Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, by canceling and restarting any cooperative-chain realization reaching the boundary with a smaller number of steps than the bulk cooperativity, we account for a purely attractive substrate, and explore the impact of the latter in the previous geometries.

中文翻译：

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各种受限几何中的合作弦乐和玻璃态动力学

以前，我们开发了一个基于随机协作串的最小模型，用于松散本体和接近自由界面中的过冷液体，并恢复了一些关键的实验观察结果。在本文中，我们回顾了协作串模型的主要成分后，研究了各种与实验相关的受限几何形状的有效玻璃化转变和表面迁移率：独立膜，支撑膜，球形颗粒和圆柱形颗粒，具有自由界面和/或被动基板。最后，通过取消并重新启动以比批量协作少的步骤数到达边界的任何协作链实现，我们可以得出一个纯粹有吸引力的基质，并探索后者在先前几何形状中的影响。