Luo Chengjie, Janssen Liesbeth M C
Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands.
J Chem Phys. 2020 Dec 7;153(21):214507. doi: 10.1063/5.0026969.
Mode-coupling theory (MCT) constitutes one of the few first-principles-based approaches to describe the physics of the glass transition, but the theory's inherent approximations compromise its accuracy in the activated glassy regime. Here, we show that microscopic generalized mode-coupling theory (GMCT), a recently proposed hierarchical framework to systematically improve upon MCT, provides a promising pathway toward a more accurate first-principles description of glassy dynamics. We present a comprehensive numerical analysis for Percus-Yevick hard spheres by performing explicitly wavenumber- and time-dependent GMCT calculations up to sixth order. Specifically, we calculate the location of the critical point, the associated non-ergodicity parameters, and the time-dependent dynamics of the density correlators at both absolute and reduced packing fractions, and we test several universal scaling relations in the α- and β-relaxation regimes. It is found that higher-order GMCT can successfully remedy some of MCT's pathologies, including an underestimation of the critical glass transition density and an overestimation of the hard-sphere fragility. Furthermore, we numerically demonstrate that the celebrated scaling laws of MCT are preserved in GMCT and that the predicted critical exponents manifestly improve as more levels are incorporated in the GMCT hierarchy. Although formally the GMCT equations should be solved up to infinite order to reach full convergence, our finite-order GMCT calculations unambiguously reveal a uniform convergence pattern for the dynamics. We thus argue that GMCT can provide a feasible and controlled means to bypass MCT's main uncontrolled approximation, offering hope for the future development of a quantitative first-principles theory of the glass transition.
模式耦合理论（MCT）是为数不多的基于第一性原理来描述玻璃化转变物理过程的方法之一，但该理论固有的近似性损害了其在活化玻璃态区域的准确性。在此，我们表明微观广义模式耦合理论（GMCT），这是最近提出的一种用于系统改进MCT的层次框架，为更准确地从第一性原理描述玻璃态动力学提供了一条有前景的途径。我们通过进行高达六阶的明确依赖波数和时间的GMCT计算，对珀西 - 耶维克硬球进行了全面的数值分析。具体而言，我们计算了临界点的位置、相关的非遍历性参数以及在绝对和约化堆积分数下密度关联函数的时间相关动力学，并在α和β弛豫区域测试了几个通用标度关系。结果发现，高阶GMCT能够成功纠正MCT的一些问题，包括对临界玻璃化转变密度的低估以及对硬球脆性的高估。此外，我们通过数值证明了MCT著名的标度律在GMCT中得以保留，并且随着GMCT层次结构中纳入更多层次，预测的临界指数明显改善。尽管从形式上讲，GMCT方程应求解到无穷阶才能达到完全收敛，但我们的有限阶GMCT计算明确揭示了动力学的一致收敛模式。因此，我们认为GMCT可以提供一种可行且可控的方法来绕过MCT的主要非受控近似，为玻璃化转变定量第一性原理理论的未来发展带来希望。
