Study of morphology and phase diagram of the H-shaped (AC)B(CA) ternary block copolymers using self-consistent field theory

Influences of the Periodicity in Molecular Architecture on the Phase Diagrams and Microphase Transitions of the Janus Double-Brush Copolymer with a Loose Graft

The backbone of the Janus double-brush copolymer may break during long-term service, but whether this breakage affects the self-assembled phase state and microphase transitions of the material is still unknown. For the Janus double-brush copolymers with a periodicity in molecular architecture ranging from 1 to 10, the influences of the architectural periodicity on their phase diagrams and order–disorder transitions (ODT) were investigated by the self-consistent mean field theory (SCFT). In total, nine microphases with long-range order were found. By comparing the phase diagrams between copolymers of different periodicity, a decrease in periodicity or breakage along the copolymer backbone had nearly no influence on the phase diagrams unless the periodicity was too short to be smaller than 3. For copolymers with neutral backbones, a decrease in periodicity or breakage along the copolymer backbone reduced the critical segregation strengths of the whole copolymer at ODT. The equations for the critical segregation strengths at ODT, the architectural periodicity, and the volume fraction of the backbone were established for the Janus double-brush copolymers. The theoretical calculations were consistent with the previous theoretical, experimental, and simulation results.

Interactions between brush-grafted nanoparticles within chemically identical homopolymers: the effect of brush polydispersity

We systematically examined the polymer-mediated interparticle interactions between polymer-grafted nanoparticles (NPs) within chemically identical homopolymer matrices through experimental and computational efforts. In experiments, we prepared thermally stable gold NPs grafted with polystyrene (PS) or poly(methyl methacrylate) (PMMA), and they were mixed with corresponding homopolymers. The nanocomposites are well dispersed when the molecular weight ratio of free to grafted polymers, α, is small. For α above 10, NPs are partially aggregated or clumped within the polymer matrix. Such aggregation of NPs at large α has been understood as an autophobic dewetting behavior of free homopolymers on brushes. In order to theoretically investigate this phenomenon, we calculated two particle interaction using self-consistent field theory (SCFT) with our newly developed numerical scheme, adopting two-dimensional finite volume method (FVM) and multi-coordinate-system (MCS) scheme which makes use of the reflection symmetry between the two NPs. By calculating the polymer density profile and interparticle potential, we identified the effects of several parameters such as brush thickness, particle radius, α, brush chain polydispersity, and chain end mobility. It was found that increasing α is the most efficient method for promoting autophobic dewetting phenomenon, and the attraction keeps increasing up to α = 20. At small α values, high polydispersity in brush may completely nullify the autophobic dewetting, while at intermediate α values, its effect is still significant in that the interparticle attractions are heavily reduced. Our calculation also revealed that the grafting type is not a significant factor affecting the NP aggregation behavior. The simulation result qualitatively agrees with the dispersion/aggregation transition of NPs found in our experiments.

Finite volume method for self-consistent field theory of polymers: Material conservation and application

For the purpose of checking material conservation of various numerical algorithms used in the self-consistent-field theory (SCFT) of polymeric systems, we develop an algebraic method using matrix and bra-ket notation, which traces the Hermiticity of the product of the volume and evolution matrices. Algebraic tests for material conservation reveal that the popular pseudospectral method in the Cartesian grid conserves material perfectly, while the finite-volume method (FVM) is the proper tool when real-space SCFT with the Crank-Nicolson method is adopted in orthogonal coordinate systems. We also find that alternating direction implicit methods combined with the FVM exhibit small mass errors in the SCFT calculation. By introducing fractional cells in the FVM formulation, accurate SCFT calculations are performed for systems with irregular geometries and the results are consistent with previous experimental and theoretical works.

Diblock and triblock copolymer thin films on a substrate with controlled selectivity

Using self-consistent field theory (SCFT), morphology development in symmetric linear ABC triblock copolymer films on neutral and selective substrates has been studied, and it is compared with the triblock copolymer morphologies in bulk. In particular, the effects of the substrate preferable to B (interior) block on nanopattern formation of the copolymer films are of our central interest. Here, we report various nanopatterns with tunable square morphologies. The domain patterns are much more diverse than those parallel to the substrate with substrate selectivity for end-block or those vertical to the substrate without substrate selectivity. Furthermore, in order to figure out an economical and efficient way to fabricate useful passive pattern transfer layers, which have potential applications in microelectronic processes and ultrahigh density storage media, we propose a two-step strategy and scrutinize the conditions for generating square symmetries using cylinder-forming or lamella-forming AB diblock copolymers deposited on substrates created from ABC triblock copolymer films. It is found that a thinner film with weak incompatibility can produce square patterns.