Site-bound ions, polyelectrolyte-counterion

These arguments for simple electrolytes can be extended to the relationship between the two types of bound counterion in polyelectrolytes the bound but mobile (atmospheric) and the localized (site-bound). Under equilibrium conditions, the relationship between site-bound and atmospheric ions is... 

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.-... 

On the other hand t and A r contain the rate constants of the equilibrium under study and, for bimolecular reactions, the concentrations of the species involved in the reaction [4b, 8]. Had counter-ion site binding been a one step process the determination of t would have provided a direct estimation of the lifetime of the bound counter-ions and, therefore, of the exchange rate between bound and free counterions. On the other hand the study of as a function of concentration would have permitted to obtain informations on the distribution of bound counterions between those bound with and without dehydration. Unfortunately, as will be shown in Section 4, site binding is a multistep process involving at least two equilibria. All of the unknown quantities involved in such a process (four rate constants, two volume changes and the concentrations of the species) cannot be obtained from ultrasonic absorption data alone. Independent measurements become necessary. For this purpose we have measured the density d of the polyelectrolyte solutions from which can be obtained the apparent molal volume FcP of the polyelectrolyte CP (C counterion, P polyion) according to ... 

A very versatile approach to the formation of multilayer films has been developed by Decher, based on polyelectrolytes. If a solid substrate with ionic groups at the surface is dipped into a solution of a complementary polyelectrolyte, an ultrathin, essentially monomolecular film of the polyion is adsorbed [340]. The adsorption is based on pairing of surface bound ionic sites with oppositely charged ions, bound to the macromolecule. The polymers adsorb in an irregular flattened coil structure and only part of the polymer ions can be paired with the surface ions (Figure 29a). Ionic sites which remain with small counterions provide anchor points for a next layer formed by a complementary polyelectrolyte [342,343]. This way multilayer polyelectrolyte films can be prepared layer-by-layer just by dipping a suitable substrate alternately in an aqueous solution of polyanions and polycations. The technique can be employed with nearly all soluble charged polymers and results in films with a... 

Equation (6) has been verified to a high degree of accuracy for simple electrolytes. It assumes a complete ionization of the salt at infinite dilution. An examination of Table II reveals that for each of the polyelectrolytes studied in this work the values of (Fp )c depend on the counter-ion. This result means that the additivity law does not hold for polyelectrolyte solutions. A simple explanation for this behaviour is provided by Manning s theory which states that even at infinite dilution part of the counter-ions remain condensed on the polyions. On the other hand, dilatometry [2], refractometry [3] and ultrasonic absorption [9, 10] have shown that part of the condensed counterions and of the sites on which they are bound are dehydrated. Therefore, the value ()c of the apparent molal volume of the polyion P, as obtained from Equation (6) >vill include the volume change dVc associated with the binding of C. This is why the subscript C was placed on the apparent molal volume of the polyion P in Equation (6). If we call (Fp )true> the true apparent molal volume of the polyion P it may be assumed that (Fp )true (Fp)tma since there are numerous evidences [9,10, 18, 4c] that a negligible volume change is associated with the condensation of TMA" ion (this ion... 

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