Time-Dependence of Boundary Tensions of Solutions I. The Role of Diffusion in Time-Effects

表面张力 扩散 热力学 表面扩散 化学 吸附 扩散过程 扩散方程 曲面(拓扑) 边界(拓扑) 统计物理学 机械 物理 数学 物理化学 数学分析 计算机科学 几何学 创新扩散 经济 知识管理 经济 服务(商务)
作者
A. F. H. Ward,L. Tordai
出处
期刊:Journal of Chemical Physics [American Institute of Physics]
卷期号:14 (7): 453-461 被引量:1384
标识
DOI:10.1063/1.1724167
摘要

The variation of surface tension of solutions with time has in some cases, where the change is over within a few seconds or less, been explained on the basis of diffusion. This paper attempts a rigorous mathematical analysis of the role that diffusion might play in such time-effects. The limitations of diffusion theories which have been proposed previously are discussed. A general theory of diffusion to the surface is derived, which allows for back-diffusion and which makes no special assumptions of a physical nature. It is possible to use Fick's equation to calculate the total amount of solute which diffuses from a semi-infinite bulk solution into the surface if the concentration immediately under the surface is known at various times throughout the process. It is shown how the latter information may be deduced from the variation of surface tension with time together with final equilibrium values of surface tension. The methods of this theory are applied to analyze recent data on time-effects of short duration. It is concluded that even in cases where the variation of the surface tension is over in less than a second the rate-determining process is not diffusion. Even for these very rapid changes one is therefore led to assume the existence of an activation barrier which determines the rate of adsorption.
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