We investigate the solution self-assembly of a mixture of positively charged homopolymers and AB diblock copolymers,in which the A blocks are negatively charged,and the B blocks are neutral.The electrostatic complexat...We investigate the solution self-assembly of a mixture of positively charged homopolymers and AB diblock copolymers,in which the A blocks are negatively charged,and the B blocks are neutral.The electrostatic complexation between oppositely charged polymers drives the formation of many ordered phases.The microstructures and phase diagrams are calculated using self-consistent field theory(SCFT)based on an ion-pair model with an equilibrium constant K to characterize the strength of binding between positively and negatively charged monomers.The effects of the charge ratio,representing the ratio of charges from the homopolymer over all charges from polymers in the system,on the ordered structure are systematically studied,both for hydrophobic and hydrophilic A blocks.The charge ratio plays an important role in determining the phase boundaries in the phase diagram of salt concentration versus polymer concentration.We also provide information about the varying tendency of the domain spacing and core size of the spherical phase when the charge ratio is changed,and the results are in good agreement with experiments.These studies provide a deep understanding of the self-assembled microstructures of oppositely charged diblock copolymer-homopolymer systems.展开更多
We study the effect of chain rigidity on tailoring the nanoparticle locations for neutral and selective particles embedded in the lamellar morphology formed by semiflexible diblock copolymer chains using self-consiste...We study the effect of chain rigidity on tailoring the nanoparticle locations for neutral and selective particles embedded in the lamellar morphology formed by semiflexible diblock copolymer chains using self-consistent field calculations. The nanoparticles are modeled through a cavity function, and the semiflexible chains are represented by the continuous Kratsky-Porod chain model. In general situation, the nanoparticles prefer to stay at the interface in order to reduce the interface areas and thus the system free energy. However, the particle distribution at the domain center is subtle, and the underlying physics is intrinsically different depending on the polymer flexibility. In the case of flexible chains, the entropy just contributes a constant shift to the free energy when the nanoparticles move around the domain center indicating that the local metastable state if appears at the domain center is wholly attributed to the local minimum in the enthalpy. If the polymers are rigid, the variation of the particle distribution at the domain center has a close relation with the polymer rigidity and nanoparticle size. In the case of strongly rigid polymers with small nanoparticles, a nearly uniform particle distribution at the domain center is observed, while in other cases, a local enhancement of particle distribution there is found. In contrast to the case of flexible chains, further analysis reveals the crucial role of entropy in controlling the shape of particle distributions at the phase domain. Specifically, the local metastable state appears in the domain center is determined by the large entropy there which arises from the weak coupling of bond orientations that allows the polymer chains to be relatively relaxed. When the particle becomes selective, its distribution in the phase domain exhibits a shift almost uniformly rather than changes its profile, and the underlying physics still holds. In all, our study establishes a strong coupling between the chain rigidity and effect of entropy.展开更多
Designing the kinetic pathways of assembling macromolecules such as block copolymers and DNA strands is crucial not only for an achievement of thermodynamically equilibrium nanostructures over macroscopic areas,but al...Designing the kinetic pathways of assembling macromolecules such as block copolymers and DNA strands is crucial not only for an achievement of thermodynamically equilibrium nanostructures over macroscopic areas,but also for a better understanding of formation process of higher-level superstructures where well-tailored assemblies act as mesoscopic building units.Theoretical analysis and computer simulations provide excellent opportunities to microscopically reveal the kinetics and mechanism of structural evolution as well as the collective behaviors of building units.In this perspective,we summarize our efforts of theoretical and computational modelling to understand the long-range ordering mechanisms and the organization kinetics of assembling macromolecules along designable pathways.First,we present the computational modelling and recent strategies of designable pathways for the achievement of long-range ordering.Then,from the computational views,we give the applications of pathway-designed strategies to explore the ordering mechanism and kinetics in the course of structural evolution,covering the block copolymers and their nanocomposites under zone annealing as well as the hierarchical self-assembly of mesoscopic building units(e.g.,patchy micelles and DNA-functionalized nanoparticles).Finally,we outlook future directions in the field of designable pathways for the achievement of long-range ordered nanostructures.This perspective could promote further efforts towards the wide applications of theoretical and computational modelling in the construction of soft hybrid metamaterials.展开更多
The self-assembly of the linear rod-coil multiblock copolymers is studied by applying self-consistent-field lattice techniques in a three-dimensional （3D） space. Compared to the copolymer with one rod, the copolymer...The self-assembly of the linear rod-coil multiblock copolymers is studied by applying self-consistent-field lattice techniques in a three-dimensional （3D） space. Compared to the copolymer with one rod, the copolymer with more rods （mrod≥ 2） exhibits rich order-order phase transitions with increasing temperature, where the ordered morphology changes from strips to perforated lamellae and finally to lamellae. In addition, taking the copolymer with mrod = 2 as a representative, we fiarther study the effects of the volume fractions of the rods, the spacer coils and the end coils on the phase behaviors respectively, by which the detailed self-assembled mechanism of the linear rod-coil multiblock copolymers is revealed. Our results are expected to provide guidance for the design of the rod-coil materials.展开更多
Dynamic self-consistent field theory(DSCFT)is a fruitful approach for modeling the structural evolution and collective kinetics for a wide variety of multicomponent polymers.However,solving a set of DSCFT equations re...Dynamic self-consistent field theory(DSCFT)is a fruitful approach for modeling the structural evolution and collective kinetics for a wide variety of multicomponent polymers.However,solving a set of DSCFT equations remains daunting because of high computational demand.Herein,a machine learning method,integrating low-dimensional representations of microstructures and long short-term memory neural networks,is used to accelerate the predictions of structural evolution of multicomponent polymers.It is definitively demonstrated that the neural-network-trained surrogate model has the capability to accurately forecast the structural evolution of homopolymer blends as well as diblock copolymers,without the requirement of“on-the-fly”solution of DSCFT equations.Importantly,the data-driven method can also infer the latent growth laws of phase-separated microstructures of multicomponent polymers through simply using a few of time sequences from their past,without the prior knowledge of the governing dynamics.Our study exemplifies how the machine-learning-accelerated method can be applied to understand and discover the physics of structural evolution in the complex polymer systems.展开更多
The different confinement shapes can induce the formation of various interesting and novel morphologies, which might inspire potential applications of materials. In this paper, we study the directed self-assembly of d...The different confinement shapes can induce the formation of various interesting and novel morphologies, which might inspire potential applications of materials. In this paper, we study the directed self-assembly of diblock copolymer confined in irregular geometries with a soft surface by using self-consistent field theory. Two types of confinement geometries are considered, namely, one is the concave pore with one groove and the other is the concave pore with two grooves. We obtain more novel and different structures which could not be produced in other two-dimensional（2D） confinements. Comparing these new structures with those obtained in regular square confinement, we find that the range of ordered lamellae is enlarged and the range of disordered structure is narrowed down under the concave pore confinement.We also compare the different structures obtained under the two types of confinement geometries, the results show that the effect of confinement would increase, which might induce the diblock copolymer to form novel structures. We construct the phase diagram as a function of the fraction of B block and the ratio of h/L of the groove. The simulation reveals that the wetting effect of brushes and the shape of confinement geometries play important roles in determining the morphologies of the system. Our results improve the applications in the directed self-assembly of diblock copolymer for fabricating the irregular structures.展开更多
ABCA tetrablock copolymers offer new opportunities for design of materials with novel structures. Using real-space self- consistent field theory and simulation, we systematically examined the self-assembly behavior of...ABCA tetrablock copolymers offer new opportunities for design of materials with novel structures. Using real-space self- consistent field theory and simulation, we systematically examined the self-assembly behavior of linear ABCA tetrablock copolymers in a 2D space. The simulation was carried out under conditions of symmetrical compositions and interactions. We focus on the influence of chain length ratio of block A and interactions between block A and other blocks B and C on the self-assembly behavior of the copolymer system. The simulation results show that most of the structures self-assembled by the ABCA tetrablock copolymers are centrosymmetric, such as diblock-like lameUa phase, two kinds of lameUae with beads at interface, two kinds of hierarchical lamella phase, hexagonal honeycomb-like phase, lamella phase with mixed BC and hexagonal spheres with mixed BC. Furthermore, we find that a novel noncentrosymmetric Janus spheres can be obtained when the interaction between blocks B and C is strong, whereas a noncentrosymmetric lamella phase was obtained at weak interaction between blocks B and C. Phase diagrams for the ABCA tetrablock copolymers with different interaction strength between blocks B and C are constructed by comparing free energies of candidate ordered structures. In addition, studies on the metastable behavior of the system reveal that enthalpy plays an important role in the metastable behavior of the ABCA tetrablock copolymer system. Our work can provide useful guide for structure control of such kind of tetrablock copolymers in experiments.展开更多
The topic of self-assembly of cylinder-forming diblock copolymers （DBCPs） under spherical shell confinement in different surface fields is explored using real-space self-consistent field theory calculations （SCFT）...The topic of self-assembly of cylinder-forming diblock copolymers （DBCPs） under spherical shell confinement in different surface fields is explored using real-space self-consistent field theory calculations （SCFT）. Using this approach we observed various microstructures of cylinder-forming DBCPs at different confinement dimensions and surface fields. From detailed searching for the microdomain morphologies, an obvious conclusion is that the interactions between the confinement surface and the polymers have a great effect on the self-assembly. Most of the microstructures are unique and not reported in bulk or under planar and cylindrical confinements.展开更多
The symmetry orbital-symmetry orbital tensor method is applied to the evaluation of molecular integrals (one-electron and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) cal...The symmetry orbital-symmetry orbital tensor method is applied to the evaluation of molecular integrals (one-electron and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) calculations. A calculation scheme is proposed to simplify the evaluation of integrals and a key equation is derived to reduce the computation efforts in SCF iterations. According to the key equation, compared with the traditional SCF method, the computation efficiencies including CPU timing and external disk (or internal memory) requirement increase in the magnitude of the square of the order of a point group. The new SOT method is expected to be useful in the theoretical calculations of large molecular systems of high point group symmetries.展开更多
A cluster model is used to calculate electron energy-loss fine structures in crystal. The multiple-scattering self-consistent-field method is employed in the calculation. Our theoretical results of N near K-edge energ...A cluster model is used to calculate electron energy-loss fine structures in crystal. The multiple-scattering self-consistent-field method is employed in the calculation. Our theoretical results of N near K-edge energy loss fine structures in hexagonal GaN crystal are in good agreement with the experimental spectra. Future possible experiments in energy-filtered transmission electron microscopy (EFTEM) are discussed and proposed because our theoretical work can provide clear assignments for transmitted electrons with different energy losses.展开更多
The self-consistent Hartree-Fock equation for the He atom is solved using the pseudospectral method. The Feshbach- type autoionization resonance parameters for doubly excited 2s2, 3s2, and 4s2 IS states of He have bee...The self-consistent Hartree-Fock equation for the He atom is solved using the pseudospectral method. The Feshbach- type autoionization resonance parameters for doubly excited 2s2, 3s2, and 4s2 IS states of He have been determined by adding a complex absorbing potential to the Hamiltonian. The Riss-Meyer iterative and Pad6 extrapolation methods are applied to obtain reliable values for the autoionization resonance parameters, which are compared to previous results in the literature.展开更多
Current mainstream method of simulating plasma is based on rigid-macroparticle approximation in which many realistic particles are merged, according to their initial space positions regardless of their initial velocit...Current mainstream method of simulating plasma is based on rigid-macroparticle approximation in which many realistic particles are merged, according to their initial space positions regardless of their initial velocities, into a macroparticle, and do a global motion. This is a distorted picture because what each macroparticle do is to break into, because of differences among velocities of contained realistic particles, pieces with different destinations at next time point, rather than a global moving to a destination at next time point. Therefore, the scientific validity of results obtained from such an approximation cannot be warranted. Here, we propose a solution to this problem. It can fundamentally warrant exact solutions of plasma self-consistent fields and hence those of microscopic distribution function.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)(Nos.22073002,51921002 and 22373008).
文摘We investigate the solution self-assembly of a mixture of positively charged homopolymers and AB diblock copolymers,in which the A blocks are negatively charged,and the B blocks are neutral.The electrostatic complexation between oppositely charged polymers drives the formation of many ordered phases.The microstructures and phase diagrams are calculated using self-consistent field theory(SCFT)based on an ion-pair model with an equilibrium constant K to characterize the strength of binding between positively and negatively charged monomers.The effects of the charge ratio,representing the ratio of charges from the homopolymer over all charges from polymers in the system,on the ordered structure are systematically studied,both for hydrophobic and hydrophilic A blocks.The charge ratio plays an important role in determining the phase boundaries in the phase diagram of salt concentration versus polymer concentration.We also provide information about the varying tendency of the domain spacing and core size of the spherical phase when the charge ratio is changed,and the results are in good agreement with experiments.These studies provide a deep understanding of the self-assembled microstructures of oppositely charged diblock copolymer-homopolymer systems.
基金financially supported by the National Natural Science Foundation of China (No.22173002)the Fundamental Research Funds for the Central Universities (No.YWF-22-K-101)the Fundamental Research Funds for the Central Universities from Beihang University。
文摘We study the effect of chain rigidity on tailoring the nanoparticle locations for neutral and selective particles embedded in the lamellar morphology formed by semiflexible diblock copolymer chains using self-consistent field calculations. The nanoparticles are modeled through a cavity function, and the semiflexible chains are represented by the continuous Kratsky-Porod chain model. In general situation, the nanoparticles prefer to stay at the interface in order to reduce the interface areas and thus the system free energy. However, the particle distribution at the domain center is subtle, and the underlying physics is intrinsically different depending on the polymer flexibility. In the case of flexible chains, the entropy just contributes a constant shift to the free energy when the nanoparticles move around the domain center indicating that the local metastable state if appears at the domain center is wholly attributed to the local minimum in the enthalpy. If the polymers are rigid, the variation of the particle distribution at the domain center has a close relation with the polymer rigidity and nanoparticle size. In the case of strongly rigid polymers with small nanoparticles, a nearly uniform particle distribution at the domain center is observed, while in other cases, a local enhancement of particle distribution there is found. In contrast to the case of flexible chains, further analysis reveals the crucial role of entropy in controlling the shape of particle distributions at the phase domain. Specifically, the local metastable state appears in the domain center is determined by the large entropy there which arises from the weak coupling of bond orientations that allows the polymer chains to be relatively relaxed. When the particle becomes selective, its distribution in the phase domain exhibits a shift almost uniformly rather than changes its profile, and the underlying physics still holds. In all, our study establishes a strong coupling between the chain rigidity and effect of entropy.
基金financially supported by the National Natural Science Foundation of China(Nos.22073028 and 21873029)。
文摘Designing the kinetic pathways of assembling macromolecules such as block copolymers and DNA strands is crucial not only for an achievement of thermodynamically equilibrium nanostructures over macroscopic areas,but also for a better understanding of formation process of higher-level superstructures where well-tailored assemblies act as mesoscopic building units.Theoretical analysis and computer simulations provide excellent opportunities to microscopically reveal the kinetics and mechanism of structural evolution as well as the collective behaviors of building units.In this perspective,we summarize our efforts of theoretical and computational modelling to understand the long-range ordering mechanisms and the organization kinetics of assembling macromolecules along designable pathways.First,we present the computational modelling and recent strategies of designable pathways for the achievement of long-range ordering.Then,from the computational views,we give the applications of pathway-designed strategies to explore the ordering mechanism and kinetics in the course of structural evolution,covering the block copolymers and their nanocomposites under zone annealing as well as the hierarchical self-assembly of mesoscopic building units(e.g.,patchy micelles and DNA-functionalized nanoparticles).Finally,we outlook future directions in the field of designable pathways for the achievement of long-range ordered nanostructures.This perspective could promote further efforts towards the wide applications of theoretical and computational modelling in the construction of soft hybrid metamaterials.
基金supported by the National Natural Science Foundation of China (Nos. 20804047, 20774096 and 20734003)Programs and the Fund for Creative Research Groups (No. 50921062)subsidized by the Special Funds for National Basic Research Program of China (Nos. 2009CB930100, 2010CB631100)
文摘The self-assembly of the linear rod-coil multiblock copolymers is studied by applying self-consistent-field lattice techniques in a three-dimensional （3D） space. Compared to the copolymer with one rod, the copolymer with more rods （mrod≥ 2） exhibits rich order-order phase transitions with increasing temperature, where the ordered morphology changes from strips to perforated lamellae and finally to lamellae. In addition, taking the copolymer with mrod = 2 as a representative, we fiarther study the effects of the volume fractions of the rods, the spacer coils and the end coils on the phase behaviors respectively, by which the detailed self-assembled mechanism of the linear rod-coil multiblock copolymers is revealed. Our results are expected to provide guidance for the design of the rod-coil materials.
基金financially supported by the National Natural Science Foundation of China(Nos.22073028,21873029 and 22073004)the Fundamental Research Funds for the Central Universities。
文摘Dynamic self-consistent field theory(DSCFT)is a fruitful approach for modeling the structural evolution and collective kinetics for a wide variety of multicomponent polymers.However,solving a set of DSCFT equations remains daunting because of high computational demand.Herein,a machine learning method,integrating low-dimensional representations of microstructures and long short-term memory neural networks,is used to accelerate the predictions of structural evolution of multicomponent polymers.It is definitively demonstrated that the neural-network-trained surrogate model has the capability to accurately forecast the structural evolution of homopolymer blends as well as diblock copolymers,without the requirement of“on-the-fly”solution of DSCFT equations.Importantly,the data-driven method can also infer the latent growth laws of phase-separated microstructures of multicomponent polymers through simply using a few of time sequences from their past,without the prior knowledge of the governing dynamics.Our study exemplifies how the machine-learning-accelerated method can be applied to understand and discover the physics of structural evolution in the complex polymer systems.
基金Project supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20121404110004)the Research Foundation for Excellent Talents of Shanxi Provincial Department of Human Resources and Social Security+2 种基金Chinathe Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi ProvinceChina
文摘The different confinement shapes can induce the formation of various interesting and novel morphologies, which might inspire potential applications of materials. In this paper, we study the directed self-assembly of diblock copolymer confined in irregular geometries with a soft surface by using self-consistent field theory. Two types of confinement geometries are considered, namely, one is the concave pore with one groove and the other is the concave pore with two grooves. We obtain more novel and different structures which could not be produced in other two-dimensional（2D） confinements. Comparing these new structures with those obtained in regular square confinement, we find that the range of ordered lamellae is enlarged and the range of disordered structure is narrowed down under the concave pore confinement.We also compare the different structures obtained under the two types of confinement geometries, the results show that the effect of confinement would increase, which might induce the diblock copolymer to form novel structures. We construct the phase diagram as a function of the fraction of B block and the ratio of h/L of the groove. The simulation reveals that the wetting effect of brushes and the shape of confinement geometries play important roles in determining the morphologies of the system. Our results improve the applications in the directed self-assembly of diblock copolymer for fabricating the irregular structures.
基金financially supported by the National Natural Science Foundation of China(No.21474107)
文摘ABCA tetrablock copolymers offer new opportunities for design of materials with novel structures. Using real-space self- consistent field theory and simulation, we systematically examined the self-assembly behavior of linear ABCA tetrablock copolymers in a 2D space. The simulation was carried out under conditions of symmetrical compositions and interactions. We focus on the influence of chain length ratio of block A and interactions between block A and other blocks B and C on the self-assembly behavior of the copolymer system. The simulation results show that most of the structures self-assembled by the ABCA tetrablock copolymers are centrosymmetric, such as diblock-like lameUa phase, two kinds of lameUae with beads at interface, two kinds of hierarchical lamella phase, hexagonal honeycomb-like phase, lamella phase with mixed BC and hexagonal spheres with mixed BC. Furthermore, we find that a novel noncentrosymmetric Janus spheres can be obtained when the interaction between blocks B and C is strong, whereas a noncentrosymmetric lamella phase was obtained at weak interaction between blocks B and C. Phase diagrams for the ABCA tetrablock copolymers with different interaction strength between blocks B and C are constructed by comparing free energies of candidate ordered structures. In addition, studies on the metastable behavior of the system reveal that enthalpy plays an important role in the metastable behavior of the ABCA tetrablock copolymer system. Our work can provide useful guide for structure control of such kind of tetrablock copolymers in experiments.
基金financially supported by the National Natural Science Foundation of China(Nos.20774066,20974081 and 20934004)the Ph.D.Programs Foundation of Ministry of Education of China(No.20090101110002)the Natural Science Foundation of Zhejiang Province(No.Y4080098)
文摘The topic of self-assembly of cylinder-forming diblock copolymers （DBCPs） under spherical shell confinement in different surface fields is explored using real-space self-consistent field theory calculations （SCFT）. Using this approach we observed various microstructures of cylinder-forming DBCPs at different confinement dimensions and surface fields. From detailed searching for the microdomain morphologies, an obvious conclusion is that the interactions between the confinement surface and the polymers have a great effect on the self-assembly. Most of the microstructures are unique and not reported in bulk or under planar and cylindrical confinements.
基金Project supported by the National Natural Science Foundation of China (Grant No. 29473119)
文摘The symmetry orbital-symmetry orbital tensor method is applied to the evaluation of molecular integrals (one-electron and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) calculations. A calculation scheme is proposed to simplify the evaluation of integrals and a key equation is derived to reduce the computation efforts in SCF iterations. According to the key equation, compared with the traditional SCF method, the computation efficiencies including CPU timing and external disk (or internal memory) requirement increase in the magnitude of the square of the order of a point group. The new SOT method is expected to be useful in the theoretical calculations of large molecular systems of high point group symmetries.
基金the National Natural Science Foundation of China ( Grant Nos.19874035, 59831020, 19734030), National 973 Project, National 863 Program, Climbing Project, The Ministry of Science and Technology of China, National High-Tec ICF Committee, the Ministry of
文摘A cluster model is used to calculate electron energy-loss fine structures in crystal. The multiple-scattering self-consistent-field method is employed in the calculation. Our theoretical results of N near K-edge energy loss fine structures in hexagonal GaN crystal are in good agreement with the experimental spectra. Future possible experiments in energy-filtered transmission electron microscopy (EFTEM) are discussed and proposed because our theoretical work can provide clear assignments for transmitted electrons with different energy losses.
文摘The self-consistent Hartree-Fock equation for the He atom is solved using the pseudospectral method. The Feshbach- type autoionization resonance parameters for doubly excited 2s2, 3s2, and 4s2 IS states of He have been determined by adding a complex absorbing potential to the Hamiltonian. The Riss-Meyer iterative and Pad6 extrapolation methods are applied to obtain reliable values for the autoionization resonance parameters, which are compared to previous results in the literature.
文摘Current mainstream method of simulating plasma is based on rigid-macroparticle approximation in which many realistic particles are merged, according to their initial space positions regardless of their initial velocities, into a macroparticle, and do a global motion. This is a distorted picture because what each macroparticle do is to break into, because of differences among velocities of contained realistic particles, pieces with different destinations at next time point, rather than a global moving to a destination at next time point. Therefore, the scientific validity of results obtained from such an approximation cannot be warranted. Here, we propose a solution to this problem. It can fundamentally warrant exact solutions of plasma self-consistent fields and hence those of microscopic distribution function.
