simulations [59]. 

An important effect not taken into account by the various models discussed in Sect. 2 is the specific interactions of the counterions with the macroion. It is well-known that counterions may even be complexated by macroions and these effects have been discussed abundantly in the early literature in the field [24]. From the above discussion it now becomes clear that these effects must be traced back to specific effects which are not related to the electrostatic interaction of counterions and macroions. Hence, hydrophobic interactions related to subtle changes in the hydratation shell of the counterions could be responsible for this small but significant discrepancy of the electrostatic theory and experiment. Further studies using the PPP-polyelectrolytes will serve for a quantitative understanding of these effects which are outside of the scope of the present review. 

The osmotic coefficient obtained experimentally from polyelectrolyte PPP-1 having monovalent counterions compares favorably with the prediction of the PB cell model [58]. The residual differences can be explained only partially by the shortcomings of the PB-theory but must back also to specific interactions between the macroions and the counterions [59]. SAXS and ASAXS applied to PPP-2 demonstrate that the radial distribution n(r) of the cell model provides a sufficiently good description of experimental data. 

The characteristics of the active centers in free-radical polymerizations depend only on the nature of the monomer and are generally independent of the reaction medium. This is not the case in ionic polymerizations because these reactions involve successive insertions of monomers between a macromolecular ion and a more or less tightly attached counterion of opposite charge. The macroion and counterion form an organic salt which may exist in several forms in the reaction medium. The degree and nature of the interaction between the cation and anion of the salt and the solvent (or monomer) can vary considerably. 

Here, we propose a more realistic model of protein-electrolyte mixture. In the present case all the ionic species (macroions, co-ions and counterions) are modelled as charged hard spheres interacting by Coulomb potential as for the primitive model (Sec. 2), but the macroions are allowed to form dimers as a result of the short-range attractive interaction. Numerical evaluation of this multicomponent version of the dimerizing-macroion model has been carried out using PROZA formalism, supplemented by the MSA closure conditions (Sec. 3). 

Theoretical considerations of the coulombic interactions of dissolved biopolymers have produced a complete picture of the distributions of counter and coions under the influence of the electrostatic charge on the macroion(56,57). The counterion condensation theory of Manning(56) has stimulated a great deal of activity in the study of dissolved macroions, especially because it provides a group of limiting laws describing the contribution of electrostatic effects to the thermodynamic and transport properties of polyelectrolyte solutions. Data... 

The theory accounts for the fact that some fraction of counterions escapes from the interior of the macromolecular coil. The macromolecular coil on the whole possesses by the electrostatic charge and interacts via the screened electrostatic potential with low-molecular ions escaped from the interior of the macroion. 

It was taken into account that counterions could leave the interior of the microgel for the external solution and that both contributions of electrostatic interaction of a macroion with escaped counterions and of the osmotic pressure of counterions contribute to the swelling law of a microgel. The swelling behavior of a microgel was analyzed as a function of the number v of polymer chains in the microgel. 

If we assume that the adsorption in this system is purely driven by attractive electrostatic interactions (pine electrosorption ), it can be considered as a kind of ion-exchange process where macroions are exchanged for lithium counterions residing at the surface, so that the adsorbed amount reflects the available surface charge. As such a process is largely driven by... 

Ionic polymerizations, as we shall see later, involve successive insertion of monomer molecules between an ionic chain end (positive in cationic and negative in anionic polymerization) and a counterion of opposite charge. The macroion and the counterion form an organic salt which may, however, exist in several forms depending on the nature and degree of interaction between the cation and anion of the salt and the reaction medium (solvent/monomer). Considering, for example, an organic salt a continuous spectrum of ionicities ( Winstein... 

The larger r is, the longer the distance two macroions can affect each other. Thus, as the ionic strength (concentration) increases, the smaller the radius with which macroions can influence each other. Another way to say this is that as r gets smaller, macroions must be closer together before they can interact with each other, due to the shielding or shell of the counterions. 

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