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