Salt-Free Solutions

Effect of Coulomb Strength on Degree of Ionization and Size 6.3.2.1 Salt-Free Solutions 

4 (dot-dashed), and 5 (circle), (c), (d) Divalent salt and overcharging dependency on Ig the degree of ionization (/) in (c), and the size expansion factor (/1) in (d),ofthe polyelectrolyte 

We now give the results of this calculation for the two cases of (a) salt-free solutions and (b) salty solutions. 

the ions in the solution are only the counterions to the charges on the surface in order to maintain the overall electroneutrality of the system. Let the valency of the counterion be z. The electric potential depends on the distance from the interface logarithmically, 

For positively charged interfaces, the counterions are negatively charged, and the electric field is normal to the surface pointing into the electrolyte solution. The opposite is true for negatively charged interfaces. The electric field at the interface Es in salt-free solutions follows from the above equation as 

The density profile of the counterions can be derived by substituting Equation 3.54 in the Boltzmann law (Equation 3.12) as 

the counterions pile up at the interface. The counterion density, due only to the electrostatic attraction and thermal motion, at the interface is proportional to the square of the surface charge density and to the Bjerrum length. 

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A value for the molecular weight which is low by a factor z + 1 is obtained for salt-free solutions if the experimental results are analyzed as if the polymer were uncharged. 

These findings can be attributed to the increase in the local concentration of MV2+ on the APh-x molecular surface caused by eletrostatic interactions. In contrast, the quenching constants for MV2 + and SPV show no such large difference in the SDS micellar and AM systems. The addition of NaCl reduces the value of kq to about one-third that for the quenching of APh-9 (APh-x with 9 mol% Phen units) by MV2 + in a salt-free solution. This effect is mainly accounted for by the screening of electrostatic attraction between APh-9 and MV2+. 

The viscosities were measured with an Ubbelohde Cannon 75-L, 655 viscometer. Formic acid was chosen as the solvent for the viscosity measurement because the polymer (VII) showed very low or no solubility in other common solvents. In a salt free solution, a plot of the reduced viscosity against the concentration of the polymer showed polyelectrolytic behavior, that is, the reduced viscosity ri sp/c increased with dilution (Figure 4). This plot passed through a maximum at 0.25 g/dL indicating that the expansion of the polyions reached an upper limit, and the effects observed on further dilution merely reflected the decreasing interference between the expanded polyions. 

The viscosity of the oxidized polymer (VIII) was determined using DMF as a solvent. Chloroform was not a good solvent because it was too volatile and resulted in poor reproducibility. The reduced viscosities are plotted against polymer concentration (Figure 6). Polymer VIII behaved like a polyelectrolyte, the reduced viscosities increased sharply on dilution in a salt free solution. The addition of 0.01 M KBr did not completely suppress the loss of mobile ions however, at 0.03 M KBr addition a linear relationship between the reduced viscosities and concentration was established. 

Competition for binding to heparin (in essentially salt-free solutions) has been studied for most physiological cations, by ion-exchange,372 equilibrium dialysis,373 c.d.,365 and 23Na-n.m.r. spectroscopy.370 The following order of affinity was generally observed Na+ < K+ < Mg2+ < Ca2+. 

In fact this "unhydrolyzed" polyacrylamide sample is slightly charged and its low polyectrolyte character is confirmed by a slight difference of red values at pH 7 and 5, for salt free solutions. A really neutral polymer should be necessary to differentiate low effects of electrostatic interactions from non ionic interactions. coordination binding at low pH and hydrogen bonds at pH 7. Nevertheless, at this pH, the adsorption of the chain on Al(0H)3 aggregates can probably be considered as the main origin of the loss of viscosity. 

Recently the wall-PRISM theory has been used to investigate the forces between hydrophobic surfaces immersed in polyelectrolyte solutions [98], Polyelectrolyte solutions display strong peaks at low wavevectors in the static structure factor, which is a manifestation of liquid-like order on long lengths-cales. Consequently, the force between surfaces confining polyelectrolyte solutions is an oscillatory function of their separation. The wall-PRISM theory predicts oscillatory forces in salt-free solutions with a period of oscillation that scales with concentration as p 1/3 and p 1/2 in dilute and semidilute solutions, respectively. This behavior is explained in terms of liquid-like ordering in the bulk solution which results in liquid-like layering when the solution is confined between surfaces. In the presence of added salt the theory predicts the possibility of a predominantly attractive force under some conditions. These predictions are in accord with available experiments [99,100]. 

Rather thorough studies have now been made of the properties of the PM of tomatoes,20 21 44 62 63 66 orange peel,21 tobacco3 61 64 and alfalfa.49 The activity of PM is profoundly affected by the pH of the reaction mixture, the salt concentration and the cation component of the salt. In salt-free solutions, the activity of the PM of higher plants is nearly zero at pH 4.25 and increases linearly with a steep slope as the pH is increased to 8. Above 8 the pectinic acids are also demethylated by the action of alkali and the enzyme activity measurements therefore become unreliable. The relationship between activity and pH is also dependent on the salt content of the reaction mixture. 

Polyelectrolytes are long chain molecules bearing ionisable sites. It is not always possible to predict with confidence the extent to which polyelectrolytes behaviour is exhibited. Thus, polyacrylic acid in water is only weakly ionised and in dioxan it behaves as a typical non-electrolyte. It is usual to overcome the complications imposed by ionic interactions by the inclusion of simple salts and LS studies in salt-free solutions are rather rare. The problems have been discussed recently by Kratochvil137), whilst the review of Nagasawa and Takahashi138 constitutes one of the few devoted exclusively to LS from polyelectrolyte solutions. LS from many biopolymers such as proteins is, of course, extremely relevant in this context. 

Ketenylidenetriphenylphosphorane and its thio-analogue (2) can be obtained from the corresponding ester ylides by treatment with sodium bis(trimethylsilyl)-amide (4).7 Salt-free solutions of alkylidenetriphenylphosphoranes can be conveni-... 

Now, the decay rate of the incoherent dynamic structure factor is proportional to fc(i+2v)/v xherefore, the -dependence of the decay rate for salt-free solutions is independent of whether the hydrodynamic interaction is present or not. 

Therefore, the coupling of polymer segments to the counterion cloud, which is directly responsible for the term N in the above equation, dominates the collective diffusion coefficient. Since Rg N for salt-free solutions, Df is independent of N. 

This value of kn is actually low by an order of magnitude for dilute suspensions of charged spheres of radius Rg. This is due to the neglect of interchain correlations for c < c in the structure factor used in the derivation of Eqs. (295)-(298). If the repulsive interaction between polyelectrolyte chains dominates, as expected in salt-free solutions, the virial expansion for viscosity may be valid over considerable range of concentrations where the average distance between chains scales as. This virial series may be approxi-... 

Therefore in this Rouse regime of unentangled semidilute solutions where hydrodynamic interaction is screened, both the reduced viscosity and reduced modulus decrease with increase in polymer concentration in salt free solutions... 

Lin Y, Liao Q, Jin X. Molecular dynamics simulations of dendritic polyelectrolytes with flexible spacers in salt free solution. J Phys Chem B 2007 111 5819-5828. 

Discuss the reasons why it is so difficult to obtain meaningful osmotic pressure data in salt-free solutions. Consider specifically the reconciliation of the electrolyte-free aspect of the experiment with the accurate control of pH. 

Collapse of Polyampholyte Gels in Salt-Free Solutions.152... 

The isoionic point of RNase-A determined as the pH of a concentrated salt-free solution is 9.60 (268). Estimates of the isoelectric point in buffers not containing phosphate all give values above 9, Anderson and Alberty (269) reporting 9.45. In phosphate buffers specific anion binding dramatically reduces the measured isoelectric point to an extent dependent on the total phosphate concentration. Values below 6 have been measured (270). 

The basis for characterizing fractionated precipitation of proteins is the Cohn-Edsall equation (Cohn, 1943) [Eq. (8.60), where S is the solubility of the protein, is the solubility in salt-free solution, Ks is the salting-out constant, and I represents the ionic strength]. 

The PB-differential equation may be solved analytically for salt-free solution [27, 28], and n(r) is given by [28]... 

Up to now, only two sets of data of the osmotic coefficient of rod-like polyelectrolytes in salt-free solution are available 1) Measurements by Auer and Alexandrowicz [68] on aqueous DNA-solutions, and 2) Measurements of polyelectrolyte PPP-1 in aqueous solution [58]. A critical comparison of these data with the PB-cell model and the theories delineated in Sect. 2.2 has been given recently [59]. Here it suffices to discuss the main results of this analysis displayed in Fig. 8. It should be noted that the measurements by the electric birefringence discussed in Sect. 4.1 are the most important prerequisite of this analysis. These data have shown that PPP-1 form a molecularly disperse solution in water and the analysis can therefore assume single rods dispersed in solution [49]. 

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...

Neutral circular cylinders in salt-free solutions... 

Schwarz S, Nagel J, Jaeger W (2004) Comparison of Polyelectrolyte Multilayers Built Up with Polydiallyldimethylammonium Chloride and Poly (ethyleneimine) from Salt-Free Solutions by in-situ Surface Plasmon Resonance Measurements. Macromolecular Symposia 211 201... 

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