Salt concentrations, polyelectrolyte dynamics

The use of computer simulations to study internal motions and thermodynamic properties is receiving increased attention. One important use of the method is to provide a more fundamental understanding of the molecular information contained in various kinds of experiments on these complex systems. In the first part of this paper we review recent work in our laboratory concerned with the use of computer simulations for the interpretation of experimental probes of molecular structure and dynamics of proteins and nucleic acids. The interplay between computer simulations and three experimental techniques is emphasized (1) nuclear magnetic resonance relaxation spectroscopy, (2) refinement of macro-molecular x-ray structures, and (3) vibrational spectroscopy. The treatment of solvent effects in biopolymer simulations is a difficult problem. It is not possible to study systematically the effect of solvent conditions, e.g. added salt concentration, on biopolymer properties by means of simulations alone. In the last part of the paper we review a more analytical approach we have developed to study polyelectrolyte properties of solvated biopolymers. The results are compared with computer simulations. 

Tj max increases [19] linearly with M. An increase in the salt concentration moves Umax toward higher c so that c ax c, and it drastically lowers the value of Analogous to the viscosity behavior, the dynamic storage and loss moduli also show [22] a peak with c. The unusual behavior at low c where the reduced viscosity increases with dilution in the polyelectrolyte concentration range between and c, along with the occurrence of a peak in the reduced viscosity versus c, has remained as one of the most perplexing properties of polyelectrolytes over many decades. 

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. 

Sedlak M, Amis EJ. Dynamics of moderately concentrated salt-free polyelectrolyte solutions molecular weight dependence. J Chem Phys 1992 96 817-825. 

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. 

We investigate here the dynamic behavior of fully charged NaPSS solutions with multivalent salt (LaCl3) measured by quasi-elastic light scattering. The bimodal decay of the correlation function of polyelectrolyte concentration (C) at constant salt concentration (Cs) is studied first. The ratio Cs/C varies from 0.2 to 10 2. Then the dynamics of the solution at constant C as a function of Cs from Cs/C approximately 10 2 to 0.2 are investigated. 

Figure 31 Concentration dependence of the correlation length (in salt-free polyelectrolyte solutions. Filled symbols corresponds to the small-angle neutron scattering (SANS) data (circles) (Nierlich, M. etal. J. Phys. (Paris) 1979, 40, 701 ) and light scattering data (squares) (Drifford, M. Dalbiez, J. P. J. Phys. Chem. 1984, 88,5368 ) in solutions of NaPSS. Open symbols represent results of the molecular dynamics simulations. The lines with slope -1/2 are shown to guide the eye. Reproduced with permission from Dobrynin, A. V. Rubinstein, M. Prog. Polym. Sci. 2005, 30,1049-1118. Copyright 2005, Elsevier.

One of the most perplexing (and not yet understood) properties of polyelectrolyte dynamics is the fact that, at a certain ratio X. of polyion-concentration Cp (in mol monomer or mol charges, abbreviated monomol/l ) to added salt concentration c (mol/1), a slow mode is observed in dynamic light scattering with a concomitant drastic increase in scattering intensity. 

Jeon, J., Dobrynin, A.V. Molecular dynamics simulations of polyelectrolyte-polyampholyte complexes. Effect of solvent quality and salt concentration. J. Phys. Chem. B 110, 24652-24665 (2006). doi 10.1021/jp064288b... 

To investigate the effect of the Debye-Huckel approximation on the solution properties, Stevens and Kremer [152] performed molecular dynamics simulations of salt-free solutions of bead-spring polyelectrolyte chains in which the presence of counterions was treated via a screened Coulomb potential, and compared the results with their simulations with explicit counterions [146,148]. To elucidate the effect of the Debye-Hiickel approximation, the dependence of the mean square end-to-end distance, R ), osmotic pressure, and chain structure factor on polymer concentration was examined. Stevens and Kremer found that (i ) tends to be larger at low densities for DH simulations and is smaller at higher densities. However, the difference in (i ) between DH simulations and simulations with explicit counterions is within 10%. This trend seems to be a generic feature for all N in their simulations. The functional form and density dependence of the chain structure factor are very close in both simulations. The most severe Debye-Huckel approximation affects the dependence of the osmotic pressure on polymer concentration. It appears that in the DH simulations not only is the magnitude of the osmotic pressure incorrect, but also the concentration dependence is wrong. 

It turned out that the dynamical behaviour of polyelectrolyte solutions is even more spectacular then theoretically anticipated. In the early 1970s mostly biopolymers such as DNA were studied and often two separate relaxations were observed which were then attributed to internal relaxations [197-202]. During the past twenty years numerous studies on synthetic polyelectrolytes (NaPSS, NaPMA, NaPAA, QPVP), proteins (BSA, PLL), polynucleotides (DNA, RNA) and charged polysaccharides (heparin, chondroitin-6-sulfate, proteoglycan hyal-onurate) have been performed. The dynamical behaviour of all these polymers exhibits common features which are attributed to the ionic character of the polyelectrolytes. So far, most studies have focused on the dependence of the apparent diffusion coefficient on polyelectrolyte concentration, salt concentra-... 

The overwhelming majority of experiments unambiguously demonstrate that the coupling of polyions and counterions is the basic mechanism which determines the dynamics of polyelectrolytes as a function of polyion concentration and added salt. The results cannot be explained by one-component theories, i.e., a dilute/semi-dilute cross-over, although the experimental scatter of some of... 

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