A generalized equation describing isotope exchange kinetics at solid-liquid interface

A generalization of the kinetic equation for the isotope exchange at solid—liquid interface is presented. The generalized equation may be used to describe kinetics of the isotope exchange process limited by surface reactions and diffusion without assumption of spherical symmetry of solid particles.

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Eine generalisierte Gleichung für die Kinetik des Isotopenaustausches an Fest-Flüssig-Phasengrenzen

Zusammenfassung Es wird eine generalisierte kinetische Gleichung angegeben, die die Kinetik des Isotopenaustausches an Fest-Flüssig-Phasengrenzen beschreibt, wobei der Austauschprozeß durch Oberflächenreaktionen und Diffusion ohne der Annahme sphärischer Symmetrie für die festen Partikel begrenzt ist.

     

Formal Mathematical Analysis of the Existence of the Common Intersection Point in Relation to Determining the Parameters Describing Ion Adsorption at the Oxide/Electrolyte Interface: Comparison of the Triple and Four-Layer Models

For most oxide/electrolyte systems potentiometric titration curves measured for different ionic strengths have a Common Intersection Point (CIP) which corresponds to the Point of Zero Charge (PZC). However, there are systems where a CIP exists but the surface charge at this point does not equal zero (PZC CIP). In this paper theoretical analysis of the systems in which the PZC and CIP do not coincide is presented. It is based on the well-known 2-pK surface charging approach and Triple Layer Model (TLM) as well as the Four Layer Model (FLM) of the electric double layer. The appropriate mathematical criterion for CIP existence was applied with detailed derivations, both for TLM and FLM. Having determined in this manner the parameter values, one can draw proper conclusions about the features of oxide/electrolyte adsorption systems, in which PZC and CIP do not coincide. The values of adsorption parameters are found by fitting simultaneously the obtained theoretical expressions to both of the experimental titration isotherms, and to the individual isotherms of electrolyte cation adsorption measured using radiometric methods.     

The Binary System BaF2/AlF3

The system BaF₂/AlF₃ is investigated by X-ray and D.T.A., and the liquid-solid phase diagram is established. Five ternary fluorides are disclosed: trimorphic BaAlF₅, Ba₃Al₂F₁₂, Ba₅AlF₁₉, polymorphic Ba₃AlF₉ and Ba₅AlF₁₃. Neutron thermodiffractometry experiments are performed to specify some parts of the diagram. The cell parameters of the fluorides are given and the results are discussed and compared with those of the previous works.     

Improvement of the spinning electrophorometer for zeta potential measurements

In this study, bubbles are held by centripetal force at the center of a rotating cylinder filled with an aqueous solution. Their velocities along the axe of rotation, after application of an electrophoretic force, are used for the calculation of the so-called electrokinetic potential. But this process necessitates the elimination of the electro-osmosis which occurs on the interior sides of the glass cylinder by superposing a concurrent force on the bubble. Efficiency of DEAE-Dextran reticulated with 1,4 Butanediol Diglycidyl Ether can be tested by the observation of a cloud of latex microspheres injected in the interior of the tube and allowed to move in respect with the application of an electric field. The experimental control of these velocity profiles proves the adequacy of the polymer for many cases such as surfactant solutions, presence of electrolytes, utilization with moderate pH.The dynamic interpretation of the electrophoretic motion of bubbles is possible by considering that small ones behave like rigid spheres moving in a rotating fluid. In the second part of this paper and in a previous publication, we have experimentally proved that the use of the theoretical expressions of the forces involved for rigid spheres is justified for small bubbles. So, the electrokinetic potential can be expressed versus the velocity, leading to possible interpretations of the adsorption on gas-water interfaces.     

Surface mixed adsorption films of 2,4,6- trimethylphenol–2,4,6-trichlorophenol at aqueous solution/air interface

 The results of experimental studies of the adsorption at the solution/air interface from an aqueous mixture: 2,4,6-trimethylphenol–2,4,6-trichlorophenol are presented. The surface properties of the above-mentioned mixture were studied by surface potential and surface tension measurements. These measurements were carried out as a function of the concentration of 2,4,6-trimethylphenol aqueous solution at a constant concentration of 2,4,6-trichlorophenol. Using the results obtained and based on the Gibbs equation, Helmholtz formula and Motomura’s method the relative surface excesses of adsorbed substances, effective dipole moments, surface molar fractions of solutes and miscibility of adsorbed films were determined. Received: 7 November 1997 Accepted: 26 February 1998     

Pb2＋在液/液界面迁移的电化学研究及其应用

用循环伏安法研究了双硫腙络合推动Pb^2＋在水/乙酰丙酮界面迁移的伏安过程. 实验证明, 该过程是受扩散控制的不可逆过程, Pb^2＋由水相转移到有机相中, 与双硫腙形成络合物Pb(DzH)₂. Pb^2＋的峰电位在－0.3 V处, 并且在5× 10^－6～0.1 mol•L^－1范围内与峰电流成正比. 这一方法为工业废水中铅的在线、现场测定提供了可靠、灵敏的检测方法.     

First‐principles study of metal/nitride polar interfaces: Ti/TiN

We have examined the optimal interface structure, ideal work of adhesion and bonding character of polar Ti(110)/TiN(111) interfaces by first‐principles density‐functional plane‐wave pseudopotential calculations. Both Ti‐ and N‐terminated interfaces, including six different interface structures, were calculated. The interface structure for each termination, continuing the TiN crystal structure across the interface, has the largest work of adhesion. Although both terminations yield substantial adhesion energies in the range 3–7 J m^?2, the N‐terminated interface is ～4 J m^?2 stronger than the Ti‐terminated interface. Analysis of the interfacial electronic structure shows that the Ti‐terminated interface is a mixed strong, metallic and weak covalent character, whereas the N‐terminated interface is a polar covalent bond similar to the Ti/TiC interface. Further study of the separation of the optimal interface shows that the cleavages will never fracture at the interface due to the strong bonding, which is consistent with the experimental results. Copyright © 2003 John Wiley & Sons, Ltd.     

曲率流的参数化有限元逼近

许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战.     

曲边区域上的多边形网格间断有限元离散及其多重网格算法

本文利用多边形网格上的间断有限元方法离散二阶椭圆方程,在曲边区域上,采用多条直短边逼近曲边的以直代曲的策略,实现了高阶元在能量范数下的最优收敛.本文还将这一方法用于带曲边界面问题的求解,同样得到高阶元的最优收敛.此外我们还设计并分析了这一方法的\linebreakW-cycle和Variable V-cycle多重网格预条件方法,证明当光滑次数足够多时,多重网格预条件算法一致收敛.最后给出了数值算例,证实该算法的可行性并验证了理论分析的结果.     

New formulation of restricted growth processes

We present a new formulation of a class of growth models-those which evolve according to an exclusion process. This formulation is based upon a transformation of the probability distribution function which involves Grassmann variables. This method is very general and enables one to derive an exact stochastic differential equation for the model of interest. We describe this method using the traffic model as an example.