基于Scilab准确计算非对称氧化还原滴定终点误差的方法

非对称氧化还原滴定终点误差不仅与滴定终点的电势有关,还与滴定产物的平衡浓度有关,这给终点误差的计算带来了困难。针对这一问题,在综合考虑氧化还原反应物料平衡、电子平衡和能斯特方程等数量关系的基础上,构建了以滴定产物平衡浓度和滴定体积比为未知量的耦合方程组。基于Scilab求解了该方程组,将求解结果代入相关计算公式,所得终点误差与文献值是相符的。     

基于改进计时电流法精确模型的数值解仿真及实验验证

根据电极表面被测物浓度变化经验公式所建立的改进计时电流法的理论模型,只能定性分析响应电流峰值与被测物浓度关系,无法准确描述响应电流峰值与反应体系及激励电势中其它参数的关系.为解决该问题,利用能斯特方程与扩散定律,建立了描述电极表面被测物浓度与响应电流关系的积分方程,通过数值分析方法求解得到该积分方程数值解.进而利用数值仿真得到精确的电流与时间关系曲线,分析了电流峰值与试剂浓度、惯性时间常数、参比电极标准电势、激励电势初始值以及稳态值之间的关系.最后,利用改进计时电流法的电路装置对K3[Fe(CN)6]试剂进行测试,实验结果表明该数值模型比经验模型更接近真实情况,也验证了由该模型推导得到的各参数之间关系的正确性.     

利用平衡移动原理判断浓度对电极电势的影响

利用平衡移动原理可以定性判断浓度对电极电势的影响。在改变除电对以外离子的浓度、改变电对其中1种离子的浓度、同时改变电对本身2种离子的浓度的3种情况下,能斯特方程和该法均可得到相同的结论,但后者更简单。     

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．     

欠电势沉积Bi-Te基体系热电材料的平衡热力学分析

基于普通的能斯特方程, 建立了单原子层平衡电势的热力学模型. 据此, 分析了单原子层覆盖度以及电吸附价与欠电势之间的相互关系, 获得了沉积物与衬底之间干涉特性. 并且分析了Bi-Te基体系欠电势沉积热力学特性. 通过对Bi欠电势沉积在几个不同的金属衬底体系的分析阐明了功函数随覆盖度的变化机制. 研究了铋离子的浓度变化对铋的欠电势及覆盖度的影响关系, 结果表明, 铋在铂上欠电势沉积的体系在整个欠电势范围内具有恒定的电吸附价, 而铋在覆盖了一层碲的铂衬底上欠电势沉积的体系其电吸附价随覆盖度的增加而降低, 从热力学理论角度对铋在碲覆盖的衬底上导致欠电势负移的特性给予了解释.     

电毛细管中非线性PB积分方程及其数值解

依据电毛细管非线性Ｐｏｉｓｓｏｎ Ｂｏｌｔｚｍａｎｎ微分方程的物理原理,导出其积分形式的ＰＢ方程．并采用数值迭代法给出相应方程的数值解．数值计算只用到电势Ψ的离散值,不需要Ψ的导数值,从根本上解决了因电势在管壁陡然变化引起数值解法的困难．文中给出的计算实例表明该算法是正确的、有效的和高精度的（相对误差小于０．０１％）,且在ＰＣ机上容易实现．     

基于氨气敏电极的氨氮在线检测仪补偿模型EI北大核心CSCD

研究了氨气敏电极的输出电位与温度、压强、空白电位值、氨氮质量浓度、搅拌速度之间的关系。根据能斯特方程,采用多元回归分析的方法,建立了氨气敏电极的输出电位与氨氮质量浓度、温度、空白电位值之间的关系模型,并对模型的准确性进行了验证,并与国标法进行对比,误差均在6%以内。     

用氯离子选择电极测定浓盐酸的活度系数及氯离子吸附效应的探讨

在25 ℃下, 用氯离子选择电极与玻璃电极组成电池测定了0.00498～15.02 molkg~(-1)浓度范围盐酸体系的电势, 发现用Nernst方程计算出的活度系数与文献值偏差极大。用氯离子吸附原理和形成吸附对的平衡原理导出的电势方程, 由此计算出的盐酸活度系数与文献值十分一致, 这表明氯离子在电极表面发生了特性吸附作用。     

基于氨气敏电极的氨氮在线检测仪补偿模型

研究了氨气敏电极的输出电位与温度、压强、空白电位值、氨氮质量浓度、搅拌速度之间的关系。根据能斯特方程,采用多元回归分析的方法,建立了氨气敏电极的输出电位与氨氮质量浓度、温度、空白电位值之间的关系模型,并对模型的准确性进行了验证,并与国标法进行对比,误差均在6%以内。     

基于Excel的化学计算方法

对化学计算中遇到的求解方程或方程组的复杂计算问题,利用Excel提供的数值计算和绘制函数图像的功能,通过单变量求解和规划求解能使问题得到圆满解决。与其它软件比较,该方法对初值的选择和计算过程中迭代方法的选择、迭代次数、精度、误差等都可以进行自由设置,更能体现出门槛低、简单、快捷的特点。     

Effect of a film layer on mono-divalent bi-ionic membrane potential

The bi-ionic potential generated across a standard cation exchange membrane was investigated in a mono-divalent bi-ionic system. Applying Henderson's theory to the film layer, the Nernst—Planck equation was solved in the film layer as well as in the membrane. The observed potentials were compared with the theoretically predicted values from parameters such as bulk concentrations, diffusion coefficients in the membrane and in solution, exchange capacity, corrected molar selectivity coefficient, and film layer thickness. The calculated potentials were not always in agreement with the experimental values, but reproduced properly the trend of potential change with concentration and stirring rate. The constituent potentials, i.e. the diffusion potentials in the film layer and in the membrane and the interfacial potentials, are also discussed. In the sodium—calcium bi-ionic system, the primary contribution to the total membrane potential was not the diffusion potential in the film layers and in the membrane, but the sum of two interfacial potentials. p]In the case of membrane-diffusion control, the bi-ionic potential was confirmed to follow the equation of Helfferich.     

Calculation of membrane potential in synaptosomes with use of a lipophilic cation (tetraphenylphosphonium)

To estimate membrane potential in synaptosomes with the use of tetraphenylphosphonium (TPP+), an equation relating the amount of TPP+ accumulated in synaptosomes with membrane potential was derived from the following two assumptions. (1) TPP+ molecules were distributed into plasma membranes, mitochondria and cytosol of synaptosomes. (2) TPP+ achieves a Nernst equilibrium across both the synaptosomal and inner mitochondrial membranes. We propose three methods for calculation of membrane potential using this equation. The concentration of TPP+ was measured under various controlled conditions with an electrode selective for TPP+. The amount of TPP+ accumulated in synaptosomes was determined by measuring the difference between its initial concentration and the concentration after addition of synaptosomes, and membrane potential was estimated by the three methods. The resting potential of synaptosomes was estimated to be -75 to -90 mV by all of these methods. Membrane potentials under various controlled conditions were calculated, and the characteristics of the methods for estimation of membrane potential and those of membrane potential obtained by the methods are discussed.     

Determination of surface potentials from the electrode potentials of a single-crystal electrode

Determination of surface potentials Psi0 at the metal oxide/aqueous solution interface from measured electrode potentials of a metal oxide single-crystal electrode (SCrE) is described. The proposed method is based on the surface complexation model and evaluates the surface potential at the isoelectric point, i.e., at pHiep. This value is used for calculation of Psi0 values from the measured electrode potentials. Both 1-pK and 2-pK models produced the same result so that the procedure does not depend on the assumed mechanism of the surface charging. It is proposed to determine the pristine point of zero charge pHeln and the isoelectric point pHiep, and use these data to set the scale of surface potentials. The value of pHeln can be obtained at a sufficiently low ionic strength where pHpzc coincides with pHiep. The method is demonstrated on the example of the anatase single-crystal electrode. From the shifts of pHiep and pHpzc with respect to the pristine point of zero charge pHeln it was concluded that Cl- ions exhibit higher affinity for association with positively charged surface groups than ClO-4 ions. Also, preferential surface association of Na+ cations compared to both anions was detected. The slopes of the Psi0(pH) functions were found to be significantly lower in magnitude with respect to the Nernst equation, which is due to the high degree of counterion association at the surface caused by their relatively high concentration.     

Computational electrochemistry: aqueous two-electron reduction potentials for substituted quinones

The electrode potentials of some quinone derivatives in aqueous solution have been calculated. The calculations are carried out at the Hartree–Fock and B3LYP levels with the inclusion of entropic and thermochemical corrections to yield free energies of redox reactions. The Polarisable Continuum Model (PCM) is used to describe the solvent. The average error of calculation of electrode potentials is less than 0.03 V and is decreased compared to the average error of methods presented previously. The role of relaxation energies and frequency calculations in improving the results has been investigated.     

Potentiometric selectivity coefficients of liquid ion-exchange membranes for univalent and divalent ions

Digital simulation has been used to calculate potential—activity responses and concentration-dependent selectivity coefficients for membranes bathed in mixtures of univalent and divalent ions. For an ideal, dissociated, univalent-site liquid ion-exchange membrane, more accurate computations, based on Nernst—Planck equations, were possible than have been reported previously. Simulation results were used with four suggested equations for the membrane potential (including the IUPAC recommendation) to determine which equation gives best fit and most nearly constant selectivity coefficients. When concentration profiles found by digital simulation are employed, improved response equations are given which closely describe the dependence of surface concentrations on the mobility ratio for the bi-ionic case. From these equations a closed form solution to the diffusion equation yields an explicit expression relating the bi-ionic selectivity coefficient to membrane loading, single ion partition coefficients, and ion mobilities.     

Pulstrodes: triple pulse control of potentiometric sensors

Ion-selective electrode membranes based on hydrophobic materials doped with chemically selective host molecules are an attractive sensing technology but normally suffer from a limited sensitivity, given by the Nernst equation, and a direct reliance on the reference electrode potential, which makes miniaturization difficult. These fundamental problems are addressed here by imposing a multipulse electrochemical excitation signal onto ion-selective membranes that lack ion-exchange properties. Current pulses are responsible for the generation of ion fluxes in the direction of the membrane, which give reproducible super-Nernstian response slopes that originate from depletion processes at the membrane surface. Membranes may also be measured at zero current after this pulse, giving super-Nernstian response regions at lower concentrations. Difference potentials obtained from subsequent pulses give about 10-fold higher sensitivities than predicted on the basis of the Nernst equation.     

考虑相关能效应的过渡态计算方法

提出了一种在X_a方法基础上,同时包含电子相关效应和考虑电子自相互作用的过渡态计算方法.由此计算的一系列原子电离势的结果表明,相关能对电离势的计算结果有很大影响,其数值为—0.41eV～0.94eV.引入相关能效应使计算结果明显趋于合理.此计算模型兼有简便和合理的特点,且能适用于分子体系的计算.     

Electrokinetic effects in membrane pores and the determination of zeta-potential

The surface charge or electrical potential properties of microfiltration, ultrafiltration and nanofiltration membranes can have a very significant influence on their separation performance. Such properties are most commonly quantified in terms of zeta-potentials obtained by calculation following experimental measurement of streaming potentials. Such calculation requires numerical solution of the equations governing fluid flow and electrical-potential distribution in the pores. A method for such calculations is presented, which includes a numerical solution of the non-linear Poisson–Boltzmann equation and allows for the mobilities of anions and cations to be individually specified. By expressing the results of such calculations in terms of a factor to be applied to a classical analytical result, it is shown to be very important to use proper numerical calculations in the interpretation of electrokinetic data for membranes. Use of a classical analytical analysis to calculate ‘relative', ‘apparent', ‘equivalent' or ‘nominal' zeta-potentials is likely to lead to substantial underestimation of the true zeta-potential and possible serious error even in the interpretation of relative changes in membrane properties. The calculations needed to avoid such difficulties may be readily carried out on a PC. It is also important to account for the individual mobilities of the anions and cations in the electrolyte used for measurements.     

Explanation of Misleading Nernst Slope by Boltzmann Equation

The common misuse in the literature of the terms Nernst slope, Nernst factor, and Nernst potential should be corrected. The membrane electrode potential is explained by the Boltzmann distribution equation. The slope of 59 mV per ionic unit is not unique to the Nernst equation. Both the Nernst equation and the Boltzmann distribution equation give the same 59-mV slope based on different mechanisms. The slope indicates only the change of −ΔGregardless of mechanisms. To avoid any misleading inference to the wrong equation mechanism, a person's name should not be used to denote a common slope. The factors affecting the slope, the electrode potential and its measurements, the importance of potential mechanism, and the modified Boltzmann equation are presented.     

Recent development of non-faradaic potentiometry

Non-faradaic potentiometry has been plagued by a great many fundamental errors and a lack of conceptualization. Of greatest concern is the second Nernst equation hiatus. Potentiometry may be generally classified as faradaic and non-faradaic. The former deals with the redox reactions using the Nernst equation to explain the potential origin. The latter deals with the non-redox reactions using the Boltzmann and modified Boltzmann equations to explain the origin of electrode potential. Redox faradaic potentiometry has been well described in the textbooks. However, non-faradaic potentiometry has been almost completely neglected in the literature. Many well-known electrodes, such as the pH glass electrode, common reference electrodes, and ion selective electrodes (ISE) have been mistakenly interpreted as redox reactions or ion exchange reactions. New theories and experimental results show their mechanisms to be non-faradaic in nature. Furthermore, the reaction mechanisms for ISE have been confused in textbooks with redox reactions and the Nernst equation. The ISE potentials originating from adsorption of ions or charged particles based on surface charge density will be explained using the double and counterion triple layers concept. The new counterion triple layer concept may be applied to the potential development of sensors. The reason for a new concept, theory, or mechanism is to better explain the phenomena. Examples will be given of how our new concept explains the capacitor, counterion triple layer, surface adsorbed layers interactions, and the interface structure. We will also discuss the new sensor development based on the new adsorption concept. For the first time a new type of Ag/AgCl reference electrode for non-faradaic potentiometry will be presented, one without a liquid junction and with a Pt wire instead of a salt bridge. They will help open up a new horizon for electrochemical sensor research and may be used under unusual conditions, such as high temperature and high pressure, stirring, etc.