Low polyelectrolyte concentrations

Equations (116) and (271) give fl in dilute and semidilute limits. For low polyelectrolyte concentrations, we have... 

At very low polyelectrolyte concentrations the reduced viscosity decreases again even for very rigid polymer chains and expanded coils, as seen in the plot of the reduced viscosity against the logarithmic concentration (Fig. 5.15) for poly(styrene sulfonate). The data shows a maximum of the reduced viscosity with a decreasing polymer concentration. At concentrations below this maximum, the polymer solution is in a dilute state, even for the nearly fully expanded polyelectrolytes. The intermolecular interactions simply decrease again with the polymer concentration [47]. 

The advantages of PECs lie in their three-dimensional structure and the relatively low polyelectrolyte concentration needed to reach this structure as compared with, for example, polymer lattices. Another major advantage is the possibility to vary the structure and properties of the complexes simply by changing their composition. This is more important than ever considering the large efforts that are needed to acquire necessary permits for the introduction of new chemicals, since the PECs can be prepared by already accepted polymers/polyelectrolytes and/or nanoparticles. The structural integrity of the PECs also allows them to retain a three-dimensional structure when adsorbed at a solid-liquid interface, which is essential, e.g., for flocculation efficiency. Hocculation is interesting in many industrial applications, not only for the paper industry but also in, e.g., waste water treatment. 

Equation (3.136) implies that the osmotic pressure of a salt containing solution approaches in the limit of low polyelectrolyte concentrations the value found for neutral polymers... 

For low-polyelectrolyte concentrations, R 00 and Eqs. [304] and [305] give the standard bulk Debye-Hiickel solution for the potential near an ion of radius a... 

Sodium alumiaate is used ia the treatment of iadustrial and municipal water suppHes and the use of sodium alumiaate is approved ia the clarification of drinking water. The FDA approves the use of sodium alumiaate ia steam generation systems where the steam contacts food. One early use of sodium alumiaate was ia lime softening processes, where it iacreases the precipitation of ions contributing to hardness and improves suspended soHds removal from the treated water (17). Sodium alumiaate reacts with siHca to leave very low residual concentrations of siHca ia hot process water softeners. Sodium alumiaate is often used with other chemicals such as alum, ferric salts, clays, and polyelectrolytes, as a coagulant aid (18,19). 

The increasing dilution of flexible polyelectrolytes at low ionic strength, the reduced viscosity may increase first, reach a maximum, and then decrease. Since a similar behavior can also be observed even for solutions of polyelectrolyte lattices at low salt concentration, the primary electroviscous effect was thought as a possible explanation for the maximum, as opposed to conformation change. 

In the limit of low salt concentrations, the conformation of polyelectrolytes is expected to be rod-like so that v = 1. In this limit, Eq. (2) is recovered. However, as the concentration of the added salt increases, the effective exponent v decreases toward 3/5. Therefore we expect from Eq. (6) that p will increase with M at higher salt concentrations, in contradiction with the experimentally observed result of Eq. (2). There are several erroneous claims in the literature... 

Tj max increases [19] linearly with M. An increase in the salt concentration moves Umax toward higher c so that c ax c, and it drastically lowers the value of Analogous to the viscosity behavior, the dynamic storage and loss moduli also show [22] a peak with c. The unusual behavior at low c where the reduced viscosity increases with dilution in the polyelectrolyte concentration range between and c, along with the occurrence of a peak in the reduced viscosity versus c, has remained as one of the most perplexing properties of polyelectrolytes over many decades. 

But p decreases with salt concentration with an apparent exponent of k which changes from 0 at low salt concentration to — at high salt concentrations. The N-independence of p arises from a cancellation between hydrodynamic interaction and electrostatic coupling between the polyelectrolyte and other ions in the solution. It is to be noted that the self-translational diffusion coefficient D is proportional to as in the Zimm model with full... 

In addition, we predict that p is independent of polyelectrolyte concentration c at low salt concentrations and decreases with c as the salt concentration is... 

Therefore we expect Df, identified as the fast diffusion coefficient measured in dynamic light-scattering experiments, in infinitely dilute polyelectrolyte solutions to be very high at low salt concentrations and to decrease to self-diffusion coefficient D KRg 1) as the salt concentration is increased. The above result for KRg 1 limit is analogous to the Nernst-Hartley equation reported in Ref. 33. The theory described here accounts for stmctural correlations inside poly electrolyte chains. 

The Huggins coefficient kn is of order unity for neutral chains and for polyelectrolyte chains at high salt concentrations. In low salt concentrations, the value of kn is expected to be an order of magnitude larger, due to the strong Coulomb repulsion between two polyelectrolyte chains, as seen in the case of colloidal solutions of charged spheres. While it is in principle possible to calculate the leading virial coefficients in Eq. (332) for different salt concentrations, the essential feature of the concentration dependence of t can be approximated by... 

The crossover between the Kirkwood-Riseman-Zimm behavior and the Rouse behavior requires a better understanding, in terms of the contributing factors for the occurrence of a maximum in the plot of reduced viscosity against polyelectrolyte concentration at low salt concentrations. A firm understanding of the structure factor of polyelectrolyte solutions at concentrations comparable to the overlap concentration is necessary. 

Since the polyelectrolytes contain only one type of mobile ion, the interpretation of conductivity data is greatly simplified. Polyelectrolytes have significant advantages for applications in electrochemical devices such as batteries. Unlike polymer-salt complexes, polyelectrolytes are not susceptible to the build up of a potentially resistive layer of high or low salt concentration at electrolyte-electrolyte interfaces during charging and discharging. Unfortunately flexible polyelectrolyte films suitable for use in devices have not yet been prepared. 

More than half a century ago, Bawden and Pirie [77] found that aqueous solutions of tobacco mosaic virus (TMV), a charged rodlike virus, formed a liquid crystal phase at as very low a concentration as 2%. To explain such remarkable liquid crystallinity was one of the central themes in the famous 1949 paper of Onsager [2], However, systematic experimental studies on the phase behavior in stiff polyelectrolyte solutions have begun only recently. At present, phase equilibrium data on aqueous solutions qualified for quantitative discussion are available for four stiff polyelectrolytes, TMV, DNA, xanthan (a double helical polysaccharide), and fd-virus. 

The amount of decrease of d.c. resistance is not or only insignificantly dependent upon polyelectrolyte concentration, as long as this is over 0.05%. The most drastic decrease in d.c. resistance may be obtained by combining polyphosphate and bovine erythrocyte ghost protein. Resistances as low as 5 X 103 ohms per sq. cm. have been obtained at pH 6.8. 

If we take into consideration that the lowest experimentally possible polyelectrolyte concentration cp is approximately 10 6 monomol L 1, it follows from Table 8 that the diluted solution state, cp 2000, i.e. if Mn >320,000 g-mol The theoretical treatment and the experimental studies of the concentration dependent behavior of polyelectrolytes in solution is usually restricted to the case with or without an excess of a low molecular electrolyte. A relatively limited amount of data exist for similar concentrations of polyelectrolytes and low molecular mass salt [97]. 

Plotting A vs. the ratio of the polyelectrolyte to the salt concentration, cp/cs, the largest change of the slope is located in the cp/cs region between 1 and 3. An example is given in Fig. 20 for the lowest molar mass and holds for all ionic strengths and molar masses that have been investigated. This implies that a linear increase of the equivalent conductivity below the overlap concentration will only be found if the polyelectrolyte concentration exceeds the concentration of monovalent low molecular electrolyte by a factor of two to three. 

We see that for Cp = 0, the concentration of sodium ion in both compartments is the same (i.e., Cn3 = C J and that there is no Donnan potential across the membrane. In other words, it is the presence of the blocked polyelectrolyte that gives rise to the Donnan potential. For low molar concentration of P and high concentration of NaCl, the squared term (zCp/2C)2 can be neglected and (6.11) then changes to... 

The net result is shown schematically in Figure 16. Instead of the array of surface charges leading to a well defined surface charge density and surface potential there is now a distribution of charges in space which contribute to the electrical double layer surrounding the particle. At low electrolyte concentrations the latter will extend into the space beyond the polyelectrolyte... 

The electrostatic repulsion between the colloids can also be strengthened by adsorption of polyelectrolytes with the same net charge as the colloids. Such adsorption has been observed experimentally by several groups [55,56]. Another example is adsorption of polyelectrolytes on clay particles and in Fig. 13 it is shown that more salt must be added to coagulate the clay particles when the polyelectrolyte concentration has been increased (except for very low concentrations of polyelectrolytes, which has been described above). The polyelectrolytes only adsorb on equally charged clay particles in the presence of salt [51]. There are many explanations to this phenomenon and one theory is that the adsorption preferentially takes place at edges of the clay particles and it has been found that the probability for adsorption is higher for short polymers [56]. 

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