泛函数迭代法求解反胶束内双电层电势

用泛函数分析理论中的迭代法求解了反胶束内关于双电层势的Poisson- Boltzmann（PB）方程，导出了泛电位下的第一、二次迭代的解析表达式。与 Debye-Huckel（DH）线性近似及计算机的数值解进行对比表明，迭代解不仅在低电 位条件下能与两者相符合，而且在高电位下与数值解在相吻合。     

Dynamic Mobility of Two Spherical Particles with Thick Double Layers

The dynamic electrophoretic mobility of a pair of nearby spherical particles is analyzed in the case when the thickness of the electrical double layer around each particle is comparable to the particle radius. By means of an integral reciprocal relation, a formal expression is obtained for the force and torque on N spheres subject to an oscillating electric field which may be spatially varying. Upon linearizing in the surface potential, this expression is shown to depend upon a set of purely hydrodynamic problems involving N neutral spheres, the calculation of the electric field around N neutral spheres, and the equilibrium charge distribution around N charged spheres. In the case of a single particle, the known analytic formula for the dynamic mobility is recovered. For a pair of identical particles, the dynamic mobility is calculated numerically, using known solutions to the required subproblems. An analytical expression for the mobility of a pair of widely separated spheres is also obtained by a method of reflections, and this is in excellent agreement with the numerical results outside the range of double layer overlap. Copyright 2000 Academic Press.     

非导电球型粒子悬浮液宽频介电谱——薄双电层理论的计算机模拟

以Shilov等提出的带有紧密层表面电导率的非导电球型粒子悬浮液宽频介电弛豫的薄双电层理论为基础, 从电动力学角度解释了粒子分散系两种典型介电弛豫(高频和低频弛豫)的机制. 在此基础上, 利用Mathcad程序将该理论定量程序化并建立了粒子/水相分散系介电谱参数与体系内部相参数的关系. 进而利用该程序模拟了溶液浓度、Zeta电位以及分散粒子半径等内相参数对两种弛豫的影响, 结合该理论阐述了不同环境下这两种弛豫的变化规律, 从而为今后更好地利用这两种弛豫表征纳米至毫米级球形粒子分散系的各相电及界面性质提供了有价值的参考.     

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,     

Low-Zeta-Potential Analytic Solution for the Electrophoretic Mobility of a Spherical Colloidal Particle in an Oscillating Electric Field

The equations developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans. 88, 3567 (1992)) to calculate the electrophoretic mobility of a solid, spherical colloidal particle subjected to an oscillating electric field are solved analytically for low zeta potential, ζ, to obtain the electrophoretic mobility correct to (eζ/k_BT). Due to severe numerical cancellation of the exponential integrals, two forms of the analytic solution are presented which are numerically stable for different regions of κa (where a is the particle radius and κ^-1 is the Debye screening length). This low-ζ analytic solution is valid for all frequencies, particle sizes, and electrolyte concentrations, and agrees to at least two significant figures with the "exact" results obtained by Mangelsdorf and White at eζ/k_BT = 1 (ζ ≈ 25 mV). A program implementing this low-zeta analytic formula for the electrophoretic mobility is available from the authors.     

Effect of Discrete Macroion Charge Distributions on Electric Double Layer of a Spherical Macroion

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ?₀ and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ?₀ and ξ potentials are increased.     

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…     

Molecular Dynamics Simulation of the Electrical Double Layer of Spherical Macroion

The structure of the electrical double layer (EDL) of a spherical macroion with a total charge of 60 elementary charges is studied by molecular dynamics methods. In calculations we used two models: continuous and discrete. In the continuous model, the total charge was concentrated in the center of the macroion; in the discrete model, elementary charges were randomly distributed over the surface of the macroion. The radial profiles of local densities and electric potential in EDL, as well as the degree of counterion binding by the macroion, are calculated with allowance for the Lennard-Jones and electrostatic interactions. It is established that the character of charge distribution significantly affects the EDL structure near the macroion, whereas its effect is much weaker at larger distances. The results obtained are compared with the experimental data on the surface potential and the diffuse part of EDL of sodium dodecyl sulfate micelles in aqueous solution, as well as on the micelle-bound charge. It is shown that even weak specific interaction between counterions and a macroion can substantially influence the structure of its EDL.     

Dynamic Electrophoretic Mobility of a Soft Particle

A theory of the dynamic electrophoretic mobility of a spherical soft particle (that is, a polyelectrolyte-coated spherical particle) in an oscillating electric field is presented. In the absence of the polyelectrolyte layer a spherical soft particle becomes a spherical hard particle, while in the absence of the particle core it tends to a spherical polyelectrolyte. The present theory thus covers two extreme cases, that is, dynamic electrophoresis of hard particles and that of spherical polyelectrolytes. Simple analytic mobility expressions are derived. It is shown how the dynamic electrophoretic mobility of a soft particle depends on the volume charge density distributed in the polyelectrolyte layer, on the frictional coefficient characterizing the frictional forces exerted by the polymer segments on the liquid flow in the polyelectrolyte layer, on the particle size, and on the frequency of the applied oscillating electric field. Copyright 2001 Academic Press.     

以多孔CaCO3微球为模板制备聚乙烯超疏水表面

以聚苯乙烯磺酸钠（PSS）掺杂的多孔碳酸钙（CaCO3）微球层为模板,通过热压低密度聚乙烯（LDPE）并结合酸蚀刻的方法制得了具有多层粘联微球结构、而非常见蜂窝状多孔结构的LDPE稳定超疏水表面（接触角152.8±2.5°,滚动角约6°）。元素分析表明,表面粘联微球为纯LDPE而非LDPE包覆的CaCO3。将多孔CaCO3微球稀疏地撒在LDPE表面并加热熔融,发现微球会自发沉降到熔体内部,酸蚀刻后形成了类似莲蓬的表面微结构,即坑内包含小球。结合CaCO3微球生成原理和多孔结构,认为粘联微球结构和莲蓬结构均是由于LDPE熔融大分子自发沉积到多孔CaCO3微球内部,“反模”形成了LDPE微球所致。本发现为多孔CaCO3微球的应用开辟了新方向。     

Dynamic Mobility of Particles with Thick Double Layers in a Nondilute Suspension

The dynamic mobility of a nondilute suspension of spherical particles is investigated in the case where the thickness of the electrical double layer around each particle is comparable to the particle radius. A formula is obtained for the O(φ) correction in a random suspension of particles with volume fraction φ, involving an integral over the dynamic mobility of a pair of spheres. This formula is then evaluated using both analytical approximations and numerical results previously obtained for the pair mobilities and valid for low surface potentials. The effect of double-layer thickness on the O(φ) coefficient is most pronounced at low frequencies, and lessens once the hydrodynamic penetration depth is smaller than the particle radius. Various approximations are considered that use the O(φ) result to predict the dynamic mobility in concentrated suspensions, and at high frequencies these approximations are shown to give results qualitatively different from those of recent cell models. Copyright 2000 Academic Press.     

An Application of Functional Analysis Method to the Potential of Electrical Double Layer for Spherical Micelles

With the help of the iterative method in functional analysis theory based on the Gouy–Chapman model in the colloid and interface chemistry an analytic solution of the potential of electrical double layer of spherical micelles has been obtained. This method has eliminated the restriction that the Poisson–Boltzmann equation, which represents the distribution of the potential in the double layer, can be solved only under the condition of zekT so far. The connections between the present results and those from Verwey and Overbeek's previous work have also been discussed. Our approach provides a simple but effective method for the calculation of the potential of electrical double layer under general potential condition.     

Dynamic Mobility of Colloidal Particles with Thick Double Layers

The dynamic mobility spectra of several colloidal systems having a ratio of particle radius to double-layer thickness between 1 and 20 have been measured using the technique of electroacoustics. Good agreement is found between the experimental mobility spectra and the theoretical spectra generated by the computer program of Manglesdorf and White for spherical monodisperse suspensions with sizes in the neighborhood of 0.1 μm. Smaller and larger particles show some minor discrepancies which are more likely to be due to limitations of the model systems being used for the test than to any basic limitation of the theoretical analysis. Copyright 2000 Academic Press.     

The Electrical Double-Layer Interaction between a Spherical Particle and a Cylinder

Based on the well-known Debye-Hückel approximation and the Derjaguin's integration method, this paper presents an integral solution for the electrical double-layer (EDL) interaction between a spherical particle and a cylinder. The effects of the relative dimensions of the cylinder to the sphere on the EDL interaction are studied using this numerical solution. The detailed numerical results indicate that, in general, the curvature effect on the EDL interaction cannot be neglected at small separation distances. The widely used sphere-flat plate approximation will considerably overestimate the actual EDL interaction between a spherical particle and a cylinder. The ratio of the radius of the particle to the EDL thickness, tau=kappaa(p), also plays an important role in determining the EDL interaction at small dimensionless separation distances (相似文献   

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.     

On the General Expression for the Electrophoretic Mobility of a Soft Particle

Electrokinetic equations for electrophoresis of a soft particle (that is, a hard particle covered with a layer of polyelectrolytes) have been solved previously under the conditions that the net force acting on the soft particle as a whole (the particle core plus the polyelectrolyte layer) must be zero and that the electrical force acting on the polymer segment is balanced with a frictional force exerted by the liquid flow (J. Colloid Interface Sci. 163, 474 (1994)). In the present work we replaced the latter condition by the alternative and more appropriate condition that pressure is continuous at the boundary between the surface layer and the surrounding electrolyte solution to solve the electrokinetic equations and obtained the general mobility expression for the electrophoretic mobility of a spherical soft particle. It is found that the general mobility expression thus obtained reproduces all of the approximate mobility expressions derived previously and, in addition, that the continuous pressure condition leads to the correct limiting behavior of the electrophoretic mobility in the case where the frictional coefficient tends to zero (this behavior cannot be derived from the force balance condition for the polyelectrolyte layer). Copyright 2000 Academic Press.     

双电层电容法在电化学生物传感器中的研究与应用

对双电层电容法在电化学生物传感器中的研究和应用进行了较全面的综述,并展望了其发展前景。     

微粒运动实验创新设计与改进

对微粒运动实验的仪器、用品作了改进,重新设计实验装置,使实验装置达到了小型化、封闭化、简洁化,实验达到了绿色环保要求,满足了大面积的学生探究实验操作使用,取得了良好的效益。     

Near-Contact Motion of Surfactant-Covered Spherical Drops: Ionic Surfactant

A lubrication analysis is presented for near-contact axisymmetric motion of spherical drops covered with an insoluble nondiffusing surfactant. The surfactant equation of state is arbitrary; detailed results are presented for ionic surfactants. The qualitative behavior of the system is determined by the dimensionless force parameter &Fcirc;, the external force normalized by the maximum resistance force generated by Marangoni stresses. For &Fcirc; > 1 drops coalesce on a time scale commensurate with the coalescence time tau0 for drops with clean interfaces. For &Fcirc; < 1, the system evolves on the time scale tau0 until Marangoni stresses approximately balance the external force; thereafter a slow evolution occurs on the Stokes time scale. In the long-time regime a self-similar surfactant concentration profile is attained that scales with the extent of the near-contact region. The gap width decreases exponentially with time but slower than for rigid particles because of surfactant backflow. For &Fcirc; < 1, drop coalescence does not occur without van der Waals attraction. Quantitative results depend only moderately on the surfactant equation of state. Copyright 1999 Academic Press.