1979.02.15《Direct experimemtal verification of the Kelvin equation for capillary condensation》

在《Nature》发表的研究中，围绕毛细凝聚这一界面与表面科学的基础性现象，针对长期仅停留在热力学推导与间接验证层面的Kelvin方程，开展了高度创新的实验研究。该工作首次实现了对Kelvin方程的直接、定量实验验证，明确揭示了受限几何条件下蒸汽-液体相变与界面曲率之间的严格定量关系，使这一经典公式从理论预言转化为可被直接检验的实验事实。依托高精度表面力测量与多光束干涉技术，研究在纳米尺度上精确控制表面间距，原位观测了毛细凝聚与蒸发的发生条件及其可逆转变。实验结果表明，即便在分子尺度受限空间中，凝聚压力与界面曲率仍严格遵循Kelvin方程的理论预测，为毛细凝聚热力学提供了首个直接而可靠的实验证据。这一成果不仅澄清了Kelvin方程适用下限的关键争议，也显著推进了对纳米受限流体相变行为的定量认知。总体而言，该研究以原创性的实验策略和极高的测量精度，完成了对毛细凝聚经典理论的首次直接实证检验，在方法学与物理认识层面均具有突出的创新性，是界面热力学与表面科学领域中具有代表性的经典工作。

作者：Leonard R. Fisher & Jacob N. Israelachvili*

In a study published in Nature, the authors presented a highly innovative experimental investigation of capillary condensation, a fundamental phenomenon in interface and surface science, by directly addressing the Kelvin equation, which had long been supported only by thermodynamic derivations and indirect experimental evidence. For the first time, the work provided a direct and quantitative experimental verification of the Kelvin equation, unambiguously establishing the strict relationship between vapor-liquid phase transitions and interfacial curvature under geometrical confinement. In this way, the Kelvin equation was elevated from a theoretical prediction to an experimentally testable physical law. By integrating high-precision surface force measurements with multiple-beam interferometry, the study achieved nanometer-scale control of surface separations and enabled in situ observation of the onset, reversibility, and evaporation of capillary condensation. The results demonstrated that even in molecularly confined geometries, the condensation pressure continues to follow the predictions of the Kelvin equation, thereby delivering the first direct and reliable experimental confirmation of capillary condensation thermodynamics. This accomplishment resolved long-standing questions regarding the lower limits of the Kelvin equation’s applicability and significantly advanced the quantitative understanding of phase transitions in nanoconfined fluids. Overall, through an original experimental strategy and exceptional measurement precision, this study accomplished the first direct experimental validation of a classic theory of capillary condensation. It stands as a landmark and highly influential contribution to interface thermodynamics and surface science, distinguished by its methodological innovation and deep physical insight.

Authors：Leonard R. Fisher & Jacob N. Israelachvili*

Direct experimental verification of the Kelvin equation for capillary condensation