Polymers and counterions

In the semidilute concentration regime. Cm > different polymer coils are strongly overlapping, but the polymer solution is still far from being concentrated. This means that the volume fraction of the monomers in solution is much smaller than unity, h Cm 1- In this concentration range, the statistics of counterions and polymer fluctuations are intimately connected. One example in which this feature is particularly prominent is furnished by neutron and X-ray scattering from semidilute PE solutions [43-48]. 

For more complex mechanisms, picturesque names such as square, ladder, fence [18] or cubic schemes [20] have been selected. In redox polymer films, additional transport of counterions, solvation, and polymer reconfiguration are important and four-dimensional hyper-cubes are needed to describe the reactions [21]. 

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... 

In the case of crystals, both intramolecular (conformational) and packing energies should be taken into account simultaneously. Such a total energy minimization method, with suitable crystallographic constraints, has been applied in different steps of the analysis of crystalline structures of three different synthetic polymers. Structures of these molecules, namely, isotactic trans-1,4-poly-penta-1,3-diene (ITPP), poly-pivalolactone (PPVL), and isotactic cis-1,4-poly(2-methyl-penta-1,3-diene)(PMPD), do not have troublesome features such as charged groups, counterions, and solvent molecules. 

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. 

The procedure used for testing the ideal Donnan theory is applicable to any model that decouples ionic effects from network elasticity and polymer/solvent interactions. Thus we require that nnet depend only on EWF and not C. While this assumption may seem natural, several models which include ionic effects do not make this assumption. For example, the state of ionization of a polymer chain in the gel and the ionic environment may affect the chain s persistence length, which in turn alters the network elasticity [26]. Similarly, a multivalent counterion can alter network elasticity by creating transient crosslinks. 

Takenaka et al. 595) used XPS to study deterioration of a thin polythiophene film on an ITO electrode, such as might be used in a display device. After 105 dopingundoping cycles at 0.5 Hz with BF4" counter-ions there was evidence of extensive fluorination of the polymer, probably due to decomposition of the counter-ion or its hydrolysis by traces of water in the electrolyte. Corradini et al. 596) carried out a similar study of polypyrrole, polythiophene and their analogues with C104 counterions and concluded that all of the polymers are unstable to cycling or to standing in contact with the electrolyte, although polypyrrole performed best. 

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