Semidilute solutions, polyelectrolyte dynamics

In scenario (c) corresponding to semidilute solutions, polyelectrolyte chains interpenetrate. Under these circumstances, there are three kinds of screening. The electrostatic interaction, excluded volume interaction, and the hydro-dynamic interaction between any two segments of a labeled polyelectrolyte chain are all screened by interpenetrating chains. Each of these three interactions is associated with a screening length, namely, and These screening... 

FIG. 2 Relaxation times of dynamic modes observed in polyelectrolyte solutions and mixtures over a broad range of experimental conditions 0 diffusion of low molecular weight salt diffusion of polyions or polyion segments in semidilute solutions 3 interaction mode in polyelectrolyte mixtures and diffusion of polyelectrolyte domains (clusters). The data are based mostly on the work on linear flexible polyelectrolytes. Relaxation times correspond to scattering at 90°. See text for more details. 

The dynamic behavior of linear charged polyelectrolytes in aqueous solution is not yet understood. The interpretation of dynamic light scattering (DLS) of aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) is particularly complicated. The intensity correlation function shows a bimodal shape with two characteristic decay rates, differing sometimes by two or three orders of magnitude, termed fast and slow modes. The hrst observations in low salt concentration or salt free solution were reported by Lin et al. [31] for aqueous solutions of poly(L-lysine). Their results are described in terms of an extraordinary-ordinary phase transition. An identical behavior was hrst observed by M. Drifford et al. in NaPSS [32], Extensive studies on this bimodal decay on NaPSS in salt-free solution, or solutions where the salt concentration is increased slowly, have been reported [33-36]. The fast mode has been attributed to different origins such as the coupled diffusion of polyions and counterions [34,37,38] or to cooperative fluctuations of polyelectrolyte network [33,39] in the semidilute solutions. 

The time dependence of the stress relaxation modulus in semidilute unentangled solution is sketched in Fig. 8.10. Experimental verification of Rouse dynamics for frequencies smaller than 1/r was shown in Fig. 8.5, for a semidilute unentangled polyelectrolyte solution. 

Polyelectrolyte chains in semidilute regime follow unentangled dynamics in a much wider concentration range and the crossover to the entangled dynamics occurs further away from the chain s overlap concentration than in solutions of uncharged polymers. 

Extensive molecular dynamics simulations of dilute and semidilute polyelectrolyte solutions of chains with degree of polymerization N ranging from 16 up to 300 were recently performed by Stevens and Kremer [146-148] and by Liao et al, [149], In these simulations the long-range electrostatic interactions were taken into account by the Ewald summation method, including interactions with all periodic images of the system, Stevens and Kremer [146-148] have used a spherical approximation of Adams and Dubey [150] for the Ewald sum while Liao et al, [149] have applied the PME method [110], In addition to Coulombic interactions, all particles, including monomers and counterions, interacted via a shifted Lennard-Jones potential with cutoff rcui = 2 a... 

Rubinstein, M., Colby, R., Dobrynin, A. Dynamics of semidilute polyelectrolyte solutions. Phys. Rev. Lett. 73, 2776-2779 (1994)... 

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