Polyelectrolyte single chains

Ha, B. Y., and Thirumalai, D. (2003). Bending rigidity of stiff polyelectrolyte chains A single chain and a bundle of multichains. Macromolecules 36, 9658—9666. 

Before we will discuss the structure of polyelectrolyte solutions at nonzero densities, we will briefly address the conformational properties of a single chain at infinite dilution in the next section. 

Qualitatively, the phase diagram fits very well to the phase diagram known for single-chain polyelectrolytes, the phase boundaries are only slightly shifted. In principle, the parameter space for polyelectrol ffes has far more dimensions, such as the solvent quality parameter, the valency of monomers or counterions, and additional salt concentration in the system. Especially for multivalent counterions, one can expect an even more complex picture, since correlation effects are known to play an important role even for single chains. 

H. J. Limbach and C. Holm (2003) Single-chain properties of polyelectrolytes in poor solvent. J. Phys. Chem. B 107(32), pp. 8041-8055 H. J. Limbach, C. Holm, and K. Kremer (2002) Structure of polyelectrolytes in poor solvent. Europhys. Lett. 60(4), pp. 566-572... 

Amphiphilic molecules contain a polar and an apolar part. As a result, such molecules have an ambiguous (amphi) affinity (philos) for water. The apolar parts behave hydrophobically the water molecules tend to escape from contact with these parts. The polar parts are hydrophilic. They interact favorably with water. The consequence of the amphiphilic character is that the molecules are preferably located at interfaces with water, where the polar parts are exposed to the aqueous phase and the apolar parts to the nonaqueous phase. Low-molecular-weight, amphiphilic compounds are often called surfactants. Well-known examples of surfactants are the classical soaps (single-chain fatty acids), phospholipids, cholesterol, bile acids, lung surfactant, and so on. In Figure 7.1, the chemical structures showing the polar and apolar parts of some of these surfactants are given. Monolayers may also be formed by polymers, polyelectrolytes, and proteins that contain polar and apolar parts. 

Limbach HI, Hohn C (2003) Single-chain properties of polyelectrolytes in poor solvent. JPhys Chem B 107(32) 8041-8055. doi 10.1021/jp027606p... 

The present review mainly, but not exclusively, deals with linear flexible polyions and focuses on single chain properties such as the "electrostatic persistence length of intermolecular interactions of a mainly electrostatic nature, on static and dynamic properties at the dilute-semidilute cross-over regime and, only briefly, on the occurrence of unidentified polyelectrolyte structures, sometimes referred to as extraordinary phase , cluster , association or, according to its most striking phenomenology, slow mode . 

Let us consider a single chain of N monomers in volume V. Each monomer is monovalently charged, and i is the distance between two successive monomers along the polymer. Due to the electroneutrality condition, there are N monovalent counterions. Let M be the number of counterions adsorbed on the polyelectrolyte so that M/N is the degree of counterion adsorption and a = 1 — M/N) is the degree of ionization of the polyelectrolyte. In addition. 

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