泛函数法研究柱状反胶束双电层

利用泛函数分析理论中的迭代方法, 建立并在泛电位下求解了柱状反胶束水池内关于双电层电位的Poisson-Boltzmann (PB)方程, 推导出了该方程的第一、二次迭代解及电荷密度表达式, 并将其与Debye-Hückel(DH)的低电位线性近似方法得到的结果进行了比较.     

Electrical Potential Distribution around a Charged Colloidal Particle: Nonlinear Integral Equation

多电解质溶液中带电胶体粒子的电势分布由球形Ｐｏｉｓｓｏｎ－Ｂｏｌｔｚｍａｎｎ方程（ＰＢＥ）描述．ＰＢＥ是一个非线性的微分方程，且难以求得其解析解．本文采用非线性Ｐ－Ｂ积分方程，计算电势分布的数值解．首先，根据静电场和热力学系统中的物理定理，导出描述电势分布的Ｐ－Ｂ积分方程（ＰＢＩＥ）；其次，用迭代方法求ＰＢＩＥ的数值解．最后，计算了在３－１型电解液中无量纲半径κａ分别为０．１２和０．２２，无量纲表面电势ξ分别为１，２，４，６时球形胶体粒子外部的电势值．为了检验数值解的精度，计算了表面电荷密度，并与Ｌｏｅｂ（１９６１）和Ｏｓｈｉｍａ（１９９５）等人的结果比较，本文结果的相对误差小于１％，优于Ｏｓｈｉｍａ的结果．     

不同边界条件下球形颗粒吸附剂内扩散方程的分析解和数值解的比较

吸附质在球形颗粒的内扩散可用固相内扩散偏微分方程描述，当使用吸附剂球心的浓度为零时，可得到解析解模型；当使用在球心的浓度梯度为零时，只能得到数值解。本文分析了在这两种不同的边界条件下导出的分析解和数值解模型之间的差别，当分别用两种模型计算颗粒内瞬时溶质浓度分布和吸附剂颗粒体积平均吸附量的结果表明：在吸附发生的初期（如τ＝０．０００１），二者的相对误差为２４％，当吸附持续较长时间时，二者的数值基本相     

大型广义特征值问题的部分特征值和特征向量的块迭代求解

将求解标准特征值问题的Davidson方法推广到求解大型广义特征值问题, 并给出了相应的块迭代算法. 经过理论分析和数值计算发现, 如果迭代过程不发散, 则块迭代算法经过有限次迭代一定收敛. 设矩阵的维数为n, 要求的特征值和相应特征向量的个数为k, 初始的子空间大小为r(r≥k),迭代次数为m,则它们之间满足关系n=r+km. 通过调节子空间大小, 就得到迭代次数m的正整数解.     

径向Hartree-Fock-Slater方程的新的数值解法

本文提出径向Hartree-Fock-Slater(HFS)方程的一种新的数值解法。使用二阶或四阶有限差分法,把HFS方程离散化,构成一组拟线性代数本征值问题。其系数矩阵与解有关,需用迭代方法求近似解。本工作对数值方法做了改进,使得数值处理比较完整和统一。已编成计算机程序,对Cu⁺和Mn²⁺进行了计算。所得结果与文献[1,2]的结果一致,表明此法的稳定性和精确性良好。还对一系列原子和离子问题进行过计算,证明此法能成功地用于中性原子和正离子的计算。     

明胶层中的扩散和反应动力学研究Ⅵ.球型扩散及扩散伴随一级反应过程的数值解

本文采用有限差分法导出了扩散物从空间一点向周围作三维球型扩散和边扩散边进行一级反应的动力学方程的数值解,并描述了其求解方法。在相同的参数下,获得的数值解与相近边界条件的分析解结果对照,一致性良好,为进而研究染料云的形成过程打下基础。     

动态复合对染料敏化太阳电池性能的影响

本文通过设计一种特殊的电池结构,动态改变电解液与导电玻璃（Tc0）的接触面积,固定Ti02薄膜面积,将TCO／OL解液界面与TiO2／电解液界面两种复合途径进行区分,从实验和理论两方面研究了复合途径变化对染料敏化太阳电池（DSC）性能的影响．采用电化学阻抗谱（EIS）表征界面电荷交换过程,研究了不同途径在复合中的作用机理．通过单色光下,1-V性能测试,对不同界面复合主导下的DSC二极管特性进行数值分析,探讨了复合过程中界面电荷交换变化对光电压（‰）的影响．研究结果表明,高光强下（Voc=700mV）改变TCO／电解液接触面积对复合影响不明显,DSC电子复合主要经由TiO2／电解液界面,电池具有明显的二极管特征;而弱光下（Voc〈400mV）增加TCO／电解液接触面积将使复合大幅增加,此时电荷交换由TCO／电解液界面主导,电池填充因子大幅降低,整流作用减弱．由于TCO／OL解液界面电荷交换明显慢于TiO2／电解液界面,通过同一电池一定光强范围内的光电压变化对比发现,高光强下光电压变化较慢,而弱光下光电压变化较快．     

两种氨基酸中[MH-CO_2H_2]~ 的特征质谱碎裂

运用低能碰撞诱导解离（CID）研究了电子轰击（EI）、快原子轰击（FAB）电离条件下质子化亮氨酸与异亮氨酸解高产生亚稳离子［MH－CO2H2］＋的单分子质谱碎裂，二种异构体呈现出了各自不同的解离特征，根据CID的特征碎片离子和氘代同位素标记实验，提出了其碎裂过程存在离子／中性（碎片）复合物中间体碎裂机理，并对有关的特征离子的形成进行了讨论．     

双显色体系迭代目标转换因子分析法测定混合稀土的研究

用双显色体系降低各组分光谱的线性相关性，并用光谱向量间的夹角描述这种特性；同时采用数值稳定性较好的迭代目标转换因子分析法（ＩＴＴＦＡ），进行混合稀土（Ｌａ、Ｇｄ、Ｙｂ、Ｙ）中单一稀土元素的光度分析。结果表明，在三氯偶氮胂—稀土（Ｌａ、Ｇｄ、Ｙｂ、Ｙ）显色体系中，采用一个酸度体系（ｐＨ３４）的光谱数据计算时，各稀土组分光谱向量间夹角平均值为４５°；而采用两个酸度体系（ｐＨ３４，ｐＨ１４）的光谱数据计算时，各稀土组分之间向量夹角平均值达到２１５°，这不仅使得ＩＴＴＦＡ中主因子的选择较为准确，且较易获得稳定的结果，并提高多组分光度分析的可靠性。     

稀土储氢合金在有机氢化物中的吸氢行为和吸氢热力学性能

研究了富镧混合稀土－镍储氢合金（MlNi5)与有机化合物（C6H6）组成的浆液体系的吸氢行为和吸氢热力学性能。测定了不同温度（10，20，30，40℃）下两个不同系统的吸氢压力－成分等温（PCT）曲线，并分别计算出气固系统和气固液系统吸氢反应的热力学函数值ΔH,ΔS。     

An Analytical Solution to the Electrical Double Layer Potential for Spherical Particles: A Functional Theoretical Approach

Based on the Gouy-Chapman electrical double layer model, an analytical solution to the Poisson-Boltzmann equation describing the distribution of the electrical potential around spherical particles has been obtained. The advantage of this method is that it is not restricted to the Debye-Hückel approximation condition, where ze ψ ? kT. The present results compare favorably to results obtained under the ze ψ ? kT condition for spherical particles and to results obtained for the general solution for flat plate geometry. This approach provides an effective method for the iterative calculation of the electrical double layer potential for spherical particles.     

Study on Electric Double Layer of a Cylindrical Particle with Functional Theoretical Approach

A new method, i.e. the iterative method in functional theory, was introduced to solve analytically the nonlinear Poisson-Boltzmann （PB） equation under general potential ψ condition for the electric double layer of a charged cylindrical colloid particle in a symmetrical electrolyte solution. The iterative solutions of ψ are expressed as functions of the distance from the axis of the particle with solution parameters： the concentration of ions c, the aggregation number of ions in a unit length m, the dielectric constant e, the system temperature T and so on. The relative errors show that generally only the first and the second iterative solutions can give accuracy higher than 97%. From the second iterative solution the radius and the surface potential of a cylinder have been defined and the corresponding values have been estimated with the solution parameters, Furthermore, the charge density, the activity coefficient of ions and the osmotic coefficient of solvent were also discussed,     

The surface potential of a spherical colloid particle: functional theoretical approach

By using the iterative method in functional analysis, the potential of the electrical double layer of a spherical colloid particle, which is represented by the so-called Poisson-Boltzmann (PB) equation, has been solved analytically under general potential conditions. With the help of the diagram method in mathematics, the surface potential of the particle has been defined from the second iterative solution. The influence of the parameters included in the solutions on the surface potential has been studied. The results show that the surface potential of the particle increases as the temperature of the system, the aggregation number, and the concentration of ions increase, but decreases with an increase in the dielectric constant and the valence of the ions. The corresponding space charge density also has been illustrated in this work.     

Numerical study of electroosmotic slip flow of fractional Oldroyd-B fluids at high zeta potentials

In this paper, an investigation of the electroosmotic flow of fractional Oldroyd-B fluids in a narrow circular tube with high zeta potential is presented. The Navier linear slip law at the walls is considered. The potential field is applied along the walls described by the nonlinear Poisson–Boltzmann equation. It's worth noting here that the linear Debye–Hückel approximation can't be used at the condition of high zeta potential and the exact solution of potential in cylindrical coordinates can't be obtained. Therefore, the Matlab bvp4c solver method and the finite difference method are employed to numerically solve the nonlinear Poisson–Boltzmann equation and the governing equations of the velocity distribution, respectively. To verify the validity of our numerical approach, a comparison has been made with the previous work in the case of low zeta potential and the excellent agreement between the solutions is clear. Then, in view of the obtained numerical solution for the velocity distribution, the numerical solutions of the flow rate and the shear stress are derived. Furthermore, based on numerical analysis, the influence of pertinent parameters on the potential distribution and the generation of flow is presented graphically.     

Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length： Functional Theoretical Approach

Introduction The electrostatic potentialΨis the most importantproperty for the electrical double layer( EDL) of acharged particle in an electrolyte solution[1—4]. Thispotential is characterized by the so-called Poisson-Bolt-zmann(PB) equation. The PB equation is a second-or-der nonlinear differential equation with a constant coef-ficient, except a flat-plate model, which cannot besolved analytically by the traditional method. To ourknowledge, apart from the numerical solution to thisequa…     

An application of the refined born approximation to the solution of coupled equations involved in electron-ion and electron-atom scattering problems

A new approach to the solution of coupled equations involved in electron-ion and electron-atom scattering problems is proposed. This method is a combination of iteration and variation procedures. The main advantage of this method is that exchange terms can be calculated in a direct and straightforward manner. The method is based on the Lippmann-Schwinger equation and does not require trial functions satisfying appropriate boundary conditions. Using the Volterra formulation one can find the solution on an interval determined by the range of the exchange potential and the long-range potential terms can be taken into account by a projection procedure giving the asymptotic value of the reactance matrix. The method is tested on the case of electron-hydrogen atom scattering in the 1s-2s and 1s-2s-2p approximation.We have adapted the method proposed originally by Rayski to obtain solutions of coupled equations involved in electron-ion and electron-atom scattering. As mentioned in section 1 the construction of the method secures an automatic fulfilment of the boundary conditions. It allows an easy calculation of the exchange potential as well as an estimation of the introduced approximation. It gives also a possibility of detecting any spurious convergence. Moreover, it is important that this formalism can be applied in the case of normalized as well as unnormalized initial integral equations. This fact is of special importance in the case of long-range interactions. When the method is used for unnormalized (Volterra) equations it allows application of a very convenient projection procedure for treating the long-range terms in the direct potential.Electron-hydrogen atom collisions are investigated as a numerical illustration of the method. In the 1s-2s approximation the normalized equations were solved, while in the 1s-2s-2p approximation the solution was obtained with the help of Volterra equations and the long-range terms of the direct potential were taken into account by the projection procedure. In both cases the calculations were performed in the first iteration step and the obtained solutions agree fairly well with the results obtained by a numerical integration. It is not clear which set of results is more accurate. The numbers of parameters needed to obtain these results was not too large (not more than twenty in each channel) and decreased with the increase of the values of angular momentum and energy. The calculations were performed without weight functions, although the use of an appropriate weight function can improve the effectiveness of the method. This effectiveness could also be improved through a more lucky choice of trial functions.     

Study of the Electrical Double Layer of a Spherical Micelle: Functional Theoretical Approach

The electrical double layer theory is the base of the colloid stability theory (DLVO theory), and the PB eq. is a key to the study of the layer1,2. For a spherical particle, the PB eq. is (1) where and are the dielectric constant of the medium, the valence of ions, the elementary charge, the concentration of ions far away from the particle, the Boltzmann's constant and the temperature of the system, respectively. Since this eq. is a second order nonlinear differential one, only the anal…     

Nomographische und numerische Korrekturen für trübungsbedingte Untergrundabsorption bei spektralphotometrischen Gehaltsbestimmungen

It is shown by the example of cyanomethaemoglobin in agreement with the literature, that light absorption of protein solutions due to turbidity is—because of the size of the particles—only in the limiting case dependent on the Rayleigh Law. The validity to correct with an exponential formula for absorption due to turbidity is confirmed. Relations are derived, permitting to correct for background absorption by measuring the sample at three wavelengths without plotting: one nomographic method without neglections, an iterative numerical method and a linear approximation sufficiently accurate. These methods are universally applicable.     

Analytical energy gradient evaluation in relativistic and nonrelativistic density functional calculations

The expressions of analytical energy gradients in density functional theory and their implementation in programs are reported. The evaluation of analytical energy gradients can be carried out in the fully 4-component relativistic, approximate relativistic, and nonrelativistic density functional calculations under local density approximation or general gradient approximation with or without frozen core approximation using different basis sets in our programs. The translational invariance condition and the fact that the one-center terms do not contribute to the energy gradients are utilized to improve the calculation accuracy and to reduce the computational effort. The calculated results of energy gradients and optimized geometry as well as atomization energies of some molecules by the analytical gradient method are in very good agreement with results obtained by the numerical derivative method.     

Highly efficient and exact method for parallelization of grid‐based algorithms and its implementation in DelPhi

The Gauss–Seidel (GS) method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the GS method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here, we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of processes or computing units. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson–Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further, we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. © 2012 Wiley Periodicals, Inc.