Correspondingly, these fluctuations suppress crystallization at high polymer concentrations, leading apparently to an amorphous rather than crystalline solid state at high polyelectrolyte concentrations. Moderately branched polymers are particle-like in many of their properties, while at the same time they exhibit large fluctuations in size and shape as in the case of linear chain polymers. This class of polymeric materials is found to exhibit rather distinct static and dynamic properties from linear and highly branched star polyelectrolyte solutions emphasized in past studies. We investigate polyelectrolyte stars having a moderate number of arms by molecular dynamics simulations of a coarse-grained model over a range of polyelectrolyte concentrations, where both the counter-ions and solvent are treated explicitly. Drawing on similar trends observed in the field of polymer nanocomposites, we propose a coarse-grained model of aqueous electrolyte solutions that captures the observed trends and that offers physical insight into the influence of salt on the thermodynamic and dynamic properties of electrolyte solutions. Recent studies have demonstrated that common atomistic models of aqueous electrolyte solutions completely fail to reproduce this basic phenomenon. In particular, experiments show that the self-diffusion coefficient, D, of water molecules in electrolyte solutions can be either enhanced or suppressed by particular salts having the same valence where the observed changes correlate with the Hofmeister series governing the relative solubility of proteins and water-soluble polymers in the same salt solutions. Nonetheless, there are fundamental unresolved issues in modeling the dynamics of aqueous salt solutions and the related problem of polymers dissolved in these solutions. Ion-specific solvation has fundamental implications in biochemistry, and the thermodynamics and dynamics of aqueous salt solutions have correspondingly been investigated intensively. Our findings demonstrate the essential role of the solvent in the description of the polyelectrolyte solutions, as well as providing a guideline for the development of a more predictive theory of the properties of the thermodynamic and transport properties of these complex fluids. We rationalize these types of polyelectrolyte association based on the impact of the selective solvent affinity on the charge distribution and polymer solvation in these solutions. Based on our coarse-grained model of polyelectrolyte solutions, we identify conditions in which three distinct types of polyelectrolyte association arise. We calculate static and dynamic correlation functions to quantify the equilibrium structure and dynamics of these complex liquids. In particular, we find that these dispersion interactions can greatly influence the nature of the association between the polyelectrolyte chains under salt-free conditions. To investigate this phenomenon, we perform molecular dynamics simulations of a minimal model of polyelectrolyte solutions that includes an explicit solvent and counter-ions, where the relative affinity of the counter-ions and the polymer for the solvent is tunable through the variation of the relative strength of the dispersion interactions of the polymer and ions. For highly charged polyelectrolytes, this leads to the formation of a diffuse "polarizable" cloud of counter-ions around these polymers, an effect having significant implications for the function of proteins and other natural occurring polyelectrolytes, as emphasized long ago by Kirkwood and co-workers. The theoretical difficulties are especially great for flexible polyelectrolytes due to the additional complex coupling between the polyelectrolyte chain configurations and the spatial distribution of the ionic species in solution. There has been significant interest in the tendency of highly charged particles having the same charge to form dynamic clusters in solution, but an accepted theoretical framework that can account for this ubiquitous phenomenon has been slow to develop.
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