Multicomponent Diffusivities from the Free Volume Theory
Multicomponent Diffusivities from the Free Volume Theory
复制标题
自由体积理论中的多分量扩散率
DOI：
10.1205/026387697524119
复制
发表时间：
1997
影响因子：
3.9
通讯作者：
A.
中科院分区：
文献类型：
--
作者：
J. Wesselingh;A.
在本文中，扩散的自由体积理论被扩展到多组分混合物。根据其表面分数，任何组件都可以使用自由体积。由此产生的方程根据摩尔质量、密度和粘度等纯组分数据预测简单液体混合物中的多组分 (Maxwell-Stefan) 扩散率。它们也可以与状态方程一起使用。对于简单的液体混合物，结果与实验非常吻合。对于粘性液体、橡胶聚合物和玻璃，可以正确预测小渗透物扩散率的数量级和主要趋势。这些方程遵循许多已知的扩散系数经验规则。 ● 在非粘性液体中，它们几乎与爱因斯坦-斯托克斯方程的经验修正一致。 ● 他们预测了具有正确活化能的阿累尼乌斯型温度依赖性。 ● 在具有相似成分的混合物中，他们预测 MS 扩散系数应该是成分的线性函数（达肯规则）。 ● 在组分之间差异较大（但不是太大）的混合物中，MS 扩散系数是成分的对数函数（Vignes 规则）。 ● 在粘性混合物和聚合物中，扩散率随着粘性成分的浓度而急剧变化（大致呈指数方式）。该理论并不完美。对于大小或化学结构差异很大的分子混合物，它会失败。它只能与水和聚合物一起使用，但有一些可疑的假设。
In this paper the free volume theory of diffusion is extended to multicomponent mixtures. The free volume is taken to be accessible for any component according to its surface fraction. The resulting equations predict multicomponent (Maxwell-Stefan) diffusivities in simple liquid mixtures from pure component data such as molar masses, densities and viscosities. They can also be used together with an equation of state. For simple liquid mixtures, the results agree closely with experiment. For viscous liquids, rubbery polymers and glasses, orders of magnitude and the main trends of diffusivities of small permeants are predicted correctly. The equations follow many of the empirical rules known for diffusion coefficients. ● In non-viscous liquids they almost coincide with an empirical modi® cation of the Einstein-Stokes equation. ● They predict an Arrhenius type of temperature dependence with correct activation energies. ● In mixtures with similar components, they predict that MS-diffusivities should be linear functions of composition (the Darken rule). ● In mixtures with larger (but not-too-large) differences between the components, the MSdiffusivities are logarithmic functions of composition (the Vignes rule). ● In viscous mixtures and polymers, diffusivities vary sharply (in a roughly exponential ● manner) with the concentration of the viscous component. The theory is not perfect. It fails for mixtures of molecules differing greatly in size or chemical structure. It can only be made to work with water and polymers with a few dubious assumptions.