Wigbers M C, MacKintosh F C, Dennison M
Department of Physics and Astronomy, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands.
Department of Applied Physics and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042145. doi: 10.1103/PhysRevE.92.042145. Epub 2015 Oct 22.
We study the elasticity of thermalized spring networks under an applied bulk strain. The networks considered are subisostatic random-bond networks that, in the athermal limit, are known to have vanishing bulk and linear shear moduli at zero bulk strain. Above a bulk strain threshold, however, these networks become rigid, although surprisingly the shear modulus remains zero until a second, higher, strain threshold. We find that thermal fluctuations stabilize all networks below the rigidity transition, resulting in systems with both finite bulk and shear moduli. Our results show a T(0.66) temperature dependence of the moduli in the region below the bulk strain threshold, resulting in networks with anomalously high rigidity as compared to ordinary entropic elasticity. Furthermore, we find a second regime of anomalous temperature scaling for the shear modulus at its zero-temperature rigidity point, where it scales as T(0.5), behavior that is absent for the bulk modulus since its athermal rigidity transition is discontinuous.
我们研究了在施加体应变下热平衡弹簧网络的弹性。所考虑的网络是亚等静压随机键网络，在无热极限下，已知其在零体应变时体模量和线性剪切模量都为零。然而，在体应变阈值以上，这些网络会变得刚性，尽管令人惊讶的是，直到第二个更高的应变阈值，剪切模量仍保持为零。我们发现热涨落使所有网络在刚性转变以下稳定，从而产生具有有限体模量和剪切模量的系统。我们的结果表明，在体应变阈值以下的区域，模量具有T(0.66)的温度依赖性，与普通熵弹性相比，导致网络具有异常高的刚性。此外，我们发现在剪切模量的零温度刚性点处，存在第二种异常温度标度 regime，其标度为T(0.5)，而体模量不存在这种行为，因为其无热刚性转变是不连续的。
