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arXiv 2102.02555cond-mat.soft
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线框玻璃的弹性响应。I.二维模型

Elastic Response of Wire Frame Glasses. I. Two Dimensional Model

David A. King, Masao Doi, Erika Eiser

摘要:

本文研究了刚性线框颗粒浓悬浮体系对阶跃应变的弹性响应。这些粒子由长度为$L$的无限细的刚性棒构成。我们专门比较了直棒状颗粒弯曲和分支线框。在稠密悬浮液中,线框被它们的臂之间的拓扑纠缠冻结在无序状态。我们提出了一个简单的几何方法来找到这些玻璃系统中的浓度的弹性应力的标度。我们将此方法应用到一个简单的二维模型系统中,其中测试粒子被放置在一个平面上,并受到随机分布的点与数密度$ν$的约束。线框悬浮液和棒悬浮液之间有两个显著的区别:1)线框悬浮液的线弹性很大,与$ν^2 L^4$相似,而棒悬浮液的线弹性小得多,与浓度无关。2)对于小于$\sim \sqrt{K/k_B T L^4}$的密度,棒总是剪切变薄,但线框剪切硬化,其中$K$是颗粒的弯曲模量。线框的变形被发现是重要的,即使是小的应变,在特定的应变,$γ$的变形颗粒的比例,由$(νL^2)^2 γ^2$。我们的结果与一个简单的模拟的二维系统吻合得很好。

英文摘要:

We study the elastic response of concentrated suspensions of rigid wire frame particles to a step strain. These particles are constructed from infinitely thin, rigid rods of length $L$. We specifically compare straight rod-like particles to bent and branched wire frames. In dense suspensions the wire frames are frozen in a disordered state by the topological entanglements between their arms. We present a simple, geometric method to find the scaling of the elastic stress with concentration in these glassy systems. We apply this method to a simple 2D model system where a test particle is placed on a plane and constrained by a random distribution of points with number density $ν$. Two striking differences between wire frame and rod suspensions are found: 1) The linear elasticity per particle for wire frames is very large, scaling like $ν^2 L^4$, whereas for rods it much smaller and independent of concentration. 2) Rods always shear thin but wire frames shear harden for densities less than $\sim \sqrt{K/k_B T L^4}$, where $K$ is the bending modulus of the particles. The deformation of wire frames is found to be important even for small strains, with the proportion of deformed particles at a particular strain, $γ$, being given by $(νL^2)^2 γ^2$. Our results agree well with a simple simulation of the 2D system.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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