Maier Manuel, Zippelius Annette, Fuchs Matthias
University of Konstanz, D-78457 Konstanz, Germany.
University Göttingen, D-37077 Göttingen, Germany.
Phys Rev Lett. 2017 Dec 29;119(26):265701. doi: 10.1103/PhysRevLett.119.265701.
A theory for the nonlocal shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. The long-ranged stress correlations can be traced to the coupling of shear stress to transverse momentum, which is ignored in the classic Maxwell model. To rescue this widely used model, we suggest a generalization in terms of a single relaxation time τ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length ξ∝τ as well as dynamic critical scaling and correctly accounts for the far-field stress correlations. It can be rephrased in terms of generalized hydrodynamic equations, which naturally couple stress and momentum and furthermore allow us to connect to fluidity and elastoplastic models.
一种关于过冷液体中非局部剪应力相关性的理论从第一原理推导得出。它捕捉了在理想化的液体到玻璃态转变时从粘性动力学到弹性动力学的转变，并解释了玻璃中长程应力相关性的出现，这正如经典连续介质弹性理论所预期的那样。长程应力相关性可追溯到剪应力与横向动量的耦合，而这在经典麦克斯韦模型中被忽略了。为了挽救这个广泛使用的模型，我们仅针对快速自由度提出了一个基于单一弛豫时间τ的推广。这个广义麦克斯韦模型意味着相关长度ξ∝τ发散以及动态临界标度，并正确地解释了远场应力相关性。它可以用广义流体动力学方程重新表述，这些方程自然地将应力和动量耦合起来，并且还使我们能够与流动性和弹塑性模型建立联系。
