Cylindrical polyelectrolytes

The problem under consideration arises in the theory of polyelectrolytes. ip in (2.3.1) is the electric potential, produced by a central cylindrical polyelectrolyte core of radius a, charged with a normalized structural linear... 

Consider the case where cylinder 1 is a soft cylinder and cylinder 2 is a cylindrical polyelectrolyte. By taking the limit Kd2 1, we obtain from Eqs. (15.66) and (15.71)... 

Note that the following exact expression for the electrostatic interaction between porous cylinder (cylindrical polyelectrolyte) 1 and hard cylinder 2 has been derived [5,10] ... 

In the limit a O, the particle core vanishes and the particle becomes a cylindrical polyelectrolyte (a porous charged cylinder) of radius b. For the low potential case, Eq.(21.79) gives... 

Finally, in the limit u 0, the cylinder core vanishes and the cyhnder becomes a cylindrical polyelectrolyte. In this limit, Eq. (22.35) becomes... 

In the following text recent progress in the field of polyelectrolyte brushes is reviewed. In the first section the theory of polyelectrolyte brushes is briefly summarized and some more recent simulation results are shown. In the next section several aspects of the synthesis and the elucidation of the physicochemical properties of polyelectrolyte brushes are discussed. In the following section adaptive and responsive polymer surfaces based on mixed polyelectrolyte brushes are introduced, followed by a section on cylindrical polyelectrolyte brushes, in which charged polymer chains are attached to the backbone of other polymers. Finally some perspectives for further developments in the field of polyelectrolyte brushes are given. 

Table 6 Light-scattering and IR characterization of cylindrical polyelectrolyte brushes prepared by quaternization of PVP brushes...

In summary, the light-scattering investigations support the results obtained by conductivity measurements that the effective charge density of cylindrical polyelectrolyte brushes is much smaller than for linear flexible polyions. 

Table 10 Light-scattering characterization of cylindrical polyelectrolyte brushes in aqueous 10-2 mol L-1 NaCl solution ...

Neither the main nor the side-chain dimensions of ionic cylindrical brushes differ significantly from their uncharged counterparts. Obviously, the osmotic swelling is not significant for the present small side-chain lengths, i.e. Psc<50. The intermolecular structure factor of ionic cylindrical brushes are difficult to interpret. The intermolecular distances derived from the peak of the structure factor is different for H+ and Cs+ counter-ions and is always significantly smaller than the mean distance calculated from the concentration of the particles and the known molar mass. Thus, a two state model may also be postulated for the present cylindrical polyelectrolyte structures. 

For any practical application of polyelectrolyte brushes the influence of multivalent ions, hydrophobic ions, and other polyelectrolyte molecules present in a contacting solution on to the structure of the surface-attached layers or the cylindrical polyelectrolyte brushes are of utmost importance. In particular, study of the interaction of brushes with other polyelectrolyte molecules in solution might open an avenue for the understanding of interaction of proteins or other charged biomolecules such as DNA, as a special form of charged macromolecules, with charged surfaces. It has become clear that not only the influence of the surface on to the conformation of the protein, but also the influence of the protein on the structure of the polymer layer is important. 

We summarize recent work showing that condensation can be derived as a natural consequence of the Poisson-Boltzmann equation applied to an infinitely long cylindrical polyelectrolyte in the following sense Nearly all of the condensed population of counter-ions is trapped within a finite distance of the polyelectrolyte even when the system is infinitely diluted. Such behavior is familiar in the case of charged plane surfaces where the trapped ions form the Gouy double layer. The difference between the plane and the cylinder is that with the former all of the charge of the double layer is trapped, while with the latter only the condensed population is trapped. 

Le Bret M, Zimm BH. Monte Carlo determination of the distribution of ions about a cylindrical polyelectrolyte. Biopolymers 1984 23 271. 

Gonzales-Tovar E, Lozada-Cassou M, Henderson D. Hypernetted chain approximation for the distribution of ions around a cylindrical electrode. II. Numerical solution for a model cylindrical polyelectrolyte. J. Chem. Phys. 1985 83 361. 

Le Bret M, Zimin BH. Distribution of counterions around a cylindrical polyelectrolyte and Manning s condensation theory. Biopolymers 1984 23 287-312. 

Inter-Poly electrolyte and Surfactant Complexes of Cylindrical Polyelectrolyte Brushes... 

Cylindrical polyelectrolyte brushes can form complexes with oppositely charged surfactants and polyelectrolytes. Although the polyelectrolyte cylindrical brushes behave similarly to their linear analogs when forming complexes with surfactants, their distinctive cylindrical nanostructures make it possible to visualize directly the morphology changes by microscopy such as AFM. 

Abstract This review reports advances in experimental and theoretical research on interpolyelectrolyte complexes based on polyionic species of star-shaped polyelectrolytes, cylindrical polyelectrolyte brushes, and micelles of ionic amphiphilic block CO- and terpolymers. 

Keywords Co-assembly Cylindrical polyelectrolyte brushes Interpolyelectrolyte complexes Ionic amphiphilic block copolymers Micelles Polyelectrolytes Star-shaped polyelectrolytes... 

IPECs Based on Cylindrical Polyelectrolyte Brushes 3.1 Experimental Results... 

Water-soluble interpolyelectrolyte complexes (IPECs) formed by cationic cylindrical polyelectrolyte bmshes and linear anionic poly(sodium styrenesulfonate) (PSSNa) have been smdied both theoretically and experimentally by using AFM. ° ° The IPECs were prepared by dialysis of... 

Xu Y, Borisov OV, Ballauff M, Muller AHE (2010) Manipulating the morphologies of cylindrical polyelectrolyte bmshes by forming interpolyelectrolyte complexes with oppositely charged linear polyelectrolytes an AFM study. Langmuir 26(10) 6919-6926... 

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