No abstract

No abstract

By making use of the developed potential theory, we investigate the polymer-mediated depletion interactions between nanoparticles and hard planar surfaces in the following settings: (i) interaction between two nanoparticles; (ii) interactions between nanoparticle and hard planar surface; (iii) interaction between two nanoparticles in the presence of hard planar surface; and (iv) interaction between nanoparticle and walls of the plane-parallel slab. For each of the listed systems, we have calculated the polymer end density, excess grand potential, and the potential of the depletion forces. On the basis of the obtained results, we have analyzed the effect of the geometric constraints imposed by hard walls on the polymer density structure and the depletion interaction between nanoparticles.

The effect of spherical and sphero-cylindrical fillers on the order–disorder transition (ODT) of a symmetric diblock copolymer melt is investigated. Self-consistent equations describing the copolymer density distribution in the presence of fillers are derived. Using these equations, we calculate the excess free energy due to the presence of the particles in the diblocks. The critical value of the segregation factor χN is recalculated with the effect of the fillers taken into account. We find that a relatively small volume fraction of fillers can cause a significant suppression of the ODT temperature. It is shown that smaller particles cause a greater suppression of the ODT temperature provided a constant particle volume fraction is maintained. The effect of the particle shape on the ODT is investigated. The ODT temperature shift is calculated for the sphero-cylindrical particles as a function of their aspect ratio at a given particle volume. It is found that sphero-cylinders with the smaller aspect ratio produce the bigger effect on the ODT. A scaling analysis of the presented results and a comparison with the experimental work are given.

We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion velocities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, orientational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocity v of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that v does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.