We report molecular dynamics simulations on completely charged polyelectrolyte brushes grafted to two parallel surfaces. The pressure $\Pi$ is evaluated as a function of separation $D$ between the two grafting planes. For decreasing separation, $\Pi$ shows several regimes distinguished by their scaling with $D$ which reflects the different physical nature of the various regimes. At weak compression the pressure obeys the $1∕D$ power law predicted by scaling theory of an ideal gas of counterions in the osmotic brush regime. In addition we find that the brushes shrink as they approach each other trying to avoid interpenetration. At higher compressions where excluded volume interactions become important, we obtain scaling exponents between $-2$ at small grafting density ${\rho }_a$ and $-3$ at large ${\rho }_a$. This behavior indicates a transition from a brush under good solvent condition to the melt regime with increasing grafting density.

We have studied the self-assembly of nano-particles (NPs) at the surface of microphase-separated AB diblock copolymer brushes in a selective solvent by means of dissipative particle dynamics (DPD) simulations. The structure of such nano-composites depends both on the morphology of the underlying brush which is basically determined by chain composition f_B and solvent selectivity τ_B, and on specific parameters of the NPs added such as polymer compatibility a_BP, solvophobicity a_PS, and concentration φ, where a_ij are the DPD interaction parameters. The immense parameter space is explored within a coarse-grained model that contains polymer A and B beads, solvent (S), nano-particle (P), and wall (W) beads. For composites with B-like nano-particles, i.e., NPs that are covered by polymer B ligands, we construct the phase diagram in the f_B − φ space. For B-unlike NPs, it is found that the solvophobicity of the particles set by a_PS is crucial for the spreading of nano-droplets. We show that in principle microphase-separated diblock copolymer brushes can be used to create ordered nano-dots as well as nano-wires and deduce some rules which should facilitate the design of such novel polymer nano-composites. Finally we suggest a new mechanism to move nano-objects on the surface of diblock copolymer brushes.

We analyze, theoretically and by means of molecular dynamics (MD) simulations, the generation of mechanical force by a polyelectrolyte (PE) chain grafted to a plane and exposed to an external electric field; the free end of the chain is linked to a deformable target body. Varying the field, one can alter the length of the non-adsorbed (bulk) part of the chain and hence the deformation of the target body and the arising force. We focus on the impact of added salt on the magnitude of the generated force, which is especially important for applications. In particular, we develop a simple variational theory for the double layer formed near electrodes to compute the electric field acting on the bulk part of the chain. Our theoretical predictions agree well with the MD simulations. Next, we study the effectiveness of possible PE-based nano-vices, comprised of two clenching planes connected by PEs exposed to an external electric field. We analyze a novel phenomenon – two-dimensional diffusion of a nano-particle, clenched between two planes, and introduce a quantitative criterion for clenching efficiency, the clenching coefficient. It is defined as a logarithm of the ratio of the diffusion coefficients of a free and clenched particle. Using first a microscopic counterpart of the Coulomb friction model, and then a novel microscopic model based on surface phonons, with the vibration direction normal to the surface, we calculate the clenching coefficient as a function of the external electric field. Our results demonstrate a dramatic decrease of the diffusion coefficient of a clenched nano-particle for the range of parameters relevant for applications; this proves the effectiveness of the PE-based nano-vices.