Free ions, polyelectrolyte-counterion

Consider a dilute suspension of polyelectrolyte-coated spherical colloidal particles (soft particles) in a salt-free medium containing counterions only. We assume that the particle core of radius a (which is uncharged) is coated with an ion-penetrable layer of polyelectrolytes of thickness d. The polyelectrolyte-coated particle has thus an inner radius a and an outer radius b = a + d (Fig. 6.4). We also assume that ionized groups of valence Z are distributed at a uniform density N in the poly electrolyte... 

Figure 4 shows the most important feature of the electro-optical effect in a suspension, stabilized by polyelectrolyte adsorption. This is the appearance of an additional LF effect near the range of particle rotation (102-104 Hz) that resembles the LF effect in free polyelectrolyte solutions. The analogy is so impressive that we supposed the same origin of the LF effect in both systems. Polarization of tightly bound counterions with lower mobility in comparison to that of the free ions is proposed to explain the LF effect in stabilized suspensions [12-18], since it cannot be found in suspensions of bare oxide particles. The overlap (full or partial) of the frequency intervals of particle hydrodynamic relaxation (RF effect) and the relaxation of this additional LF effect means that the tightly bound counterions have close mobility to that of the whole colloid-polymer complex. A saturable ionic induced dipole moment probably arises due to the polarization of these coun-... 

The polyelectrolyte also affects the distribution of coions (small ions having a charge of the same sign). This is known as the Donnan effect, which may be illustrated by envisaging a system with two compartments that are separated by a semipermeable membrane. This membrane does not allow passage of polymers but is permeable for small ions. Assume that one compartment initially contains the polyelectrolyte (PEZ ) and sufficient counterions (Na+) to neutralize the charge, while the other compartment initially contains NaCl. At equilibrium, the activity of NaCl (which means the free ion activity a+) must be equal in both compartments. This implies that CD will diffuse towards the other compartment, and the condition of... 

The aqueous phase contains free (or dissolved ) counterions. These ions are either dissociated from the polyelectrolyte or result from the dissolution of the salt S. Their contribution to the Gibbs energy of the solution is ... 

Solutions of polyelectrolytes contain polyions and the free (individual) counterions. The dissociation of a polyacid or its salt yields polyanions, and that of a polybase or its salt yields polycations, in addition to the simple counterions. The polyampholytes are amphoteric their dissociation yields polyions that have anionic and cationic functions in the same ion and often are called zwitterions (as in the case of amino acids having HjN and COO groups in the same molecule). Such an amphoter will behave as a base toward a stronger acid and as an acid toward a stronger base its solution properties (particularly its effective charge) will be pH dependent, and an isoelectric point (pH value) exists where anionic and cationic dissociation is balanced so that the polyion s charges add up to zero net charge (and solubility is minimal). 

A synthetic ion-selective (ion-exchange) membrane is a dense, nonporous, mechanically stable polymer film about 0.01 —0.04 cm thick. By nonporosity we mean the absence of pores (possibly very tortuous transmembrane channels) with a typical radius above 5 — KM (10-8 cm). Structurally the membrane material is a cross-linked polyelectrolyte. This latter is a polymer containing chemical groups that while in contact with an aqueous solvent are capable of dissociation into charges which remain fixed to the polymer core and counterions which are free to move in the solution. 

The fifth term describes the free energy of a polyelectrolyte chain associated with M dipoles and N-M charges. The chain is in aqueous solution of N-M counterions and salt ions [48]. This free energy is obtained from the Edwards Hamiltonian [49]... 

Two plates grafted with polymer chains on their surface are immersed in an electrolyte solution. The two plates are considered to be located at x = 0 and D, respectively, and the system is considered to be in contact with a large reservoir containing an electrolyte solution free of polymer. Compared to the concentration of the ions of the electrolyte, the concentration of the counterions dissociated from the grafted polyelectrolyte is neglected. 

CE is a predestinate for study of polyelectrolyte counter-ion dissociation in free solution and study of the speed of this dissociation process. Counterion dissociation was studied with sodium poly(styrenesulfonates) of different molecular mass using indirect UV detection for quantification of sodium ions in the sample solution. The separation [39] was performed in an unmodified fused-silica capillary using a 0.005 mol L-1 imidazole buffer at pH 4.5 with potassium chloride as internal standard. In the electrophero-... 

Tabulated are polyelectrolyte concentration c, temperature /. Manning parameter t. ion diameter cr, distance of closest approach dca between ions and the rod, and cell radius R corresponding to the given concentration. The experiments have been performed under salt-free aqueous conditions with monovalent counterions. Source Ref. 34. 

Many theoretical models have been developed to describe the electrical polarizability of polyelectrolytes [2-4,13-40], The problem is, however, extremely complex and difficult, even if simple models are assumed for the geometry of the polyions [37]. This is because many fields are involved concentrations of small ions, the electrical potential, and the solvent velocity, to be determined as functions of space and time, which are coupled with each other through essentially nonlinear equations. Our numerical approach, however, need not introduce, as in most of the theories, somewhat ad hoc approximations such that counterions are classified into free and bound ions, only the latter contributing to the polarizability, nor neglect interactions between counterions. 

Our simulation has shown that polyions are on average completely shielded electrostatically by counterions even in salt-free solutions. Two kinds of counterions, condensed and those forming a diffuse ion atmosphere, are distinguished not only by their spatial distributions but also by their fluctuation or polarization behaviors. The contribution from condensed counterions to the radial components of the electrical polarizability tensor is very small, as has often been postulated in various theories previously. But that from the diffuse ion cloud is very large and cannot be neglected in the calculation of the anisotropy. We have succeeded in the computational reproduction of one of the characteristic properties of polyelectrolytes in salt-... 

On the contrary, that an excess of monovalent ions can compete with condensed divalent ones is out of the range of validity of Manning s model. However, the model of Iwasa (l. ) which introduces an entropic term contributing to the free energy of polyelectrolyte systems can explain that an excess NaCl displaces condensed divalent counterions. In the experiment described in Fig. 6, NaCl was added to a solution of chondroitin sulfate containing Sr " " counterions, a fraction of which are condensed. The variation of Dg shows that Sr2+ are "decondensed" by an excess NaCl, in good agreement with Iwasa s model. 

More recently, Manning has extended his theory to include those counterions that are "territorially bound" or trapped in the domain of the polyelectrolyte, but are somewhat free to move along the polyion.- Counterions that are neither condensed site-bound nor territorially-bound are in the ion atmosphere, along with the coions, if simple salt is added. The idea of counterion condensation has recently received substantiation from theoretical investigations of the Poisson-Boltzmann equation for polyelectrolyte solutions.-... 

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