Self-consistent field theory of adsorption of flexible polyelectrolytes onto an oppositely charged sphere

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.

Application of self-consistent field theory to self-assembled bilayer membranes

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.

Self-assembly of lipids and nanoparticles in aqueous solution:Self-consistent field simulations

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.

Effect of interaction and temperature on quantum phase transition in anisotropic square-octagon lattice

We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard model through using the combination of cellular dynamical mean field theory and a continuous time Monte Carlo algorithm. The competition between interaction and temperature shows that with the increase of the anisotropic parameter, the critical on-site repulsive interaction for the metal-insulator transition increases for fixed temperature. The interaction-anisotropic parameter phase diagram reveals that with the decrease of temperature, the critical anisotropic parameter for the Mott transition will increase for fixed interaction cases.

Mott transition in ruby lattice Hubbard model

Mott transition in a ruby lattice with fermions described by the Hubbard model including on-site repulsive interaction is investigated by combining the cellular dynamical mean-field theory and the continuous-time quantum Monte Carlo algorithm. The effect of temperature and on-site repulsive interaction on the metallic–insulating phase transition in ruby lattice with fermions is discussed based on the density of states and double occupancy. In addition, the magnetic property of each phase is discussed by defining certain magnetic order parameters. Our results show that the antiferromagnetic metal is found at the low temperature and weak interaction region and the antiferromagnetic insulating phase is found at the low temperature and strong interaction region. The paramagnetic metal appears in whole on-site repulsive interaction region when the temperature is higher than a certain value and the paramagnetic insulator appears at the middle scale of temperature and on-site repulsive interaction.

Magnetic hysteresis, compensation behaviors, and phase diagrams of bilayer honeycomb lattices

Magnetic behaviors of the Ising system with bilayer honeycomb lattice（BHL） structure are studied by using the effective-field theory（EFT） with correlations. The effects of the interaction parameters on the magnetic properties of the system such as the hysteresis and compensation behaviors as well as phase diagrams are investigated. Moreover, when the hysteresis behaviors of the system are examined, single and double hysteresis loops are observed for various values of the interaction parameters. We obtain the L-, Q-, P-, and S-type compensation behaviors in the system. We also observe that the phase diagrams only exhibit the second-order phase transition. Hence, the system does not show the tricritical point（TCP）.

Numerical Study of Two Opposing Weak Polyelectrolyte Brushes by the Self-consistent Field Theory

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.

Theoretical Study of Electron Paramagnetic Resonance Spectra and Local Lattice Distortion for Mn^(2+) in Zn(ClO_4)_2·6(H_2O)Mg(ClO_4)_2·6(H_2O)

The electron paramagnetic resonance（EPR） spectra of trigonal Mn^（2＋） centers in Zn（ClO4）2·6（H2O） and Mg（ClO4）2·6（H2O） crystals were studied on the basis of the complete energy matrices for a d^5 configuration ion in a trigonal ligand field. It was demonstrated that the local lattice structure around a trigonal Mn^（2＋） center has an compressed distortion along the crystalline c3 axis, and when Mn^（2＋） is doped in the Zn（ClO4）2·6（H2O） and Mg（ClO4）2·6（H2O） crystals, there is a similar local distortion. From the EPR calculation, the local lattice structure parameters R=2.183 2 ？, for Zn（ClO4）2·6（H2O）, R=2.130 2 ？, for Mg（ClO4）2·6（H2O） have been determined.

Applications of self-consistent field theory in polymer systems

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.

Response of Bi-disperse Polyelectrolyte Brushes to External Electric Fields A Numerical Self-consistent Field Theory Study

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.

An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts

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.

Self-consistent field theory and its applications in polymer systems

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.

Towards the continuum coupling in nuclear lattice effective field theory Ⅰ: A three-particle model

Weakly bound states often occur in nuclear physics.To precisely understand their properties,the coupling to the continuum should be worked out explicitly.As the first step,we use a simple nuclear model in the continuum and on a lattice to investigate the influence of a third particle on a loosely bound state of a particle and a heavy core.Our approach is consistent with the Lüscher formalism.

二维稀磁Ising铁磁体的磁化行为

对处于外磁场中,自旋为1/2的具有二维正方晶格结构的稀磁Ising铁磁体模型,采用相关有效场理论,推导出了不同浓度下系统的磁矩、磁化率的理论公式·对磁化过程中系统主要物理量随温度、浓度等因素变化的情况进行了探讨·对给定的浓度和温度,磁矩随外场强度增大而变大;而对给定的浓度和磁场,磁矩随温度升高而减小·得到了基态时系统的序参量随浓度的变化曲线及该结构在不同浓度下的相图·

双轴分子构成液晶薄层的分子场理论

本文以分子场理论研究双轴分子构成的液晶薄层。双轴分子通过色散力作用，使分子质心固定在简单立方晶格的格点上。在液晶薄层的一侧是基板，它对界面层上的分子提供吸引作用，另一侧为自由表面。给出了各分子层上序参数随温度变化的情况。

黄铁矿中晶格金的萃取实验及有关问题的初步研究

尽管某些研究者认为黄铁矿中确实存在有晶格金,但以前的研究都没有取得直接而充分的证据。为此,作者做了晶格金的萃取实验,使黄铁矿中的晶格金(离子金)形成[AuCl_4]-络合物,然后利用紫外—可见光谱证实了[AuCl_4]-的存在,从而取得了晶格金存在较为直接而充分的证据。作者认为,象黄铁矿中Fe^(2+)与Au^(+)的取代关系的理论解释不应局限于类质同象的传统理论上,而应用现代的配位场理论解释之。计算表明,只要温度足够高,Au^(+)是可以取代Fe^(2+)形成晶格金的。本文还通过穆斯鲍尔谱的研究,探讨了晶格金的形成机理。

一种基于平均场理论的格栅材料均匀化方法

将颗粒材料中发展的一种基于平均场理论的解析均匀化方法应用于二维周期格栅材料;依据尺度分离原理和统计均匀表征元概念构建了格栅材料的两尺度均匀化模型,包括细观杆件单元的本构关系、细观位移-宏观应变关系式以及应力的细观力学表达式;推导了两种二维周期格栅材料等效弹性参数包括弹性模量、泊松比和剪切弹性模量的细观力学表达式。结果表明:等边三角形结构等效为各向同性连续体时,弹性参数表达式与文献中其他方法所得结果一致;正方形结构均匀化为正交各向异性连续体时,主平面内弹性模量等于杆件单元轴向刚度,泊松比和剪切弹性模量分别由杆件单元的泊松比和剪切刚度决定,符合正方形格栅材料的力学特性;对于非主平面内的正方形本构矩阵,选取坐标轴与材料主轴夹角为45°的方向为例进行推导,本文方法与坐标变换方法所得结果一致。以上结果均验证了本文所发展方法的有效性。

过渡离子Fe^(3+)在KMgF_3中局域晶体结构理论的研究

通过对角化能量矩阵研究了KMgF3:Fe3+系统的EPR谱.引入了双层配体模型,即6个F离子为第一层配体和8个K离子为第二层配体,来描述KMgF3:Fe3+系统.通过同时模拟第二和第四个EPR参量D和(a-F),在理论上发现了沿C3轴的一个K+离子向Fe3+离子的移动,并且这个移动导致了第一层的六个F配体的移动.用Fe3+-F-键和C3轴的夹角θ1和θ2描述这个畸变.在室温下,得到两个畸变角Δθ1=5.54~6.07°,Δθ2=-4.60^-5.00°.这个结果与重叠模型估计的角度具有可比性.

ZnO:Fe^(3+)体系局域晶格结构的研究

本文采用对角化三角场中d5组态离子的完全能量矩阵的方法,研究了Fe3+离子在Zn O:Fe3+体系的局域结构与EPR参量的关系,结果表明:在Zn O:Fe3+体系中,Fe3+取代了Zn2+离子后整个晶体显示出压缩畸变,其畸变参量ΔR=-0.119和Δθ=0.339°被确定.

高自旋BC模型基态相变的研究

采用相关有效场理论,对具有正方点阵结构的S=2横向BC模型,推导出系统的磁矩公式,并利用数值计算方法得到了基态相图。研究发现三种相变线将相图分成三个区域:有序铁磁相O1、有序铁磁相O2及无序顺磁相P,一级有序-有序相变线将铁磁相分成了O1及O2,并使铁磁相O2的区域非常狭窄。