Electrostatic interactions polyelectrolytes

Thus, depending on the strength of the electrostatic interaction, polyelectrolytes may form intermolecular structures caused by pure hard-core or by crystalline-like lattice potentials. Accordingly, the concepts describing the structure of polyelectrolyte solutions may be divided into lattice models and polymer models with the application of liquid state theories. 

Lattice theories apply to the limit of strong electrostatic interactions where the polyions form lattice-like structures. Polymer theories combine concepts developed for neutral polymers together with results from liquid-state theory. The latter focus on weak interactions, the rationale being that, in the case of vanishing electrostatic interaction, polyelectrolytes should behave like neutral polymers. So far there is no theory that covers the whole range from weak to... 

The existing theoretical models may be characterized by the number of dynamic components (polyions, co-ions, counterions) being considered explicitly. One-component theories most closely resemble the theories developed for neutral polymer solutions. A rationale for using this approach is that, in the limit of vanishing electrostatic interactions, polyelectrolytes behave as neutral polymers. On the other hand, multi-component theories are based on models developed for low molecular weight electrolytes. This approach is most powerful for strong electrostatic interactions, where polymer effects are less important. 

The existence of electric charges on the chemical backbone modifies considerably the properties of the polymers because of the long range character of the electrostatic interactions. Polyelectrolytes are of major importance in biology. While their static properties are now better understood, little is known about their hydrodynamic behavior. At low concentrations the specific viscosity of a polyelectrolyte solution varies according to Fuoss law [>y] 1/y/c there does not seem to be any... 

Morishima et al. [75, 76] have shown a remarkable effect of the polyelectrolyte surface potential on photoinduced ET in the laser photolysis of APh-x (8) and QPh-x (12) with viologens as electron acceptors. Decay profiles for the SPV (14) radical anion (SPV- ) generated by the photoinduced ET following a 347.1-nm laser excitation were monitored at 602 nm (Fig. 13) [75], For APh-9, the SPV- transient absorption persisted for several hundred microseconds after the laser pulse. The second-order rate constant (kb) for the back ET from SPV- to the oxidized Phen residue (Phen+) was estimated to be 8.7 x 107 M 1 s-1 for the APh-9-SPV system. For the monomer model system (AM(15)-SPV), on the other hand, kb was 2.8 x 109 M-1 s-1. This marked retardation of the back ET in the APh-9-SPV system is attributed to the electrostatic repulsion of SPV- by the electric field on the molecular surface of APh-9. The addition of NaCl decreases the electrostatic interaction. In fact, it increased the back ET rate. For example, at NaCl concentrations of 0.025 and 0.2 M, the value of kb increased to 2.5 x 108 and... 

In the following paper, the possibility of equilibration of the primarily adsorbed portions of polymer was analyzed [20]. The surface coupling constant (k0) was introduced to characterize the polymer-surface interaction. The constant k0 includes an electrostatic interaction term, thus being k0 > 1 for polyelectrolytes and k0 1 for neutral polymers. It was found that, theoretically, the adsorption characteristics do not depend on the equilibration processes for k0 > 1. In contrast, for neutral polymers (k0 < 1), the difference between the equilibrium and non-equilibrium modes could be considerable. As more polymer is adsorbed, excluded-volume effects will swell out the loops of the adsorbate, so that the mutual reorientation of the polymer chains occurs. 

The linearity of L with N is maintained at the theta point. Relative to Eq. 5, the chains have shrunk by a factor of (a/d),/3 but the linear variation indicates that the chains are still distorted at the theta point and characteristic dimensions do not shrink through a series of decreasing power laws as do free chains [29-31]. Experimentally, Auroy [25] has produced evidence for this linearity even in poor solvents. Pincus [32] has recently applied this type of analysis to tethered polyelectrolyte chains, where the electrostatic interactions can produce even stronger stretching effects than those that have been discussed for good solvents. Tethered polyelectrolytes have also been studied by others [33-35],... 

Note that when the concentration of added salt is very low, Debye length needs to be modified by including the charge contribution of the dissociating counterions from the polyelectrolytes. Because the equilibrium interaction is used, their theory predicts that the intrinsic viscosity is independent of ion species at constant ionic strength. At very high ionic strength, the intrachain electrostatic interaction is nearly screened out, and the chains behave as neutral polymers. Aside from the tertiary effect, the intrinsic viscosity will indeed be affected by the ionic cloud distortion and thus cannot be accurately predicted by their theory. 

Theoretical treatment of the viscosity-concentration relationship for polyelectrolyte solutions would involve both the cumbersome statistics of highly elongated chains beyond the range of usefulness of the Gaussian approximation and the even more difficult problem of their electrostatic interactions when highly charged. There appears to be little hope for a satisfactory solution of this problem from theory. Fuoss has shown, however, that experimental data may be handled satisfactorily through the use of the empirical relation ... 

Water-soluble polymers in general, and especially polyelectrolytes, are often difficult due to their specific and long range electrostatic interactions, which complicate all analytical techniques that rely on single particle properties that are usually realized by high dilution. In most cases the ionic strength of the solution must be increased by the addition of salt in order to screen electrostatic forces. Ideally, SEC separation is predominantly governed by entropic interactions,... 

Fig. 3. Schematics of the influence of electrostatic interactions on adsorption isotherms of polyelectrolytes. Effect of charge contrast between the polyelectrolyte and the sorbent surface in media of (a) low and (b) high ionic strength.

The presence of polymers or polyelectrolytes have important effects on the Van der Waal interaction and on the electrostatic interaction. Bacterial adhesion, as discussed in Chapter 7.9 may be interpreted in terms of DLVO theory. Since the interaction in bacterial adhesion occurs at larger distances, this interaction may be looked at as occurring in the secondary minimum of the net interaction energy (Fig. 7.4). Particle Size. The DLVO theory predicts an increase of the total interaction energy with an increase in particle size. This effect cannot be verified in coagulation studies. 

Polyelectrolytes provide excellent stabilisation of colloidal dispersions when attached to particle surfaces as there is both a steric and electrostatic contribution, i.e. the particles are electrosterically stabilised. In addition the origin of the electrostatic interactions is displaced away from the particle surface and the origin of the van der Waals attraction, reinforcing the stability. Kaolinite stabilised by poly(acrylic acid) is a combination that would be typical of a paper-coating clay system. Acrylic acid or methacrylic acid is often copolymerised into the latex particles used in cement sytems giving particles which swell considerably in water. Figure 3.23 illustrates a viscosity curve for a copoly(styrene-... 

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 scenario (c) corresponding to semidilute solutions, polyelectrolyte chains interpenetrate. Under these circumstances, there are three kinds of screening. The electrostatic interaction, excluded volume interaction, and the hydro-dynamic interaction between any two segments of a labeled polyelectrolyte chain are all screened by interpenetrating chains. Each of these three interactions is associated with a screening length, namely, and These screening... 

In 1991 Decher and coworkers introduced a new method to prepare multilayered thin films by electrostatic interaction between oppositely charged polyelectrolytes [3, 62, 63]. In this fashion, thin molecular films comprised of charged polymers. 

For polyelectrolytes, electrostatic interactions provide the driving force for their salient features and have to be included in any theoretical description. The reduced electrostatic interaction between two point-like charges can be written as qiq2v r) where... 

Fig.2.16. Behavior of a polyelectrolyte in dilution viscosimetry in water (a) without, (b) with a low quantity and (c) with a higher quantity of a low-molecular-weight electrolyte (salt) which screens the electrostatic interactions...

Miura N, Dubin PL, Mooiefield CN, Newkome GR. Complex formation by electrostatic interaction between carboxyl-terminated dendrimers and oppositely charged polyelectrolytes. Langmuir 1999 15 4245-4250. 

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