Lubchenko Vassiliy, Wolynes Peter G
Departments of Chemistry and Physics , University of Houston , Houston , Texas 77204 , United States.
Departments of Chemistry, Physics and Astronomy, and Center for Theoretical Biological Physics , Rice University , Houston , Texas 77005 , United States.
J Phys Chem B. 2018 Apr 5;122(13):3280-3295. doi: 10.1021/acs.jpcb.7b09553. Epub 2018 Jan 9.
Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily far away from equilibrium and require a description of the history of the conditions under which they formed. In this paper we describe how the locality of interactions intrinsic to finite-dimensional systems affects the stability of amorphous solids far off equilibrium. Our analysis encompasses both structural glasses formed by cooling and colloidal assemblies formed by compression. A diagram outlining regions of marginal stability can be adduced which bears some resemblance to the quasi-equilibrium replica meanfield theory phase diagram of hard sphere glasses in high dimensions but is distinct from that construct in that the diagram describes not true phase transitions but kinetic transitions that depend on the preparation protocol. The diagram exhibits two distinct sectors. One sector corresponds to amorphous states with relatively open structures, the other to high density, more closely packed ones. The former transform rapidly owing to there being motions with no free energy barriers; these motions are string-like locally. In the dense region, amorphous systems age via compact activated reconfigurations. The two regimes correspond, in equilibrium, to the collisional or uniform liquid and the so-called landscape regime, respectively. These are separated by a spinodal line of dynamical crossovers. Owing to the rigidity of the surrounding matrix in the landscape, high-density part of the diagram, a sufficiently rapid pressure quench adds compressive energy which also leads to an instability toward string-like motions with near vanishing barriers. Conversely, a dilute collection of rigid particles, such as a colloidal suspension leads, when compressed, to a spatially heterogeneous structure with percolated mechanically stable regions. This jamming corresponds to the onset of activation when the spinodal line is traversed from the low density side. We argue that a stable glass made of sufficiently rigid particles can also be viewed as exhibiting sporadic and localized buckling instabilities that result in local jammed structures. The lines of instability we discuss resemble the Gardner transition of meanfield systems but, in contrast, do not result in true criticality owing to being short-circuited by activated events. The locally marginally stable modes of motion in amorphous solids correspond to secondary relaxation processes in structural glasses. Their relevance to the low temperature anomalies in glasses is also discussed.
除了尚未结晶外，过冷液体可被视为处于适当的平衡状态，因此可用几个热力学控制变量来描述。相比之下，玻璃和其他非晶态固体可能远离平衡态，需要描述其形成时的条件历史。在本文中，我们描述了有限维系统固有的相互作用局部性如何影响远离平衡态的非晶态固体的稳定性。我们的分析涵盖了通过冷却形成的结构玻璃和通过压缩形成的胶体聚集体。可以得出一个概述边缘稳定区域的图，它与高维硬球玻璃的准平衡复本平均场理论相图有一些相似之处，但又有所不同，因为该图描述的不是真正的相变，而是依赖于制备协议的动力学转变。该图展示了两个不同的区域。一个区域对应具有相对开放结构的非晶态，另一个对应高密度、堆积更紧密的非晶态。前者由于存在无自由能垒的运动而快速转变；这些运动在局部呈线状。在致密区域，非晶态系统通过紧凑的活化重排而老化。这两种状态在平衡时分别对应碰撞或均匀液体状态以及所谓的能景观状态。它们由动态交叉的旋节线分隔开。由于在能景观中周围基质的刚性，在图的高密度部分，足够快速的压力猝灭会增加压缩能量，这也会导致向具有近乎消失能垒的线状运动的不稳定性。相反，诸如胶体悬浮液之类的稀刚性颗粒集合在被压缩时会导致具有机械稳定渗流区域的空间非均匀结构。这种堵塞对应于从低密度侧穿过旋节线时活化的开始。我们认为，由足够刚性的颗粒制成的稳定玻璃也可被视为表现出导致局部堵塞结构的零星和局部屈曲不稳定性。我们讨论的不稳定线类似于平均场系统的加德纳转变，但与之不同的是，由于被活化事件短路，不会导致真正的临界性。非晶态固体中局部边缘稳定的运动模式对应于结构玻璃中的二级弛豫过程。还讨论了它们与玻璃中低温异常的相关性。
