The dependence of the contact angle on the size of a nanoscopic droplet residing on a flat substrate is traditionally ascribed solely to line tension. Other contributions, stemming from the droplet geometry dependence of the surface tension and line tension, are typically ignored. Here, we perform molecular dynamics simulations of water droplets of cylindrical morphology on surfaces of a wide range of polarities. In the cylindrical geometry, where the line tension is not operative directly, we find significant contact angle dependence on the droplet size. The effect is most pronounced on hydrophilic surfaces, with the contact angle increase of up to $10^{°}$ with a decreasing droplet size. On hydrophobic surfaces, the trend is reversed and considerably weaker. Our analysis suggests that these effects can be attributed to the Tolman correction due to the curved water–vapor interface and to a generalized line tension that possesses a contact angle dependence. The latter is operative also in the cylindrical geometry and yields a comparable contribution to the contact angle as the line tension itself in case of spherical droplets.

中文翻译：

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超出标准线张力：纳米水滴的尺寸依赖性接触角

接触角对驻留在平坦基底上的纳米液滴的尺寸的依赖性传统上仅归因于线张力。由表面张力和线张力的液滴几何形状相关性引起的其他贡献通常被忽略。在这里，我们对极性范围很广的圆柱状水滴进行分子动力学模拟。在线张力不能直接作用的圆柱几何形状中，我们发现液滴的大小与接触角有很大关系。这种作用在亲水性表面上最为明显，接触角最大增加到$\mathrm{1个}{0}^{°}$液滴尺寸减小。在疏水性表面上，趋势被逆转并且明显减弱。我们的分析表明，这些影响可归因于弯曲的水-蒸汽界面和具有接触角依赖性的广义线张力所致的托尔曼修正。后者在圆柱几何形状中也是有效的，并且在球形液滴的情况下，对接触角的贡献与线张力本身相当。