Polyelectrolyte chains, annealed

Molecular Dynamics Simulations of Annealed Polyelectrolyte Chains... 

If the pearl-necklace structure contains only a few pearls, there are always pearls at the end of the chains and these pearls are slightly larger than the inner pearls. This can be proved by doing an explicit calculation of the local electrostatic potential along the necklace very similar to that done in the following section on annealed polyelectrolytes. 

The fraction / of charged monomers on an annealed polyelectrolyte is measured in a titration experiment. The simplest description of this experiment [90] is to assume that the polymer is homogeneous and to minimize its grand canonical free energy (its free energy at constant pH). In a mean field approach, the free energy of one chain is... 

So far we implicitly assumed that once a copolymer stmcture is formed (e.g., by copolymerization), it does not change any more (i.e., it is quenched ). A variable ( annealed ) copol3mier stmcmre is another important possibility. In the latter case each chemical unit can reversibly transform between A and B states. This transition can be associated, for example, with (i) ionization of a hydrophobic group of a weak polyelectrolyte (ii) hydration of an amphiphilic unit and (iii) reversible attachment of a surfactant moiety to a main-chain group (by, say, a hydrogen-bond formation). An instantaneous primary stmcture (sequence) of an annealed copolymer is close to that of a statistical copolymer (and it can often be described by eqn [1]). 

Abstract This introductory chapter provides a brief (textbook-like) survey of important facts concerning the conformational and dynamic behavior of polymer chains in dilute solutions. The effect of polymer-solvent interactions on the behavior of polymer solutions is reviewed. The physical meanings of the terms good, 9-, and poor thermodynamic quality of the solvent are discussed in detail. Basic assumptions of the Kuhn model, which describes the conformational behavior of ideal flexible chains, are outlined first. Then, the correction terms due to finite bond angles and excluded volume of structural units are introduced, and their role is discussed. Special attention is paid to the conformational behavior of polyelectrolytes. The pearl necklace model, which predicts the cascade of conformational transitions of quenched polymer chains (i.e., of those with fixed position of charges on the chain) in solvents with deteriorating solvent quality, is described and discussed in detail. The incomplete (up-to-date) knowledge of the behavior of annealed (i.e., weak) polyelectrolytes and some characteristics of semiflexible chains are addressed at the end of the chapter. 

Keywords Ideal polymer chain Realistic polymer chain Chain conformations Solvent quality Quenched polyelectrolyte Annealed polyelectrolyte Pearl necklace model Persistence length... 

The chains of polyelectrolytes (PEs) contain charged groups. PEs can be divided in two classes Those with permanently charged groups, e.g., sulfonated polystyrene, are called strong or quenched polyelectrolytes. The term quenched PE reflects the fact that the positions of the charges are fixed (predetermined by the synthesis). Weak or annealed PEs contain ionizable groups that can dissociate in polar... 

Computer studies (both Monte Carlo and molecular dynamic simulations) have become a very powerful tool for studying the conformational and dynamic behavior of polymer chains. They can be used for testing the predictions of theoretical models concerning the equilibrium properties and moreover they provide information on dynamic characteristics, e.g., on instantaneous fluctuations of chain shapes which is important because most experimental techniques (e.g., scattering techniques) yield the ensemble-average characteristics only. Large numbers of studies have been performed on neutral chains— not only on linear ones but also on stars, combs, etc. [78-85]. The most important advances in understanding the behavior of polyelectrolytes have been made mainly thanks to computer studies. As aheady mentioned, quenched PEs have been studied both by Monte Carlo [86-89] and by molecular dynamics simulations [59, 63, 71, 73, 87, 90]. Simulation of annealed... 

It has also long been acknowledged that the presence of a small amount of salt leads to a more uniform distribution of the short chain components among the polyelectrolyte with the longer chains, and thus thermodynamic equilibrium [23], More recently it has also been demonstrated that temperature annealing can lead to more organized liquid crystalline structures of DNA—lipid systems [55] and single-molecule structures of xanthan—chitosan systems [56] (see below). 

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