Counterions, polyelectrolyte solutions

High sorption capacities with respect to protein macromolecules are observed when highly permeable macro- and heteroreticular polyelectrolytes (biosorbents) are used. In buffer solutions a typical picture of interaction between ions with opposite charges fixed on CP and counterions in solution is observed. As shown in Fig. 13, in the acid range proteins are not bonded by carboxylic CP because the ionization of their ionogenic groups is suppressed. The amount of bound protein decreases at high pH values of the solution because dipolar ions proteins are transformed into polyanions and electrostatic repulsion is operative. The sorption maximum is either near the isoelectric point of the protein or depends on the ratio of the pi of the protein to the pKa=0 5 of the carboxylic polyelectrolyte [63]. It should be noted that this picture may be profoundly affected by the mechanism of interaction between CP and dipolar ions similar to that describedby Eq. (3.7). 

In polyelectrolyte solutions, the counterion condensation on linear polyelectrolyte chains is known to occur when the charge density along the chain exceeds the critical value [40]. Our work indicates the existence of a critical value for the separation distance between chains, where the interchain interaction changes drastically, most likely due to the transition in the binding mode of the counterions (see Fig. 13). Many peculiar forms of behavior, which are often interpreted by the cluster formation or the interchain organization of polyelectrolytes, have been reported for high concentrations of aqueous polyelectrolytes... 

Kagawa, I. Katsuura, K. (1955). Activity of counterions in polyelectrolyte solutions. Journal of Polymer Science, 17, 365-74. 

Manning, G. S. (1969). Limiting laws and counterion condensation in polyelectrolyte solutions. 1. Colligative properties. Journal of Chemical Physics, 51, 924-33. 

Satoh, M., Komiyama, J. lijima, T. (1984). Counterion condensation in polyelectrolyte solutions a theoretical prediction of the dependences on the ionic strength and degree of polymerization. Macromolecules, 18, 1195-2000. 

By definition, in a solution all ions belong to the same phase, even though counterions may cluster more or less diffusely around the macroions. When significant amounts of a simple 1 1 electrolyte (such as KCl) are added to a polyelectrolyte solution, dissociation of the polyelectrolyte macromolecule is repressed in an extreme case the polyelectrolyte may be salted out. An undissociated polyacid may be precipitated by generous addition of a simple acid such as HCl. 

In order to resolve these challenges, it is essential to account for chain connectivity, hydrodynamic interactions, electrostatic interactions, and distribution of counterions and their dynamics. It is possible to identify three distinct scenarios (a) polyelectrolyte solutions with high concentrations of added salt, (b) dilute polyelectrolyte solutions without added salt, and (c) polyelectrolyte solutions above overlap concentration and without added salt. If the salt concentration is high and if there is no macrophase separation, the polyelectrolyte solution behaves as a solution of neutral polymers in a good solvent, due to the screening of electrostatic interaction. Therefore for scenario... 

We discuss below how this law is modified by counterions for the case of polyelectrolyte solutions. 

A polyelectrolyte solution contains the salt of a polyion, a polymer comprised of repeating ionized units. In dilute solutions, a substantial fraction of sodium ions are bound to polyacrylate at concentrations where sodium acetate exhibits only dissoci-atedions. Thus counterion binding plays a central role in polyelectrolyte solutions [1], Close approach of counterions to polyions results in mutual perturbation of the hydration layers and the description of the electrical potential around polyions is different to both the Debye-Huckel treatment for soluble ions and the Gouy-Chapman model for a surface charge distribution, with Manning condensation of ions around the polyelectrolyte. 

Formula (2.3.41) implies that in a system with added electrolyte of a higher valency z, the magnitude of the effective linear charge density is determined by the latter. Upon reduction of the concentration of the added electrolyte (N —> 0) a transition occurs in the way prescribed by (2.3.41) to the effective linear charge as determined by the proper counterions of valency Q in a polyelectrolyte solution free from added low molecular electrolyte. 

Strong evidence of ionic association was found by Stilbs and Lindman 69) in their PGSE study of aqueous polyelectrolyte solutions, polyacrylic acid and poly-methacrylic acid, neutralized by tetramethylammonium hydroxide, with or without sodium counterions. While polymer diffusion could not be detected since its T2 was too short, TMAOH and water diffusion was measured as function of degree of neutralization a, or Na+ content. A pronounced minimum of D(TMAOH) near a = 1 was interpreted in terms of a two-site model, leading to the determination that at a = 1, approximately half of the counterions are bound in both systems. Fourier transform techniques permitted the simultaneous measurement of diffusion of water and TMAOH. 

Counterions are necessary to ensure electroneutrality in polyelectrolyte solutions. Therefore, it can be energetically advantageous if a fraction of counterions are situated in the vicinity, or at the surface, of the polyion in order to reduce the charge of the polyion. To answer the question under which conditions this occurs, the concept of the counterion condensation has been introduced by Fuoss, Katchalsky and Lifson [98],Alexandrowicz and Katchalsky [99] or Oosawa [100] and subsequently theoretically developed by Manning [101-108]. 

The cell model is a commonly used way of reducing the complicated many-body problem of a polyelectrolyte solution to an effective one-particle theory [24-30]. The idea depicted in Fig. 1 is to partition the solution into subvolumes, each containing only a single macroion together with its counterions. Since each sub-volume is electrically neutral, the electric field will on average vanish on the cell surface. By virtue of this construction different sub-volumes are electrostatically decoupled to a first approximation. Hence, the partition function is factorized and the problem is reduced to a singleparticle problem, namely the treatment of one sub-volume, called cell . Its shape should reflect the symmetry of the polyelectrolyte. Reviews of the basic concepts can be found in [24-26]. 

This rather simple scheme of solution behavior is complicated by various interesting aspects. It is not at all clear that the number of dissociated or non-condensed counterions remain constant with added salt. Likewise, at high salt concentrations, the polyelectrolyte solution may no longer represent a quasi binary solution but rather a ternary mixture with the added salt representing a third component with distinctly different solvation properties as compared to water. This scenario is supported by the fact that for some salts the ordinary salting out is reversed if the inert monovalent salt concentration is further increased. In other words the chains become redissolved at an even higher salt concentration [21, 22]. Consequently, this redissolution is denoted as salting in . 

The present review deals mainly with two examples of polyelectrolyte phase behavior as discussed above. As an example for an H-type precipitation, the solution properties of polyvinylpyridinium chains are monitored as function of added inert salt. Here, we focus on the determination of the effective charge density and of the solvent quality parameter which are supposed to play a central role for the understanding of polyelectrolyte solution without specific counterion interactions. The second system under investigation comprises the interaction of polyacrylic acid with alkaline earth cations which exhibit very specific interactions, thus representing an example for type L-precipitation. Here the coil dimensions close to the phase boundary are compared to those close to type H-precipitation with inert added salt. 

The PRISM (Polymer-Reference-Interaction-Site model) theory is an extension of the Ornstein-Zernike equation to molecular systems [20-22]. It connects the total correlation function h(r)=g(r) 1, where g(r) is the pair correlation function, with the direct correlation function c(r) and intramolecular correlation functions (co r)). For a primitive model of a polyelectrolyte solution with polymer chains and counterions only, there are three different relevant correlation functions the monomer-monomer, the counterion-counterion, and the monomer-counterion correlation function [23, 24]. Neglecting chain end effects and considering all monomers as equivalent, we obtain the following three PRISM equations for a homogeneous and isotropic system in Fourier space ... 

Our model of a polyelectrolyte solution consists of Np flexible bead-spring-chains which are located in a simulation box of length L with periodic boundary conditions. For each chain, a fraction / of the N monomers is monovalently charged (v=l), and fN oppositely charged monovalent counterions are added to obtain an electrically neutral system. In some cases Ns pairs of salt ions were added. The density is given in form of the charged... 

G. S. Manning, Biophys. Chem., 7, 95 (1977). Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. 4. Approach to Limit and Extraordinary Stability of Charge Fraction. 

One of the simplest ways to observe the electrostatic effect inherent in polyion systems is to measure the activity of the counterion of the polyelectrolyte solution in the absence of simple salt. Single ion activities of these sodium salt solutions, a a, measured electrochemically by use of a Na" ion selective glass electrode can be expressed by the foUowing equation ... 

Moeawetz, H., and J. A. Shafer Characterization of counterion distribution in polyelectrolyte solution II. The effect of the distribution of the electrostatic potential on the solvolysis of cationic esters in pol3nneric acid solution. J. Phys. Chem. 67, 1293 (1963). 

This effect has been known for quite some time [76-81] and used to influence the reaction rate between the charged particles. Examples include some hydrolysis reactions [80] where a small addition of polyelectrolyte causes a dramatic acceleration of the chemical reaction between equally charged divalent counterions in solution. The effect of a polyelectrolyte on ion-ion collision frequencies has also been used to probe the distribution of ions around the polyion. For example, Meares and coworkers [82] probed the electrosta-... 

Before presenting numerical results, it is worth summarizing the main characteristics of the experimental results for the osmotic pressure of polyelectrolyte solutions [9, 17, 18, 57, 107], The measured osmotic coefficients most often exhibit strong negative deviations from ideality. The measured values are a) lower than it was predicted by the cylindrical cell model theory, b) rather (but not completely) insensitive to the nature of the counterions, and c) also insensitive to the polyelectrolyte concentration in a dilute regime and/or for... 

Nishio, T., and Minakata, A. Effects of ion size and valence on ion distribution in mixed counterion systems of a rodlike polyelectrolyte solution. 2. mixed-valence counterion systems. Journal of Physical Chemistry B, 2003, 107, No. 32, p. 8140-8145. 

Liao, Q., Dobrynin, A.V., and Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions Osmotic coefficient and counterion condensation. Macromolecules, 2003, 36, No. 9, p. 3399-3410. 

Hribar, B., and Vlachy, V. Properties of polyelectrolyte solutions as determined by the charge of counterions. Revista de la Sociedad Quimica de Mexico, 2000, 44, p. 11-15. 

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... 

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