A Numerical Study Of Two Opposing Polyelectrolyte Brushes By The Self-consistent Field Theory

In recent years, the interactions between polyelectrolyte brushes have attracted much attention and research interest, because this force is directly related to the lubricity of brush surface. Interactions between polyelectrolyte brushes depend on the polymer chain flexibility, the electrostatic force, the counter-ions entropy effect and spatial steric factor. In the last two decades, there are many theoretical, experimental and simulation studies of polymer brushes.In this thesis, the self-consistent field theory (SCFT) is employed to numerically study the interaction and interpenetration between two opposing polyelectrolyte (PE) brushes formed by grafting PE chains onto the surfaces of two infinitely long and parallel columns with rectangular-shaped cross-section immersed in a good solvent. The thesis is organized as follows:Section1, the concept and applications of polymers are briefly introduced. The scaling laws of poly electrolyte brushes are discussed.Section2, the self-consistent field theory for flexible and weakly charged polyelectrolytes and its detailed derivation are provided. The numerical method for solving the self-consistent field equations is briefly discussed.Section3, in this section, the self-consistent field theory (SCFT) is employed to numerically study the interactions between two PE brushes grafted on the surfaces of two opposing infinitely long and parallel columns with rectangular cross-sections immersed in a solvent. The dependences of the brush height and the mutual interpenetration between the two PE brushes on various system parameters such as the grafting density, the chain length, the charge fraction of PE chains, and the size of grafted substrates can be fully explored.Section4, the average concentration of charged monomers and that of counter-ions trapped inside the brushes are examined. The percentage of counter-ions trapped inside the brushes and the charge neutrality inside the brush are investigated.