Theory of Complex Spherical Packing Phases in Diblock Copolymer/Homopolymer Blends

The formation of complex spherical packing phases in binary and ternary diblock copolymer/homopolymer blends is studied using self-consistent field theory (SCFT). The polymeric blends are composed of A-sphere-forming AB diblock copolymers mixed with B-selective (C) homopolymers and A-selective (D) homopolymers, resembling surfactant/water and surfactant/water/oil systems. It is observed that the addition of C homopolymers stabilizes the Frank–Kasper (FK) σ and A15 phases, and further addition of D homopolymers enables the appearance of the Laves C14 and C15 phases. Compared with neat AB diblock copolymers, the FK σ phase is predicted to become an equilibrium phase in the AB/C blends at lower conformational asymmetry. In the AB/C/D blends, the C and D homopolymers are localized in the B-rich matrix and A-rich cores, respectively, synergistically stabilizing the complex spherical packing phases. The theoretically predicted phase behaviors of the AB/C and AB/C/D blends are consistent with experiments on polymeric blends and surfactant systems. These results provide insights into the emergence of complex spherical packings in soft matter systems composed of amphiphiles and selective additives

Theory of Complex Spherical Packing Phases in Diblock Copolymer/Homopolymer Blends

The formation of complex spherical packing phases in binary and ternary diblock copolymer/homopolymer blends is studied using self-consistent field theory (SCFT). The polymeric blends are composed of A-sphere-forming AB diblock copolymers mixed with B-selective (C) homopolymers and A-selective (D) homopolymers, resembling surfactant/water and surfactant/water/oil systems. It is observed that the addition of C homopolymers stabilizes the Frank–Kasper (FK) σ and A15 phases, and further addition of D homopolymers enables the appearance of the Laves C14 and C15 phases. Compared with neat AB diblock copolymers, the FK σ phase is predicted to become an equilibrium phase in the AB/C blends at lower conformational asymmetry. In the AB/C/D blends, the C and D homopolymers are localized in the B-rich matrix and A-rich cores, respectively, synergistically stabilizing the complex spherical packing phases. The theoretically predicted phase behaviors of the AB/C and AB/C/D blends are consistent with experiments on polymeric blends and surfactant systems. These results provide insights into the emergence of complex spherical packings in soft matter systems composed of amphiphiles and selective additives

Origin of Microstructures from Confined Asymmetric Diblock Copolymers

The self-assembly of asymmetric diblock copolymers confined within cylindrical pores is studied using the self-consistent-field theory. The cylinder-forming asymmetric diblock copolymer is chosen to be near the cylinder−gyroid phase boundary in the intermediate segregation region. This choice makes the self-assembled cylindrical structure highly deformable, leading to very rich morphologies under confinement. A rich variety of structures, such as helices, stacked toroids, and perforated tubes, is observed as a function of the degree of confinement characterized by the ratio between the pore diameter D and bulk period L (D/L) as well as pore surface−polymer interactions. The origin of these confinement-induced structures is elucidated. The theoretical results are in good agreement with available experimental observations

Rotational Dynamics of Discoid Colloidal Particles in Attractive Quasi-Two-Dimensional Plastic Crystals

Plastic crystals formed from anisotropic molecules or particles are an important state of matter characterized by the presence of long-range positional order and the lack of long-range orientational order. The rotational motion of molecules or particles in plastic crystals is the most attractive characteristic of the system. Here the rotational dynamics of the discoid particles in quasi-two-dimensional colloidal plastic crystals stabilized via depletion interactions are quantitatively studied using time-resolved confocal microscopy. The measured probability distribution of particle orientation reveals the existence of a strong coupling between the lattice symmetry and particle rotation, resulting in anisotropic rotational dynamics modes resembling the underlying hexagonal crystalline symmetry. Furthermore, the orientational distribution function provides information about the potential surface of rotational dynamics. The observed slow rotational diffusion can be attributed to the presence of orientational minima and potential barriers on the potential surface. Our findings with a real experimental system provide important insights into the role of attraction in the phase behaviors of plastic crystals

Microstructures of a Cylinder-Forming Diblock Copolymer under Spherical Confinement

Self-assembly of cylinder-forming diblock copolymers under spherical confinement is studied using real-space self-consistent field theory calculations (SCFT). Various microstructures are found at different confinement dimensions and surface fields. Most of these microstructures are center-symmetric and they could not be formed in bulk or under planar and cylindrical confinements. It is also observed that the interactions between the confinement surface and the polymers have a large effect on the self-assembly. When the spherical confinement’s surface attracts the short blocks, the self-assembled structures become similar to those under a neutral surface field. On the other hand, when the spherical confinement’s surface attracts the long blocks, the equilibrium structures become different from those under a neutral surface field

Rotational Dynamics of Discoid Colloidal Particles in Attractive Quasi-Two-Dimensional Plastic Crystals

Plastic crystals formed from anisotropic molecules or particles are an important state of matter characterized by the presence of long-range positional order and the lack of long-range orientational order. The rotational motion of molecules or particles in plastic crystals is the most attractive characteristic of the system. Here the rotational dynamics of the discoid particles in quasi-two-dimensional colloidal plastic crystals stabilized via depletion interactions are quantitatively studied using time-resolved confocal microscopy. The measured probability distribution of particle orientation reveals the existence of a strong coupling between the lattice symmetry and particle rotation, resulting in anisotropic rotational dynamics modes resembling the underlying hexagonal crystalline symmetry. Furthermore, the orientational distribution function provides information about the potential surface of rotational dynamics. The observed slow rotational diffusion can be attributed to the presence of orientational minima and potential barriers on the potential surface. Our findings with a real experimental system provide important insights into the role of attraction in the phase behaviors of plastic crystals

Rotational Dynamics of Discoid Colloidal Particles in Attractive Quasi-Two-Dimensional Plastic Crystals

Plastic crystals formed from anisotropic molecules or particles are an important state of matter characterized by the presence of long-range positional order and the lack of long-range orientational order. The rotational motion of molecules or particles in plastic crystals is the most attractive characteristic of the system. Here the rotational dynamics of the discoid particles in quasi-two-dimensional colloidal plastic crystals stabilized via depletion interactions are quantitatively studied using time-resolved confocal microscopy. The measured probability distribution of particle orientation reveals the existence of a strong coupling between the lattice symmetry and particle rotation, resulting in anisotropic rotational dynamics modes resembling the underlying hexagonal crystalline symmetry. Furthermore, the orientational distribution function provides information about the potential surface of rotational dynamics. The observed slow rotational diffusion can be attributed to the presence of orientational minima and potential barriers on the potential surface. Our findings with a real experimental system provide important insights into the role of attraction in the phase behaviors of plastic crystals

Rotational Dynamics of Discoid Colloidal Particles in Attractive Quasi-Two-Dimensional Plastic Crystals

Plastic crystals formed from anisotropic molecules or particles are an important state of matter characterized by the presence of long-range positional order and the lack of long-range orientational order. The rotational motion of molecules or particles in plastic crystals is the most attractive characteristic of the system. Here the rotational dynamics of the discoid particles in quasi-two-dimensional colloidal plastic crystals stabilized via depletion interactions are quantitatively studied using time-resolved confocal microscopy. The measured probability distribution of particle orientation reveals the existence of a strong coupling between the lattice symmetry and particle rotation, resulting in anisotropic rotational dynamics modes resembling the underlying hexagonal crystalline symmetry. Furthermore, the orientational distribution function provides information about the potential surface of rotational dynamics. The observed slow rotational diffusion can be attributed to the presence of orientational minima and potential barriers on the potential surface. Our findings with a real experimental system provide important insights into the role of attraction in the phase behaviors of plastic crystals

Polymer Translocation Time

The force- and flow-induced translocation processes of linear and ring polymers are studied using a combination of multiparticle collision dynamics and molecular dynamics, focusing on the behavior of the polymer translocation time. We compare the force- and flow-induced translocations of linear and ring polymers. It is found that when the translocation time (τ*) is characterized by scaling exponents, δ, δ′, and α, via the relations τ* ∼ fδNα and τ* ∼ Jδ′Nα, the scaling exponents are not constants. For long chains tested, α = 1.0 for both force- and flow-induced translocations. The difference between the force- and flow-induced translocations stems from different monomer crowding effects due to distinct flow patterns outside the channel. Furthermore, general relations for polymer translocation time are derived for these two translocation processes, which are in good agreement with the simulation results. Our results provide clear molecular pictures for the force- and flow-induced translocations, which shed light on the understanding of translocation dynamics and provide guidance for practical applications such as molecular sequencing and ultrafiltration

Origin of Microstructures from Confined Asymmetric Diblock Copolymers

The self-assembly of asymmetric diblock copolymers confined within cylindrical pores is studied using the self-consistent-field theory. The cylinder-forming asymmetric diblock copolymer is chosen to be near the cylinder−gyroid phase boundary in the intermediate segregation region. This choice makes the self-assembled cylindrical structure highly deformable, leading to very rich morphologies under confinement. A rich variety of structures, such as helices, stacked toroids, and perforated tubes, is observed as a function of the degree of confinement characterized by the ratio between the pore diameter D and bulk period L (D/L) as well as pore surface−polymer interactions. The origin of these confinement-induced structures is elucidated. The theoretical results are in good agreement with available experimental observations