Search

The self-consistent field theory (SCFT) is employed to numerically study the response of weak polybase type polymer chains grafted on a sphere to electric fields generated by the uniform positive or negative charges on the grafting substrate in the planar polyelectrolyte brush limit. Also the effect of curvature of the grafting sphere on the brush height of weak polybase brushes in the absence of surface charges is investigated. The numerical study reveals interesting and nontrivial dependence of the brush height on the radius of the grafting substrate. Consistent with experimental results, in the parameter range of the surface charge density examined, the brush height is found to be independent of the applied electric field at intermediate and high grafting densities. At relatively low grafting density, the applied negative surface charge which is termed as negative bias in this study results in a reduction of the brush height. At rather low grafting density, the positive bias corresponding to applied positive surface charges can lead to a slight increase in the brush height. The underlining mechanism governing the response of weak polybase brushes to the applied electric field is elucidated.

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., (© 2011 American Chemical Society)

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 electrostatics and density correlations of dipolar solvent molecules in weakly charged polyelectrolyte solutions and charged gels are studied using a field-theoretical approach. For miscible dipolar solvent mixtures, an exact expression for the effective dielectric permittivity is obtained on the mean-field level, which depends upon the individual volume of each solvent species before mixing and the final volume of the mixture. If the effect of volume change is small during mixing, the dielectric permittivity is approximately equal to the volume-averaged dielectric permittivity of the individual components of the dipolar solvent mixture. It is found that the electrostatic interaction between the dipolar solvent molecules or any charged species in the polyelectrolyte solution is screened by both counterions (and co-ions if salt is added) and polyions, and there exists a total screening length for any charged species in the system which contains the contribution from the polyions. The screening from the polyions is as important as that from the counterions on the length scale of the polymer coil size. For uniaxially stretched charged gels, it is shown that there is an enhanced orientational ordering of the dipolar solvent molecules along the stretching direction, and the correlation length (r(cor)) of this enhanced orientational ordering is about the product of the total screening length (xi(-1)) due to the counterions and polyions times the square root of the dielectric constant of the medium, that is, r(cor)approximately equal to (epsilon(r)xi(-1))1/2.