Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bangalore 560064, India.
J Chem Phys. 2013 Mar 28;138(12):12A548. doi: 10.1063/1.4792356.
The breakdown of the Stokes-Einstein (SE) relation between diffusivity and viscosity at low temperatures is considered to be one of the hallmarks of glassy dynamics in liquids. Theoretical analyses relate this breakdown with the presence of heterogeneous dynamics, and by extension, with the fragility of glass formers. We perform an investigation of the breakdown of the SE relation in 2, 3, and 4 dimensions in order to understand these interrelations. Results from simulations of model glass formers show that the degree of the breakdown of the SE relation decreases with increasing spatial dimensionality. The breakdown itself can be rationalized via the difference between the activation free energies for diffusivity and viscosity (or relaxation times) in the Adam-Gibbs relation in three and four dimensions. The behavior in two dimensions also can be understood in terms of a generalized Adam-Gibbs relation that is observed in previous work. We calculate various measures of heterogeneity of dynamics and find that the degree of the SE breakdown and measures of heterogeneity of dynamics are generally well correlated but with some exceptions. The two-dimensional systems we study show deviations from the pattern of behavior of the three- and four-dimensional systems both at high and low temperatures. The fragility of the studied liquids is found to increase with spatial dimensionality, contrary to the expectation based on the association of fragility with heterogeneous dynamics.
在低温下，扩散率和粘度之间的斯托克斯-爱因斯坦（SE）关系的破裂被认为是液体玻璃动力学的特征之一。理论分析将这种破裂与非均匀动力学的存在联系起来，并由此推断与玻璃形成体的脆性有关。我们在 2、3 和 4 维空间中对 SE 关系的破裂进行了研究，以了解这些相互关系。对模型玻璃形成体的模拟结果表明，SE 关系破裂的程度随着空间维度的增加而降低。通过在三维和四维中的 Adam-Gibbs 关系中扩散率和粘度（或弛豫时间）的激活自由能之间的差异，可以对 SE 关系的破裂进行合理化解释。二维的行为也可以根据先前工作中观察到的广义 Adam-Gibbs 关系来理解。我们计算了动力学异质性的各种度量，并发现 SE 关系破裂的程度和动力学异质性的度量通常高度相关，但也存在一些例外。我们研究的二维系统在高温和低温下都表现出与三维和四维系统的行为模式的偏离。研究液体的脆性随着空间维度的增加而增加，这与基于脆性与非均匀动力学相关的预期相反。
