Polyelectrolyte dynamics dilute solutions

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. 

Chang R, Yethiraj A (2006) Dilute solutions of strongly charged flexible polyelectrolytes in poor solvents molecular dynamics simulations with explicit solvent. Macromolecules 39 821-828. doi 10.1021/ma051095y... 

Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute 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. 

Because the configurations of the chains which predominantly contain the trans and gauche conformations of short parts formed by four C atoms (in sp hybridization) fit fairly well to the tetrahedral lattice (see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions, Fig. 3), to a first approximation they assumed that the basic motion of the fluorophore can be described as a jump-like rotation on the tetrahedral lattice with one characteristic time, p (which depends on the characteristic jump frequency and the conformation structure of the chain), in the form [100, 101] ... 

Two general classical bead-spring models have been developed for the description and analysis of the motions of flexible chains (see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions ). The Rouse model [54] is simpler (it does not take into account hydrodynamic correlations). The more advanced Zimm model accounts for hydrodynamic correlations and provides better description of the behavior [55]. In both cases, solution of the derived equations provides the so-called normal modes (relaxation times of different types of motions). The first mode describes the slowest motion of the... 

Fujita and coworkers [79] smdied fluorescently labeled polyoxyethylene chains and found a good correlation between the concentration dependence of the friction coefficient evaluated from the anisotropy measurements and from the macroscopic viscosity. Fujita developed the fi ee-volume theory which describes reasonably well the concentration dependence of in the whole concentration region, [80] but it does not enable prediction of the parameters at a molecular level. Hyde et al. [81] used the Fujita theory for fairly successful interpretation of the experimental data. An interesting paper has been published by Viovy and Moimerie [82]. The authors studied concentrated solutions of anthracene-labeled polystyrene in toluene. They found good correlation of the local dynamics with the viscosity in the range of high concentrations and made one very important observation the local dynamics are unaffected by the overlap of the polymer chains that occurs at concentrations higher than c (concentration of the first overlap—see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions ). 

The conformational behavior of polymer and polyelectrolyte chains in dilute solutions is an interesting and practically important aspect and has been a subject of numerous studies since early 1950s. While the dynamics of polymers can be studied more or less directly by time-resolved depolarization measurements, the conformations and conformational transitions are studied indirectly via changes in the reorientation correlation times. However, because the correlation times depend sensitively on the chain conformations and the changes accompanying the structural transitimis are usually quite pronounced, the conclusions concerning the conformational behavior are reliable in the overwhelming majority of cases. 

Studies of viscoelasticity of dilute solutions are being extended to polyelectrolytes and biopolymers to determine the degree of molecular flexibility of substances such as DNA and muscle proteins. Various polymeric systems will be investigated in the future to seek further understanding of the relations between molecular dynamics and macroscopic physical properties. 

Although the direct consequences of the Einsteinian dynamics of the center-of-mass diffusion of a polyelectrolyte chain in dilute solutions. 

At higher polymer concentrations with chains interpenetrating, the intrachain hydrodynamic interaction is screened. Under these conditions, the model chain dynamics, called the Rouse model, may be used as far as the molecular weight dependence is concerned, and not for the dependence of the polymer concentration. The Rouse model is inapplicable for describing any dynamical properties of polyelectrolyte chains or uncharged macromolecules in dilute solutions. 

In order to resolve these challenges, it is essential to account for chain connectivity, hydrodynamic interactions, electrostatic interactions, and distribution of counterions and their dynamics. It is possible to identify three distinct scenarios (a) polyelectrolyte solutions with high concentrations of added salt, (b) dilute polyelectrolyte solutions without added salt, and (c) polyelectrolyte solutions above overlap concentration and without added salt. If the salt concentration is high and if there is no macrophase separation, the polyelectrolyte solution behaves as a solution of neutral polymers in a good solvent, due to the screening of electrostatic interaction. Therefore for scenario... 

Therefore we expect Df, identified as the fast diffusion coefficient measured in dynamic light-scattering experiments, in infinitely dilute polyelectrolyte solutions to be very high at low salt concentrations and to decrease to self-diffusion coefficient D KRg 1) as the salt concentration is increased. The above result for KRg 1 limit is analogous to the Nernst-Hartley equation reported in Ref. 33. The theory described here accounts for stmctural correlations inside poly electrolyte chains. 

Dilute polyelectrolyte solutions, such as solutions of tobacco mosaic virus (TMV) in water and other solvents, are known to exhibit interesting dynamic properties, such as a plateau in viscosity against concentration curve at very low concentration [196]. It also shows a shear thinning at a shear strain rate which is inverse of the relaxation time obtained from the Cole-Cole plot of frequency dependence of the shear modulus, G(co). 

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