Searcy Alan W, Beruto Dario T, Barberis Fabrizio
Lawrence Berkeley National Laboratory and Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.
J Chem Phys. 2009 May 14;130(18):184713. doi: 10.1063/1.3123389.
In order to obtain consistency with the force balance theory of Young and Laplace, which quantitatively predicts the height of capillary rise from the contact angles of drops on solid surfaces, Gibbs made chemical potentials in interface functions of the integral interface free energies. We cite evidence that equilibrium chemical potentials in one-component systems are identical at interfaces to equilibrium chemical potentials in bulk phases. We evaluate two postulates. (1) Partial free energies of liquids at an interface with a solid are functions of the strength and range of attractive fields outside solid phase boundaries. (2) At equilibrium, the chemical potentials in all interfaces of a one-component liquid equal the chemical potential in its interior when the liquid is bonded to one or more immiscible solids. These postulates yield equations for partial equilibrium (PE) states of drops, films, and liquids. The PE equations yield the same prediction of the height of a meniscus from the contact angle of drops as does Young-Laplace theory and also the same dependence of the volume of capillary condensate on vapor pressure as does the Kelvin equation. But our measurements of the contact angles of water on glass and Teflon and between their close-spaced surfaces contradict the YL supposition that meniscus angles are the same as angles of drops on glass and Teflon surfaces and support the PE postulate that attraction by the external fields of solids, not meniscus curvature, is responsible for capillary rise. We use published data to illustrate the validity of the PE conclusion that divergence or convergence at the saturation pressure of a parent liquid depends on whether or not the attractive field of a solid surface imparts to the liquid more than twice the energy required to create two liquid-vapor interfaces. For divergent water films on quartz, the PE equation provides a quantitative fit to experimental data for films of any thickness greater than 1.5 nm. No previous theory has accomplished that. In an appendix, we illustrate applications of PE theory to evaluating the complex interactions between inherently reversible chemical diffusion and inherently irreversible forces introduced by strains.
为了与杨氏和拉普拉斯的力平衡理论保持一致，该理论从液滴在固体表面的接触角定量预测毛细上升高度，吉布斯在积分界面自由能的界面函数中引入了化学势。我们引用证据表明，单组分系统中界面处的平衡化学势与体相中的平衡化学势相同。我们评估两个假设。（1）液体与固体界面处的部分自由能是固相边界外吸引力场的强度和范围的函数。（2）在平衡时，当单组分液体与一种或多种不混溶的固体结合时，其所有界面中的化学势等于其内部的化学势。这些假设得出了液滴、液膜和液体的部分平衡（PE）状态方程。PE方程从液滴接触角对弯月面高度的预测与杨氏 - 拉普拉斯理论相同，并且毛细凝聚体积对蒸气压的依赖关系也与开尔文方程相同。但是我们对水在玻璃和聚四氟乙烯上以及它们紧密间隔表面之间的接触角测量结果与杨氏 - 拉普拉斯假设相矛盾，即弯月面角度与玻璃和聚四氟乙烯表面上液滴的角度相同，并且支持PE假设，即固体的外部场的吸引力而非弯月面曲率导致毛细上升。我们使用已发表的数据来说明PE结论的有效性，即母液在饱和压力下的发散或收敛取决于固体表面的吸引力场是否赋予液体超过创建两个液 - 气界面所需能量的两倍。对于石英上的发散水膜，PE方程对任何厚度大于1.5 nm的膜的实验数据提供了定量拟合。以前没有理论做到这一点。在附录中，我们说明了PE理论在评估固有可逆化学扩散与应变引入的固有不可逆力之间复杂相互作用方面的应用。
