Arzash Sadjad, Gannavarapu Anupama, MacKintosh Fred C
Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.
Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA.
Phys Rev E. 2023 Nov;108(5-1):054403. doi: 10.1103/PhysRevE.108.054403.
At zero temperature, spring networks with connectivity below Maxwell's isostatic threshold undergo a mechanical phase transition from a floppy state at small strains to a rigid state for applied shear strain above a critical strain threshold. Disordered networks in the floppy mechanical regime can be stabilized by entropic effects at finite temperature. We develop a scaling theory for this mechanical phase transition at finite temperature, yielding relationships between various scaling exponents. Using Monte Carlo simulations, we verify these scaling relations and identify anomalous entropic elasticity with sublinear T dependence in the linear elastic regime. While our results are consistent with prior studies of phase behavior near the isostatic point, the present work also makes predictions relevant to the broad class of disordered thermal semiflexible polymer networks for which the connectivity generally lies far below the isostatic threshold.
在零温度下，连通性低于麦克斯韦等静阈值的弹簧网络会经历机械相变，从小应变时的柔软状态转变为施加的剪切应变高于临界应变阈值时的刚性状态。在有限温度下，柔软机械状态下的无序网络可通过熵效应实现稳定。我们针对这种有限温度下的机械相变发展了一种标度理论，得出了各种标度指数之间的关系。通过蒙特卡罗模拟，我们验证了这些标度关系，并在线性弹性区域中识别出具有亚线性温度依赖性的反常熵弹性。虽然我们的结果与等静点附近相行为的先前研究一致，但本工作也做出了与广泛的无序热半柔性聚合物网络相关的预测，这类网络的连通性通常远低于等静阈值。
