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首页> 外文期刊>The journal of physical chemistry, B. Condensed matter, materials, surfaces, interfaces & biophysical >Sieverts Law Empirical Exponent for Pd-Based Membranes: Critical Analysis in Pure H2 Permeation
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Sieverts Law Empirical Exponent for Pd-Based Membranes: Critical Analysis in Pure H2 Permeation

机译：Pd基膜的Sieverts法则经验指数：纯H2渗透的临界分析

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摘要

In this paper, the physical meaning of the Sieverts-type driving force exponent n is analyzed for hydrogen permeation through Pd-based membranes by considering a complex model involving several elementary permeation steps (adsorption on the membrane surface on the feed side, desorption from the surface on the permeate side, diffusion through the metal lattice, and the two transition phenomena surface-to-bulk and bulk-to-surface). First, the characteristic driving force of each step is evaluated, showing that adsorption and desorption singularly considered and the adsorption and desorption considered at the same time are characterized by driving forces depending on the ratio of feed and permeate hydrogen pressure. On the contrary, the diffusion step is found to present a driving force that is composed of two terms, one which corresponds to the original Sieverts law (with an exponent of 0.5) and the other which is the product of the pressure difference and a temperature-dependent factor. Then, the characteristic n is evaluated by applying the multistep model to two different membranes from the literature in several cases, (a) considering each permeation step as the only limiting one and (b) considering the overall effect of all steps. The results of the analysis show that for a low temperature and thin membrane thickness, the effect of the surface phenomena is, in general, a decrease of the overall exponent n toward values lower than 0.5, even though, under particular operating conditions, the n theoretical value of the surface phenomena is equal to unity. At a higher temperature and thickness (diffusion-controlled permeation), n tends to 0.5, even though the rapidity of this tendency depends strictly on the membrane diffusional parameters. In this frame, the expression developed for the diffusion step provides a theoretical reason why n values higher than 0.5 are found even for thick membranes and high temperature, where diffusion is the only rate-determining step.
机译：在本文中，通过考虑涉及几个基本渗透步骤（在进料侧的膜表面上的吸附，从膜表面脱附的解吸）的复杂模型，分析了Sieverts型驱动力指数n的物理意义，以了解氢在Pd基膜上的渗透。渗透侧的表面，通过金属晶格扩散，以及两个过渡现象（从表面到本体和从本体到表面）。首先，评估每个步骤的特征驱动力，表明单独考虑的吸附和解吸以及同时考虑的吸附和解吸的特征在于，驱动力取决于进料和渗透氢压力之比。相反，发现扩散步骤呈现的驱动力由两个项组成，一个项对应于原始的Sieverts定律（指数为0.5），另一项是压差和温度的乘积依赖因素。然后，在几种情况下，通过将多步模型应用于文献中的两种不同的膜来评估特性n，（a）将每个渗透步骤视为唯一的限制条件，（b）考虑所有步骤的整体效果。分析结果表明，对于低温和薄膜厚度，表面现象的影响通常是总指数n朝小于0.5的值减小，即使在特定的操作条件下，n表面现象的理论值等于1。在较高的温度和厚度下（扩散控制的渗透），n趋于0.5，即使这种趋势的速度严格取决于膜的扩散参数。在此框架中，为扩散步骤开发的表达式提供了理论上的原因，即使对于厚膜和高温，n值仍高于0.5，而扩散是唯一决定速率的步骤。

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