Chain conformation, polyelectrolyte-counterion

Schiessel H. Counterion condensation on flexible polyelectrolytes dependence on ionic strength and chain conformation. Macromolecules 1999 32 5673— 5680. 

For the polyion equivalent conductivity, conditions are different. Here an appreciable concentration dependence is expected even in very dilute solutions. This is partly due to the direct dependence of Ap on a, a quantity that may vary with concentration, and partly due to the concentration dependence of the friction coefficient/p. As in the case of polymeric solutes in general, the friction coefficient depends on the polyion chain conformation, which for flexible polyelectrolytes is strongly concentration dependent. Furthermore, the polyion friction coefficient also includes contributions from the fraction (1 — a) of the counterions, which form a kinetic unit with the polyion. The friction coefficient can therefore be written in the form... 

The first part of the book is devoted to the basic properties of polyelectrolytes in general, namely to the factors influencing the chain conformation of charged polymers in solution and to their counterion selectivity. It also contains methods of synthesis and new concepts of charge stabilized polymer colloids and of polyelectrolyte catalysis. 

The situadon is even more interesting in the case of polyelectrolyte chains. In this case, chain conformations are dirertly coupled with the intrachain electrostatic interactions between charges that are controlled by the amount of the condensed counterions. ° ° 5-72,86,88-93 jjj addition to counterion... 

An example of the conformation of long polyelectrolyte chains attached to colloidal latex particles is also shown here by cryo-TEM [590]. The dense grafting of the polyelectrolyte chains ( spherical polyelectrolyte brush, or SPB) leads to a confinement of the counterions... 

These experiments show the effect of the counterion on the structure of the charges stored on the polymer chain. On the other hand tiie electrostatic interaction between charges, as for polyelectrolyte, must change the chain conformation. Then, one can ask the influence of the chain conformation in die neutral state on the stracture of the charges and the way the chains are sensitive to the different kinds of charges. 

Wang XW, Liu GM, Zhang GZ (2011) Conformational behavior of grafted weak polyelectrolyte chains effects of counterion condensation and nonelectrostatic anion adsorption. Langmuir 27 9895-9901... 

Random coil conformations can range from the spherical contracted state to the fully extended cylindrical or rod-like form. The conformation adopted depends on the charge on the polyion and the effect of the counterions. When the charge is low the conformation is that of a contracted random coil. As the charge increases the chains extend under the influence of mutually repulsive forces to a rod-like form (Jacobsen, 1962). Thus, as a weak polyelectrolyte acid is neutralized, its conformation changes from that of a compact random coil to an extended chain. For example poly(acrylic acid), degree of polymerization 1000, adopts a spherical form with a radius of 20 nm at low pH. As neutralization proceeds the polyion first extends spherically and then becomes rod-like with a maximum extension of 250 nm (Oosawa, 1971). These pH-dependent conformational changes are important to the chemistry of polyelectrolyte cements. 

Recently, the stiff-chain polyelectrolytes termed PPP-1 (Schemel) and PPP-2 (Scheme2) have been the subject of a number of investigations that are reviewed in this chapter. The central question to be discussed here is the correlation of the counterions with the highly charged macroion. These correlations can be detected directly by experiments that probe the activity of the counterions and their spatial distribution around the macroion. Due to the cylindrical symmetry and the well-defined conformation these polyelectrolytes present the most simple system for which the correlation of the counterions to the macroion can be treated by analytical approaches. As a consequence, a comparison of theoretical predictions with experimental results obtained in solution will provide a stringent test of our current model of polyelectrolytes. Moreover, the results obtained on PPP-1 and PPP-2 allow a refined discussion of the concept of counterion condensation introduced more than thirty years ago by Manning and Oosawa [22, 23]. In particular, we can compare the predictions of the Poisson-Boltzmann mean-field theory applied to the cylindrical cell model and the results of Molecular dynamics (MD) simulations of the cell model obtained within the restricted primitive model (RPM) of electrolytes very accurately with experimental data. This allows an estimate when and in which frame this simple theory is applicable, and in which directions the theory needs to be improved. 

A survey over the area of stiff-chain polyelectrolytes has been given. Such rod-like polyelectrolytes can be realized by use of the poly(p-phenylene) backbone [9-13]. The PPP-polyelectrolytes present stable systems that can be studied under a wide variety of conditions. Moreover, electric birefringence demonstrates that these macroions form molecularly disperse solution in water [49]. The rod-like conformation of these macroions allows the direct comparison with the predictions of the Poisson-Boltzmann cell model [27-30] which has been shown to be a rather good approximation for monovalent counterions but which becomes an increasingly poor approximation for higher valent counterions [29]. Here it was shown in Sect. 2.2 that the basic problem of the PB model, namely the neglect of correlations, can be remedied in a systematic fashion. 

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