Finite size effects in critical fiber networks
Finite size effects in critical fiber networks
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DOI：
10.1039/d0sm00764a
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发表时间：
2020-08-07
期刊：
影响因子：
3.4
通讯作者：
MacKintosh, Fred C.
中科院分区：
文献类型：
--
作者：
Arzash, Sadjad;Shivers, Jordan L.;MacKintosh, Fred C.
胶原蛋白等纤维网络在生理系统中很常见。这些网络的一项重要功能是为细胞和组织提供机械稳定性。在连接的生理水平上，这样的网络在仅具有中心力相互作用的情况下将是机械不稳定的。虽然网络可以通过弯曲相互作用来稳定，但也有研究表明，它们随着施加应变的变化而表现出从软到刚性的关键转变。超过某个应变阈值后，预计仅具有中心力相互作用的欠约束网络会表现出剪切模量的不连续性。我们研究了这种转变的有限尺寸缩放行为，并确定了热力学极限中的机械不连续性和临界指数。我们发现了非平均场行为和临界指数超尺度关系的证据，其中网络刚度类似于热相变的热容量。光纤网络的自平均特性也可以证明这一点。
Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.