Dynamic properties of polyelectrolytes

Sedlak M. Static and Dynamic Properties of Polyelectrolyte Solutions. Ph.D. dissertation, Institute of Macromolecular Chemistry, Prague, 1989. 

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. 

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. 

The role of semiflexibility of the polymer backbone on the dynamical properties is necessary to explore the dynamical properties of biologically relevant polyelectrolytes. Orientational correlations among molecules are expected to enhance the richness of the dynamical properties. 

As discussed extensively in this chapter, most of the surprising properties of polyelectrolyte dynamics are due to the coupling of counterion dynamics with polymer dynamics. But, there is no adequate understanding of how much of the counterions are mobile and how much are effectively condensed on polymer chain backbone. Theoretical attempts [77, 78] on counterion condensation need to be extended to concentrated poly electrolyte solutions. 

Relatively little use has been made of the phase-space kinetic theory to study solvent elTects m polymer solution dynamics. Also much more can be done with regard to wall effects, flow of polymers m constrictions, behavior of polymers at interfaces, and the thermal and diffiisional properties of polyelectrolytes. 

Buhler E., Rinaudo M., Structural and dynamical properties of semirigid polyelectrolyte solutions A light-scattering study. 

Despite the increasing theoretical and experimental effort, particularly during the last ten years, the solution properties of polyelectrolytes are not well understood. Investigations of various polyelectrolytes by different experimental methods very often lead to controversial conclusions which are sometimes subject to the bias of individual scientists. This situation is favoured by the fact that experiments on polyelectrolytes almost always turned out to be extremely difficult and the usually enormous scatter of experimental data effectively prohibited, for a long time, a unique picture on the structure and dynamical behaviour of polyelectrolyte solutions. 

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. 

Usually, the mesoscopic, kinetic models are considered to be well suited for predicting dynamic properties of polymer solutions on macroscopic scales. Details of the fast solvent dynamics are in most cases irrelevant for macroscopic properties. Exceptions are polyelectrolytes, where the motion of counterions in the solvent can have a major influence on polymer conformation. Therefore, more microscopic models of polyelectrolytes with explicit counterions are sometimes employed [34] (see also the contribution by M. Muthukumar in this volume). Another exception is the dynamics of individual biopolymers, for example, protein folding, which is modeled with an all atomistic model including an explicit treatment of the (water) solvent molecules [35]. 

The best approach is, therefore, to compare the results of simulations made at different length scales with real measurements to determine the validity of the approach since the causes for changes in e.g. viscosity can be caused by changes in local interaction energy or with the PE structure or both [103]. In this section, the results of computer simulations with relation to the PE structure, complex formation and dilution behavior are summarized. The focus lies on molecular dynamics simulations since Monte Carlo simulations [102, 113] are discussed in detail in chapter Thermodynamic and Rheological Properties of Polyelectrolyte Systems . 

Horvath J, Nagy M (2006) Role of linear charge density and counterion quality in thermo dynamic properties of strong acid type polyelectrolytes divalent transition metal cations. Langmuir 22 10%3 10971... 

The problems involved in formulating a consistent theory of binding are illustrated when one measures the thermodynamic and dynamic properties of a limited number of polyelectrolytes with different counter-ions and then attempts to formulate a simple theory. For example, Gregor measured the selective uptake, self diffusion coefficients, electrical conductivity and electro-osmotic coefficients of a number of different ions in ion-exchange membrane and resin systems. The measurement of selective uptake is unequivocal and its correlation with binding is straightforward. Data on self-diffusion coefficients are complicated to interpret because the narrow pores of these insolu-bilized polyelectrolytes place steric and hydrodynamic restrictions upon the diffusive process. These can be overcome, at least in a semi-quantitative manner, by the use of appropriate correction terms [7]. The measurement of the electro-osmotic coefficient is simple and its interpretation is similarly straightforward. Data on electrical conductivity require interpretation because of the steric and hydrodynamic restraints of the pore nature of the system there is an electro-osmotic correction to the electrical conductivity. Table I tabulates normalized values for different counter-ions with... 

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. 

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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