论文标题
通用$ l^{ - 3} $在受限无定形系统的粘弹性中有限尺寸效果
Universal $L^{-3}$ finite-size effects in the viscoelasticity of confined amorphous systems
论文作者
论文摘要
我们提出了无定形介质的粘弹性理论，该理论考虑了沿三个空间维度之一的限制的影响。该框架基于晶格动力学对无定形系统或非承包反应理论的非承物扩展。通过剪切模量$ g'$的非承包部分考虑了由于限制而产生的尺寸效果。非承包供款以$ k $ -space中的模式写成。通过基于对模式上$ K $ - 空间积分的分析的严格论点，这表明限制大小$ l $在一个空间维度中，例如$ z $轴可导致对非借条（软化）校正的模式的红外截止，该模量校正为缩放为$ l^{ - 3} $的模量。有限样本量$ d $的校正在两个垂直尺寸的比例为$ \ sim（l/d）^4 $，对于$ l \ ll d $而言是可忽略的。对于液体，可以预测，$ g'\ sim l^{ - 3} $与以前的更近似分析一致，而对于无定形材料，$ g'\ sim g'_ {bulk} +βl^{ - 3} $。对于液体的情况，$ l^{ - 3} $ Law证明了四个不同的实验系统。
We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous systems, or nonaffine response theory. The size effects due to the confinement are taken into account via the nonaffine part of the shear storage modulus $G'$. The nonaffine contribution is written as a sum over modes in $k$-space. With a rigorous argument based on the analysis of the $k$-space integral over modes, it is shown that the confinement size $L$ in one spatial dimension, e.g. the $z$ axis, leads to a infrared cut-off for the modes contributing to the nonaffine (softening) correction to the modulus that scales as $L^{-3}$. Corrections for finite sample size $D$ in the two perpendicular dimensions scale as $\sim (L/D)^4$, and are negligible for $L \ll D$. For liquids it is predicted that $G'\sim L^{-3}$ in agreement with a previous more approximate analysis, whereas for amorphous materials $G' \sim G'_{bulk} + βL^{-3}$. For the case of liquids, four different experimental systems are shown to be very well described by the $L^{-3}$ law.
