No abstract

In this paper, we used combined self-consistent-field and hybrid particle-field theory to explore the self-assembly behavior of diblock copolymer-nanoparticle mixtures confined between two concentric circular walls. The simulation reveals that the structural frustration, the loss of conformational entropy of the copolymer, and the radii of the two concentric circles have great influence on the morphologies of the system. We also discuss the underlying mechanism of controlling the self-assembly of such a system in terms of enthalpic interaction between particles and copolymers, steric repulsive interactions between particles, and the conformational entropy of copolymers, and a representative phase diagram in terms of block ratio and the particle volume fraction is constructed. This study suggests a route to help experimentalists better create high-performance nanodevices.

The continuum self-consistent field theory (SCFT) is applied to the study of the adsorption of flexible polyelectrolyte (PE) onto the surfaces of two two-dimensional charged square objects with a constant electric field strength immersed in a weakly charged polyelectrolyte solution. The dependences of the different chain conformations, that is, bridging, loop, tail, and train, and in particular, the bridging chain conformation, on various system parameters (the charge fraction of the PE chains, the surface charge density, the object size, the salt concentration, etc.) are investigated. The efficient multigrid method is adopted to numerically solve the modified diffusion equation and the Poisson equation. It is found that the thickness L(B) of the boundary layer of the adsorbed PE chains is independent of the chain length and scales with the surface charge density σ and the fraction of charges on PE chains α(P) as L(B) ~ σ(-0.36) and L(B) ~ α(P)(-0.36), respectively. Simulation results reveal that the total amount of bridging chain conformation in the system scales linearly with respect to the size of the charge objects and scales linearly with the chain length in the long polymer chain regime. Simulation results reveal that the total amount of the bridging chain conformation in the system scales with the charge fraction of PE chains as a power law and the scaling exponent is dependent on all of the other system parameters. Simulation results show that the total amount of charges on the adsorbed chains in the system can overcompensate the surface charges for relatively long chains with high charge fractions.

The response of strong polyelectrolyte (PE) brushes grafted on an electrode to electric fields generated by opposite surface charges on the PE-grafted electrode and a second parallel electrode has been numerically investigated by self-consistent field theory. The influences of grafting density, average charge fraction, salt concentration, and mobile ion size on the variation of the brush height against an applied voltage bias were investigated. In agreement with molecular dynamics simulation results, a higher grafting density requires a larger magnitude of voltage bias to achieve the same amount of relative change in the brush height. In the experimentally relevant parameter regime of the applied voltage, the brush height becomes insensitive to the voltage bias when the grafting density is high. Including the contribution of surface charges on the grafting electrode, overall charge neutrality inside the PE brushes is generally maintained, especially for PE brushes with high grafting density and high average charge fraction. Our numerical study further reveals that the electric field across the two electrodes is highly non-uniform because of the complex interplay between the surface charges on the electrodes, the charges on the grafted PE chains, and counterions.