Modeling of Charged Polymers in Aqueous Solutions in the Presence of Salt Ions and Substrates

Polyelectrolytes (PEs) are charged macromolecules. They interact with surrounding ions in aqueous solutions, playing a pivotal role in various scientific and industrial applications. Examples of PEs include biologically relevant molecules such as DNA, RNA, and proteins, as well as synthetic PEs like poly(styrene sulfonate) and poly(diallyl dimethyl ammonium chloride), which are widely used in industrial applications. The interactions of PEs with ions and substrates are governed by a complex interplay of electrostatic, steric, and dielectric effects, making it essential to develop a comprehensive understanding of these processes at the molecular level. This thesis aims to enhance our understanding of PE interactions through theoretical models and molecular dynamics simulations. It explores the influence of ion characteristics and investigates how they affect PE behavior in bulk solutions and at interfaces. To this end, a soft-potential-enhanced Poisson-Boltzmann model is developed and optimized using coarse-grained molecular dynamics (CGMD) simulations and atomistic models. This model captures the influence of ion size in monovalent salt solutions, providing accurate predictions of ion distributions around rodlike PEs. Beyond mean-field theory, CGMD simulations are used to study the effect of correlations arising from multivalent ions and ions with varying shapes on PE interactions. The results highlight the critical role of ion shape and concentration in controlling the range of PE interactions, offering valuable insights for designing PE-based systems, with potential applications in drug delivery, material science, and beyond. In addition, the research highlights the role of ion valency on the electrophoretic mobility (EM) of PEs. Contrary to the conventional assumption that EM is controlled by counterion valency, we show that coion valency can significantly influence EM. Specifically, we find that increasing the coion valency can reverse EM in systems with high salt concentrations, revealing a complex, non-monotonic relationship between ion valency and EM. Moreover, we examine how dielectric discontinuities between the solvent and solid substrates influence PE adsorption. The findings demonstrate that the dielectric mismatch, as well as salt concentration, ion valency, and PE charge, play a crucial role in determining whether PEs are attracted to or repelled from the substrate. This understanding provides practical guidelines for optimizing PE adsorption and monolayer formation on neutral, polarizable substrates, which is essential for applications in material science, biotechnology, and beyond. Overall, this thesis contributes to a deeper understanding of the fundamental mechanisms governing PE interactions in complex environments, offering strategies for controlling and optimizing PE behavior in various scientific and industrial applications, paving the way for the development of more efficient and targeted PE-based systems.