Hierarchical superstructures assembled by binary mixed homopolymer-grafted nanoparticles are investigated by using a self-consistent field theory (SCFT). Our results demonstrate that grafting mixed homopolymer brushes provides an effective way to program the spatial lattice arrangement of the nanoparticles. For the polymer-grafted nanoparticles with specific interaction parameter and total grafting density, the unusual non-close-packed simple cubic (SC) crystal lattice is obtained at small spherical core/polymer size ratios (R/( N b) < 1). As the size ratio increases to R N b /() > 1, the nanoparticle arrangement transforms into a body-centered cubic (BCC) crystal lattice. Meanwhile, some unconventional microphases are formed in the polymer matrix, such as the tetragonal cylinder and simple cubic sphere phases. Furthermore, the two-dimensional (2D) model calculations reveal that the binary hairy nanoparticles prefer to arrange into the lattice in a way they can maintain the free energy-minimizing morphology as an isolated particle. Our findings suggest a possible strategy to design hierarchical nanomaterials composed of unique inorganic/organic hybrid superstructures.

Binary polymer brushes, including mixed homopolymer brushes and diblock copolymer brushes, are an attractive class of environmentally responsive nanostructured materials. Owing to microphase separation of the two chemically distinct components in the brush, multifaceted nanomaterials with functionalized and patterned surfaces can be obtained. This review summarizes recent progress on the theory and simulations related to binary polymer brushes grafted to flat, spherical, and cylindrical substrates, with a focus on patterned morphologies of multifaceted hairy nanoparticles, an intriguing class of hybrid nanostructured particles (e.g., nanospheres and nanorods). In particular, powerful field theory and particlebased simulations suitable for revealing novel structures on these patterned surfaces, including self-consistent field theory and dissipative particle dynamics simulations, are emphasized.The unsolved yet critical issues in this research field, such as dynamic response of binary polymer brushes to environmental stimuli and the hierarchical self-assembly of binary hairy nanoparticles, are briefly discussed.

A classical density functional theory (DFT) is applied to investigate the behavior of compressed polymer brushes composed of hard-sphere chains. The excluded volume interactions among the chain segments are explicitly treated. Two compression systems are used to study the behavior of brush-wall and brush-brush interactions. For the brush-brush systems, an obvious interpenetration zone has been observed. The extent of the interpenetration depends strongly on the grafting density. Furthermore, the repulsive force between the brush and wall or between the two brushes has been obtained as a function of the compression distance. Compared to the prediction of the analytic self-consistent field theory, such force increases more rapidly in the brush-wall compression with high polymer grafting densities or at higher compressions. In the brush-brush compression system, the interpenetration between the two compressed brushes creates a "softer" interaction. The influence of hard-sphere solvents on the behavior of compressed brushes is also discussed.

The conformation of homodendrimers and amphiphilic dendrimers in various solvents is studied using classical density functional theory (DFT), in which the excluded-volume effects are treated explicitly. For homodendrimers in an athermal solvent, DFT results predict a remarkable fold-back behavior for the outer generation of segments, supporting the dense-core model. A coil-to-globule transition is observed for homodendrimers in a poor solvent. The size of the dendrimers, characterized by the radius of gyration, ⟨Rg⟩, is found to follow the scaling relationship, ⟨Rg⟩ ∼ N(ν), where N is the total number of segments of the dendrimers. For amphiphilic dendrimers, DFT results show that chemical modification in the outermost generation is an effective method to drive the ends toward the periphery of the dendrimers. In particular, a conformation with a hollow interior structure could be formed for amphiphilic dendrimers with longer end spacers in a selective solvent. The resulting unimolecular micelles with a hollow core and dense shell could serve as a unique candidate for encapsulation applications, such as sustained-drug-release nanocontainers.

We report on microphase separation behaviors of mixed polymer brushes grafted onto an infinitely long cylindrical rod by performing polymer self-consistent field theory (SCFT) calculation with "masking" technique. The "masking" technique is especially suitable to deal with systems of confined polymers grafted onto curved surfaces. We have developed a method to solve the morphology of block copolymers confined into complicated topographic surfaces with SCFT. In this paper, this unique technique is extended to solve the SCFT for nanorod grafted by mixed polymer brushes. Furthermore, the use of simple Cartesian grids in a cubic computational cell with periodic boundary conditions makes it possible to solve diffusion equations in SCFT by utilizing an efficient and highly accurate pseudo-spectral method involving fast Fourier transform. Both parallel rippled phase and ring-shaped phase are predicted. We have investigated the influences of the cylinder radius, grafting density and interaction between the two incompatible grafting polymers on the stability of the two typical phases. Our results show that the system prefers the ring-shaped phase with the increase of the cylinder radius, grafting density and interaction between the two grafting polymers. Phase diagrams involving these parameters are constructed, and we explain the reason of the transition between the parallel rippled phase and ring-shaped phase in terms of the degree of phase segregation. Again, the degree of phase segregation is higher with larger cylinder radius, grafting density and interaction between the two grafting polymers. By comparing the degree of phase segregation and free energy of the parallel rippled and ring-shaped phases at the same condition, we found that the ring-shaped phase favors the entropic part of the free energy while the parallel rippled phase significantly reduces the enthalpy. Therefore, when the degree of phase segregation is low, the free energy of the system is dominated by the enthalpy, leading to the parallel rippled phase; when the degree of phase segregation is high, the free energy of the system is dominated by the entropic part and the ring-shaped phase is stable. We also found that the domain numbers of parallel rippled phase and the period of alternating ring-shaped phase vary with the radius of cylinder. These predictions are expected to be helpful in rational design and fabrication of such novel polymer brushes.

We employed the strong segregation theory (SST) to study the phase structures of mixed homopolymer brushes grafted on cylindrical surfaces. We considered a simplified case in which two incompatible homopolymers have the same chain length and grafting density. Under these conditions, micro-phase separation in the brush may result in either ripple or helix structures. By comparing the free energy of the possible candidate structures, we found that the helix structure is never the most stable one, while the stability of the perpendicular and parallel ripple structures are sensitive to the curvature of the grafting substrate. It was found that the morphology orientation of the mixed homopolymer brushes can be controlled by attuning the geometry of the substrates.

Nonsequential response is the phenomenon where the change of soil water content at the lower layer is larger than that of the upper layer within a set time interval. It is often ignored because of the lack of spatially distributed measurements at the watershed scale, especially in mountainous areas where extensive monitoring network is expensive and difficult to deploy. In this study, the subsurface nonsequential response in a mountainous watershed in Southwest China was investigated by combining field monitoring and numerical simulation. A physics-based numerical model (InHM) was employed to simulate the soil water movement to explore the occurrence of the subsurface nonsequential response. The topographic wetness index [TWI = ln (a/tan b)] was used to distinguish the topographic zone corresponding to the nonsequential response at different depths. The nonsequential response mainly came from the subsurface lateral flow initiated at the soil–bedrock interface or at a relatively impermeable layer. The results showed that the occurrence depth of the nonsequential response increased with precipitation intensity when the time since last event was more than 24 h and the total amount of this event exceeded 37 mm. During a rainfall event, the nonsequential response occurred at the middle layer in the hillslope zone and the deep soil layer beneath the channel. In case of a rainfall event with two peaks, the region observed with nonsequential response expanded. The soil layer at the interface of the bedrock could be saturated quickly, and became saturated upward. This kind of nonsequential response can be observed on the hillslope at the beginning of rainfall events, and then found beneath stream channels afterward. Furthermore, nonsequential response could also happen after rainfall events. The results improved our understanding of nonsequential response and provided a scientific basis for flash flood research in mountainous areas.