In this study,we investigate the ef-ficacy of a hybrid parallel algo-rithm aiming at enhancing the speed of evaluation of two-electron repulsion integrals(ERI)and Fock matrix generation on the Hygon C86/DCU(deep compu...In this study,we investigate the ef-ficacy of a hybrid parallel algo-rithm aiming at enhancing the speed of evaluation of two-electron repulsion integrals(ERI)and Fock matrix generation on the Hygon C86/DCU(deep computing unit)heterogeneous computing platform.Multiple hybrid parallel schemes are assessed using a range of model systems,including those with up to 1200 atoms and 10000 basis func-tions.The findings of our research reveal that,during Hartree-Fock(HF)calculations,a single DCU ex-hibits 33.6 speedups over 32 C86 CPU cores.Compared with the efficiency of Wuhan Electronic Structure Package on Intel X86 and NVIDIA A100 computing platform,the Hygon platform exhibits good cost-effective-ness,showing great potential in quantum chemistry calculation and other high-performance scientific computations.展开更多
The morphological changes of ABA amphiphilic triblock copolymer micelles in dilute solution were systematically studied by tuning the solvent property using self-consistent field simulation. The solvent property was t...The morphological changes of ABA amphiphilic triblock copolymer micelles in dilute solution were systematically studied by tuning the solvent property using self-consistent field simulation. The solvent property was tuned by changing the Flory-Huggins interaction parameters between each type of blocks and solvent, respectively. The simulation results show that by changing the solvent properties, a series of micelle morphologies such as vesicle, cage-like, ring-shaped, rod-like and spherical micelle morphologies can be obtained. Variations of the free energy of the solution system and the surface area of micelles with the Flory-Huggins interaction parameters were calculated to better understand the effect of solvent property on micelle morphologies. In addition, a phase diagram showing the morphological changes of micelles with the Flory-Huggins interaction parameters is provided.展开更多
Self-assembled nanostructures of lipids and nanoparticles hold great promise for applications in such fields as nanomedicine. This paper uses the self-consistent field theory to investigate the self-assembly behavior ...Self-assembled nanostructures of lipids and nanoparticles hold great promise for applications in such fields as nanomedicine. This paper uses the self-consistent field theory to investigate the self-assembly behavior of lipid molecules and nanoparticles with different shapes in an aqueous solution. It is found that the lipid molecules can form monolayered and bilayered nanostructures around the nanopartieles with different shapes （e.g., triangular, square, hexagonal and octangular）. With decreasing the size of nanoparticles or increasing the number of polygon edges, the shape of lipid layers will approach an approximately spherical shape. These findings may help to predict and design novel drug delivery nanocarriers.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
The self-consistent field theory has been employed to numerically study the response of bi-disperse flexible polyelectrolyte （PE） brushes grafted on an electrode to electric fields generated by opposite surface char...The self-consistent field theory has been employed to numerically study the response of bi-disperse flexible polyelectrolyte （PE） brushes grafted on an electrode to electric fields generated by opposite surface charges on the PE-grafted electrode and a second parallel electrode. The numerical study reveals that, under a positive external electric field, the shorter and negatively charged PE chains are more responsive than the longer PE chains in terms of the relative changes in their respective brush heights. Whereas under a negative external electric field, the opposite was observed. The total electric force on the grafted PE chains was calculated and it was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The underlying mechanism was unraveled through analyzing the total electric field across the two oppositely charged electrodes.展开更多
Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depen...Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such as surface tension, bending moduli, and line tension. Understanding how the molecular properties of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting the mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.展开更多
Self-consistent field theory（SCFT）, as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to improve its accuracy and efficiency. Here we present a four...Self-consistent field theory（SCFT）, as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to improve its accuracy and efficiency. Here we present a fourth-order exponential time differencing Runge-Kutta algorithm（ETDRK4） to solve the modified diffusion equation（MDE） which is the most time-consuming part of a SCFT calculation. By making a careful comparison with currently most efficient and popular algorithms, we demonstrate that the ETDRK4 algorithm significantly reduces the number of chain contour steps in solving the MDE, resulting in a boost of the overall computation efficiency, while it shares the same spatial accuracy with other algorithms. In addition, to demonstrate the power of our ETDRK4 algorithm, we apply it to compute the phase boundaries of the bicontinuous gyroid phase in the strong segregation regime and to verify the existence of the triple point of the O70 phase, the lamellar phase and the cylindrical phase.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 adsorption of flexible polyelectrolyte （PE） with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory...The adsorption of flexible polyelectrolyte （PE） with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.展开更多
The self-consistent field theory(SCFT)was employed to numerically study the interaction and interpenetration between two opposing weak polyelectrolyte(PE)brushes formed by grafting weak PE chains onto the surfaces of ...The self-consistent field theory(SCFT)was employed to numerically study the interaction and interpenetration between two opposing weak polyelectrolyte(PE)brushes formed by grafting weak PE chains onto the surfaces of two long and parallel columns with rectangularshaped cross-section immersed in a salty aqueous solution.The dependences of the brush heights and the average degree of ionization on various system parameters were also investigated.When the brush separation is relatively large compared with the unperturbed brush height,the degree of interpenetration between the two opposing PE brushes was found to increase with increasing grafting density and bulk degree of ionization.The degree of interpenetration also increases with the bulk salt concentration in the osmotic brush regime.Numerical results further revealed that,at a brush separation comparable to the unperturbed brush height,the degree of interpenetration does not increase further with increasing bulk degree of ionization,bulk salt concentration in the osmotic regime and grafting density.The saturation of the degree of interpenetration with these system parameters indicates that the grafted PE chains in the gap between the two columns retract and tilt in order to reduce the unfavorable electrostatic and steric repulsions between the two opposing PE brushes.Based on salt ion concentrations at the midpoint between the two opposing brushes,a quantitative criterion in terms of the unperturbed brush height and Debye screening length was established to determine the threshold value of the brush separation beyond which they are truly independent from each other.展开更多
As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency...As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔE_(ST))of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔE_(ST)would be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S_(1)state energy(E(S_(1))),T_(1)state ener-gy(E(T_(1))),andΔE_(ST)using three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S_(1)),E(T_(1)),andΔE_(ST)for 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S_(1)state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T_(1)state energy.TheΔE_(ST)derived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔE_(ST)of MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.展开更多
In this paper,we develop an adaptive high-order surface finite element method(FEM)incorporating spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations o...In this paper,we develop an adaptive high-order surface finite element method(FEM)incorporating spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved surfaces.The high-order surface FEM is obtained by the high-order surface geometrical approximation and the high-order function space approximation.Numerical results demonstrate that the precision order of these methods is consistent with theoretical prediction.In order to describe the sharp interface in the strongly segregated system more accurately,an adaptive FEM equipped with a new Log marking strategy is proposed.The Log marking strategy can not only label the elements that need to be refined or coarsened,but also give the refined or coarsened times,which can make full use of the information of a posterior error estimator and improve the efficiency of the adaptive algorithm.To demonstrate the power of our approach,we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces.Numerical results illustrate the efficiency of the proposed method,especially for strongly segregated systems with economical discretization nodes.展开更多
This review article addresses the widely used self-consistent field theory(SCFT)in interacting polymer systems.The theoretical framework and numerical method of solving the self-consistent equations are presented.In t...This review article addresses the widely used self-consistent field theory(SCFT)in interacting polymer systems.The theoretical framework and numerical method of solving the self-consistent equations are presented.In this paper,different structures of polymer can be considered,such as homopolymer,block copolymer,polydisperse polymer and charged polymer.Several systems,micro/macro phase separation,interface,self-assembly,are presented as examples to demonstrate its applications in details.Besides,the fluctuation effects are considered.The first order is Gaussian fluctuation theory,which can be used to determine the stability of the mean-field solution and predict the kinetics of unstable structure.The derivation and applications of Gaussian fluctuation theory are presented as well.展开更多
The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction.However,the counterintuitive like-charge attraction in electrolytes has been frequently observed in e...The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction.However,the counterintuitive like-charge attraction in electrolytes has been frequently observed in experiments,which has been theoretically debated for a long time.It is widely known that the mean field Poisson-Boltzmann theory cannot explain and predict this anomalous feature since it ignores many-body properties.In this paper,we develop efficient algorithm and perform the force calculation between two interfaces using a set of self-consistent equations which properly takes into account the electrostatic correlation and the dielectric-boundary effects.By solving the equations and calculating the pressure with the Debye-charging process,we show that the self-consistent equations could be used to study the attraction between like-charge surfaces from weak-coupling to mediate-coupling regimes,and that the attraction is due to the electrostatics-driven entropic force which is significantly enhanced by the dielectric depletion of mobile ions.A systematic investigation shows that the interaction forces can be tuned by material permittivity,ionic size and valence,and salt concentration,and that the like-charge attraction exists only for specific regime of these parameters.展开更多
The self-consistent field theory (SCFT) based upon coarse-grained model is especially suitable for investigating thermodynamic equilibrium morphology and the phase diagram of inhomo-geneous polymer systems subjected t...The self-consistent field theory (SCFT) based upon coarse-grained model is especially suitable for investigating thermodynamic equilibrium morphology and the phase diagram of inhomo-geneous polymer systems subjected to phase separation. The advantage of this model is that the details of the chain such as the architecture of the chain and the sequence of blocks can be consid-ered. We present here an overview of SCFT approach and its applications in polymeric systems. In particular, we wish to focus on our group’s achievements in applications of SCFT in such fields: simulation of microphase separation morphologies of multiblock copolymers with a complex molecular architecture, interactions between brush-coated sheets in a polymer matrix, mixtures of flexible poly-mers and small molecular liquid crystals at the interface, shapes of polymer-chain-anchored fluid vesicles, self-assembled morphologies of block copolymers in dilute solution, and so on. Finally, the further developments as well as the perspective applications of SCFT are discussed.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
Based on 'the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens (cylindrical coordinates)' proposed by one of the authors (1981), the propagation of the self-cons...Based on 'the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens (cylindrical coordinates)' proposed by one of the authors (1981), the propagation of the self-consistent field in PCR is analyzed, and a matrix eigen-equation of the self-consistent field is presented. By solving the eigen-equation, the axisymmetrical PCR with finite aperture is calculated, and the diffraction losses, phase shifts, relative amplitude and phase distributions on each mirror surface of various order transverse modes (including high-order modes, whose l≥2, p≥1) are introduced.A quasi-equivalence relation of PCR is also given. According to this relation, some characteristics (as the diffraction loss, the field distribution on the surface of spherical mirror) of all transverse modes in a PCR are just the same as those in some of the other PCR with different g_1.Some examples of calculation results are also given. They show that (ⅰ) the convengence of the above-mentioned equation is very good, (ⅱ) the calculation results with very high precision can be obtained practically, and the characteristics of TEM with very small or large losses can also be calculated precisly and (ⅲ) the choice of the reference light field does not affect correctness of the theory but affects the amount of calculation.Only the PCR with only one PCM being one of the two endreflectors of resonators is discussed, and the effect of response time of the PCM is ignored in this paper.展开更多
We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implemen...We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implementedthe charge self-consistent DFT+DMFT formalism by interfacing a full-potential all-electron DFT code with threehybridization expansion-based continuous-time quantum Monte Carlo impurity solvers.The benchmarks on several 3d,4fand 5f strongly correlated electron systems validated our formalism and implementation.Furthermore,within the LCANOframework,our formalism is general and the code architecture is extensible,so it can work as a bridge merging differentLCNAO DFT packages and impurity solvers to do charge self-consistent DFT+DMFT calculations.展开更多
In ultrasonic non-destructive testing of high-temperature industrial equipment,sound velocity drift induced by non-uniform temperature fields can severely compromise defect localization accuracy.Conventional approache...In ultrasonic non-destructive testing of high-temperature industrial equipment,sound velocity drift induced by non-uniform temperature fields can severely compromise defect localization accuracy.Conventional approaches that rely on room-temperature sound velocities introduce systematic errors,potentially leading to misjudgment of safety-critical components.Two primary challenges hinder current methods:first,it is difficult to monitor real-time changes in sound velocity distribution within a thermal gradient;second,traditional uniform-temperature correction models fail to capture the nonlinear dependence of material properties on temperature and their effect on ultrasonic velocity fields.Here,we propose a defect localization correction method based on multiphysics coupling.A two-dimensional coupled heat transfer–wave propagation model is established in COMSOL,and a one-dimensional steady-state heat transfer condition is used to design a numerical pulse–echo experiment in 1020 steel.Temperature-dependent material properties are incorporated,and the intrinsic relationship between sound velocity and temperature is derived,confirming consistency with classical theories.To account for gradient temperature fields,a micro-element integration algorithm discretizes the propagation path into segments,each associated with a locally computed temperature from the steady-state heat conduction solution.Defect positions are dynamically corrected through cumulative displacement along the propagation path.By integrating heat conduction and elastic wave propagation in a multiphysics framework,this method overcomes the limitations of uniform-temperature assumptions.The micro-element integration approach enables dynamic tracking of spatially varying sound velocities,offering a robust strategy to enhance ultrasonic testing accuracy in high-temperature industrial environments.展开更多
The deformation characteristics and thermal response of anchor rods are crucial for ensuring the stability and safety of surrounding rock support structures.However,existing research has predominantly concentrated on ...The deformation characteristics and thermal response of anchor rods are crucial for ensuring the stability and safety of surrounding rock support structures.However,existing research has predominantly concentrated on the mechanical performance of anchor rods,with limited attention to the coupled evolution of strain and temperature fields during tensile deformation.This knowledge gap hinders a comprehensive understanding of the synergistic mechanical-thermal response mechanisms in anchor rods under loading conditions.To address this limitation,the present study systematically investigated the evolution of strain and temperature fields,along with their correlation,during the test of micro-negative Poisson's ratio(NPR)and ordinary Poisson's ratio(PR)anchor rods.Digital image correlation(DIC)and infrared thermography(IRT)techniques were employed for this exploration.The uniaxial tensile tests were conducted at two different rates,and the ordinary PR anchor rod(Q235 anchor rod)was established as a control group for comparative analysis.The findings reveal that the micro-NPR anchor rod exhibit strain localization at multiple locations during the tensile process,whereas Q235 anchors show local strain concentration in only one region.The standard deviation evolution curves for both the strain and temperature field exhibit two distinct phases in the two anchor rods.The evolution patterns between these two types of curves are basically consistent.The two standard deviation curves for the micro-NPR anchor rod display a wavy increase in the second phase,while for the Q235 anchor rod,they increase steadily until the specimen is damaged.The correlation analysis reveals that the standard deviations of strain and temperature differences for both types of anchor rods are significantly correlated.These findings demonstrate the synergistic evolution mechanism of deformation and thermal response,providing a potential foundation for utilizing thermal monitoring to assess the stability of rock support structures.展开更多
基金supported by the National Natural Science Foundation of China(No.22373112 to Ji Qi,No.22373111 and 21921004 to Minghui Yang)GH-fund A(No.202107011790)。
文摘In this study,we investigate the ef-ficacy of a hybrid parallel algo-rithm aiming at enhancing the speed of evaluation of two-electron repulsion integrals(ERI)and Fock matrix generation on the Hygon C86/DCU(deep computing unit)heterogeneous computing platform.Multiple hybrid parallel schemes are assessed using a range of model systems,including those with up to 1200 atoms and 10000 basis func-tions.The findings of our research reveal that,during Hartree-Fock(HF)calculations,a single DCU ex-hibits 33.6 speedups over 32 C86 CPU cores.Compared with the efficiency of Wuhan Electronic Structure Package on Intel X86 and NVIDIA A100 computing platform,the Hygon platform exhibits good cost-effective-ness,showing great potential in quantum chemistry calculation and other high-performance scientific computations.
基金financially supported by the National Natural Science Foundation of China(No.21104078)the Project of Science and Technology of Jilin Province,China(No.201201096)the Scientific Research Starting Foundation for the Jilin Agricultural University,China(No.201212)
文摘The morphological changes of ABA amphiphilic triblock copolymer micelles in dilute solution were systematically studied by tuning the solvent property using self-consistent field simulation. The solvent property was tuned by changing the Flory-Huggins interaction parameters between each type of blocks and solvent, respectively. The simulation results show that by changing the solvent properties, a series of micelle morphologies such as vesicle, cage-like, ring-shaped, rod-like and spherical micelle morphologies can be obtained. Variations of the free energy of the solution system and the surface area of micelles with the Flory-Huggins interaction parameters were calculated to better understand the effect of solvent property on micelle morphologies. In addition, a phase diagram showing the morphological changes of micelles with the Flory-Huggins interaction parameters is provided.
基金supported by the National Natural Science Foundation of China(10972121)the Ministry of Education (SRFDP 20090002110047)the 973 Program of MOST(2012CB934101)
文摘Self-assembled nanostructures of lipids and nanoparticles hold great promise for applications in such fields as nanomedicine. This paper uses the self-consistent field theory to investigate the self-assembly behavior of lipid molecules and nanoparticles with different shapes in an aqueous solution. It is found that the lipid molecules can form monolayered and bilayered nanostructures around the nanopartieles with different shapes （e.g., triangular, square, hexagonal and octangular）. With decreasing the size of nanoparticles or increasing the number of polygon edges, the shape of lipid layers will approach an approximately spherical shape. These findings may help to predict and design novel drug delivery nanocarriers.
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.
基金financially supported by the National Natural Science Foundation of China(No.21374052)the support from K.C.Wong Magna Fund in Ningbo University
文摘The self-consistent field theory has been employed to numerically study the response of bi-disperse flexible polyelectrolyte （PE） brushes grafted on an electrode to electric fields generated by opposite surface charges on the PE-grafted electrode and a second parallel electrode. The numerical study reveals that, under a positive external electric field, the shorter and negatively charged PE chains are more responsive than the longer PE chains in terms of the relative changes in their respective brush heights. Whereas under a negative external electric field, the opposite was observed. The total electric force on the grafted PE chains was calculated and it was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The underlying mechanism was unraveled through analyzing the total electric field across the two oppositely charged electrodes.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11421101 and 21274005)the Natural Sciences and Engineering Research Council(NSERC)of Canada
文摘Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such as surface tension, bending moduli, and line tension. Understanding how the molecular properties of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting the mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.
基金financially supported by the China Scholarship Council (No. 201406105018)the National Natural Science Foundation of China (No. 21004013)the National Basic Research Program of China (No. 2011CB605701)
文摘Self-consistent field theory（SCFT）, as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to improve its accuracy and efficiency. Here we present a fourth-order exponential time differencing Runge-Kutta algorithm（ETDRK4） to solve the modified diffusion equation（MDE） which is the most time-consuming part of a SCFT calculation. By making a careful comparison with currently most efficient and popular algorithms, we demonstrate that the ETDRK4 algorithm significantly reduces the number of chain contour steps in solving the MDE, resulting in a boost of the overall computation efficiency, while it shares the same spatial accuracy with other algorithms. In addition, to demonstrate the power of our ETDRK4 algorithm, we apply it to compute the phase boundaries of the bicontinuous gyroid phase in the strong segregation regime and to verify the existence of the triple point of the O70 phase, the lamellar phase and the cylindrical phase.
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Project supports by the National Natural Science Foundation of China(Grant Nos.21074062 and 11174163)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of Chinathe Scientific Research Fund of Zhejiang Provincial Educational Department,China(Grant No.Y200907455)
文摘The adsorption of flexible polyelectrolyte （PE） with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.
基金supported by the National Natural Science Foundation of China(No.21774067)The Foundation of Key Laboratory of Flexible Electronics of Zhejiang Province(No.2023FE004)C.T.acknowledges the support from K.C.Wong Magna at Ningbo University。
文摘The self-consistent field theory(SCFT)was employed to numerically study the interaction and interpenetration between two opposing weak polyelectrolyte(PE)brushes formed by grafting weak PE chains onto the surfaces of two long and parallel columns with rectangularshaped cross-section immersed in a salty aqueous solution.The dependences of the brush heights and the average degree of ionization on various system parameters were also investigated.When the brush separation is relatively large compared with the unperturbed brush height,the degree of interpenetration between the two opposing PE brushes was found to increase with increasing grafting density and bulk degree of ionization.The degree of interpenetration also increases with the bulk salt concentration in the osmotic brush regime.Numerical results further revealed that,at a brush separation comparable to the unperturbed brush height,the degree of interpenetration does not increase further with increasing bulk degree of ionization,bulk salt concentration in the osmotic regime and grafting density.The saturation of the degree of interpenetration with these system parameters indicates that the grafted PE chains in the gap between the two columns retract and tilt in order to reduce the unfavorable electrostatic and steric repulsions between the two opposing PE brushes.Based on salt ion concentrations at the midpoint between the two opposing brushes,a quantitative criterion in terms of the unperturbed brush height and Debye screening length was established to determine the threshold value of the brush separation beyond which they are truly independent from each other.
基金support provided by the National Natural Science Foundation of China(No.22273043).
文摘As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔE_(ST))of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔE_(ST)would be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S_(1)state energy(E(S_(1))),T_(1)state ener-gy(E(T_(1))),andΔE_(ST)using three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S_(1)),E(T_(1)),andΔE_(ST)for 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S_(1)state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T_(1)state energy.TheΔE_(ST)derived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔE_(ST)of MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.
基金supported by the National Natural Science Foundation of China(Nos.11871413 and 12171412)supported by the Postgraduate Scientific Research Innovation Project of Hunan Province(No.CX20210602)+1 种基金Postgraduate Scientific Research Innovation Project of Xiangtan University(XDCX2021B106)supported by the Natural Science Foundation for Distinguished Young Scholars of Hunan Province(No.2021JJ10037).
文摘In this paper,we develop an adaptive high-order surface finite element method(FEM)incorporating spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved surfaces.The high-order surface FEM is obtained by the high-order surface geometrical approximation and the high-order function space approximation.Numerical results demonstrate that the precision order of these methods is consistent with theoretical prediction.In order to describe the sharp interface in the strongly segregated system more accurately,an adaptive FEM equipped with a new Log marking strategy is proposed.The Log marking strategy can not only label the elements that need to be refined or coarsened,but also give the refined or coarsened times,which can make full use of the information of a posterior error estimator and improve the efficiency of the adaptive algorithm.To demonstrate the power of our approach,we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces.Numerical results illustrate the efficiency of the proposed method,especially for strongly segregated systems with economical discretization nodes.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant Nos.20973176,20990234,50821062,and 20874111)973 Program of the Ministry of Science and Technology(MOST)(Grant No.2011CB808502)the Fundamental Research Funds for the Central Universities.
文摘This review article addresses the widely used self-consistent field theory(SCFT)in interacting polymer systems.The theoretical framework and numerical method of solving the self-consistent equations are presented.In this paper,different structures of polymer can be considered,such as homopolymer,block copolymer,polydisperse polymer and charged polymer.Several systems,micro/macro phase separation,interface,self-assembly,are presented as examples to demonstrate its applications in details.Besides,the fluctuation effects are considered.The first order is Gaussian fluctuation theory,which can be used to determine the stability of the mean-field solution and predict the kinetics of unstable structure.The derivation and applications of Gaussian fluctuation theory are presented as well.
基金The authors acknowledge the financial support from the Natural Science Foundation of China(Grant Numbers:11101276,and 91130012),Youth Talents Program by Chinese Organization Department,and the HPC center of Shanghai Jiao Tong University.
文摘The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction.However,the counterintuitive like-charge attraction in electrolytes has been frequently observed in experiments,which has been theoretically debated for a long time.It is widely known that the mean field Poisson-Boltzmann theory cannot explain and predict this anomalous feature since it ignores many-body properties.In this paper,we develop efficient algorithm and perform the force calculation between two interfaces using a set of self-consistent equations which properly takes into account the electrostatic correlation and the dielectric-boundary effects.By solving the equations and calculating the pressure with the Debye-charging process,we show that the self-consistent equations could be used to study the attraction between like-charge surfaces from weak-coupling to mediate-coupling regimes,and that the attraction is due to the electrostatics-driven entropic force which is significantly enhanced by the dielectric depletion of mobile ions.A systematic investigation shows that the interaction forces can be tuned by material permittivity,ionic size and valence,and salt concentration,and that the like-charge attraction exists only for specific regime of these parameters.
基金This work was supported by the National Basic Research Program of China (Grant No. 2005CB623800) the National Natural Science Foundation of China (Grant Nos. 20474012, 20374016 & 20104002)This review was recommended by Prof.Li Lemin,member of editorial of Science in China.
文摘The self-consistent field theory (SCFT) based upon coarse-grained model is especially suitable for investigating thermodynamic equilibrium morphology and the phase diagram of inhomo-geneous polymer systems subjected to phase separation. The advantage of this model is that the details of the chain such as the architecture of the chain and the sequence of blocks can be consid-ered. We present here an overview of SCFT approach and its applications in polymeric systems. In particular, we wish to focus on our group’s achievements in applications of SCFT in such fields: simulation of microphase separation morphologies of multiblock copolymers with a complex molecular architecture, interactions between brush-coated sheets in a polymer matrix, mixtures of flexible poly-mers and small molecular liquid crystals at the interface, shapes of polymer-chain-anchored fluid vesicles, self-assembled morphologies of block copolymers in dilute solution, and so on. Finally, the further developments as well as the perspective applications of SCFT are discussed.
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.
文摘Based on 'the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens (cylindrical coordinates)' proposed by one of the authors (1981), the propagation of the self-consistent field in PCR is analyzed, and a matrix eigen-equation of the self-consistent field is presented. By solving the eigen-equation, the axisymmetrical PCR with finite aperture is calculated, and the diffraction losses, phase shifts, relative amplitude and phase distributions on each mirror surface of various order transverse modes (including high-order modes, whose l≥2, p≥1) are introduced.A quasi-equivalence relation of PCR is also given. According to this relation, some characteristics (as the diffraction loss, the field distribution on the surface of spherical mirror) of all transverse modes in a PCR are just the same as those in some of the other PCR with different g_1.Some examples of calculation results are also given. They show that (ⅰ) the convengence of the above-mentioned equation is very good, (ⅱ) the calculation results with very high precision can be obtained practically, and the characteristics of TEM with very small or large losses can also be calculated precisly and (ⅲ) the choice of the reference light field does not affect correctness of the theory but affects the amount of calculation.Only the PCR with only one PCM being one of the two endreflectors of resonators is discussed, and the effect of response time of the PCM is ignored in this paper.
文摘We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implementedthe charge self-consistent DFT+DMFT formalism by interfacing a full-potential all-electron DFT code with threehybridization expansion-based continuous-time quantum Monte Carlo impurity solvers.The benchmarks on several 3d,4fand 5f strongly correlated electron systems validated our formalism and implementation.Furthermore,within the LCANOframework,our formalism is general and the code architecture is extensible,so it can work as a bridge merging differentLCNAO DFT packages and impurity solvers to do charge self-consistent DFT+DMFT calculations.
基金supported by the following projects:National Natural Science Foundation of China[U24A20135]Science and Technology Program of the State Administration for Market Regulation[2024MK016]+9 种基金Basic Scientific Research Fund Project for Higher Education Institutions of Inner Mongolia(2024YXXS057)Key Project of Natural Science Foundation of Inner Mongolia[2023ZD12]2023 Inner Mongolia Autonomous Region Key R&D and Achievement Transformation Program[2023YFHH0090]Natural Science Foundation of Inner Mongolia[2022MS05006]Talent Development Fund of Inner Mongolia Autonomous RegionFundamental Research Funds for Universities[2023RCTD012]Fundamental Research Funds for Universities[2023QNJS075]Inner Mongolia Autonomous Region Postgraduate Research Innovation Project[KC2024053B]Fundamental Research Funds for Universities[2024YXXS012]Open Project of the National Key Laboratory of Special Vehicle Design and Manufacturing Integration Technology[GZ2023KF012].
文摘In ultrasonic non-destructive testing of high-temperature industrial equipment,sound velocity drift induced by non-uniform temperature fields can severely compromise defect localization accuracy.Conventional approaches that rely on room-temperature sound velocities introduce systematic errors,potentially leading to misjudgment of safety-critical components.Two primary challenges hinder current methods:first,it is difficult to monitor real-time changes in sound velocity distribution within a thermal gradient;second,traditional uniform-temperature correction models fail to capture the nonlinear dependence of material properties on temperature and their effect on ultrasonic velocity fields.Here,we propose a defect localization correction method based on multiphysics coupling.A two-dimensional coupled heat transfer–wave propagation model is established in COMSOL,and a one-dimensional steady-state heat transfer condition is used to design a numerical pulse–echo experiment in 1020 steel.Temperature-dependent material properties are incorporated,and the intrinsic relationship between sound velocity and temperature is derived,confirming consistency with classical theories.To account for gradient temperature fields,a micro-element integration algorithm discretizes the propagation path into segments,each associated with a locally computed temperature from the steady-state heat conduction solution.Defect positions are dynamically corrected through cumulative displacement along the propagation path.By integrating heat conduction and elastic wave propagation in a multiphysics framework,this method overcomes the limitations of uniform-temperature assumptions.The micro-element integration approach enables dynamic tracking of spatially varying sound velocities,offering a robust strategy to enhance ultrasonic testing accuracy in high-temperature industrial environments.
基金supported by State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining&Technology,Beijing(Grant No.SKLGDUEK2120)。
文摘The deformation characteristics and thermal response of anchor rods are crucial for ensuring the stability and safety of surrounding rock support structures.However,existing research has predominantly concentrated on the mechanical performance of anchor rods,with limited attention to the coupled evolution of strain and temperature fields during tensile deformation.This knowledge gap hinders a comprehensive understanding of the synergistic mechanical-thermal response mechanisms in anchor rods under loading conditions.To address this limitation,the present study systematically investigated the evolution of strain and temperature fields,along with their correlation,during the test of micro-negative Poisson's ratio(NPR)and ordinary Poisson's ratio(PR)anchor rods.Digital image correlation(DIC)and infrared thermography(IRT)techniques were employed for this exploration.The uniaxial tensile tests were conducted at two different rates,and the ordinary PR anchor rod(Q235 anchor rod)was established as a control group for comparative analysis.The findings reveal that the micro-NPR anchor rod exhibit strain localization at multiple locations during the tensile process,whereas Q235 anchors show local strain concentration in only one region.The standard deviation evolution curves for both the strain and temperature field exhibit two distinct phases in the two anchor rods.The evolution patterns between these two types of curves are basically consistent.The two standard deviation curves for the micro-NPR anchor rod display a wavy increase in the second phase,while for the Q235 anchor rod,they increase steadily until the specimen is damaged.The correlation analysis reveals that the standard deviations of strain and temperature differences for both types of anchor rods are significantly correlated.These findings demonstrate the synergistic evolution mechanism of deformation and thermal response,providing a potential foundation for utilizing thermal monitoring to assess the stability of rock support structures.
