Determining the onset of rigidity in gels is a fundamental challenge with significant practical implications across different applications. Limited-valence, or patchy-particle systems have proven to be a valuable model to study the relationship between microscopic interactions and macroscopic mechanical properties. It has been suggested that the emergence of rigidity coincides with the formation of an infinitely spanning cluster of particles with at least three bonds. This work explores this hypothesis, its implications, and its broader applicability across a range of system parameters, by associating the emergence of rigidity with m-percolation transition for m=3. The properties of m-percolation are developed using a mean-field theoretical approach validated with numerical simulations, and used to build phase and rigidity diagrams for different particle valences of both single-component systems and binary mixtures of patchy particles. The difference between connectivity and rigidity percolation thresholds is found to reduce with increasing valence, providing an explanation for the challenges encountered in experimental attempts to distinguish isotropic connectivity percolation from the onset of rigidity. For binary mixtures, we found a robust minimum average valence, below which the gel is never rigid.
Percolation with trapping mechanism drives active gels to the critically connected state
细胞运动和组织形态发生关键取决于肌动球蛋白网络的动态重塑。肌动球蛋白网络由通过交联蛋白和马达蛋白肌球蛋白连接的肌动蛋白聚合物网络组成，马达蛋白肌球蛋白在网络上产生内应力。最近的发现表明，对于一系列实验参数，肌动球蛋白网络收缩成具有幂律尺寸分布的簇[Alvarado J. et al.（2013）Nature Physics 9 591]。在这里，我们认为，肌动球蛋白网络可以表现出强大的关键签名没有微调，因为系统的动态可以映射到一个修改后的版本的渗流与捕获（PT），这是已知的临界行为属于静态渗流普适类，而不需要微调的控制参数。我们进一步使用我们的PT模型来生成实验可检验的预测。
