Effective chain dynamics, dilute polyelectrolyte solutions

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. 

In this article I review some of the simulation work addressed specifically to branched polymers. The brushes will be described here in terms of their common characteristics with those of individual branched chains. Therefore, other aspects that do not correlate easily with these characteristics will be omitted. Explicitly, there will be no mention of adsorption kinetics, absorbing or laterally inhomogeneous surfaces, polyelectrolyte brushes, or brushes under the effect of a shear. With the purpose of giving a comprehensive description of these applications, Sect. 2 includes a summary of the theoretical background, including the approximations employed to treat the equifibrium structure of the chains as well as their hydrodynamic behavior in dilute solution and their dynamics. In Sect. 3, the different numerical simulation methods that are appHcable to branched polymer systems are specified, in relation to the problems sketched in Sect. 2. Finally, in Sect. 4, the appHcations of these methods to the different types of branched structures are given in detail. 

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