Polyelectrolyte flexible chains

This result is contrary to that found in the solution proposed by Heller and coworkers, of attaching the mediator to the enzyme on a flexible chain (49), and adsorbing die modified species on an electrode in a polyelectrolyte. In this instance the O2 induced decrease in signal was constant with glucose concentration. 

Theories of conformations of polyelectrolytes fall into two groups. In the first group [32-34] the chain is assumed to be a flexible chain and the consequence of electrostatic interaction is calculated. In the second category [35-42], the chain is assumed to be a stiff chain and calculations are performed to obtain the effect of the electrostatic interaction between charges on the chain backbone. To date, there is no satisfactory theory in the literature to describe the electrostatic effect on conformations of polyelectrolyte chains with arbitrary intrinsic stiffness. In the following we briefly outline the developments for both groups of theories. 

The alternative method [46] of analyzing the data is based on the treatment by Odijk and Houwaart [36] of the excluded volume effect on the electrostatic stiffening of semi flexible chains. The total persistence length lt of a stiff polyelectrolyte is the sum of the intrinsic persistence length lp=hl2 and the electrostatic persistence length le,... 

The monomer-monomer correlation functions of flexible polyelectrolytes exhibit qualitatively the same behavior as those for rod-like molecules. The conformational changes, however, result in more pronounced and shifted peaks. From Fig. 8 we deduce a shift of the peaks of flexible chains to larger distances compared to those of rod-like chains. This is a consequence of a smaller overlap between flexible chains compared to the one between rodlike molecules. Naturally, the effect is most pronounced for densities larger than the overlap densities. The increased peak intensity corresponds to a more pronounced order in the system of flexible chains, and is a result of the more compact structure of a polymer coil. (The structural properties of flexible polyelectrolytes without medium-induced potential have been studied in [48].)... 

The situation is more favourable for the study of EB in solutions of flexible-chain polyelectrolytes for which the value of K may be higher by several orders of msg-nitude than for molecules bearing no charge This seems plausible since the uncoiling of a flexible-chain polyion by electrostatic repulsion of ionc enic groups increases the persistent length of the chain and the optical and hydrodynamic properties of the molecule approach those of a rigid-chain polymer ... 

Table 8). This permits the interpretation of experimental data by using the electro-optical properties of flexible-chain polymers in terms of a worm-like chain model However, EB in solutions of polyelectrolytes is of a complex nature. The high value of the observed effect is caused by the polarization of the ionic atmosphere surrounding the ionized macromolecule rather than by the dipolar and dielectric structure of the polymer chain. This polarization induced by the electric field depends on the ionic state of the solution and the ionogenic properties of the polymer chain whereas its dependence on the chain structure and conformation is slight. Hence, the information on the optical, dipolar and conformational properties of macromoiecules obtained by using EB data in solutions of flexible-chain polyelectrolytes is usually only qualitative. Studies of the kinetics of the Kerr effect in polyelectrolytes (arried out by pulsed technique) are more useful since in these... 

In the case of intrinsically rigid polyelectrolytes, such as DNA, experimental results [67] show that electrostatic persistence length calculated from the data shows no unique power law dependence on cs. Compared to the OSF theory [60,61], a much better agreement with these data was achieved later by the calculation of Le via numerical solution of the Poisson-Boltzmann equation for a toroidal polyion geometry [59,62], These calculations showed that the exponent ft in the scaling Rg cs p varies from -1 to -1/4 upon increase of cs. A breakdown of the OSF theory for flexible chains (unless Le /.p) was indicated by taking into account fluctuations in the chain configuration [63]. 

A species (e.g., a colloidal particle or a flexible chain) that is partially ionizable when placed in a solution. The polyelectrolyte dissociates into a macroion and counterions. 

H. Morawetz, Theoretical Aspects of Chain Configuration and Counterion Distribution in Solutions of Flexible Chain Polyelectrolytes, in Polyelectrolyte Solutions, Rice, S.A., Nagasawa, M., Eds., Academic Press, New York, 1961. Morawetz, H., Polymers the Origins and Growth of a Science, John Wiley Sons, New York, 1985. 

Polyelectrolytes with flexible chains and high charge density are more expanded in water than nonionic polymers, especially at low ionic strength. Determination of intrinsic viscosity is difficult in this regime (Fig. 5c). Electrostatic repulsions not only cause increases in hydrodynamic volume but also increases in shear sensitivity or non-Newtonian behavior. 

To verify the predictions of eqn [69] for the osmotic coefficient, Figure 16 shows a universal plot of the reduced osmotic coefficient yo ° /yR as a function of the normalized polymer concentration cjc. For the rodlike chains, we define the overlap concentration c as monomer concentration in the cylindrical zone 4NI nL ), which is an overlap concentration for rodlike polyions. All points collapse onto the universal curve as predicted by eqn [69] for rodlike polyelectrolyte solutions (see Figure 16(a)). However, the size Re of flexible chains is a function of the polymer concentration because polyelectrolytes contract with increasing polymer concentration. To collapse all points into one universal curve and to take into account the chain contraction in Figure 16(b), the reduced osmotic coefficient yo ° /yR is plotted against the ratio of... 

Figure 36 Comparison of the total osmotic pressure n in semidilute polyelectrolyte solutions with the polymeric contribution estimated as /(b77i for fully charged (f=1) flexible chains with /V=300. Reproduced with permission from Liao, Q. Dobrynin, A. V. Rubinstein, M. Macromolecules 2003, 36,3399-3410. ° Copyright 2003, American Chemical Society.

Nature and synthetic chemistry have provided polyelectrolytes of different shapes They can be rod-like as, for example, DNA, or flexible (chain-like) as are many of the synthetic polyelectrolytes. Moreover, they can change their conformation in solution and, under the influence of external conditions such as nature of the... 

Abstract This introductory chapter provides a brief (textbook-like) survey of important facts concerning the conformational and dynamic behavior of polymer chains in dilute solutions. The effect of polymer-solvent interactions on the behavior of polymer solutions is reviewed. The physical meanings of the terms good, 9-, and poor thermodynamic quality of the solvent are discussed in detail. Basic assumptions of the Kuhn model, which describes the conformational behavior of ideal flexible chains, are outlined first. Then, the correction terms due to finite bond angles and excluded volume of structural units are introduced, and their role is discussed. Special attention is paid to the conformational behavior of polyelectrolytes. The pearl necklace model, which predicts the cascade of conformational transitions of quenched polymer chains (i.e., of those with fixed position of charges on the chain) in solvents with deteriorating solvent quality, is described and discussed in detail. The incomplete (up-to-date) knowledge of the behavior of annealed (i.e., weak) polyelectrolytes and some characteristics of semiflexible chains are addressed at the end of the chapter. 

Two general classical bead-spring models have been developed for the description and analysis of the motions of flexible chains (see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions ). The Rouse model [54] is simpler (it does not take into account hydrodynamic correlations). The more advanced Zimm model accounts for hydrodynamic correlations and provides better description of the behavior [55]. In both cases, solution of the derived equations provides the so-called normal modes (relaxation times of different types of motions). The first mode describes the slowest motion of the... 

The HPAM molecule is a flexible chain structure sometimes known as a random coil in polymer chemistry. There is essentially no permanent secondary structure in polyacrylamide which affords it some degree of rigidity in the way that the helical structure acts in xanthan. Like xanthan, HPAM is a polyelectrolyte, and as such it will interact quite strongly with ions in solution. However, since the polyacrylamide chain is flexible, it may respond much more to the ionic strength of the aqueous solvent, and its solution properties are much more sensitive to salt/hardness than are those of xanthan. This is illustrated schematically in Figure 2.11, in which the effect of ionic strength on the hydrodynamic size of the molecule is shown. The effects of ions on the solution properties of polyacrylamide are discussed in more detail in Chapter 3. 

---