Polyelectrolyte concentration

Recently, the quaternized poly-4-vinylpyridine, 50-54 (QPVP) was found to be an electron acceptor in the charge-transfer interactions 104 Ishiwatari et al.105) studied alkaline hydrolyses of p-nitrophenyl-3-indoleacetate 58 (p-NPIA) and N-(indole-3-acryloyl) imidazole 59 (IAI) (electron donor) in the presence of QPVP. The fcobs vs. polyelectrolyte concentration plots are shown in Fig. 12. As is seen in... 

The slow diffusion coefficient is measurable only at high enough polyelectrolyte concentrations. The value of c at which the slow mode appears is higher if Cj is higher. When the ratio X = c/cg is about 1, the onset of the slow mode and the crossover between the smaller Df for A, < 1 and higher Df for A > 1 occur. Dj depends [33] on c strongly. 

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. 

The virial series of viscosity in polyelectrolyte concentration c can be obtained from Eq. (229) by iterating S(k) to the desired order in c and then combining with Eq. (38). To the leading order in c, Eq. (229) yields... 

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... 

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

Thus in salt-free semidilute solutions, the fast diffusion coefficient is expected to be independent of both N and c, although the polyelectrolyte concentration is higher than the overlap concentration. This remarkable result is in agreement with experimental data [31, 33, 34] discussed in the Introduction. Upon addition of salt, Df decreases from this value as given by the above formulas. 

These expectations are indicated as regime III in Figs. 1 and 2 for polyelectrolyte concentrations greater than the entanglement concentration c. ... 

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. 

Fig. 15. Inhibition of the lysis of Micrococcus luteus by lysozyme, kiko (ko = activity in the absence of inhibitor) (A, 0), and optical density increase of an M. luteus suspension at 500 nm, both as a function of polyelectrolyte concentration. Poly(Lys), O Poly(Glu), pH 8.5, I = 0.01, lysozyme 0.55 x 10" M. M. luteus 100 mg liter", +20°C. Inset Recording vs time of the optical density increase of an M. luteus suspension on addition of poly(Lys) at 2.5 X 10" M, at +20°C.

Significantly, counterion activity coefficients generally are not strongly affected by polyelectrolyte concentration. In contrast, simple salts exhibit a monotonic increase in activity upon dilution. This effect may be attributed to the fact that the charge density in the vicinity of the polyelectrolyte coil is insensitive to dilution, while dilution of a simple salt solution results in uniform separation of all of the charges and hence weaker ionic interactions. 

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. 

In Oil/Water Separation by Induced-Air Flotation by Sylvester and Byeseda, an induced-air flotation pilot unit was used to study the separation of oil from bnne solutions. Variations in the inlet oil concentration, vessel, residence time, air flow rate, bubble diameter, oil-drop diameter, temperature. NaCI concentration, and cationic polyelectrolyte concentration were evaluated. On a multistage unit, the majority of the oil removal occurred in the first stage. Oil-drop and air-bubble diameters have the most significant effects on oil-removal rates. 

The adsorption isothems obtained first rise with the polyelectrolyte concentration and level off to a plateau, as shown in Fig. 24. The adsorbance at the polymer concentration of 0.1 g/dl, which is well in the plateau region, decreases as the salt concentration is lowered, and it varies linearly with the square root of the salt concentration, as shown in Fig. 25. This linear relationship agrees with the theoretical prediction by Hesselink23. ... 

Fig. 26. Plots of thickness of the adsorbed layer v. polyelectrolyte concentration at various ionic strengths114). Symbols are the same as in Fig. 24...

In pure polyelectrolyte solutions a decreasing polyelectrolyte concentration cp is followed by an increase of the Debye length 1D and an increase in chain stiffness. Applying scaling concepts [109] and considering an electrostatic contribution to the persistence length Lp [110-113] various concentration regimes could be identified for polyelectrolyte solutions. Odijk derived different critical con-... 

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]. 

The plot of the equivalent conductivity vs. the polyelectrolyte concentration, however, is more suitable to demonstrate the concentration dependent changes of the polyelectrolyte conductivity [129]. Generally, the equivalent conductivity (Eq. (17)) can be written as [128]... 

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. 

First of all, the comparison of the PB-theory and experiment shown in Fig. 8 proceeds virtually without adjustable parameters. The osmotic coefficient (j) is solely determined by the charge parameter parameter determines the cell radius R0 (see the discussion in Sect. 2.1) Figure 8 summarizes the results. It shows the osmotic coefficient of an aqueous PPP-1 solution as a function of counterion concentration as predicted by Poisson-Boltzmann theory, the DHHC correlation-corrected treatment from Sect. 2.2, Molecular Dynamics simulations [29, 59] and experiment [58]. 

Fig. 11 Interaction of polyelectrolyte rods in salt-free solution SAXS-intensities measured for different polyelectrolyte concentrations at smallest scattering angles [71]. The respective concentrations are filled trangles 3 g/L hollow triangles lOg/L crosses 15 g/ L circles 20 g/L. The inset displays the maximum of the scattering intensity as function of the reduced concentration c/c where c=L 3...

Fig. 7. The segment concentration distribution between the plates for various bulk polyelectrolyte concentrations. >=20 A, and the other parameter values used in calculations are as for Fig. 6. (1) qf= x.W 6 A-3 (2)

Abstract Investigations of alternate adsorption regularities of cationic polyelectrolytes a) copolymer of styrene and dimethylaminopropyl-maleimide (CSDAPM) and b) poly(diallyldimethylammonium chloride) (PDADMAC) and anionic surfactant - sodium dodecyl sulfate (SDS) on fused quartz surface were carried out by capillary electrokinetic method. The adsorption/desorption kinetics, structure and properties of adsorbed layers for both polyelectrolytes and also for the second adsorbed layer were studied in dependence on different conditions molecular weight of polyelectrolyte, surfactant and polyelectrolyte concentration, the solution flow rate through the capillary during the adsorption, adsorbed layer formation... 

There is a range of parameters other than polyelectrolyte charge density that has an important influence on the generated surface interactions, for instance, counterion valency and ionic strength of solution [121-123], the order of addition of polyelectrolyte and salt [124], polyelectrolyte concentration [125], presence of surfactants [31, 119, 126], and finally, the chemical structure of the polyelectrolyte itself [127]. A rich literature is available on these topics (see Ref. [115] and references therein). 

FIG. 13 The amount of NaCl needed to flocculate a clay (i.e., sodium bentonite suspension) as a function of the polyelectrolyte concentration (i.e., sodium car-boxymethylcellulose). The inserted figure is an enlargement of the initial addition of the polyelectrolyte. The lines are redrawn from An Introduction to Clay Colloid Chemistry by van Olphen [51]. 

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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