Effect of particle size and shape on the order–disorder phase transition in diblock copolymers

Abstract

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.

Conductivity of Insulating Diblock Copolymer System Filled with Conductive Particles Having Different Affinities for Dissimilar Copolymer Blocks

“…When the above affinity contrast is sufficiently large, the filler particles are found to be preferentially localized within polymer domains that have larger affinity for these particles. Note that this observation is in agreement with our previous results independently obtained by the self-consistent field theory [23]. The described enthalpic effect causes an essentially non-uniform distribution of particles in the DBC system resulting in the formation of the aforementioned filler-rich domains.…”

“…Depending on the copolymer composition, the thus formed micro-phases can have well-defined geometrical form of lamellae, spherical or cylindrical domains having a typical size of several hundreds of nanometers. The microphase separation of DBC, in turn, can cause [22,23] the redistribution of fillers through the formation of well-defined domains enriched with fillers. We demonstrate that DBC system containing the described filler-rich domains have larger conductance relative to the homogeneous counterpart of this system.…”

Conductivity of diblock copolymer system filled with conducting nano‐particles: Effect of copolymer morphology

“…This possibility relies on the propensity of DBC to spontaneously separate into mesoscopic phases upon lowering temperature. 3,4 When one of the copolymer blocks has larger entalpic or entropic affinity for fillers, these fillers tend 5,6 to be localized in DBC microphases rich in these blocks. These selective microphases can therefore serve as "containers" for fillers formed in DBC host systems.…”

Mean-field models of structure and dispersion of polymer-nanoparticle mixtures

“…Seminal steps towards a theoretical description of this problem was taken by Balazs and coworkers, who extended the self-consistent field theory of multicomponent polymers to include the presence of hard particles of different shapes and delineated the resulting particle and block copolymer selfassemblies for a variety of physical parameters which included confinement effects. 37,[163][164][165][166][167] Broadly, the results of their analyses suggested a rich self-assembly behavior determined by an interplay between the shape, size and selectivity of the particles and the other physicochemical features of the block copolymers. Recently, molecular dynamics simulations, 156 cell dynamics based approaches, 168 density functional theories 169 and Monte Carlo simulations 170,171 have also been used to study similar issues.…”