The precise determination of the line tension of sessile droplets still represents a major challenge. At present, the estimates of the line tension from contact angle measurements can differ by 4–5 orders of magnitude. Here we show that the pinning effect of the droplet contact line caused by the substrate inhomogeneities influences the apparent contact angle of the droplet, affecting the determination of the line tension via the corrected Young’s equation. We introduce the contribution of pinning effects into the Gibbs free energy differential and derive a modified version of the Young’s equation. Using classical density functional theory, we isolate the line tension and the pinning force contributions for substrates with different heterogeneity. The pinning effect leads to metastability of wetting states and influences the contact angle, hence introducing errors in the estimation of line tensions using the traditional analysis of contact angles, based on the modified Young’s equation.

中文翻译：

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接触线钉扎效应对确定吸附在基材上的液滴的线张力的影响

精确测定无蒂液滴的线张力仍然是一个重大挑战。目前，通过接触角测量得出的线张力估计值可以相差4-5个数量级。在这里，我们显示了由基材不均匀性引起的液滴接触线的钉扎效应会影响液滴的表观接触角，从而影响通过修正的杨氏方程式确定线张力。我们将钉扎效应的贡献引入吉布斯自由能微分，并推导了杨氏方程的修正形式。使用经典的密度泛函理论，我们隔离了具有不同异质性的基板的线张力和钉扎力的贡献。钉扎效应导致润湿状态的亚稳定性，并影响接触角，