Polyelectrolyte dynamics theoretical model

Computer studies (both Monte Carlo and molecular dynamic simulations) have become a very powerful tool for studying the conformational and dynamic behavior of polymer chains. They can be used for testing the predictions of theoretical models concerning the equilibrium properties and moreover they provide information on dynamic characteristics, e.g., on instantaneous fluctuations of chain shapes which is important because most experimental techniques (e.g., scattering techniques) yield the ensemble-average characteristics only. Large numbers of studies have been performed on neutral chains— not only on linear ones but also on stars, combs, etc. [78-85]. The most important advances in understanding the behavior of polyelectrolytes have been made mainly thanks to computer studies. As aheady mentioned, quenched PEs have been studied both by Monte Carlo [86-89] and by molecular dynamics simulations [59, 63, 71, 73, 87, 90]. Simulation of annealed... 

The existing theoretical models may be characterized by the number of dynamic components (polyions, co-ions, counterions) being considered explicitly. One-component theories most closely resemble the theories developed for neutral polymer solutions. A rationale for using this approach is that, in the limit of vanishing electrostatic interactions, polyelectrolytes behave as neutral polymers. On the other hand, multi-component theories are based on models developed for low molecular weight electrolytes. This approach is most powerful for strong electrostatic interactions, where polymer effects are less important. 

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. 

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