Titrating Polyelectrolytes - Variational Calculations and Monte Carlo Simulations

Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being used as variational parameters to minimize the free energy. For the titrating charges, a mean field approach is used. The accuracy is tested against Monte Carlo data for up to 1000 monomers. For an unscreened chain, excellent agreement is obtained for the end-to-end distance and the apparent dissociation constant. With screening, the thermodynamical properties are invariably well described, although the structural agreement deteriorates. A very simple rigid-rod approximation is also considered, giving surprisingly good results for certain properties.Comment: 22 pages, PostScript, 9 figure

Osmotic pressure in polyelectrolyte solutions: cell-model and bulk simulations

The osmotic pressure of polyelectrolyte solutions as a function of concentration has been calculated by Monte Carlo simulations of a spherical cell model and by molecular dynamics simulations with periodic boundary conditions. The results for the coarse-grained polyelectrolyte model are in good agreement with experimental results for sodium polyacrylate and the cell model is validated by the bulk simulations. The cell model offers an alternative perspective on osmotic pressure and also forms a direct link to even simpler models in the form of the Poisson–Boltzmann approximation applied to cylindrical and spherical geometries. As a result, the non-monotonic behaviour of the osmotic coefficient seen in simulated salt-free solutions is shown not to rely on a transition between a dilute and semi-dilute regime, as is often suggested when the polyion is modelled as a linear flexible chain. The non-monotonic behaviour is better described as the combination of a finite-size effect and a double-layer effect. Parameters that represent the linear nature of the polyion, including an alternative to monomer concentration, make it possible to display a generalised behaviour of equivalent chains, at least at low concentrations. At high concentrations, local interactions become significant and the exact details of the model become important. The effects of added salt are also discussed and one conclusion is that the empirical additivity rule, treating the contributions from the polyelectrolyte and any salt separately, is a reasonable approximation, which justifies the study of salt-free solutions

Rezension zu: Katja Kröss, Die politische Rolle der stadtrömischen Plebs

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Statistical Mechanical Studies of Titrating Polyelectrolytes

Different models and statistical mechanical approximations for titrating polyelectrolytes are studied and the results compared with Monte Carlo simulations and experimental data. Three types of models have been used in the simulations: i) rigid structures and freely jointed chains with ii) rigid bonds and iii) flexible, harmonic bonds. Sampling is facilitated for the latter two by the use of pivot algorithms, which allow simulations of literally thousands of monomers. Electrostatic interactions are treated within the primitive model. There are no interactions between macromolecules; only single chain properties are investigated. The main part of the thesis is devoted to the study of flexible polyelectrolytes, which represent systems like polyacrylic acid and polyglutamic acid. The apparent dissociation constant and the end-to-end separation are calculated for varying degree of dissociation, bond length/bond strength, number of monomers and salt concentration. Simple scaling relations obtained by a Flory type approach are investigated as well as the results of more elaborate variational calculations using a Gaussian Ansatz where all interactions are modelled by harmonic springs. Various rigid models that have appeared in the literature are also examined. The last part of the thesis deals with integral equation theory in the form of RISM-MSA for proteins and other more or less rigid polyelectrolytes. The theory is applied to the calcium binding and titrational behaviour of the protein calbindin D9k

Comments on the scaling behavior of flexible polyelectrolytes within the Debye-Huckel approximation

Over the years, there has been much debate regarding the conformational behavior of flexible polyelectrolytes with electrostatic interactions described by the D bye-Huckel approximation. In particular, the electrostatic persistence length has been reported to depend both quadratically and linearly on the screening length as well as having no consistent power-law dependence at all. On the basis of simulation results together with a careful analysis of analytical approaches, including Odijk-Skolnick-Fixman (OSF) theory, variational calculations, and renormalization group results, it is possible to present a consistent picture, which contains a better understanding of the true behavior as well as an explanation for the diverse results. The projection length of long chains can be described by power laws in three regimes, and an expression by Odijk is qualitatively correct in two of these regimes. Scaling arguments based on OSF theory and excluded volume considerations give good agreement with the third power law, but the underlying assumptions are not entirely correct. More than one parameter is required to describe the internal chain behavior, which is characterized b short-range flexibility and long-range stiffness. Still, most analytical approaches end up in one of two one-parameter approximations, either an OSF-like perturbation expansion around a rigid-rod state or a Flory-type variational calculation based on an unperturbed chain. The latter describes at best the short-range behavior. A field-theoretic renormalization group treatment, which has suggested that there should be no power law behavior, is not valid in three dimensions. Previous support from simulation results were obtained through an unfortunate mistake