Jamming in confined geometry: Criticality of the jamming transition and implications of structural relaxation in confined supercooled liquids

In marginally jammed solids confined by walls, we calculate the particle and ensemble averaged value of an order parameter, 〈Ψ(r)〉, as a function of the distance to the wall, r. Being a microscopic indicator of structural disorder and particle mobility in solids, Ψ is by definition the response of the mean square particle displacement to the increase of temperature in the harmonic approximation and can be directly calculated from the normal modes of vibration of the zero-temperature solids. We find that, in confined jammed solids, 〈Ψ(r)〉 curves at different pressures can collapse onto the same master curve following a scaling function, indicating the criticality of the jamming transition. The scaling collapse suggests a diverging length scale and marginal instability at the jamming transition, which should be accessible to sophisticatedly designed experiments. Moreover, 〈Ψ(r)〉 is found to be significantly suppressed when approaching the wall and anisotropic in directions perpendicular and parallel to the wall. This finding can be applied to understand the r-dependence and anisotropy of the structural relaxation in confined supercooled liquids, providing another example of understanding or predicting behaviors of supercooled liquids from the perspective of the zero-temperature amorphous solids.

在壁面约束的临界堵塞固体中，我们计算了序参量〈Ψ(r)〉的粒子平均值和系综平均值，它是到壁面距离r的函数。Ψ作为固体中结构无序和粒子迁移率的微观指标，根据定义，它是在简谐近似下均方粒子位移对温度升高的响应，并且可以从零温固体的振动简正模式直接计算得出。我们发现，在受限堵塞固体中，不同压力下的〈Ψ(r)〉曲线可以按照一个标度函数坍缩到同一条主曲线上，这表明堵塞转变的临界性。标度坍缩表明在堵塞转变处存在一个发散的长度尺度和临界不稳定性，这应该可以通过精心设计的实验来探测。此外，发现当靠近壁面时〈Ψ(r)〉会被显著抑制，并且在垂直和平行于壁面的方向上是各向异性的。这一发现可用于理解受限过冷液体中结构弛豫的r依赖性和各向异性，为从零温非晶固体的角度理解或预测过冷液体的行为提供了又一个实例。