Polyelectrolyte molecule

Fig. 15. Energy of proton dissociation (Ez) from Z times ionized polyelectrolyte molecules as function of the degree of dissociation (a). (A) - PPAL (1), PPAS (2), PPA (3), polyfmethacrylic acid) (4), copolymer of acrylic acid with ethylenesulfonic acid (50 50) in aqueous solutions (5), (B) - PPAL (1), PPAS (2), PPA in the presence of NaCl (3) ( ) INaClj = 0 (X) fNaCll = 0.25 mmol/1 (o) 0.50 mmol/1...

As seen in the preceding section, the counterions play a crucial role in the mobility of the polyelectrolyte molecules. Even in the absence of an external electric field, the counterions exert an induced electric field in the immediate environment of a charged segment which in turn significantly modifies the collective diffusion coefficient of the polymer. This additional contribution is absent for uncharged polymers, where the cooperative diffusion coefficient Dc is given by the Stokes-Einstein law in dilute solutions. 

The local concentration of the polyelectrolyte molecules, in number of chains per unit volume, as defined by... 

There is evidence that random mixing of partially charge-neutralized hydrated polyelectrolyte complexes inside the coacervate phase imparts higher configurational entropy to these less stiff polyelectrolyte molecules as compared to those in the pre-coacervation phase (Kaibara et al.,... 

FIG. 3.1 Donnan equilibrium and regulation of ionic concentrations resulting from the presence of a semipermeable membrane (a) conditions in the absence of polyelectrolyte molecules and (b) ionic concentrations and electrical gradients in the presence of the polyelectrolyte. The membrane is permeable to water and K+ and Cl , but not to the polyelectrolyte Pz. ... 

The molecular characterization of polyelectrolytes in general, and of DADMAC polymers in particular is complicated for several reasons. First, in aqueous solution the individual properties of the macromolecules are dominated by Coulom-bic interactions. Therefore, the resulting polyelectrolyte effects have to be suppressed through the addition of low molecular electrolyte, such as NaCl. The increase of the ionic strength results in a decrease of the chain stiffness of the polyelectrolyte molecules (see Sect. 5). The chains then revert to the coil dimensions of neutral macromolecules in dilute solutions. However, problems may still arise, particularly since the mode of action of these effects is quite different in various characterization methods [27]. 

Transport of salt and water into a capsule was considered in [3], Osmotic swelling of the capsule was assumed to be due to Donnan equilibrium between the salt solution outside the capsule and the interior solution which also contained polyelectrolyte molecules. The polyelectrolyte was unable to pass through the membrane which formed the wall of the capsule, but salt could pass freely. A model similar to that used for the clay membrane predicts two relaxation rates, only one of which was observed in experiments in which the salt concentration was varied in the external reservoir [4],... 

We now consider a capsule which consists of liquid surrounded by a closed semi-permeable membrane (figure 2) details are provided in [3,4], Water and salt can pass through the membrane from side 1 (inside the capsule) to side 2 (outside), and vice versa, but large polymer molecules cannot. Trapped inside the capsule are n p polyelectrolyte molecules of valence zp and partial molar volume Tip. The resulting Donnan equilibrium is reviewed in [5, 6], Inside the capsule, electroneutrality requires zpn p + z+n + + Z-ri - = 0. We now assume the salt to be monovalent. At equilibrium there is a jump in electrical potential across the membrane inside the capsule x +xi- r X2+X2- x2 with x = (Q =F zpX p) where... 

The stabilization of a dispersed species by a combination of electrostatic and steric repulsions. An example is the stabilization of suspended solids by adsorbed polyelectrolyte molecules. 

It may be concluded, therefore, that an electron that encounters a polyelectrolyte molecule is removed from solution by an irreversible process and, although it may not be incorporated into any particular orbital for a considerable length of time (> 10-9 sec), it has little chance to escape the high concentration of trapping sites provided by the polyelectrolyte. Another explanation would be that the polyelectrolyte has a kind of conductivity band. In the latter case, it is expected that the reactivity of the polymer should be the sum of the reactivities of the individual trapping sites. 

The scattering intensity I(q) measured for a solution of N polyelectrolyte molecules dispersed in a volume V may be rendered by... 

The number of counterions associated with the tetrahedral junction was less than sensitive not only to parameters that define the junction region, but also to the interbranch angle between 90° and 109.5° [74] The number of associated counterions is substantially larger in the four-way junction than other junction geometries and constructs studied [74]. As salt concentration is increased, the stability of the junction is enhanced over a linear polyelectrolyte molecule of identical length as the junction [74], For junctions with symmetrical branches, the counterions associated with the junction in excess of that of a linear construct increases with the length of the branches and then saturates [74],... 

Figure 4. A configuration of a polyelectrolyte molecule, grafted on a surface, whose last monomer is located at the distance z, immersed in a finite reservoir of length L.

Polyelectrolyte molecules affect in a more complicated manner than the neutral ones the bridging interactions between colloidal particles because they influence through their dissociation the electrical potential of the electrical double layer [24 27] which, in turn, affects the conformation of the chains and the overall electrostatic interaction. 

Using a self-consistent field theory, Varoqui et al. [46] calculated the segment density profile of polyelectrolyte molecules adsorbed on one plate and Podgomik [9] extended the procedure to the interaction between two plates. 

Borukhov et al. [11] investigated the effect of polyelectrolyte adsorption on the intercolloidal forces. They assume that the adsorption of polyelectrolyte molecules on the surface of the plates was solely due to the electrostatic interactions between the negatively charged plates and the positively charged polyelectrolyte segments. However, there are additional interactions between the surfaces of the plates and the segments, such as the van der Waals interactions. 

Two infinite-size plates are immersed in a semidilute solution of polyelectrolyte in a good solvent which also contains the small ions of a salt. One of the plates is located at x=0 and the other one at x=D. The system is considered to be in contact with a large reservoir, which contains a polyelectrolyte/salt solution. In addition to the electrostatic interactions, the segments of the polymer have a van der Waals interaction —UkT with the plates. In the mean field approach, the intra- and interchain interactions together with the electric field induced by the surface charges of the plates and polyelectrolyte molecules are expressed as an external potential. Within the mean-field approximation, the free energy of the system with respect to that in the reservoir can be expressed as the sum of three contributions, the polymer contribution Fpol, the salt ions contribution Fion and the electrostatic field contribution Fels,... 

Eq. (10) represents the self-consistent field equation for the local segment density of the polymer chains subject to an external electrical potential ip, a van der Waals interaction with the plates —UkT and an excluded volume interaction. Eq. (11) is a modified Poisson-Boltzmann equation in which the first term accounts for the charges of the small ions of the salt, the second term for the charges of the polyelectrolyte chains and the third one for the charges of the ions dissociated from the polyelectrolyte molecules. 

According to these data, one may draw a conclusion that at low concentrations PE molecules adsorb in flat conformation and at high concentrations more extended layer with loops and tails is formed. These data about conformation of polyelectrolyte molecules are in a good agreement with other experimental and theoretical works [21-23], Note that the curves are reversible and f potential values establish immediately at each pressure value after pressure rising and decreasing. This is the argument that the deformation of adsorbed layers but not desorption of macromolecules takes place on experimental time scale, since our measurements are carried out in polyelectrolyte-free solution. 

The polyelectrolytes used in this study are displayed in Table 1. Hydrophobic flexible polyelectrolyte molecules of poly(methacryloyloxyethyl dimethylbenzylammonium chloride) (PMBQ) with a molecular weight of 4.2 Mio g/mol was synthesized by free radical polymerization in water solution as described elsewhere [18,19], Poly(so-dium styrenesulfonate) (PSS) with molecular weight of 70 000 g/mol was purchased from Aldrich and was used without further purification. Water purified and deionized (reverse osmosis followed by ion exchange and filtration) by means of Milli-RO 5Plus and Milli-Q Plus systems (Millipore GmbH, Germany) was used as a solvent. 

Kiriy A, Gorodyska G, Minko S, Jaeger W, Stepanek P, Stamm M (2002) Cascade of Coil-Globule Conformational Transitions of Single Flexible Polyelectrolyte Molecules in Poor Solvent. J Am Chem Soc 124(45) 13454... 

Minko S, Gorodyska G, Kiriy A, Jaeger W, Stamm M (2002) Visualization of single polyelectrolyte molecules. Polymeric Materials Science and Engineering 87 185... 

Layer-by-layer Assembly on Isolated Polyelectrolyte Molecules... 

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