A generalized Young’s equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions
A generalized Young’s equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions
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DOI：
10.1080/01694243.2018.1476036
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发表时间：
2018-05
影响因子：
2.3
通讯作者：
M. Iwamatsu
中科院分区：
文献类型：
--
作者：
M. Iwamatsu
摘要：从热力学自由能最小化推导出一个广义的杨氏方程，该方程考虑了由液 - 气表面张力的曲率依赖性以及本征线张力的接触角依赖性对线张力的两种修正。利用托尔曼公式可以定性地估计曲率依赖性的修正。对于纳米级液滴，可以估计接触角依赖性的修正，因为对于这些液滴，由范德华相互作用确定的本征线张力的解析公式是可用的。对这种范德华纳米液滴的表观线张力的两种修正小到纳牛量级，并导致表观线张力为正或为负。还考虑了由重力加速度引起的毫米级液滴的重力线张力。重力线张力为牛的量级，因此曲率依赖性的修正可以忽略。然而，接触角依赖性非常大，以至于尽管未经修正的本征线张力总是正的，但表观线张力总是负的。这两个例子清楚地表明了理论计算的本征线张力与实验确定的包含这两种修正的表观线张力之间的区别。对实验确定的和理论计算的线张力进行简单比较并不总是可行的。
Abstract A generalized Young’s equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid–vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from the thermodynamic free-energy minimization. The correction from the curvature dependence can be qualitatively estimated using Tolman’s formula. The correction from the contact angle dependence can be estimated for nanometer-scale droplets for which the analytical formula for the intrinsic line tension determined from the van der Waals interaction is available. The two corrections to the apparent line tension of this van der Waals nano-droplets are as small as nN, and lead to either a positive or a negative apparent line tension. The gravitational line tension for millimeter-scale droplets by the gravitational acceleration is also considered. The gravitational line tension is of the order of N so that the correction from the curvature dependence can be neglected. Yet, the contact angle dependence is so large that the apparent line tension becomes always negative though the intrinsic line tension without the correction is always positive. These two examples demonstrate clear distinction between the theoretically calculated intrinsic line tension and the experimentally determined apparent line tension which includes these two corrections. Naive comparison of the experimentally determined and the theoretically calculated line tension is not always possible.