Polyelectrolyte theory, application

Korolev N, Lyubartsev AP, Nordenskiold L (1998) Application of polyelectrolyte theories for analysis of DNA melting in the presence of Na-t and Mg ions. Biophys J 75 3041-3056... 

Part V, by Andrey Dobrynin, focuses on simulations of charged polymer systems (polyelectrolytes, polyampholytes). Chains at infinite dilution are examined first, and how electrostatic interactions at various salt concentrations affect conformation is discussed, according to scaling theory and to simulations. Simulation methods for solutions of charged polymers at finite concentration, including explicitly represented ions, are then presented. Summation methods for electrostatic interactions (Ewald, particle-particle particle mesh, fast multipole method) are derived and discussed in detail. Applications of simulations in understanding Manning ion condensation and bundle formation in polyelectrolyte solutions are presented. This chapter puts the recent simulations results, and methods used to obtain them, in the context of the state of the art of the polyelectrolyte theory. 

G.S. Manning, The molecular theory of polyelectrolyte solution with applications to the properties of polynucleotides. Quart. Rev. Biophys. II, 179—246 (1978). 

Further details of the theory and application of Raman spectroscopy in polymer studies can be found elsewhere (1. 9). However, vibrational frequencies of functional groups in polymers can be characterized from the spacing of the Raman lines and thus information complementary to IR absorption spectroscopy can be obtained. In addition, since visible radiation is used the technique can be applied to aqueous media in contrast to IR spectroscopy, allowing studies of synthetic polyelectrolytes and biopolymers to be undertaken. Conformation and crystallinity of polymers have also been shown to influence the Raman spectra Q.) while the possibility of studying scattering from small sample volumes in the focussed laser beam (-100 pm diameter) can provide information on localized changes in chemical structure. 

The second question concerns one particular aspect of general applicability of the simple mean field equations outlined above as opposed to more sophisticated statistical mechanical descriptions. In particular, the equilibrium Poisson-Boltzmann equation (1.24) is often used in treatments of some very short-scale phenomena, e.g., in the theory of polyelectrolytes, with a typical length scale below a few tens of angstroms (1A = 10-8 cm). On the other hand, the Poisson-Boltzmann equation implicitly relies on the assumption of a pointlike ion. Thus a natural question to ask is whether (1.24) could be generalized in a simple manner so as to account for a finite ionic size. The answer to this question is positive, with several mean field modifications of the Poisson-Boltzmann equation to be found in [5], [6] and references therein. Another ultimately simple naive recipe is outlined below. 

Aside from their potential therapeutic applications, these hydrophobic polyelectrolyte gels have proved to be interesting in their own right. We have made a rather extensive study of their equilibrium and kinetic swelling properties in response to various chemical stimuli. We have found that their behavior cannot always be explained by theories that have been put forth for more hydrophilic systems. 

Recently, the stiff-chain polyelectrolytes termed PPP-1 (Schemel) and PPP-2 (Scheme2) have been the subject of a number of investigations that are reviewed in this chapter. The central question to be discussed here is the correlation of the counterions with the highly charged macroion. These correlations can be detected directly by experiments that probe the activity of the counterions and their spatial distribution around the macroion. Due to the cylindrical symmetry and the well-defined conformation these polyelectrolytes present the most simple system for which the correlation of the counterions to the macroion can be treated by analytical approaches. As a consequence, a comparison of theoretical predictions with experimental results obtained in solution will provide a stringent test of our current model of polyelectrolytes. Moreover, the results obtained on PPP-1 and PPP-2 allow a refined discussion of the concept of counterion condensation introduced more than thirty years ago by Manning and Oosawa [22, 23]. In particular, we can compare the predictions of the Poisson-Boltzmann mean-field theory applied to the cylindrical cell model and the results of Molecular dynamics (MD) simulations of the cell model obtained within the restricted primitive model (RPM) of electrolytes very accurately with experimental data. This allows an estimate when and in which frame this simple theory is applicable, and in which directions the theory needs to be improved. 

In this section we introduce integral equation theories (IETs) and approximate closures applicable for various models of polyelectrolyte solutions. A theory for linear polyelectrolytes based on the polymer reference interaction site model has also been proposed [58, 59], but this approach will not be reviewed here. 

Here we review the application of ASAXS as applied to the analysis of stiff chain polyelectrolyte in solution. The data discussed here [19] have been obtained using the polyelectrolyte the chemical structure of which is shown in Fig. 1. This system has already been under scrutiny by conventional SAXS some time ago [14]. The paper is organized as follows first we summarize the theory of ASAXS and its application to the problem at hand [18]. Moreover, we will briefly summarize the treatment of rod-like polyelectrolytes within the frame of the Poisson-Boltzmann cell model. An important point for the present analysis is the influence of mutual interaction of the dissolved polyelectrolytes. ASAXS-measurements need to be done at rather higher concentrations so that the interaction of the solute rods may come into play. Here it will be shown that this problem is negligible for the present system. Next possible difficulties encountered in an ASAXS experiment will be discussed and experimental results will be presented. A brief final section will conclude the present discussion. 

Compared to most cases addressed by the above researchers, the behavior of polyelectrolytes are more complex. One of the most prominent differences is the occurrence of long-range electrostatic interactions, whereas in the case of nncharged polymers only nearest-neighbor interactions play a role. Becanse of the wide application of polyelectrolytes, some attempts have been made to describe the adsorption of polyelectrolytes. Most theories have been developed by incorporating the electrostatic free energy into the models for uncharged polymers. ... 

Several chapters of this book discuss applications and extensions of the theory of polyelectrolyte solutions. Counterion condensation theory postulates that for a cylindrical macroion, if the linear charge density exceeds a well-defined critical value, a sufficient fraction of the counterions will "condense" into the immediate domain of the macroion so as to reduce the net charge density due to the macroion and Its condensed counterions to the critical value. No condensation is predicted for macroions with less than the critical charge density. 

This brings us to the question about the applicability of the Flory-Huggins theory for food polymers. For polyelectrolytes, the theory is invalid, unless ionic strength is very high. In Section 7.3 the solubility of proteins will be discussed. Very few polysaccharides are simple homo-... 

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