Dynamics Of Polyelectrolyte Solutions Research Articles

Dynamics of polyelectrolyte solutions under a constant gradient of base concentration.

Phase-separation dynamics of weakly charged polyacid solutions under a constant gradient of base concentration is studied both theoretically and numerically. The time-evolution equation of polymer volume fraction is derived by assuming that the chemical equilibrium of the dissociation reaction is locally established. Numerical simulations of the system in contact with two reservoirs in which the base concentrations differ are performed. The numerical results show that the polymer volume fraction can be transported by the concentration gradient of the base, which leads to the dynamic behavior of mesophase domain structures.

Length scale dependence of the dynamic properties of hyaluronic acid solutions in the presence of salt.

In solutions of the charged semirigid biopolymer hyaluronic acid in salt-free conditions, the diffusion coefficient D(NSE) measured at high transfer momentum q by neutron spin echo is more than an order of magnitude smaller than that determined by dynamic light scattering, D(DLS). This behavior contrasts with neutral polymer solutions. With increasing salt content, D(DLS) approaches D(NSE), which is independent of ionic strength. Contrary to theoretical expectation, the ion-polymer coupling, which dominates the low q dynamics of polyelectrolyte solutions, already breaks down at distance scales greater than the Debye-Hückel length.

Dynamics of polyelectrolyte solutions

We have derived a theory of dynamics of dilute and semidilute polyelectrolyte solutions by explicitly considering triple screening associated with electrostatic, excluded volume, and hydrodynamic interactions. The three screening lengths corresponding to these interactions are coupled among themselves differently at different polyelectrolyte (c) and salt (cs) concentrations. We have derived expressions for the self-translational diffusion coefficient D, electrophoretic mobility μ, coupled diffusion coefficient Df, and the viscosity η of the solution by accounting for the coupling between electrostatics and hydrodynamics. In infinitely dilute solutions, we show that Zimm dynamics is applicable and D∼1/Rg, μ∼M0, and η−η0∼cRg3/M for all values of cs, where Rg and M, respectively, are the radius of gyration and molecular weight of the polyelectrolyte and η0 is the solvent viscosity. Df is derived to be M0 at low cs and to approach D at higher cs. As the polyelectrolyte concentration is increased to semidilute conditions, excluded volume and hydrodynamic interactions get progressively screened. In the Rouse regime, where hydrodynamic interaction is screened and entanglement effects are weak, we have derived expressions for the various transport coefficients. In this regime, at low cs, D∼c0M−1, Df∼c0M0, μ∼c0M0, and η−η0∼cM; at high cs, D∼c−1/2M−1, Df∼c/(c+2cs), μ∼c−1/2M0, and η−η0∼c5/4M. The crossover formulas between these asymptotic laws with numerical prefactors are derived. We have demonstrated that the Rouse law applicable to semidilute unentangled polyelectrolyte solutions at low cs is the empirical Fuoss law. The slow diffusion coefficient observed in light scattering studies of polyelectrolyte solutions is attributed to the emergence of an effective attractive interaction between similarly charged segments of topologically correlated objects such as polyelectrolytes at sufficiently high c and low cs. The consequences of entanglements at very high polyelectrolyte concentrations are briefly mentioned. The theoretical formulas derived here are in qualitative agreement with all known phenomenological results of polyelectrolyte dynamics, and some fresh predictions are made.

The ionic strength dependence of the structure and dynamics of polyelectrolyte solutions as seen by light scattering: The slow mode dilemma

The ionic strength dependence of the structure and dynamics of polyelectrolyte solutions was investigated by static and dynamic light scattering. Narrow molecular weight distribution sodium poly(styrenesulfonate) (NaPSS) standards in aqueous NaCl solutions were chosen as model systems. The study covers moderate polymer concentrations (∼0.5–50 g/L) where interparticle interactions rather than single-polyion properties are dominant. Two diffusive modes characterized as fast and slow were detected in most cases. Scattering amplitudes of these modes were evaluated from light scattering data, which was not done in previous investigations. Amplitudes were normalized by the scattering of a benzene standard. Attention was paid mainly to the occurrence of the slow diffusive mode, which is interpreted as the dynamics of large multichain domains. Experimental results show that the occurrence of the slow mode is not connected with any kind of a sharp transition at some critical conditions. The amplitude of the slow mode (scattering intensity associated with the slow mode) changes smoothly as a function of the ratio of the polymer concentration to the solution ionic strength. At sufficiently high polymer concentrations, the slow mode can even persist until theta conditions are reached (4.17 M NaCl at 25 °C). It was shown that the absolute scattering intensity associated with the slow mode increases upon decreasing ionic strength, which is a direct proof that the structures responsible for the slow mode (domains) really form in solution and cannot be associated with the presence of some impurities, stable aggregates due to the polymer incomplete solubility, etc. Multiangle dynamic light scattering data show that dimensions of the domains increase upon decreasing ionic strength, too. The fast and slow diffusive modes are always widely separated on the time scale and the ionic strength dependence of diffusion coefficient cannot be characterized as a ‘‘splitting of diffusion coefficient.’’

Structure and dynamics of polyelectrolyte solutions with multivalent salts

AbstractAqueous solutions of highly charged polyelectrolyte solutions phase separate in the presence of multivalent salts. Phase diagrams of sodium polystyrene sulfonate (Na+PSS−) with LaCl3, Th(NO3)4 were studied over a wide range of polyelectrolyte and salt concentrations. The concentration of salt at the transition C was found to be proportional to the monomer concentration Cm and nearly molecular weight independent: C/Cm≅0.23 for La3+ and C/Cm≅0.12 for Th4+. With further addition of salt a new transition from a two phase system back to a single phase was observed at constant salt concentration independent of NaPSS concentration but sensitive to molecular weight. A theoretical model which explains this behavior in termes of electrostatic attractive interaction between monomers due to the high valency of condensated counterions has been developped recently. The form of the phase diagram results from a competition between the classical long range Coulombic interaction, the short range bridging attraction via the condensed counterion and the electrostatic screening.Dynamic light scattering measurements were performed in the lower monophase solution as a function of NaPSS concentration and over a wide LaCl3 concentration range. Two relaxation times were observed at very low salt concentration.The dynamic studies reveal some interesting behaviours of apparent diffusion coefficient as a function of polyelectrolyte and salt concentrations (Cm, Cs): i) a q2 dependence of the fast mode and a q3 dependence of the slow mode; ii) the power law Dfast varies approximately as C1/2m at constant low salt concentration. This mode can be explained assuming cooperative diffusion in a transient polyelectrolyte network.The slow mode of the bimodal decay disappears increasing the added salt (LaCl3) concentration at constant Cm. It is concluded that the slow mode is related to labile clusters or temporal domains of polyelectrolyte chains which are formed in solutions at low concentration of added salt. Both the disappearance of the slow mode on a very long time scale and the non reappearance of this mode when cycling at constant Cs/Cm between high and low salt concentration indicate that low salt or salt free polyelectrolyte solutions tend very slowly to thermodynamic equilibrium.

Dynamics of polyelectrolyte solutions by neutron spin echo: molecular weight dependence

La transition entre la region diluee et la region semidiluee se produit a une masse moleculaire critique. Etude avec du polystyrenesulfonate de sodium sans addition de sel

Addendum to the paper ‘‘On the dynamics of polyelectrolyte solutions’’

Hydrodynamic effect on the relaxation modes for a system of charged particles is reexamined. This effect is shown to produce a decrease in the diffusion coefficient due to the cloud of particles surrounding each charge.

On the effect of small ions in the dynamics of polyelectrolyte solutions

Formules exprimant le coefficient de diffusion mutuelle des polyions en fonction des concentrations de polyelectrolyte et de sel ajoute

Dynamics of polyelectrolyte solutions by light scattering

Diffusion quasi elastique pour du polystyrene sulfonate de sodium. En regime concentre sans sel ajoute, on observe deux temps de relaxation. L'addition de sel met en evidence une transition des temps de relaxation

Dynamics of Polyelectrolyte Solutions. I. A Dynamical Model for Polyelectrolyte

A new model is proposed for the polyelectrolyte solutions in order to explain their dynamical behavior. The electrolytic solvent is assumed to be decomposed into the ordinary viscous fluid and a charged fiuid superposed on it. Each of the polymer molecules dissolved into these two fluids is represented by a point-charge distribution {τ α i } on i -th segment in α-th chain. The charge τ α i =1 or 0 is treated as a stochastic variable. It is assumed that the two fluids are independent of each other when any electric matter is absent in the solvent and that they are coupled only via charged polymers. Dynamical equations of these three constituents are set up in a self-consistent manner. Edwards and Freed's theory is used to solve them.

Correlations and dynamics of polyelectrolyte solutions

The dynamics of polyelectrolyte solutions have been studied using a neutron spin echo spectrometer for wave vectors q around the maximum of the static structure factor (qm). The q dependent diffusion coefficient D(q) decreases sharply below q = qm, and is nearly constant above qm. All these features can be understood in terms of a new picture for the correlations, based on : i) the notion of a correlation hole, of diameter ξ = aO-1/2 ; ii) locally rigid chains with a persistence length b = aO-1 (where O is the polymer volume fraction and a the monomer size).