Linear polyelectrolyte

Polyelectrolytes Linear polyelectrolytes in solution can provide a scaffold for the adsorption of metal ions with opposite charges. Thereafter, the ion-absorbed polyelectrolyte templates can transform to ID metal or semiconductor NP assemblies either by a reduction reaction or by chemical combination of ion pairs. Minko and co-workers explored this strategy to prepare 1D Pd NP assemblies. Colfen and co-workers adopted double-hydrophihc block copolymers (DHBCs) with more complex structures, in which one hydrophilic block interacted strongly with appropriate inorganic materials and the... 

The exponent b depends also on the polyelectrolyte linear charge density p and on the polyelectrolyte stiffness [130], which make it a nonuniversal characteristic for the used polyelectrolytes. Typically, polyelectrolytes with smaller p reveal a stronger dependence of <7 on The polyelectrolyte-sphere binding affinity was shown to decrease with the polymer persistence length and to increase with the polyelectrolyte linear charge density. Note that for complexation of polyelectrolytes of different p with the spherical dimethyl dodecylamine oxide (DMDAO) micelles, a modified dependence on the critical micelle charge density has been suggested, namely cT(. [128]. 

Usually the acid-base properties of poly electrolyte are studied by potentiometric titrations. However it is well known, that understanding of polyelectrolyte properties in solution is based on the knowledge of the thermodynamic properties. Up to now, there is only a small number of microcalorimetry titrations of polyelectrolyte solutions published. Therefore we carried out potentiometric and microcalorimetric titrations of hydrochloric form of the linear and branched polyamines at 25°C and 65°C, to study the influence of the stmcture on the acid-base properties. 

The interpretation of the relationships obtained here is based on the same principles of polyfunctional interaction between CP and organic ions which are considered in sections 3.1-3.3. The dispersion of CP grains to a certain size (1-10 pm) yields particles retaining the ability of polyfunctional interaction with organic ions. Simultaneously with increasing dispersion, the mobility of elements of the crosslinked structure also increases, which favors additional interaction. Further dispersion of CP (d 0.1 pm) gives so weak networks that the spatial effect of polyfunctional interaction with organic ions drastically decreases similar to linear polyelectrolytes [64]. 

The polyelectrolyte chain is often assumed to be a rigid cylinder (at least locally) with a uniform surface charge distribution [33-36], On the basis of this assumption the non-linearized Poisson-Boltzmann (PB) equation can be used to calculate how the electrostatic potential

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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],... 

Equations for the evaluation of formation constants of complexed ion species in cross-linked and linear polyelectrolyte systems. J. A. Marinsky, Ion Exch. Solvent Extr., 1973,4, 227-243 (18). 

It was found earlier by experiment and theory that the viscosity intrinsic of polyelectrolyte solutions is nearly linear with the reciprocal square root of the ionic strength over a certain range, such as... 

Surface force profiles between these polyelectrolyte brush layers have consisted of a long-range electrostatic repulsion and a short-range steric repulsion, as described earlier. Short-range steric repulsion has been analyzed quantitatively to provide the compressibility modulus per unit area (T) of the poly electrolyte brushes as a function of chain density (F) (Fig. 12a). The modulus F decreases linearly with a decrease in the chain density F, and suddenly increases beyond the critical density. The maximum value lies at F = 0.13 chain/nm. When we have decreased the chain density further, the modulus again linearly decreased relative to the chain density, which is natural for chains in the same state. The linear dependence of Y on F in both the low- and the high-density regions indicates that the jump in the compressibility modulus should be correlated with a kind of transition between the two different states. 

In polyelectrolyte solutions, the counterion condensation on linear polyelectrolyte chains is known to occur when the charge density along the chain exceeds the critical value [40]. Our work indicates the existence of a critical value for the separation distance between chains, where the interchain interaction changes drastically, most likely due to the transition in the binding mode of the counterions (see Fig. 13). Many peculiar forms of behavior, which are often interpreted by the cluster formation or the interchain organization of polyelectrolytes, have been reported for high concentrations of aqueous polyelectrolytes... 

Branched polyelectrolytes have become of special interest because of their industrial importance and scientifically interesting properties. Poly(ethyl-eneimine), which is important in various industrial applications, can provide an excellent example branched and linear polyelectrolytes have quite different properties due to both their different topographies and structures [89-91]. As another practical point, branched polyelectrolytes can act as precursor or fragments of polyelectrolyte gels. A variety of theoretical approaches have been reported on the investigations of branched polyelectrolytes [92-97]. However,... 

The most investigated examples are to be formd in the precipitation of polyelectrolytes by metal ions. Here, networks are formed by the random crosslinking of linear polymer chains, and the theory requires some modification. The condition for the formation of an infinite network is that, on average, there must be more than two crosslinks per chain. Thus, the greater the length of a polymer chain the fewer crossUnks in the system as a whole are required. 

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. 

In conclusion one can say that SEC is a very powerful method for polymer characterization, especially in combination with other composition sensitive or absolute calibration methods. A big advantage is also that the sample amount is fairly small, typically 10 mg. For more complex polymers, such as polyelectrolytes, enthalpic effects often become dominant and also for rather high molecular weight polymers chromatographic methods such as field-flow fraction (FFF) techniques might be more suitable. For fast routine measurements linear columns are often used. 

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