The interaction between polyelectrolytes and surfaces

The interactions between surfaces and polymer chains are at the heart of many polymer problems, such as flow in confined geometries, development of new nano-lithography methods, understanding of the structure of block copolymer grains, polyelectrolyte adsorption, and modeling polymer brushes. The latter two systems will be the focus of this dissertation. The physical properties of each system are studied using statistical mechanics, and results from computer simulations are presented.; The first topic of this thesis is the study of adsorption of a polyelectrolyte chain in an electrolyte solution to a uniformly charged surface. By using off-lattice Monte Carlo simulations, the conditions of adsorption of a uniformly charged polyelectrolyte onto oppositely charged planar and spherical surfaces have been investigated. These conditions are functions of the strength of the electrostatic interaction, Debye screening length, chain length, charge density and curvature of the surface. The adsorption can be tuned by using anyone of these parameters. The chain's conformation, adsorption energy and thickness of the adsorbed polymer are obtained under different adsorption conditions. We find the Monte Carlo simulation data to be in good agreement with the theoretical prediction derived previously by using the assumptions of ground state dominance and separability.; The second topic is on the adsorption transition of a uniformly charged polyelectrolyte onto heterogeneously charged planar surfaces investigated with Monte Carlo simulations. Each of these surfaces contains both positive and negative charges. In addition to the usual case of adsorption of a polyelectrolyte to a surface with net charge opposite to that of the polymer, we show that a polyelectrolyte can adsorb onto a surface with net surface charge density similar to that of the polyelectrolyte. This adsorption is due to the spatial inhomogeneity of the surface charges which creates attractive regions with charge density different from the overall charge density of the surface. The spatial inhomogeneity of the surface charges also leads to differences in the conformation of the adsorbed polyelectrolyte. The critical conditions of strength and range of electrostatic interactions and chain length necessary for adsorption of a polyelectrolyte to a heterogeneously charged surface are determined.; The last topic deals with applying self-consistent field theory (SCFT) to polyelectrolyte brushes grafted onto uncharged curved surfaces with no added salt. The goal of this study is to test the validity of the Debye-Hückel approximation for the electrostatic interaction in polyelectrolyte brushes. Our results show that the Debye-Hückel approximation is a good approximation for a weakly charged polymer brush grafted on a surface with small radius. The geometry of the system also plays an important role in the validity of the Debye-Hückel approximation. The approximation gives better results in spherical geometry then cylindrical.